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@book{Alberts,
  author = "Alberts, Bruce and Johnson,Alexander and  Lewis,Julian and Morgan, David and  Raff, Martin and  Roberts, Keith and  Walter, Peter",
  title = "Molecular Biology of the Cell. 6th edition",
  publisher = "Garland Science",
  year = 2014,
  } 

@article{davis2014traffic,
  title={A traffic flow model for bio-polymerization processes},
  author={Davis, Lisa and Gedeon, Tom{\'a}{\v{s}} and Gedeon, Jakub and Thorenson, Jennifer},
  journal={Journal of mathematical biology},
  volume={68},
  pages={667--700},
  year={2014},
  publisher={Springer}
}

@article{roussel2006validation,
  title={Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression},
  author={Roussel, Marc R and Zhu, Rui},
  journal={Phys. Biol.},
  volume={3},
  pages={274},
  year={2006},
  publisher={IOP Publishing}
}

@article{hoffmann2000computational,
  title={Computational Fluid Dynamics Volume I},
  author={Hoffmann, Klaus A and Chiang, Steve T},
  journal={Engineering Education System, Wichita, Kan, USA},
  year={2000}
}

@article{courant1952solution,
  title={On the solution of nonlinear hyperbolic differential equations by finite differences},
  author={Courant, Richard and Isaacson, Eugene and Rees, Mina},
  journal={Communications on Pure and Applied Mathematics},
  volume={5},
  pages={243--255},
  year={1952},
  publisher={Wiley Online Library}
}

@article{Neuman2003,
title = "Ubiquitous Transcriptional Pausing Is Independent of {RNA} Polymerase Backtracking ",
journal = "Cell ",
volume = "115",
pages = "437 - 447",
year = "2003",
doi = "http://dx.doi.org/10.1016/S0092-8674(03)00845-6",
author = "Keir C. Neuman and Elio A. Abbondanzieri and Robert Landick and Jeff Gelles and Steven M. Block",
abstract = "\{RNA\} polymerase ({{RNAP}}) transcribes \{DNA\} discontinuously, with periods of rapid nucleotide addition punctuated by frequent pauses. We investigated the mechanism of transcription by measuring the effect of both hindering and assisting forces on the translocation of single Escherichia coli transcription elongation complexes, using an optical trapping apparatus that allows for the detection of pauses as short as one second. We found that the vast majority of pauses are brief (1–6 s at 21°C, 1 mM NTPs), and that the probability of pausing at any particular position on a \{DNA\} template is low and fairly constant. Neither the probability nor the duration of these ubiquitous pauses was affected by hindering or assisting loads, establishing that they do not result from the backtracking of \{{RNAP}\} along the \{DNA\} template. We propose instead that they are caused by a structural rearrangement within the enzyme. "
}

@article{landick2006regulatory,
  title={The regulatory roles and mechanism of transcriptional pausing},
  author={Landick, R},
  journal={Biochem. Soc. Trans.},
  volume={34},
  number={6},
  pages={1062--1066},
  year={2006},
  publisher={London: The Society, 1973-}
}

@article{Klumpp18112008,
author = {Klumpp, Stefan  and Hwa, Terence }, 
title = {Stochasticity and traffic jams in the transcription of ribosomal {RNA}: Intriguing role of termination and antitermination},
year = {2008}, 
doi = {10.1073/pnas.0806084105}, 
abstract ={In fast-growing bacteria, ribosomal {RNA} (r{RNA}) is required to be transcribed at very high rates to sustain the high cellular demand on ribosome synthesis. This results in dense traffic of RNA polymerases ({{RNAP}}). We developed a stochastic model, integrating results of single-molecule and quantitative in vivo studies of Escherichia coli, to evaluate the quantitative effect of pausing, termination, and antitermination (AT) on rRNA transcription. Our calculations reveal that in dense {{RNAP}} traffic, spontaneous pausing of {{RNAP}} can lead to severe “traffic jams,” as manifested in the broad distribution of inter-{{RNAP}} distances and can be a major factor limiting transcription and hence growth. Our results suggest the suppression of these pauses by the ribosomal AT complex to be essential at fast growth. Moreover, unsuppressed pausing by even a few nonantiterminated {{RNAP}}s can already reduce transcription drastically under dense traffic. However, the termination factor Rho can remove the nonantiterminated {{RNAP}}s and restore fast transcription. The results thus suggest an intriguing role by Rho to enhance rather than attenuate rRNA transcription.}, 
journal = {Proceedings of the National Academy of Sciences} 
}

@article{McAdams04021997,
author = {McAdams, Harley H. and Arkin, Adam}, 
title = {Stochastic mechanisms in gene expression},
volume = {94}, 
number = {3}, 
pages = {814-819}, 
year = {1997}, 
journal = {Proceedings of the National Academy of Sciences} 
}



@article{Elowitz16082002,
author = {Elowitz, Michael B. and Levine, Arnold J. and Siggia, Eric D. and Swain, Peter S.}, 
title = {Stochastic Gene Expression in a Single Cell},
volume = {297}, 
number = {5584}, 
pages = {1183-1186}, 
year = {2002}, 
doi = {10.1126/science.1070919}, 
abstract ={Clonal populations of cells exhibit substantial phenotypic variation. Such heterogeneity can be essential for many biological processes and is conjectured to arise from stochasticity, or noise, in gene expression. We constructed strains of Escherichia coli that enable detection of noise and discrimination between the two mechanisms by which it is generated. Both stochasticity inherent in the biochemical process of gene expression (intrinsic noise) and fluctuations in other cellular components (extrinsic noise) contribute substantially to overall variation. Transcription rate, regulatory dynamics, and genetic factors control the amplitude of noise. These results establish a quantitative foundation for modeling noise in genetic networks and reveal how low intracellular copy numbers of molecules can fundamentally limit the precision of gene regulation.}, 
journal = {Science} 
}

@article{mcclure1985mechanism,
  title={Mechanism and control of transcription initiation in prokaryotes},
  author={McClure, William R},
  journal={Annual Review of Biochemistry},
  volume={54},
  number={1},
  pages={171--204},
  year={1985},
  publisher={Annual Reviews 4139 El Camino Way, PO Box 10139, Palo Alto, CA 94303-0139, USA}
}

@article{Revyakin17112006,
author = {Revyakin, Andrey and Liu, Chenyu and Ebright, Richard H. and Strick, Terence R.}, 
title = {Abortive Initiation and Productive Initiation by {RNA} Polymerase Involve {DNA} Scrunching},
volume = {314}, 
number = {5802}, 
pages = {1139-1143}, 
year = {2006}, 
doi = {10.1126/science.1131398}, 
abstract ={Using single-molecule {DNA} nanomanipulation, we show that abortive initiation involves {DNA} “scrunching”—in which {RNA} polymerase ({{RNAP}}) remains stationary and unwinds and pulls downstream {DNA} into itself—and that scrunching requires {RNA} synthesis and depends on RNA length. We show further that promoter escape involves scrunching, and that scrunching occurs in most or all instances of promoter escape. Our results support the existence of an obligatory stressed intermediate, with approximately one turn of additional {DNA} unwinding, in escape and are consistent with the proposal that stress in this intermediate provides the driving force to break {{RNAP}}-promoter and {{RNAP}}-initiation-factor interactions in escape.}, 
journal = {Science} 
} 


@article{margeat2006direct,
  title={Direct observation of abortive initiation and promoter escape within single immobilized transcription complexes},
  author={Margeat, Emmanuel and Kapanidis, Achillefs N and Tinnefeld, Philip and Wang, You and Mukhopadhyay, Jayanta and Ebright, Richard H and Weiss, Shimon},
  journal={Biophys. J.},
  volume={90},
  number={4},
  pages={1419--1431},
  year={2006},
  publisher={Elsevier}
}

@article{luse1987abortive,
  title={Abortive initiation by {RNA} polymerase {II} in vitro at the adenovirus 2 major late promoter.},
  author={Luse, D S and Jacob, George A},
  journal={J. Biol. Chem.},
  volume={262},
  pages={14990--14997},
  year={1987},
  publisher={ASBMB}
}


@article{epshtein2003transcription,
  title={Transcription through the roadblocks: the role of {RNA} polymerase cooperation},
  author={Epshtein, Vitaly and Toulm{\'e}, Francine and Rahmouni, A Rachid and Borukhov, Sergei and Nudler, Evgeny},
  journal={EMBO J.},
  volume={22},
  pages={4719--4727},
  year={2003},
  publisher={Wiley Online Library}
}


@article{klumpp2008stochasticity,
  title={Stochasticity and traffic jams in the transcription of ribosomal {RNA}: Intriguing role of termination and antitermination},
  author={Klumpp, Stefan and Hwa, Terence},
  journal={Proceedings of the National Academy of Sciences},
  volume={105},
  number={47},
  pages={18159--18164},
  year={2008},
  publisher={National Acad Sciences}
}
%
%
%
@MastersThesis{Vashishtha,
  title={Stochastic modeling of eukaryotic transcription at the single nucleotide level},
  author={Vashishtha, Saurabh},
  year={2011},
  school={University of Lethbridge},
  type={{M.Sc.}\ thesis},
  url       = {https://www.uleth.ca/dspace/handle/10133/3190}
}

@article{rosonina2006terminating,
  title={Terminating the transcript: breaking up is hard to do},
  author={Rosonina, Emanuel and Kaneko, Syuzo and Manley, James L},
  journal={Genes Dev.},
  volume={20},
  number={9},
  pages={1050--1056},
  year={2006},
  publisher={Cold Spring Harbor Lab}
}

@article{luo2006role,
  title={The role of Rat1 in coupling m{RNA} 3'-end processing to transcription termination: Implications for a unified allosteric--torpedo model},
  author={Luo, Weifei and Johnson, Arlen W and Bentley, David L},
  journal={Genes Dev.},
  volume={20},
  number={8},
  pages={954--965},
  year={2006},
  publisher={Cold Spring Harbor Lab}
}

@article{gillespie1976general,
  title={A general method for numerically simulating the stochastic time evolution of coupled chemical reactions},
  author={Gillespie, Daniel T},
  journal={J. Comput. Phys.},
  volume={22},
  number={4},
  pages={403--434},
  year={1976},
  publisher={Elsevier}
}

@article{gillespie1977exact,
  title={Exact stochastic simulation of coupled chemical reactions},
  author={Gillespie, Daniel T},
  journal={J. Phys. Chem.},
  volume={81},
  number={25},
  pages={2340--2361},
  year={1977},
  publisher={ACS Publications}
}

@Article{Sneppen2005399,
  Title                    = {A Mathematical Model for Transcriptional Interference by \{RNA\} Polymerase Traffic in Escherichia coli },
  Author                   = {Kim Sneppen and Ian B. Dodd and Keith E. Shearwin and Adam C. Palmer and Rachel A. Schubert and Benjamin P. Callen and J. Barry Egan},
 Journal = {Journal of Molecular Biology },
 Year = {2005},
 Number = {2},
 Pages = {399 - 409},
 Volume = {346},

 Abstract = {Interactions between \{RNA\} polymerases ({{RNAP}}) resulting from tandem or convergent arrangements of promoters can cause transcriptional interference, often with important consequences for gene expression. However, it is not known what factors determine the magnitude of interference and which mechanisms are likely to predominate in any situation. We therefore developed a mathematical model incorporating three mechanisms of transcriptional interference in bacteria: occlusion (in which passing \{{RNAP}s\} block access to the promoter), collisions between elongating {{RNAP}}s, and ‚Äúsitting duck‚Äù interference (in which \{{RNAP}\} complexes waiting to fire at the promoter are removed by passing {RNAP}). The predictions of the model are in good agreement with a recent quantitative in vivo study of convergent promoters in E. coli. Our analysis predicts that strong occlusion requires the interfering promoter to be very strong. Collisions can also produce strong interference but only if the interfering promoter is very strong or if the convergent promoters are far apart (andgt;200 bp). For moderate strength interfering promoters and short inter-promoter distances, strong interference is dependent on the sitting duck mechanism. Sitting duck interference is dependent on the relative strengths of the two promoters. However, it is also dependent on the ‚Äúaspect ratio‚Äù (the relative rates of \{{RNAP}\} binding and firing) of the sensitive promoter, allowing promoters of equal strength to have very different sensitivities to transcriptional interference. The model provides a framework for using transcriptional interference to investigate various dynamic processes on \{DNA\} in vivo. },
 Doi = {http://dx.doi.org/10.1016/j.jmb.2004.11.075},
 Keywords = {transcriptional interference},
  Keywords                 = {transcriptional interference},
  Owner                    = {hossein},
  Timestamp                = {2016.02.12},
}

@article{Kim11111997,
author = {Kim, Tae-Kyung and Lagrange, Thierry and Wang, Yuh-Hwa and Griffith, Jack D. and Reinberg, Danny and Ebright, Richard H.}, 
title = {Trajectory of {DNA} in the RNA polymerase {II} transcription preinitiation complex},
volume = {94}, 
number = {23}, 
pages = {12268-12273}, 
year = {1997}, 
abstract ={By using site-specific protein-{DNA} photocrosslinking, we define the positions of TATA-binding protein, transcription factor {IIB}, transcription factor {IIF}, and subunits of RNA polymerase {II} ({RNAP}{II}) relative to promoter {DNA} within the human transcription preinitiation complex. The results indicate that the interface between the largest and second-largest subunits of {{RNAP}}II forms an extended, ≈240 Å channel that interacts with promoter {DNA} both upstream and downstream of the transcription start. By using electron microscopy, we show that {{RNAP}}II compacts promoter {DNA} by the equivalent of ≈50 bp. Together with the published structure of {{RNAP}}II, the results indicate that {{RNAP}}II wraps {DNA} around its surface and suggest a specific model for the trajectory of the wrapped DNA.}, 
journal = {Proceedings of the National Academy of Sciences} 
}

@article{Dvir2001209,
title = "Mechanism of transcription initiation and promoter escape by {RNA} polymerase {II} ",
journal = "Curr. Opin. Genet. Dev.",
volume = "11",
pages = "209 - 214",
year = "2001",
doi = "http://dx.doi.org/10.1016/S0959-437X(00)00181-7",
author = "Arik Dvir and Joan Weliky Conaway and Ronald C Conaway",
keywords = "\{RNA\} polymerase II",
keywords = "basal transcriptional machinery",
keywords = "mRNA synthesis",
keywords = "initiation",
keywords = "cross-linking studies",
keywords = "promoter escape ",
abstract = "Recently, key advances in biochemical and structural studies of \{RNA\} polymerase \{II\} (pol II) and the basal transcriptional machinery have shed considerable light on the basic mechanisms underlying the initiation stage of eukaryotic mRNA synthesis. The development of methods for obtaining crystal structures of pol \{II\} and its complexes has revolutionized transcriptional studies and holds promise that aspects of initiation will soon be understood at atomic resolution; crosslinking studies have revealed intriguing features of the topology of the pol \{II\} initiation complex and provided working models for dynamic steps of initiation; and mechanistic studies have identified promoter escape as a critical step during initiation and brought to light novel roles for the general initiation factors TFIIE, TFIIF, and \{TFIIH\} in this process. "
}

@Article{Potts2011,
  Title                    = {An anti-symmetric exclusion process for two particles on an infinite 1D lattice},
  Author                   = {J R Potts and S Harris and L Giuggioli},
  Journal                  = {Journal of Physics A: Mathematical and Theoretical},
  Year                     = {2011},
  Number                   = {48},
  Pages                    = {485003},
  Volume                   = {44},

  Abstract                 = {A system of two biased, mutually exclusive random walkers on an infinite 1D lattice is studied whereby the intrinsic bias of one particle is equal and opposite to that of the other. The propagator for this system is solved exactly and expressions for the mean displacement and mean square displacement (MSD) are found. Depending on the nature of the intrinsic bias, the system‚Äôs behaviour displays two regimes, characterised by (i) the particles moving towards each other and (ii) away from each other, both qualitatively different from the case of no bias. The continuous-space limit of the propagator is found and is shown to solve a Fokker‚ÄìPlanck equation for two biased, mutually exclusive Brownian particles with equal and opposite drift velocity. Connections to territorial dynamics in animal populations are discussed.},
  Owner                    = {hossein},
  Timestamp                = {2016.02.29}
}


@article{roussel2006stochastic,
  title={Stochastic kinetics description of a simple transcription model},
  author={Roussel, Marc R and Zhu, Rui},
  journal={Bull. Math. Biol.},
  volume={68},
  number={7},
  pages={1681--1713},
  year={2006},
  publisher={Springer}
}


@article{greive2011development,
  title={Development of a ``modular'' scheme to describe the kinetics of transcript elongation by {RNA} polymerase},
  author={Greive, Sandra J and Goodarzi, Jim P and Weitzel, Steven E and von Hippel, Peter H},
  journal={Biophys. J.},
  volume={101},
  pages={1155--1165},
  year={2011}
}

@article{yin2004structural,
  title={The structural mechanism of translocation and helicase activity in T7 RNA polymerase},
  author={Yin, Y Whitney and Steitz, Thomas A},
  journal={Cell},
  volume={116},
  number={3},
  pages={393--404},
  year={2004},
  publisher={Elsevier}
}

@article{guajardo1997model,
  title={A model for the mechanism of polymerase translocation},
  author={Guajardo, Richard and Sousa, Rui},
  journal={Journal of Molecular Biology},
  volume={265},
  number={1},
  pages={8--19},
  year={1997},
  publisher={Elsevier}
}

@article{brueckner2009structure,
  title={Structure--function studies of the {RNA} polymerase {II} elongation complex},
  author={Brueckner, Florian and Armache, K-J and Cheung, Alan and Damsma, Gerke E and Kettenberger, Hubert and Lehmann, Elisabeth and Sydow, Jasmin and Cramer, Patrick},
  journal={Acta Crystallographica Section D: Biological Crystallography},
  volume={65},
  number={2},
  pages={112--120},
  year={2009},
  publisher={International Union of Crystallography}
}

@article{Wang30101998,
author = {Wang, Michelle D. and Schnitzer, Mark J. and Yin, Hong and Landick, Robert and Gelles, Jeff and Block, Steven M.}, 
title = {Force and Velocity Measured for Single Molecules of {RNA} Polymerase},
volume = {282}, 
number = {5390}, 
pages = {902-907}, 
year = {1998}, 
doi = {10.1126/science.282.5390.902}, 
abstract ={{RNA} polymerase ({{RNAP}}) moves along {DNA} while carrying out transcription, acting as a molecular motor. Transcriptional velocities for single molecules of Escherichia coli {{RNAP}} were measured as progressively larger forces were applied by a feedback-controlled optical trap. The shapes of {{RNAP}} force-velocity curves are distinct from those of the motor enzymes myosin or kinesin, and indicate that biochemical steps limiting transcription rates at low loads do not generate movement. Modeling the data suggests that high loads may halt {{RNAP}} by promoting a structural change which moves all or part of the enzyme backwards through a comparatively large distance, corresponding to 5 to 10 base pairs. This contrasts with previous models that assumed force acts directly upon a single-base translocation step.}, 
journal = {Science} 
}

@article{Arimbasseri2016546,
title = "{RNA} Polymerase {III} Advances: Structural and t{RNA} Functional Views ",
journal = "Trends in Biochemical Sciences ",
volume = "41",
number = "6",
pages = "546 - 559",
year = "2016",
doi = "http://dx.doi.org/10.1016/j.tibs.2016.03.003",
author = "Aneeshkumar G. Arimbasseri and Richard J. Maraia",
abstract = "\{RNA\} synthesis in eukaryotes is divided among three \{RNA\} polymerases ({{RNAP}}s). \{{RNAP}\} \{III\} transcribes hundreds of t{RNA} genes and fewer additional short \{RNA\} genes. We survey recent work on transcription by \{{RNAP}\} \{III\} including an atomic structure, mechanisms of action, interactions with chromatin and retroposons, and a conserved link between its activity and a t{RNA} modification that enhances m{RNA} decoding. Other new work suggests important mechanistic connections to oxidative stress, autoimmunity and cancer, embryonic stem cell pluripotency, and tissue-specific developmental effects. We consider that, for some of its complex functions, variation in \{RNAP\} \{III\} activity levels lead to nonuniform changes in tRNAs that can shift the translation profiles of key codon-biased mRNAs with resultant phenotypes or disease states. "
}


@article{Vannini2012439,
title = "Conservation between the {RNA} Polymerase {I}, {II}, and {III} Transcription Initiation Machineries ",
journal = "Molecular Cell ",
volume = "45",
number = "4",
pages = "439 - 446",
year = "2012",
doi = "http://dx.doi.org/10.1016/j.molcel.2012.01.023",
author = "Alessandro Vannini and Patrick Cramer",
abstract = "Recent studies of the three eukaryotic transcription machineries revealed that all initiation complexes share a conserved core. This core consists of the \{RNA\} polymerase (I, II, or III), the {TATA} box-binding protein (TBP), and transcription factors TFIIB, TFIIE, and\{TFIIF} (for Pol II) or proteins structurally and functionally related to parts of these factors (for Pol I and Pol III). The conserved core initiation complex stabilizes the open \{DNA\} promoter complex and directs initial \{RNA\} synthesis. The periphery of the core initiation complex is decorated by additional polymerase-specific factors that account for functional differences in promoter recognition and opening, and gene class-specific regulation. This review outlines the similarities and differences between these important molecular machines. "
}

@article{Nechaev201134,
title = "Pol {II} waiting in the starting gates: Regulating the transition from transcription initiation into productive elongation ",
journal = "Biochim. Biophys. Acta",
volume = "1809",
number = "1",
pages = "34 - 45",
year = "2011",
doi = "http://dx.doi.org/10.1016/j.bbagrm.2010.11.001",
author = "Sergei Nechaev and Karen Adelman",
keywords = "\{RNA\} polymerase II",
keywords = "Gene regulation",
keywords = "Transcription elongation",
keywords = "Polymerase pausing ",
abstract = "Proper regulation of gene expression is essential for the differentiation, development and survival of all cells and organisms. Recent work demonstrates that transcription of many genes, including key developmental and stimulus-responsive genes, is regulated after the initiation step, by pausing of \{RNA\} polymerase \{II\} during elongation through the promoter-proximal region. Thus, there is great interest in better understanding the events that follow transcription initiation and the ways in which the efficiency of early elongation can be modulated to impact expression of these highly regulated genes. Here we describe our current understanding of the steps involved in the transition from an unstable initially transcribing complex into a highly stable and processive elongation complex. We also discuss the interplay between factors that affect early transcript elongation and the potential physiological consequences for genes that are regulated through transcriptional pausing. "
}

@article{robert1969multiple,
  title={Multiple forms of DNA-dependent {RNA} polymerase in eukaryotic organisms},
  author={Robert, G and William, J},
  journal={Nature},
  volume={224},
  pages={235},
  year={1969}
}
@article{Roeder2005909,
title = "Transcriptional regulation and the role of diverse coactivators in animal cells ",
journal = "\{FEBS\} Letters ",
volume = "579",
number = "4",
pages = "909 - 915",
year = "2005",
note = "Molecular Mechanisms of Biological Systems. 130th Nobel Symposium ",
doi = "http://dx.doi.org/10.1016/j.febslet.2004.12.007",
author = "Robert G. Roeder",
keywords = "Transcriptional activators",
keywords = "Coactivators",
keywords = "{RNA} polymerase II",
keywords = "Mediator",
keywords = "Histone acetyltransferases",
keywords = "Histone methyltransferases ",
abstract = "Transcriptional regulation in eukaryotes involves structurally and functionally distinct nuclear \{RNA\} polymerases, corresponding general initiation factors, gene-specific (DNA-binding) regulatory factors, and a variety of coregulatory factors that act either through chromatin modifications (e.g. histone acetyltransferases and methyltransferases) or more directly (e.g. Mediator) to facilitate formation and function of the preinitiation complex. Biochemical studies with purified factors and \{DNA\} versus recombinant chromatin templates have provided insights into the nature and mechanism of action of these factors, including pathways for their sequential function in chromatin remodeling and preinitiation complex formation/function (transcription) steps and a possible role in facilitating the transition between these steps. "
}

@article{Li2007707,
title = "The Role of Chromatin during Transcription ",
journal = "Cell ",
volume = "128",
number = "4",
pages = "707 - 719",
year = "2007",
doi = "http://dx.doi.org/10.1016/j.cell.2007.01.015",
author = "Bing Li and Michael Carey and Jerry L. Workman",
abstract = "Chromatin structure imposes significant obstacles on all aspects of transcription that are mediated by \{RNA\} polymerase II. The dynamics of chromatin structure are tightly regulated through multiple mechanisms including histone modification, chromatin remodeling, histone variant incorporation, and histone eviction. In this review, we highlight advances in our understanding of chromatin regulation and discuss how such regulation affects the binding of transcription factors as well as the initiation and elongation steps of transcription. "
}

@Article{kim1993a,
  author  = {Kim, Joseph L. and Nikolov, Dimitar B. and Burley, Stephen K.},
  title   = {Co-crystal structure of TBP recognizing the minor groove of a TATA element},
  journal = {Nature},
  year    = {1993},
  volume  = {365},
  number  = {6446},
  pages   = {520--527},
  month   = oct,
}

@article{Pal2005101,
title = "The Role of the Transcription Bubble and \{TFIIB\} in Promoter Clearance by \{RNA\} Polymerase \{II\} ",
journal = "Mol. Cell",
volume = "19",
pages = "101 - 110",
year = "2005",
doi = "http://dx.doi.org/10.1016/j.molcel.2005.05.024",
author = "Mahadeb Pal and Alfred S. Ponticelli and Donal S. Luse",
abstract = "Summary We have studied promoter clearance at a series of \{RNA\} polymerase \{II\} promoters with varying spacing of the \{TATA\} box and start site. We find that regardless of promoter spacing, the upstream edge of the transcription bubble forms 20 bp from TATA. The bubble expands downstream until 18 bases are unwound and the \{RNA\} is at least 7 nt long, at which point the upstream ∼8 bases of the bubble abruptly reanneal (bubble collapse). If either bubble size or transcript length is insufficient, bubble collapse cannot occur. Bubble collapse coincides with the end of the requirement for the \{TFIIH\} helicase for efficient transcript elongation. We also provide evidence that bubble collapse suppresses pausing at +7 to +9 caused by the presence of the B finger segment of \{TFIIB\} within the complex. Our results indicate that bubble collapse defines the \{RNA\} polymerase \{II\} promoter clearance transition. "
}

@article{Pal13052003,
author = {Pal, Mahadeb and Luse, Donal S.}, 
title = {The initiation–elongation transition: Lateral mobility of {RNA} in {RNA} polymerase {II} complexes is greatly reduced at +8/+9 and absent by +23},
volume = {100}, 
number = {10}, 
pages = {5700-5705}, 
year = {2003}, 
doi = {10.1073/pnas.1037057100}, 
abstract ={{RNA} polymerase II transcription complexes stalled shortly after initiation over a repetitive segment of the template can undergo efficient transcript slippage, during which the 3'-end of the {RNA} slides upstream and then re-pairs with the template, allowing transcription to continue. In the present study, we have used transcript slippage as an assay to identify possible structural transitions that occur as the polymerase passes from the initiation to the elongation phase of transcription. We reasoned that transcript slippage would not occur in fully processive complexes. We constructed a series of templates that allowed us to stall {RNA} polymerase II after the synthesis of a repetitive sequence (5′-CUCUCU-3′) at varying distances downstream of +1. We found that polymerase must synthesize at least a 23-nt {RNA} to attain resistance to transcript slippage. The ability to undergo slippage was lost in two discrete steps, suggestive of two distinct transitions. The first transition is the formation of the 8- to 9-bp mature RNA–{DNA} hybrid, when slippage abruptly dropped by 10-fold. However, easily detectable slippage continued until 14 more bonds were made. Thus, although the transcript becomes tightly constrained within the transcription complex once the hybrid reaches its final length, much more {RNA} synthesis is required before the {RNA} is no longer able to slip upstream along the template. This last point may reflect an important stabilizing role for the interaction of the polymerase with the transcript well upstream of the RNA–{DNA} hybrid.}, 
journal = {Proceedings of the National Academy of Sciences} 
}

@article{Marshall01051992,
author = {Marshall, N F and Price, D H}, 
title = {Control of formation of two distinct classes of {RNA} polymerase II elongation complexes.},
volume = {12}, 
number = {5}, 
pages = {2078-2090}, 
year = {1992}, 
doi = {10.1128/MCB.12.5.2078}, 
abstract ={We have examined elongation by {RNA} polymerase II initiated at a promoter and have identified two classes of elongation complexes. Following initiation at a promoter, all polymerase molecules enter an abortive mode of elongation. Abortive elongation is characterized by the rapid generation of short transcripts due to pausing of the polymerase followed by termination of transcription. Termination of the early elongation complexes can be suppressed by the addition of 250 mM KCl or 1 mg of heparin per ml soon after initiation. Elongation complexes of the second class carry out productive elongation in which long transcripts can be synthesized. Productive elongation complexes are derived from early paused elongation complexes by the action of a factor which we call P-TEF (positive transcription elongation factor). P-TEF is inhibited by 5,6-dichloro-1-beta-D-ribofuranosylbenzimidazole at concentrations which have no effect on the initiation of transcription. By using templates immobilized on paramagnetic particles, we show that isolated preinitiation complexes lack P-TEF and give rise to transcription complexes which can carry out only abortive elongation. The ability to carry out productive elongation can be restored to isolated transcription complexes by the addition of P-TEF after initiation. A model is presented which describes the role of elongation factors in the formation and maintenance of elongation complexes. The model is consistent with the available in vivo data concerning control of elongation and is used to predict the outcome of other potential in vitro and in vivo experiments.}, 
journal = {Molecular and Cellular Biology} 
}

@article{Rahl2010432,
title = "c-{Myc} Regulates Transcriptional Pause Release ",
journal = "Cell ",
volume = "141",
number = "3",
pages = "432 - 445",
year = "2010",
doi = "http://dx.doi.org/10.1016/j.cell.2010.03.030",
author = "Peter B. Rahl and Charles Y. Lin and Amy C. Seila and Ryan A. Flynn and Scott McCuine and Christopher B. Burge and Phillip A. Sharp and Richard A. Young",
keywords = "DNA",
keywords = "RNA",
keywords = "STEMCELL ",
abstract = "Summary Recruitment of the \{RNA\} polymerase \{II\} (Pol II) transcription initiation apparatus to promoters by specific DNA-binding transcription factors is well recognized as a key regulatory step in gene expression. We report here that promoter-proximal pausing is a general feature of transcription by Pol \{II\} in mammalian cells and thus an additional step where regulation of gene expression occurs. This suggests that some transcription factors recruit the transcription apparatus to promoters, whereas others effect promoter-proximal pause release. Indeed, we find that the transcription factor c-Myc, a key regulator of cellular proliferation, plays a major role in Pol \{II\} pause release rather than Pol \{II\} recruitment at its target genes. We discuss the implications of these results for the role of c-Myc amplification in human cancer. PaperClip "
}


@article{Proudfoot01092011,
author = {Proudfoot, Nick J.}, 
title = {Ending the message: poly(A) signals then and now},
volume = {25}, 
number = {17}, 
pages = {1770-1782}, 
year = {2011}, 
doi = {10.1101/gad.17268411}, 
abstract ={Polyadenylation [poly(A)] signals (PAS) are a defining feature of eukaryotic protein-coding genes. The central sequence motif AAUAAA was identified in the mid-1970s and subsequently shown to require flanking, auxiliary elements for both 3'-end cleavage and polyadenylation of premessenger {RNA} (pre-mRNA) as well as to promote downstream transcriptional termination. More recent genomic analysis has established the generality of the PAS for eukaryotic mRNA. Evidence for the mechanism of m{RNA} 3'-end formation is outlined, as is the way this {RNA} processing reaction communicates with {RNA} polymerase II to terminate transcription. The widespread phenomenon of alternative poly(A) site usage and how this interrelates with pre-m{RNA} splicing is then reviewed. This shows that gene expression can be drastically affected by how the message is ended. A central theme of this review is that while genomic analysis provides generality for the importance of PAS selection, detailed mechanistic understanding still requires the direct analysis of specific genes by genetic and biochemical approaches.}, 
journal = {Genes and Development} 
}

@article {Ezeokonkwo2012,
author = {Ezeokonkwo, Chukwudi and Ghazy, Mohamed A. and Zhelkovsky, Alexander and Yeh, Pei-Chun and Moore, Claire},
title = {Novel interactions at the essential N-terminus of poly(A) polymerase that could regulate poly(A) addition in Saccharomyces cerevisiae},
journal = {FEBS Letters},
volume = {586},
number = {8},
doi = {10.1016/j.febslet.2012.03.036},
pages = {1173--1178},
keywords = {CF I, cleavage factor I, CPF, cleavage/polyadenylation factor, CPSF, cleavage/polyadenylation specificity factor, DTT, dithiothreitol, GAD, gal activation domain, GBD, gal binding domain, GST, glutathione S-transferase, PAP, poly(A) polymerase, PMSF, phenylmethylsulfonyl fluoride, SDS, sodium dodecyl sulfate, Poly(A) polymerase, Polyadenylation},
year = {2012},
abstract = {
PTA1
 binds to 
PAP1
 by pull down (View interaction)},
}

@article{Keller1997329,
title = "A comparison of mammalian and yeast pre-m{RNA} 3'-end processing ",
journal = "Current Opinion in Cell Biology ",
volume = "9",
number = "3",
pages = "329 - 336",
year = "1997",
doi = "http://dx.doi.org/10.1016/S0955-0674(97)80004-X",
author = "Walter Keller and Lionel Minvielle-Sebastia",
abstract = "Many components of the mammalian and yeast pre-m{RNA} 3'-end-processing machinery have recently been purified and cDNAs or genes coding for these factors have been cloned. Most of the factors consist of multiple subunits, some of which serve to bind the \{RNA\} substrate, others of which are involved in forming a complex network of protein—protein interactions. Most of the mammalian 3'-end-processing factors, are similar in their amino acid sequence to the yeast factors, indicating that they have a common evolutionary history. "
}

@article{Greger18072000,
author = {Greger, Ingo H. and Aranda, Agustín and Proudfoot, Nick}, 
title = {Balancing transcriptional interference and initiation on the
 GAL7 promoter of
 Saccharomyces cerevisiae},
volume = {97}, 
number = {15}, 
pages = {8415-8420}, 
year = {2000}, 
doi = {10.1073/pnas.140217697}, 
abstract ={Transcriptional termination of the GAL10 gene in
 Saccharomyces cerevisiae depends on the efficiency of
 polyadenylation. Either cis mutations in the poly(A)
 signal or trans mutations of m{RNA} 3'-end cleavage
 factors result in GAL10 read-through transcripts into
 the adjacent GAL7 gene and inactivation (occlusion) of
 the GAL7 promoter. Herein, we present a molecular
 explanation of this transcriptional interference phenomenon. In
 vivo footprinting data reveal that GAL7 promoter
 occlusion is associated with the displacement of Gal4p transcription
 factors from the promoter. Interestingly, overexpression of Gal4p
 restores promoter occupancy, activates GAL7 expression,
 and rescues growth on the otherwise toxic galactose substrate. Our data
 therefore demonstrate a precise balance between transcriptional
 interference and initiation.}, 
journal = {Proceedings of the National Academy of Sciences} 
}

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@article{tripathi2008interacting,
  title={Interacting {RNA} polymerase motors on a {DNA} track: Effects of traffic congestion and intrinsic noise on {RNA} synthesis},
  author={Tripathi, Tripti and Chowdhury, Debashish},
  journal={Physical Review E},
  volume={77},
  number={1},
  pages={011921},
  year={2008},
  publisher={APS}
}

@incollection{risken1984fokker,
  title={Fokker-planck equation},
  author={Risken, Hannes},
  booktitle={The Fokker-Planck Equation},
  pages={63--95},
  year={1984},
  publisher={Springer}
}
@article{fokker1914fokker,
  title={Fokker-planck equation},
  author={Fokker, AD},
  journal={Ann. Physik},
  volume={43},
  pages={810},
  year={1914}
}
@article{planck1917sitzungsber,
  title={Sitzungsber},
  author={Planck, M},
  journal={Preuss. Akad. Wiss. Phys. Math. Kl},
  volume={325},
  pages={3},
  year={1917}
}
@article{shahrezaei2008analytical,
  title={Analytical distributions for stochastic gene expression},
  author={Shahrezaei, Vahid and Swain, Peter S},
  journal={Proceedings of the National Academy of Sciences},
  volume={105},
  number={45},
  pages={17256--17261},
  year={2008},
  publisher={National Acad Sciences}
}

@Book{vanKampen81,
  title     = {Stochastic Processes in Physics and Chemistry},
  publisher = {North-Holland},
  year      = {1981},
  author    = {N. G. van Kampen},
  address   = {Amsterdam},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@article{peskin1993cellular,
  title={Cellular motions and thermal fluctuations: the Brownian ratchet.},
  author={Peskin, Charles S and Odell, Garrett M and Oster, George F},
  journal={Biophysical Journal},
  volume={65},
  number={1},
  pages={316},
  year={1993},
  publisher={The Biophysical Society}
}
@article{elston2002brownian,
  title={The brownian ratchet and power stroke models for posttranslational protein translocation into the endoplasmic reticulum},
  author={Elston, Timothy C},
  journal={Biophysical Journal},
  volume={82},
  number={3},
  pages={1239--1253},
  year={2002},
  publisher={Elsevier}
}
@incollection{howard2011motor,
  title={Motor proteins as nanomachines: the roles of thermal fluctuations in generating force and motion},
  author={Howard, Jonathon},
  booktitle={Biological Physics},
  pages={47--59},
  year={2011},
  publisher={Springer}
}
@book{bender1999advanced,
  title={Advanced mathematical methods for scientists and engineers I},
  author={Bender, Carl M and Orszag, Steven A},
  year={1999},
  publisher={Springer Science \& Business Media}
}

@book{MATLAB2016,
year = {2016},
author = {MATLAB},
title = {version 9.0.0.341360 (R2016a)},
publisher = {The MathWorks Inc.},
address = {Natick, Massachusetts, https://www.mathworks.com/}
}

@book{Maple2016,
year = {2016},
author = {Maple},
title = {},
publisher = {The Maplesoft Inc.},
address = {Waterloo, ON, http://www.maplesoft.com/products/Maple}
}
@article{artsimovitch2000pausing,
  title={Pausing by bacterial {RNA} polymerase is mediated by mechanistically distinct classes of signals},
  author={Artsimovitch, Irina and Landick, Robert},
  journal={Proc. Natl. Acad.  Sci. U.S.A.},
  volume={97},
  number={13},
  pages={7090--7095},
  year={2000},
  publisher={National Acad Sciences}
}

@article{toulokhonov2003flap,
  title={The flap domain is required for pause {RNA} hairpin inhibition of catalysis by {RNA} polymerase and can modulate intrinsic termination},
  author={Toulokhonov, Innokenti and Landick, Robert},
  journal={Mol. Cell},
  volume={12},
  number={5},
  pages={1125--1136},
  year={2003},
  publisher={Elsevier}
}
@article{toulokhonov2001allosteric,
  title={Allosteric control of {RNA} polymerase by a site that contacts nascent {RNA} hairpins},
  author={Toulokhonov, Innokenti and Artsimovitch, Irina and Landick, Robert},
  journal={Science},
  volume={292},
  number={5517},
  pages={730--733},
  year={2001},
  publisher={American Association for the Advancement of Science}
}

@article{vitreschak2004attenuation,
  title={Attenuation regulation of amino acid biosynthetic operons in proteobacteria: comparative genomics analysis},
  author={Vitreschak, Alexey G and Lyubetskaya, Elena V and Shirshin, Maxim A and Gelfand, Mikhail S and Lyubetsky, Vassily A},
  journal={FEMS Microbiology Letters},
  volume={234},
  number={2},
  pages={357--370},
  year={2004},
  publisher={The Oxford University Press}
}

@book{plischke2006equilibrium,
  title={Equilibrium statistical physics},
  author={Plischke, Michael and Bergersen, Birger},
  year={2006},
  publisher={World Scientific}
}

@article{gowrishankar2004transcription,
  title={Why is transcription coupled to translation in bacteria?},
  author={Gowrishankar, J and Harinarayanan, R},
  journal={Molecular Microbiology},
  volume={54},
  number={3},
  pages={598--603},
  year={2004},
  publisher={Wiley Online Library}
}
@article{sims2004elongation,
  title={Elongation by {RNA} polymerase {II}: the short and long of it},
  author={Sims III, Robert J and Belotserkovskaya, Rimma and Reinberg, Danny},
  journal={Genes Dev.},
  volume={18},
  number={20},
  pages={2437--2468},
  year={2004},
  publisher={Cold Spring Harbor Lab}
}

@article{richard2009transcription,
  title={Transcription termination by nuclear {RNA} polymerases},
  author={Richard, Patricia and Manley, James L},
  journal={Genes Dev.},
  volume={23},
  number={11},
  pages={1247--1269},
  year={2009},
  publisher={Cold Spring Harbor Lab}
}
@article{tennyson1995human,
  title={The human dystrophin gene requires 16 hours to be transcribed and is cotranscriptionally spliced.},
  author={Tennyson, Christine N and Klamut, Henry J and Worton, Ronald G},
  journal={Nat. Genet.},
  volume={9},
  pages={184--190},
  year={1995}
}

@article{klumpp2011pausing,
  title={Pausing and backtracking in transcription under dense traffic conditions},
  author={Klumpp, Stefan},
  journal={J. Stat. Phys.},
  volume={142},
  number={6},
  pages={1252--1267},
  year={2011},
  publisher={Springer}
}

@Article{Larson-etal2011,
  author    = {Daniel R. Larson and Daniel Zenklusen and Bin Wu and Jeffrey A. Chao and Robert H. Singer},
  journal   = {Science},
  title     = {Real-Time Observation of Transcription Initiation and Elongation on an Endogeneous Yeast Gene},
  year      = {2011},
  volume    = {332},
  pages     = {475-478},
  abstract  = {Cellular messenger RNA levels are achieved by the combinatorial complexity of factors controlling transcription, yet the small number of molecules involved in these pathways fluctuates stochastically. It has not yet been experimentally possible to observe the activity of single polymerases on an endogenous gene to elucidate how these events occur in vivo. Here, we describe a method of fluctuation analysis of fluorescently labeled RNA to measure dynamics of nascent RNA---including initiation, elongation, and termination---at an active yeast locus. We find no transcriptional memory between initiation events, and elongation speed can vary by threefold throughout the cell cycle. By measuring the abundance and intranuclear mobility of an upstream transcription factor, we observe that the gene firing rate is directly determined by trans-activating factor search times.},
  annote    = {This paper uses a fluorescence method to image transcription events in yeast cells. A number of rate constants or, equivalently, of mean time periods, are extracted from the data, including the elongation rate, termination time and initiation rate. Initiation is much slower than the other steps. The authors' data is consistent with a model in which transcription activation is determined by rate-limiting recruitment of a factor (perhaps TBP?), followed by assembly of the pre-initiation complex (PIC). They also find that elongation is much less stochastic (the authors say ``deterministic'') than initiation.},
  doi       = {10.1126/science.1202142},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{Buratowski-etal1989,
  author    = {Stephen Buratowski and Steven Hahn and Leonard Guarente and Phillip A. Sharp},
  title     = {Five Intermediate Complexes in Transcription Initiation by {RNA} Polymerase {II}},
  journal   = {Cell},
  year      = {1989},
  volume    = {56},
  pages     = {549-561},
  annote    = {This paper studies the interactions of the various transcription factors needed for a minimal eukaryotic \emph{in vitro} transcription system with each other, with a DNA strand containing a TATA box, and with RNA polymerase II. The factors studied are TFIID (including TATA-binding protein, TBP), TFIIA, TFIIB and TFIIE. The footprints of various complexes on the DNA are obtained, leading to a model of a mimimal pre-initiation complex.},
  doi       = {10.1016/0092-8674(89)90578-3},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{Darzacq-etal2007,
  author    = {Xavier Darzacq and Yaron Shav-Tal and Valeria de Turris and Yehuda Brody and Shailesh M. Shenoy and Robert D. Phair and Robert H. Singer},
  journal   = {Nat. Struct. Mol. Biol.},
  title     = {\emph{In vivo} Dynamics of {RNA} Polymerase {II} Transcription},
  year      = {2007},
  volume    = {14},
  pages     = {796-806},
  abstract  = {We imaged transcription in living cells using a locus-specific reporter system, which allowed precise, single-cell kinetic
measurements of promoter binding, initiation and elongation. Photobleaching of fluorescent RNA polymerase II revealed several
kinetically distinct populations of the enzyme interacting with a specific gene. Photobleaching and photoactivation of fluorescent
MS2 proteins used to label nascent messenger RNAs provided sensitive elongation measurements. A mechanistic kinetic model
that fits our data was validated using specific inhibitors. Polymerases elongated at 4.3 kilobases min$^{-1}$, much faster than
previously documented, and entered a paused state for unexpectedly long times. Transcription onset was inefficient, with only
1\% of polymerase-gene interactions leading to completion of an mRNA. Our systems approach, quantifying both polymerase and
mRNA kinetics on a defined DNA template
\emph{in vivo}
with high temporal resolution, opens new avenues for studying regulation of
transcriptional processes \emph{in vivo}.},
  annote    = {A set of clever fluorescence experiments was used to study the transcription of an artificial construct introduced into a human tumor cell. The data were analyzed with the help of some simple mathematical models, which allowed the recovery of a number of kinetic parameters, including rate constants for initiation and for various channels leading to premature termination, elongation rates, and pausing frequencies and durations.},
  doi       = {10.1038/nsmb1280},
  owner     = {roussel},
  timestamp = {2012.07.25}
}

@Article{Venter-etal2001,
  author    = {Venter, J. Craig and Adams, Mark D. and Myers, Eugene W. and Li, Peter W. and Mural, Richard J. and Sutton, Granger G. and Smith, Hamilton O. and Yandell, Mark and Evans, Cheryl A. and Holt, Robert A. and Gocayne, Jeannine D. and Amanatides, Peter and Ballew, Richard M. and Huson, Daniel H. and Wortman, Jennifer Russo and Zhang, Qing and Kodira, Chinnappa D. and Zheng, Xiangqun H. and Chen, Lin and Skupski, Marian and Subramanian, Gangadharan and Thomas, Paul D. and Zhang, Jinghui and Gabor Miklos, George L. and Nelson, Catherine and Broder, Samuel and Clark, Andrew G. and Nadeau, Joe and McKusick, Victor A. and Zinder, Norton and Levine, Arnold J. and Roberts, Richard J. and Simon, Mel and Slayman, Carolyn and Hunkapiller, Michael and Bolanos, Randall and Delcher, Arthur and Dew, Ian and Fasulo, Daniel and Flanigan, Michael and Florea, Liliana and Halpern, Aaron and Hannenhalli, Sridhar and Kravitz, Saul and Levy, Samuel and Mobarry, Clark and Reinert, Knut and Remington, Karin and Abu-Threideh, Jane and Beasley, Ellen and Biddick, Kendra and Bonazzi, Vivien and Brandon, Rhonda and Cargill, Michele and Chandramouliswaran, Ishwar and Charlab, Rosane and Chaturvedi, Kabir and Deng, Zuoming and Francesco, Valentina Di and Dunn, Patrick and Eilbeck, Karen and Evangelista, Carlos and Gabrielian, Andrei E. and Gan, Weiniu and Ge, Wangmao and Gong, Fangcheng and Gu, Zhiping and Guan, Ping and Heiman, Thomas J. and Higgins, Maureen E. and Ji, Rui-Ru and Ke, Zhaoxi and Ketchum, Karen A. and Lai, Zhongwu and Lei, Yiding and Li, Zhenya and Li, Jiayin and Liang, Yong and Lin, Xiaoying and Lu, Fu and Merkulov, Gennady V. and Milshina, Natalia and Moore, Helen M. and Naik, Ashwinikumar K and Narayan, Vaibhav A. and Neelam, Beena and Nusskern, Deborah and Rusch, Douglas B. and Salzberg, Steven and Shao, Wei and Shue, Bixiong and Sun, Jingtao and Wang, Zhen Yuan and Wang, Aihui and Wang, Xin and Wang, Jian and Wei, Ming-Hui and Wides, Ron and Xiao, Chunlin and Yan, Chunhua and Yao, Alison and Ye, Jane and Zhan, Ming and Zhang, Weiqing and Zhang, Hongyu and Zhao, Qi and Zheng, Liansheng and Zhong, Fei and Zhong, Wenyan and Zhu, Shiaoping C. and Zhao, Shaying and Gilbert, Dennis and Baumhueter, Suzanna and Spier, Gene and Carter, Christine and Cravchik, Anibal and Woodage, Trevor and Ali, Feroze and An, Huijin and Awe, Aderonke and Baldwin, Danita and Baden, Holly and Barnstead, Mary and Barrow, Ian and Beeson, Karen and Busam, Dana and Carver, Amy and Center, Angela and Cheng, Ming Lai and Curry, Liz and Danaher, Steve and Davenport, Lionel and Desilets, Raymond and Dietz, Susanne and Dodson, Kristina and Doup, Lisa and Ferriera, Steven and Garg, Neha and Gluecksmann, Andres and Hart, Brit and Haynes, Jason and Haynes, Charles and Heiner, Cheryl and Hladun, Suzanne and Hostin, Damon and Houck, Jarrett and Howland, Timothy and Ibegwam, Chinyere and Johnson, Jeffery and Kalush, Francis and Kline, Lesley and Koduru, Shashi and Love, Amy and Mann, Felecia and May, David and McCawley, Steven and McIntosh, Tina and McMullen, Ivy and Moy, Mee and Moy, Linda and Murphy, Brian and Nelson, Keith and Pfannkoch, Cynthia and Pratts, Eric and Puri, Vinita and Qureshi, Hina and Reardon, Matthew and Rodriguez, Robert and Rogers, Yu-Hui and Romblad, Deanna and Ruhfel, Bob and Scott, Richard and Sitter, Cynthia and Smallwood, Michelle and Stewart, Erin and Strong, Renee and Suh, Ellen and Thomas, Reginald and Tint, Ni Ni and Tse, Sukyee and Vech, Claire and Wang, Gary and Wetter, Jeremy and Williams, Sherita and Williams, Monica and Windsor, Sandra and Winn-Deen, Emily and Wolfe, Keriellen and Zaveri, Jayshree and Zaveri, Karena and Abril, Josep F. and Guig{\'o}, Roderic and Campbell, Michael J. and Sjolander, Kimmen V. and Karlak, Brian and Kejariwal, Anish and Mi, Huaiyu and Lazareva, Betty and Hatton, Thomas and Narechania, Apurva and Diemer, Karen and Muruganujan, Anushya and Guo, Nan and Sato, Shinji and Bafna, Vineet and Istrail, Sorin and Lippert, Ross and Schwartz, Russell and Walenz, Brian and Yooseph, Shibu and Allen, David and Basu, Anand and Baxendale, James and Blick, Louis and Caminha, Marcelo and Carnes-Stine, John and Caulk, Parris and Chiang, Yen-Hui and Coyne, My and Dahlke, Carl and Mays, Anne Deslattes and Dombroski, Maria and Donnelly, Michael and Ely, Dale and Esparham, Shiva and Fosler, Carl and Gire, Harold and Glanowski, Stephen and Glasser, Kenneth and Glodek, Anna and Gorokhov, Mark and Graham, Ken and Gropman, Barry and Harris, Michael and Heil, Jeremy and Henderson, Scott and Hoover, Jeffrey and Jennings, Donald and Jordan, Catherine and Jordan, James and Kasha, John and Kagan, Leonid and Kraft, Cheryl and Levitsky, Alexander and Lewis, Mark and Liu, Xiangjun and Lopez, John and Ma, Daniel and Majoros, William and McDaniel, Joe and Murphy, Sean and Newman, Matthew and Nguyen, Trung and Nguyen, Ngoc and Nodell, Marc and Pan, Sue and Peck, Jim and Peterson, Marshall and Rowe, William and Sanders, Robert and Scott, John and Simpson, Michael and Smith, Thomas and Sprague, Arlan and Stockwell, Timothy and Turner, Russell and Venter, Eli and Wang, Mei and Wen, Meiyuan and Wu, David and Wu, Mitchell and Xia, Ashley and Zandieh, Ali and Zhu, Xiaohong},
  title     = {The Sequence of the Human Genome},
  journal   = {Science},
  year      = {2001},
  volume    = {291},
  pages     = {1304-1351},
  abstract  = {A 2.91-billion base pair (bp) consensus sequence of the euchromatic portion of the human genome was generated by the whole-genome shotgun sequencing method. The 14.8-billion bp DNA sequence was generated over 9 months from 27,271,853 high-quality sequence reads (5.11-fold coverage of the genome) from both ends of plasmid clones made from the DNA of five individuals. Two assembly strategies---whole-genome assembly and a regional chromosome assembly---were used, each combining sequence data from Celera and the publicly funded genome effort. The public data were shredded into 550-bp segments to create a 2.9-fold coverage of those genome regions that had been sequenced, without including biases inherent in the cloning and assembly procedure used by the publicly funded group. This brought the effective coverage in the assemblies to eightfold, reducing the number and size of gaps in the final assembly over what would be obtained with 5.11-fold coverage. The two assembly strategies yielded very similar results that largely agree with independent mapping data. The assemblies effectively cover the euchromatic regions of the human chromosomes. More than 90% of the genome is in scaffold assemblies of 100,000 bp or more, and 25% of the genome is in scaffolds of 10 million bp or larger. Analysis of the genome sequence revealed 26,588 protein-encoding transcripts for which there was strong corroborating evidence and an additional $\sim$12,000 computationally derived genes with mouse matches or other weak supporting evidence. Although gene-dense clusters are obvious, almost half the genes are dispersed in low G+C sequence separated by large tracts of apparently noncoding sequence. Only 1.1\% of the genome is spanned by exons, whereas 24\% is in introns, with 75\% of the genome being intergenic DNA. Duplications of segmental blocks, ranging in size up to chromosomal lengths, are abundant throughout the genome and reveal a complex evolutionary history. Comparative genomic analysis indicates vertebrate expansions of genes associated with neuronal function, with tissue-specific developmental regulation, and with the hemostasis and immune systems. DNA sequence comparisons between the consensus sequence and publicly funded genome data provided locations of 2.1 million single-nucleotide polymorphisms (SNPs). A random pair of human haploid genomes differed at a rate of 1 bp per 1250 on average, but there was marked heterogeneity in the level of polymorphism across the genome. Less than 1\% of all SNPs resulted in variation in proteins, but the task of determining which SNPs have functional consequences remains an open challenge.},
  annote    = {I haven't read this very lengthy paper in detail. I have pulled out the following statistics: \begin{itemize} \item The average human gene has a length of 28\,kb. \item Only about 4\% of the regions containing genes are exonic. The rest, about 96\%, of the gene is intronic. \end{itemize}},
  doi       = {10.1126/science.1058040},
  owner     = {roussel},
  timestamp = {2015.08.12},
}

@Article{LB2015,
  author    = {Jean-Fran\c{c}ois Lemay and Fran\c{c}ois Bachand},
  title     = {Fail-Safe Transcription Termination: Because One Is Never Enough},
  journal   = {RNA Biol.},
  year      = {2015},
  volume    = {12},
  pages     = {927-932},
  abstract  = {Termination of RNA polymerase II (RNAPII) transcription is a fundamental step of gene expression that involves the release of the nascent transcript and dissociation of RNAPII from the DNA template. As transcription termination is intimately linked to RNA 3' end processing, termination pathways have a key decisive influence on the fate of the transcribed RNA. Quite remarkably, when reaching the 3' end of genes, a substantial fraction of RNAPII fail to terminate transcription, requiring the contribution of alternative or ``fail-safe'' mechanisms of termination to release the polymerase. This point of view covers redundant mechanisms of transcription termination and how they relate to conventional termination models. In particular, we expand on recent findings that propose a reverse torpedo model of termination, in which the 3'5' exonucleolytic activity of the RNA exosome targets transcription events associated with paused and backtracked RNAPII.},
  annote    = {This paper starts by reviewing the literature on transcription termination in genes transcribed by RNA polymerase II (RNAPII). The reasons why timely termination is important are given as follows: ``transcriptional directionality'' (not sure what they mean here), splicing efficiency (again, no explanation of what this has to do with termination, although there are references), control of cryptic transcription events, RNA polymerase recycling, avoiding transcriptional interference, and avoiding collisions between polymerases. The three major mechanisms for terminating RNAPII transcription are briefly reviewed, namely the allosteric, torpedo, and NNS mechanisms. The NNS mechanism is a torpedo-like mechanism in which the Nrd1-Nab3-Sen1 complex, which gives its name to this mechanism, translocates along the nascent transcript in a 5' to 3' direction, eventually catching up to the polymerase and causing it to disengage. The authors have recently added a fourth termination mechanism to these three. In this mechanism, the 3' to 5' exosome engages with the 3' end of RNA extruded from a backtracked elongation complex, degrading the RNA and causing the polymerase to disengage once the exosome reaches the polymerase. They call this the ``reverse torpedo'' model.},
  doi       = {10.1080/15476286.2015.1073433},
  keywords  = {3' end processing, backtracking, fail-safe termination, Nrd1, Rat1, RNA polymerase II, RNA exosome, TFIIS, transcription termination},
  owner     = {roussel},
  timestamp = {2017.10.06},
}

@Article{Schmidt-etal2011,
  author    = {Ute Schmidt and Eugenia Basyuk and Marie-C{\'e}cile Robert and Minoru Yoshida and Jean-Philippe Villemin and Didier Auboeuf and Stuart Aitken and Edouard Bertrand},
  title     = {Real-Time Imaging of Cotranscriptional Splicing Reveals a Kinetic Model That Reduces Noise: Implications for Alternative Splicing Regulation},
  journal   = {J. Cell Biol.},
  year      = {2011},
  volume    = {193},
  pages     = {819-829},
  annote    = {This paper starts with one of the clearest descriptions of the first few steps of splicing I have seen anywhere. The authors then look at a number of constitutive and alternatively spliced introns in a human cell line using RT-PCR and find that most of them are spliced co-transcriptionally. (They find just one exception, although they admit that they needed to focus on short introns for technological reasons and thus that their results may be biased by the set of introns they examined.) They then engineer a construct which is designed to have a high co-transcriptional splicing efficiency and whose intron has four MS2 binding sites. These binding sites can thus be detected using an MS2-GFP fusion protein. FRAP experiments are then used to study the kinetics of intron splicing. The MS2 signal is never seen in free introns, i.e.\ intron degradation is rapid after they have been cut out. A very simple stochastic model with consecutive steps with equal rate constants was used to model the FRAP data. It was found that a three-step process provided an optimal model, as judged by the Akaike information criterion. A multi-step model has a smaller variance than a one-step model, all other things being equal. It is believed that alternative splicing involves competition between splice sites. That being the case, the first splice site synthesized has an advantage over its competitors. A situation in which a weak acceptor site is in competition with a strong downstream acceptor was simulated. The one-step model requires a much larger adjustment in its kinetic parameters in order to favor the downstream site than does the multi-step model, i.e.\ the multi-step model is easier to optimize for a desired splicing outcome.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{BDS2012,
  author    = {Anna Babour and Catherine Dargemont and Fran\c{c}oise Stutz},
  title     = {Ubiquitin and Assembly of Export Competent {mRNP}},
  journal   = {Biochim. Biophys. Acta},
  year      = {2012},
  volume    = {1819},
  pages     = {521-530},
  abstract  = {The production of mature and export competent mRNP (mRNA ribonucleoprotein) complexes depends on a series of highly coordinated processing reactions. RNA polymerase II (RNAPII) plays a central role in this process by mediating the sequential recruitment of mRNA maturation and export factors to transcribing genes, thereby establishing a strong functional link between transcription and export through nuclear pore complexes (NPC). Growing evidence indicates that post-translational modifications participate in the dynamic association of processing and export factors with mRNAs ensuring that the transitions and rearrangements undergone by the mRNP occur at the right time and place. This review mainly focuses on the role of ubiquitin conjugation in controlling mRNP assembly and quality control from transcription down to export through the NPC. It emphasizes the central role of ubiquitylation in organizing the chronology of events along this highly dynamic pathway. This article is part of a Special Issue entitled: Nuclear Transport and RNA Processing.},
  annote    = {This is a very dense review of the formation of the export-competent mRNP complex, focusing particularly on the role of ubiquitylation. The opening section however is a rather general (and, again, very dense) review of mRNA packaging into mRNP. A clear theme is that most of this processing and packaging is co-transcriptional.},
  doi       = {10.1016/j.bbagrm.2011.12.006},
  keywords  = {Ubiquitin, Transcription, mRNP assembly, mRNA export, Quality control, Nuclear pore complex},
  owner     = {roussel},
  timestamp = {2017.10.06},
}

@Article{Cramer-etal2001,
  author    = {P. Cramer and A. Srebrow and S. Kadener and S. Werbajh and M. de la Mata and G. Melen and G. Nogu\'es and A. R. Kornblihtt},
  journal   = {FEBS Lett.},
  title     = {Coordination Between Transcription and Pre-{mRNA} Processing},
  year      = {2001},
  volume    = {498},
  pages     = {179-182},
  abstract  = {A large body of work has proved that transcription by RNA polymerase II and pre-mRNA processing are coordinated events within the cell nucleus. Capping, splicing and polyadenylation occur while transcription proceeds, suggesting that RNA polymerase II plays a role in the regulation of these events. The presence and degree of phosphorylation of the carboxy-terminal domain of RNA polymerase II large subunit is important for functioning of the capping enzymes, the assembly of spliceosomes and the binding of the cleavage/polyadenylation complex. Nuclear architecture and gene promoter structure have also been shown to play key roles in coupling between transcription and splicing.},
  annote    = {RNA polymerase II (RNAP II) has a C-terminal domain (CTD) consisting of 52 repeats of the peptide YSPTSPS in mammals. The presence of both serines and threonines in this repeat means that the CTD can be phosphorylated. In fact, both hyper- and hypophosphorylated forms of the CTD have been observed in vivo. Elongating complexes generally involve the hyperphosphorylated form, while complexes in a promoter-proximal pause are generally in the hypophosphorylated form. This CTD and its phosphorylation state appear to be critical in coordinating transcription with capping, splicing and polyadenylation. All three of the latter processes occur while the polymerase is actively transcribing the gene.},
  doi       = {10.1016/S0014-5793(01)02485-1},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{PCP2010,
  author    = {Vicent Pelechano and Sebasti{\'a}n Ch{\'a}vez and Jos{\'e} E. P{\'e}rez-Ort{\'\i}n},
  journal   = {PLoS One},
  title     = {A Complete Set of Nascent Transcription Rates for Yeast Genes},
  year      = {2010},
  volume    = {5},
  pages       = {e15442},
  abstract  = {The amount of mRNA in a cell is the result of two opposite reactions: transcription and mRNA degradation. These reactions are governed by kinetics laws, and the most regulated step for many genes is the transcription rate. The transcription rate, which is assumed to be exercised mainly at the RNA polymerase recruitment level, can be calculated using the RNA polymerase densities determined either by run-on or immunoprecipitation using specific antibodies. The yeast \emph{Saccharomyces cerevisiae} is the ideal model organism to generate a complete set of nascent transcription rates that will prove useful for many gene regulation studies. By combining genomic data from both the GRO (Genomic Run-on) and the RNA pol ChIP-on-chip methods we generated a new, more accurate nascent transcription rate dataset. By comparing this data set with the indirect ones obtained from the mRNA stabilities and mRNA amount datasets, we are able to obtain biological information about posttranscriptional regulation processes and a genomic snapshot of the location of the active transcriptional machinery. We have obtained nascent transcription rates for 4,670 yeast genes. The median RNA polymerase II density in the genes is 0.078 molecules/kb, which corresponds to an average of 0.096 molecules/gene. Most genes have transcription rates of between 2 and 30 mRNAs/hour and less than 1\% of yeast genes have $>1$ RNA polymerase molecule/gene. Histone and ribosomal protein genes are the highest transcribed groups of genes and other than these exceptions the transcription of genes is an infrequent phenomenon in a yeast cell.},
  annote    = {This paper presents a set of measurements and analyses of genomic run-on and ChIP-on-chip data used to determine transcription rates and polymerase occupancies for over 5000 yeast genes. The overall conclusion is that most genes, even when actively transcribed, rarely have one and almost never two RNA polymerases on them. The most actively transcribed genes during exponential growth are the histones, followed by the ribosomal RNA genes.},
  doi       = {10.1371/journal.pone.0015442},
  owner     = {marcroussel},
  timestamp = {2017.10.06},
}


@Article{AIB+2010,
  author    = {Ross D. Alexander and Steven A. Innocente and J. David Barrass and Jean D. Beggs},
  journal   = {Mol. Cell},
  title     = {Splicing-Dependent {RNA} Polymerase Pausing in Yeast},
  year      = {2010},
  volume    = {40},
  pages     = {582-593},
  abstract  = {In eukaryotic cells, there is evidence for functional coupling between transcription and processing of pre-mRNAs. To better understand this coupling, we performed a high-resolution kinetic analysis of transcription and splicing in budding yeast. This revealed that shortly after induction of transcription, RNA polymerase accumulates transiently around the 3' end of the intron on two reporter genes. This apparent transcriptional pause coincides with splicing factor recruitment and with the first detection of spliced mRNA and is repeated periodically thereafter. Pausing requires productive splicing, as it is lost upon mutation of the intron and restored by suppressing the splicing defect. The carboxy-terminal domain of the paused polymerase large subunit is hyperphosphorylated on serine 5, and phosphorylation of serine 2 is first detected here. Phosphorylated polymerase also accumulates around the 3' splice sites of constitutively expressed, endogenous yeast genes. We propose that transcriptional pausing is imposed by a checkpoint associated with cotranscriptional splicing.},
  annote    = {The authors find that splicing causes pausing in several genes. The pause occurs in a fairly broad region following the 3' splice site. The pause is not sequence-dependent. Rather, it depends on the splicing event. These splicing-associated pauses last less than 30\,s. The pauses recur periodically every two to three minutes, presumably because that's the interval between polymerases passing the splice site. This paper also contains some data on the accumulation of pre-mRNA and of mRNA.},
  doi       = {10.1016/j.molcel.2010.11.005},
  owner     = {marcroussel},
  timestamp = {2017.10.09},
}

@Article{GCR2009,
  author    = {Ashok Garai and Debashish Chowdhury and T. V. Ramakrishnan},
  journal   = {Phys. Rev. E},
  title     = {Fluctuations in Protein Synthesis from a Single {RNA} Template: Stochastic Kinetics of Ribosomes},
  year      = {2009},
  volume    = {79},
  pages       = {011916},
  abstract  = {Proteins are polymerized by cyclic machines called ribosomes, which use their messenger RNA (mRNA) track also as the corresponding template, and the process is called translation. We explore, in depth and detail, the stochastic nature of the translation. We compute various distributions associated with the translation process; one of them---namely, the dwell time distribution---has been measured in recent single-ribosome experiments. The form of the distribution, which fits best with our simulation data, is consistent with that extracted from the experimental data. For our computations, we use a model that captures both the mechanochemistry of each individual ribosome and their steric interactions. We also demonstrate the effects of the sequence inhomogeneities of real genes on the fluctuations and noise in translation. Finally, inspired by recent advances in the experimental techniques of manipulating single ribosomes, we make theoretical predictions on the force-velocity relation for individual ribosomes. In principle, all our predictions can be tested by carrying out in vitro experiments.},
  annote    = {The authors describe a model of translation elongation in \emph{Escherichia coli} that includes five states of the ribosome at each codon. The rate constant corresponding to loading of the correct tRNA is adjusted for tRNA abundances. They study their model by simulation, and obtain distributions of the dwell time at a single codon, of the run time (total translation time from initiation to termination), and of the headway (time between termination events). They find that, for the sequence of the \emph{E. coli} \emph{crr} gene, taking into account codon-to-codon tRNA loading rate variability, there is much more traffic on the mRNA than for an mRNA of similar length in which tRNA loading rate variability was neglected. Correspondingly, there is much more noise in the three distributions, as measured by the width of the distributions, i.e.\ more variability in dwell time, run time and headway. They also modify their model to take into account a load force, and generate velocity vs force curves.},
  doi       = {10.1103/PhysRevE.79.011916},
  owner     = {marcroussel},
  timestamp = {2017.06.21},
}

@Article{TSH2010,
  author    = {Mier{-}y{-}Ter{\'a}n{-}Romero, Luis and Mary Silber and Vassily Hatzimanikatis},
  journal   = {PLoS Comput. Biol.},
  title     = {The Origins of Time-Delay in Template Biopolymerization Processes},
  year      = {2010},
  volume    = {6},
  pages       = {e1000726},
  abstract  = {Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70\%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models.},
  annote    = {The authors start with a mechanistic (master equation) description of translation, which considers variable codon translation rates as well as mutual exclusion by ribosomes. They derive a PDE in the continuum limit. Except for initiation, their PDE formulation neglects ribosome-ribosome interactions, i.e.\ it's valid in the low-density limit. It does however take into account the finite ribosome pool. I'm not sure if it makes sense to do this since there isn't a fixed number of ribosomes ``assigned'' to a particular mRNA, and diffusion will result in exchange of ribosomes between the region of a ribosome binding site and the rest of the cytoplasm. By using the method of characteristics, they solve their PDE to obtain an integral equation of the delay type. This equation includes a term representing exclusion at the ribosome binding site, and another representing the finite pool of ribosomes assumed here. The delay model generally performs well. Ribosome wavefronts after initiation of translation are too sharp relative to a stochastic model. With an oscillating rate of initiation, the stochastic model rapidly damps out the oscillations along the length of the gene, while the delay model transmits them as a wave of ribosome density. On the other hand, for a self-repressing gene, the two models predict oscillations with essentially identical amplitudes.},
  doi       = {10.1371/journal.pcbi.1000726},
  owner     = {marcroussel},
  timestamp = {2017.05.05},
}

@Article{CW2011,
  author    = {L. Stirling Churchman and Jonathan S. Weissman},
  title     = {Nascent Transcript Sequencing Visualizes Transcription at Nucleotide Resolution},
  journal   = {Nature},
  year      = {2011},
  volume    = {469},
  pages     = {368-373},
  abstract  = {Recent studies of transcription have revealed a level of complexity not previously appreciated even a few years ago, both in the intricate use of post-initiation control and the mass production of rapidly degraded transcripts. Dissection of these pathways requires strategies for precisely following transcripts as they are being produced. Here we present an approach (native elongating transcript sequencing, NET-seq), based on deep sequencing of 3' ends of nascent transcripts associated with RNA polymerase, to monitor transcription at nucleotide resolution. Application of NET-seq in \emph{Saccharomyces cerevisiae} reveals that although promoters are generally capable of divergent transcription, the Rpd3S deacetylation complex enforces strong directionality to most promoters by suppressing antisense transcript initiation. Our studies also reveal pervasive polymerase pausing and backtracking throughout the body of transcripts. Average pause density shows prominent peaks at each of the first four nucleosomes, with the peak location occurring in good agreement with \emph{in vitro} biophysical measurements. Thus, nucleosome-induced pausing represents a major barrier to transcriptional elongation \emph{in vivo}.},
  annote    = {The authors describe a new method for sequencing transcripts still being synthesized. In a nutshell, they freeze and lyse cells, then extract a desired RNA polymerase (in this case, RNAP II in yeast) by immunoprecipitation. The RNAs bound to the polymerase are then separated out and sequenced. Using this technique, they find that bidirectional transcription (i.e.\ transcription of both the sense and antisense strand) occur frequently \emph{in vivo}, although sense transcription is much more common. They investigate the mechanism that suppresses antisense transcription. They also find that pausing is ubiquitous during transcription, occurring in all regions of a gene. In fact, a polymerase may spend as much time paused as actively transcribing. Pauses occur particularly frequently at nucleosome dyads.},
  doi       = {10.1038/nature09652},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{LG2011,
  author    = {Jian Li and David S Gilmour},
  title     = {Promoter Proximal Pausing and the Control of Gene Expression},
  journal   = {Curr. Opin. Genet. Dev.},
  year      = {2011},
  volume    = {21},
  pages     = {231-235},
  annote    = {This is a review of promoter-proximal pausing, emphasizing its possible functions.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{ZBI+2012,
  author    = {Bradley Zamft and Lacramioara Bintu and Toyotaka Ishibashi and Carlos Bustamante},
  journal   = {Proc. Natl. Acad. Sci. U.S.A.},
  title     = {Nascent {RNA} Structure Modulates the Transcriptional Dynamics of {RNA} Polymerases},
  year      = {2012},
  volume    = {109},
  pages     = {8948-8953},
  abstract  = {RNA polymerase pausing represents an important mechanism of transcriptional regulation. In this study, we use a single-molecule transcription assay to investigate the effect of template base-pair composition on pausing by RNA polymerase II and the evolutionarily distinct mitochondrial polymerase Rpo41. For both enzymes, pauses are shorter and less frequent on GC-rich templates. Significantly, incubation with RNase abolishes the template dependence of pausing. A kinetic model, wherein the secondary structure of the nascent RNA poses an energetic barrier to pausing by impeding backtracking along the template, quantitatively predicts the pause densities and durations observed. The energy barriers extracted from the data correlate well with RNA folding energies obtained from cotranscriptional folding simulations. These results reveal that RNA secondary structures provide a cis-acting mechanism by which sequence modulates transcriptional elongation. },
  annote    = {The basic experiment used in this study involves an RNAP polymerase and a DNA strand, each of which is bound to a different polystyrene bead such that transcription pulls the two beads together. This allows for very precise measurement of elongation velocities as well as pause duration and frequency. Two different polymerases were studied, namely RNA polymerase II and the mitochondrial polymerase Rpo41. Three different RNA sequences were used, one of which is AT-rich, the other GC-rich, while the last one has roughly equal GC and AT content. For each polymerase, the elongation velocity (pauses removed) is independent of the GC content ($18.3\pm 1.6\,\mathrm{bp\,s^{-1}}$ for Pol II, and $23.9\pm 2.4\,\mathrm{bp\,s^{-1}}$ for Rpo41). For both polymerases, pause duration and frequency both decrease with increasing GC content. The authors explain this by the tendency of GC-rich sequences to form secondary RNA structures, which would inhibit backtracking. This hypothesis is supported by a loss in the sequence dependence when the experiment is carried out in the presence of RNase A, with pause duration comparable in the presence of RNase A to that of AT-rich sequences in the absence of the RNase. They also show that the kinetic barrier to backtracking inferred from their data correlates very well to the free energy of secondary structure formation computed from a cotranscriptional folding simulation.},
  doi       = {10.1073/pnas.1205063109},
  keywords  = {enzyme kinetics, Pol II, transcriptional pausing, yeast },
  owner     = {marcroussel},
  timestamp = {2013.08.22},
}

@Article{GWP2006,
  author    = {Natalia Gromak and Steven West and Nick J. Proudfoot},
  title     = {Pause Sites Promote Transcriptional Termination of Mammalian {RNA} Polymerase {II}},
  journal   = {Mol. Cell. Biol.},
  year      = {2006},
  volume    = {26},
  pages     = {3986-3996},
  annote    = {Pausing after a poly(A) signal increases the probability of transcriptional termination following cleavage at the poly(A) site in a process involving degradation of the transcript on the distal side of the cleavage.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{Luse2013,
  author    = {Donal S. Luse},
  title     = {Promoter Clearance by {RNA} Polymerase {II}},
  journal   = {Biochim. Biophys. Acta},
  year      = {2013},
  volume    = {1829},
  pages     = {63--68},
  abstract  = {Many changes must occur to the RNA polymerase II (pol II) transcription complex as it makes the transition
from initiation into transcript elongation. During this intermediate phase of transcription, contact with initiation
factors is lost and stable association with the nascent transcript is established. These changes collectively
comprise promoter clearance. Once the transcript elongation complex has reached a point where its
properties are indistinguishable from those of complexes with much longer transcripts, promoter clearance
is complete. The clearance process for pol II consists of a number of steps and it extends for a surprisingly
long distance downstream of transcription start. This article is part of a Special Issue entitled: RNA polymerase
II Transcript Elongation.},
  annote    = {This paper reviews the current state of knowledge on eukaryotic transcription initiation. It contains a very nice figure summarizing the key events, and where they occur on the template. It appears that abortive initiation may only be significant in eukaryotes in the very early stages (2--3 nucleotides). The helicase TFIIH probably eliminates the need for scrunching, and thus avoids abortive initiation of longer transcripts as is seen in prokaryotes. Because Mediator is often involved in initiation and appears to continue to be associated with the polymerase during elongation, the author speculates that it is involved in a mechanism for rapid reinitiation.},
  doi       = {10.1016/j.bbagrm.2012.08.010},
  keywords  = {Transcript initiation, Abortive initiation, Transcript elongation, TFIIB, TFIIH},
  owner     = {Marc},
  publisher = {Elsevier {BV}},
  timestamp = {2017.05.23},
}

@Article{GH2005,
  author    = {Sandra J. Greive and Peter H. von Hippel},
  journal   = {Nat. Rev. Mol. Cell Biol.},
  title     = {Thinking Quantitatively About Transcriptional Regulation},
  year      = {2005},
  volume    = {6},
  pages     = {221-232},
  abstract  = {By thinking about the chemical and physical mechanisms that are involved in the
stepwise elongation of RNA transcripts, we can begin to understand the way that these
mechanisms are controlled within the cell to reflect the different requirements for transcription
that are posed by various metabolic, developmental and disease states. Here, we focus on the
mechanistic details of the single-nucleotide addition (or excision) cycle in the transcription
process, as this is the level at which many regulatory mechanisms function and can be explained
in quantitative terms.},
  annote    = {This review paper summarizes the steps in both prokaryotic and eukaryotic transcription, including alternative pathways like pausing, arrest and editing. A thermodynamic framework is used to understand various effects, including the selection of alternative pathways. Some data on the rates of various steps are also given, with references to the primary literature.},
  doi       = {10.1038/nrm1588},
  owner     = {roussel},
  timestamp = {2012.07.25}
}

@Article{LZK+2012,
  author    = {Matthew H. Larson and Jing Zhou and Craig D. Kaplan and Murali Palangat and Roger D. Kornberg and Robert Landick and Steven M. Block},
  journal   = {Proc. Natl. Acad. Sci. U.S.A.},
  title     = {Trigger Loop Dynamics Mediate the Balance between the Transcriptional Fidelity and Speed of {RNA} Polymerase {II}},
  year      = {2012},
  volume    = {109},
  pages     = {6555-6560},
  abstract  = {During transcription, RNA polymerase II (RNAPII) must select the correct nucleotide, catalyze its addition to the growing RNA transcript, and move stepwise along the DNA until a gene is fully transcribed. In all kingdoms of life, transcription must be finely tuned to ensure an appropriate balance between fidelity and speed. Here, we used an optical-trapping assay with high spatiotemporal resolution to probe directly the motion of individual RNAPII molecules as they pass through each of the enzymatic steps of transcript elongation. We report direct evidence that the RNAPII trigger loop, an evolutionarily conserved protein subdomain, serves as a master regulator of transcription, affecting each of the three main phases of elongation, namely: substrate selection, translocation, and catalysis. Global fits to the force-velocity relationships of RNAPII and its trigger loop mutants support a Brownian ratchet model for elongation, where the incoming NTP is able to bind in either the pre- or posttranslocated state, and movement between these two states is governed by the trigger loop. Comparison of the kinetics of pausing by WT and mutant RNAPII under conditions that promote base misincorporation indicate that the trigger loop governs fidelity in substrate selection and mismatch recognition, and thereby controls aspects of both transcriptional accuracy and rate.},
  annote    = {A single-molecule technique is used to obtain position vs time plots for individual RNA polymerase II molecules subjected to either an assistive or retarding force during transcription. The authors consider four different microscopic models of transcription elongation. The traces only fit to a model in which NTPs can bind either to the pre- or post-translocated state. Catalysis and phosphate release are modeled as a single rate-limiting step. Equilibrium constants connecting the various pre-catalysis states and the rate constant for catalysis are recovered. Two populations of pauses are observed: short pauses, with an exponential distribution and a decay time of 1.1\,s, and much less common long pauses (about 5\% of all pauses) with durations of over 10\,s (supplementary data). The frequency of the long pauses corresponds roughly to the frequency of misincorporation (about once every 10 kb).},
  doi       = {10.1073/pnas.1200939109},
  keywords  = {optical trap, optical tweezers, Pol II},
  owner     = {marcroussel},
  timestamp = {2017.07.11},
}

@Article{CP1997,
  author    = {Robert A. Coleman and B. Franklin Pugh},
  title     = {Slow Dimer Dissociation of the {TATA} Binding Protein Dictates the Kinetics of {DNA} Binding},
  journal   = {Proc. Natl. Acad. Sci. U.S.A.},
  year      = {1997},
  volume    = {94},
  pages     = {7221-7226},
  annote    = {Kinetic measurements on the dissociation of the TBP dimer and on the association of TBP with the TATA box are presented. The authors conclude that TBP dimer dissociation may be rate-limiting for transcription.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{FKG2001,
  author    = {Heather A. Ferguson and Jennifer F. Kugel and James A. Goodrich},
  title     = {Kinetic and Mechanistic Analysis of the {RNA} Polymerase {II} Transcription Reaction at the Human Interleukin-2 Promoter},
  journal   = {J. Mol. Biol.},
  year      = {2001},
  volume    = {314},
  pages     = {993-1006},
  annote    = {This paper analyzes in detail the \emph{in vitro} kinetics of a short sequence (28\,nt) transcribed from the interleukin-2 (IL-2) promoter. For this system, pre-initiation complex (PIC) assembly is slow. Escape commitment occurred after the incorporation of the first four nucleotides into the RNA. Promoter escape (transition to productive elongation) was fast. Previous results with an adenovirus promoter and a different \emph{in vitro} transcription system had given the opposite results: fast PIC assembly and slow promoter escape. When the viral promoter was studied using the same \emph{in vitro} system as for the IL-2 promoter, PIC assembly was roughly as slow for the two promoters, and promoter escape was slower by one order of magnitude for the viral promoter than for IL-2.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{CC2011,
  author    = {Alan C. M. Cheung and Patrick Cramer},
  title     = {Structural Basis of {RNA} Polymerase {II} Backtracking, Arrest and Reactivation},
  journal   = {Nature},
  year      = {2011},
  volume    = {471},
  pages     = {249-253},
  annote    = {This paper presents the results of an X-ray crystallographic study of RNAP II arrested complex, and of a reactivation intermediate. A model of arrest and reactivation by TFIIS is presented. During backtracking of paused transcription complexes, a tyrosine acts as a gate, stopping backtracking at a single nucleotide. The two nucleotides at the 3' end of the transcript can be cleaved by the polymerase's intrinsic RNAase activity. However, at arrest sites where the DNA-RNA hybrid is weak, the transcript can escape this gating tyrosine and backtrack further. It then ends up in a conformational state from which it cannot escape unassisted. TFIIS reestablishes a conformation where the transcript can be cleaved and transcription can resume.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{Li-etal1996,
  author    = {Baiyong Li and Janet A. Weber and Yan Chen and Arno L. Greenleaf and David S. Gilmour},
  title     = {Analyses of Promoter-Proximal Pausing by {RNA} Polymerase {II} on the \emph{hsp70} Heat Shock Gene Promoter in a \emph{Drosophila} Nuclear Extract},
  journal   = {Mol. Cell. Biol.},
  year      = {1996},
  volume    = {16},
  pages     = {5433-5443},
  annote    = {The authors study transcriptional pausing of the \emph{hsp70} gene in a cell-free system. They find that most polymerases pause somewhere in the region 20--40 nucleotides downstream of the transcription start site. Paused polymerases remain stably bound for 25 minutes or more. The authors also disprove an earlier hypothesis that the C-terminal domain of the polymerase tethers the polymerase to the DNA in the paused state.},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{BS2015,
  author    = {Grzegorz Brzy{\.z}ek and Szymon {\'S}wie{\.z}ewski},
  journal   = {Transcription},
  title     = {Mutual Interdependence of Splicing and Transcription Elongation},
  year      = {2015},
  volume    = {6},
  pages     = {37-39},
  abstract  = {Transcription and splicing are intrinsically linked, as splicing needs a pre-mRNA substrate to commence. The more nuanced view is that the rate of transcription contributes to splicing regulation. On the other hand there is accumulating evidence that splicing has an active role in controlling transcription elongation by DNA-dependent RNA polymerase II (RNAP II). We briefly review those mechanisms and propose a unifying model where splicing controls transcription elongation to provide an optimal timing for successive rounds of splicing.},
  annote    = {This is a brief review about the coupling between transcription and splicing. The speed of transcription is known to affect splice site selection, with faster a faster transcription favoring later splice sites. Splicing also sometimes induces transcriptional pausing. The authors propose a model in which a first round of splicing leaves behing a marker---they favor histone modification, but the mark could equally well be a splicing protein left at the splice site, DNA methylation, or more exotic things---which causes subsequent polymerases to pause. Splicing-mediated transcriptional pausing may play a role in ensuring correct splicing.},
  doi       = {10.1080/21541264.2015.1040146},
  keywords  = {chromatin and transcription, chromatin marks, co-trancriptional splicing, Eukaryotic transcription, PolII, splicing, transcription and RNA processing, transcription elongation},
  owner     = {marcroussel},
  timestamp = {2017.09.21},
}

@Article{IKL+2013,
  author    = {Masahiko Imashimizu and Maria L. Kireeva and Lucyna Lubkowska and Deanna Gotte and Adam R. Parks and Jeffrey N. Strathem and Mikhail Kashlev},
  title     = {Intrinsic Translocation Barrier as an Initial Step in Pausing by {RNA} Polymerase {II}},
  journal   = {J. Mol. Biol.},
  year      = {2013},
  volume    = {425},
  pages     = {697-712},
  abstract  = {Pausing of RNA polymerase II (RNAP II) by backtracking on DNA is a major regulatory mechanism in control of eukaryotic transcription. Backtracking occurs by extrusion of the 3' end of the RNA from the active center after bond formation and before translocation of RNAP II on DNA. In several documented cases, backtracking requires a special signal such as A/T-rich sequences forming an unstable RNA-DNA hybrid in the elongation complex. However, other sequence-dependent backtracking signals and conformations of RNAP II leading to backtracking remain unknown. Here, we demonstrate with \emph{S. cerevisiae} RNAP II that a cleavage-deficient elongation factor TFIIS (TFIIS$^\mathrm{AA}$) enhances backtracked pauses during regular transcription. This is due to increased efficiency of formation of an intermediate that leads to backtracking. This intermediate may involve misalignment at the 3' end of the nascent RNA in the active center of the yeast RNAP II, and TFIIS$^\mathrm{AA}$ promotes formation of this intermediate at the DNA sequences, presenting a high-energy barrier to translocation. We proposed a three-step mechanism for RNAP II pausing in which a prolonged dwell time in the pre-translocated state increases the likelihood of the 3' RNA end misalignment facilitating a backtrack pausing. These results demonstrate an important role of the intrinsic blocks to forward translocation in pausing by RNAP II.},
  annote    = {The authors study ternary elongation complexes consisting of a DNA template, a short complementary RNA, and RNA polymerase II, and the behavior of these complexes in the presence of a TFIIS mutant that stimulates backtracking. Many of the key experiments are based on a footprinting technique that can detect backtracking due to the protection of an extra base of the template in the backtracked state. These studies are consistent with a model (Fig.\ 6) in which pausing involves a transition from the pre-translocated state to a pause-prone state (which they call Pre$^*$) from which the polymerase can backtrack by one nucleotide. If the polymerase backtracks more than that, it goes into an irreversible arrest state. Interestingly, the authors hypothesize that recovery from the Pre$^*$ state is directly to the post-translocated state. Structurally (Fig. 7(a)), the Pre$^*$ state corresponds to a state in which the last nucleotide at the 3' end of the nascent transcript has become misaligned with its template.},
  doi       = {10.1016/j.jmb.2012.12.002},
  owner     = {roussel},
  timestamp = {2017.10.17},
}

@Article{Roberts2014,
  author    = {Jeffrey W. Roberts},
  title     = {Molecular Basis of Transcriptional Pausing},
  journal   = {Science},
  year      = {2014},
  volume    = {344},
  pages     = {1226-1227},
  annote    = {This short review discusses recent advances in understanding transcriptional pausing. Much of the discussion centres around the pretranslocated (A, in our models) and posttranslocated (O) state. One key finding is that pausing proceeds from the pretranslocated state.},
  owner     = {roussel},
  timestamp = {2014.07.10},
}

@Article{SP2009,
  author    = {Jarnail Singh and Richard A. Padgett},
  journal   = {Nat. Struct. Mol. Biol.},
  title     = {Rates of \emph{in situ} Transcription and Splicing in Large Human Genes},
  year      = {2009},
  volume    = {16},
  pages     = {1128-1133},
  annote    = {DRB blocks the transition from transcription initiation to elongation. Here, cells are treated with DRB, elongating transcripts are allowed to complete, and then the DRB is washed away. PCR was then used to analyze the RNA complement of the cell at various time points in large genes, some of which had large introns. It was found that elongation proceeds are a remarkably uniform rate of 3.4--4.4\,$\mathrm{kb\,min^{-1}}$ (average 3.8\,$\mathrm{kb\,min^{-1}}$). Splicing by the major (U2) spliceosome was found to take about 5 minutes from the time of synthesis of the 3' splice site and was independent of intron size. Splicing by the minor (U12) spliceosome was a bit slower, averaging 10 minutes, but was clearly co-transcriptional (refuting an earlier study suggesting that U12-dependent splicing might occur in the cytoplasm).},
  doi       = {10.1038/nsmb.1666},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@MastersThesis{Hosseini2016,
  author    = {Seyed Hossein Hosseini},
  title     = {Analytic Solutions for Stochastic Models of Transcription},
  school    = {University of Lethbridge},
  year      = {2016},
  owner     = {marcroussel},
  timestamp = {2017.10.11},
  url       = {https://www.uleth.ca/dspace/handle/10133/4791},
}

@Article{Bratsun-etal2005,
  author    = {Dmitri Bratsun and Dmitri Volfson and Lev S. Tsimring and Jeff Hasty},
  title     = {Delay-induced stochastic oscillations in gene regulation},
  journal   = {Proc. Natl. Acad. Sci. U.S.A.},
  year      = {2005},
  volume    = {102},
  pages     = {14593-14598},
  abstract  = {The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.},
  annote    = {The main point of this paper is to compare the dynamics of delay-differential equation (DDE) models to those of stochastic models with delays. To this purpose, approximate delayed master equations are derived and a delayed Gillespie algorithm is developed. Some very simple abstract models are studied. In one model with inhibition of protein production by dimers of the protein, a Hopf bifurcation occurs. This bifurcation can be detected in the stochastic model by analyzing the autocorrelation function. It is shifted somewhat in the stochastic model relative to the deterministic DDE model.},
  doi       = {10.1073/pnas.0503858102},
  keywords  = {master equation, stochastic delay equations, noise, time delay, systems biology},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{RL2007a,
  author    = {Andre S. Ribeiro and Jason Lloyd-Price},
  title     = {{SGN} {Sim}, a Stochastic Genetic Networks Simulator},
  journal   = {Bioinformatics},
  year      = {2007},
  volume    = {23},
  pages     = {777-779},
  annote    = {This article describes SGN Sim, a simulator for genetic networks that implements the Roussel-Zhu delay stochastic simulation algorithm \cite{RZ2006b}. The program can also model mass transfer between compartments, and it has the ability of generating random gene networks with specified statistical properties.},
  doi       = {10.1093/bioinformatics/btm004},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@Article{LGR2012,
  author    = {Jason Lloyd-Price and Abhishekh Gupta and Andre S. Ribeiro},
  title     = {SGNS2: A Compartmental Stochastic Chemical Kinetics Simulator for Dynamic Cell Populations},
  journal   = {Bioinformatics},
  year      = {2012},
  volume    = {28},
  pages     = {3004-3005},
  annote    = {SGNS2 is simulation software that implements the delayed stochastic simulation algorithm as well as allowing for partitioning of chemicals among the daughter cells at cell division.},
  doi       = {10.1093/bioinformatics/bts556},
  owner     = {marcroussel},
  timestamp = {2013.09.21},
}

@manual{StochPy,
author="Timo Maarleveld",
title="StochPy User Guide, Release 2.3.0",
year=2015,
url="https://sourceforge.net/projects/stochpy/files/stochpy_userguide_2.3.pdf/download"}

@Article{Roussel96b,
  author    = {Marc R. Roussel},
  journal   = {J. Phys. Chem.},
  title     = {The Use of Delay Differential Equations in Chemical Kinetics},
  year      = {1996},
  volume    = {100},
  pages     = {8323-8330},
  doi       = {10.1021/jp9600672},
  owner     = {roussel},
  timestamp = {2012.07.25},
}

@MastersThesis{Murphy2017,
  author    = {Reba-Jean Murphy},
  title     = {Stochastic Modeling of the Torpedo Mechanism of Eukaryotic Transcription Termination},
  school    = {University of Lethbridge},
  year      = {2017},
  abstract  = {The torpedo mechanism is a type of eukaryotic transcription termination completed by RNAPII and consists of a chase-down of RNAPII by the exonuclease Xrn2 on the 3' flanking region of the RNA transcript. A biochemical model of the mechanism is detailed. By applying Gillespie simulations and using a one-dimensional biased random walk, the effects of the relative speeds of RNAPII to Xrn2 and the size of the intergenic region on termination via the torpedo mechanism are explored. The success rates of termination in terms of the likelihood of downstream gene interference, the distribution of successful termination times, and the distribution of nucleotides synthesized by RNAPII in the termination region are discussed.},
  owner     = {marcroussel},
  timestamp = {2017.10.24},
  url       = {https://www.uleth.ca/dspace/handle/10133/4906},
}

@Article{RT2012,
  author    = {Marc R. Roussel and Terry Tang},
  title     = {Simulation of {mRNA} Diffusion in the Nuclear Environment},
  journal   = {IET Syst. Biol.},
  year      = {2012},
  volume    = {6},
  pages     = {125--133},
  owner     = {marcroussel},
  timestamp = {2012.10.08},
}

@Article{Jennings2013,
  author    = {Barbara H. Jennings},
  title     = {Pausing For Thought: Disrupting the Early Transcription Elongation Checkpoint Leads to Developmental Defects and Tumourigenesis},
  journal   = {BioEssays},
  year      = {2013},
  volume    = {35},
  pages     = {553-560},
  annote    = {A large number of eukaryotic genes are controlled at least partly via promoter-proximal pausing. The core biochemical interactions involve pausing induced by DSIF (a complex of Spt4 and Spt5) and NELF acting in concert to stop RNA polymerase II 20 to 60 nucleotides downstream of the transcription start site. P-TEFb phosphorylates NELF, causing it to dissociate from the RNA polymerase, the C-terminal domain of the polymerase, and Spt5, causing the latter to become an activator rather than a repressor of transcription. This review focuses largely on the developmental consequences of various defects in this pause-control system, many of which are lethal. The regulators of P-TEFb activity 7SK (a small non-coding RNA), Brd4 and c-Myc are also briefly reviewed, as is the involvement of P-TEFb in super-elongation complexes.},
  owner     = {roussel},
  timestamp = {2013.08.29},
}

@PhdThesis{Tang2010,
  author    = {Shouchun Tang},
  title     = {Mathematical Modeling of Eukaryotic Gene Expression},
  school    = {University of Lethbridge},
  year      = {2010},
  owner     = {roussel},
  timestamp = {2012.07.25},
  url       = {https://www.uleth.ca/dspace/handle/10133/2567},
}

@Article{HS2014,
  author    = {D. Holcman and Z. Schuss},
  title     = {The Narrow Escape Problem},
  journal   = {SIAM Rev.},
  year      = {2014},
  volume    = {56},
  pages     = {213-257},
  annote    = {The authors review the literature on the problem of escape through one or several narrow openings in a container. This problem would be relevant, e.g., to nuclear export. They treat several variations on this problem, including escape through narrow necks, and diffusion through an array of obstacles, which can be reformulated as escape from a region bounded by some obstacles, with small spaces between them.},
  owner     = {roussel},
  timestamp = {2014.10.08},
}

@Article{Daneholt2001,
  author       = {Bertil Daneholt},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {Assembly and Transport of a Premessenger {RNP} Particle},
  year         = {2001},
  pages        = {7012-7017},
  volume       = {98},
  annote       = {This review paper covers a number of aspects of the packaging of mRNA with proteins in the nucleus, including the localization and functions of these proteins. This packaging into a ribonucleoprotein results in a compact conformation which must be unfolded for translocation through the nuclear pore. There are proteins that dissociate prior to binding to the pore, while others dissociate during translocation through the pore, suggesting different roles for some of these proteins in the translocation process. Yet other proteins travel through the pore with the mRNA and function in localization of the transcript to the appropriate location within the cytoplasm. Interestingly, the proteins involved in the mRNP complex consist of both proteins that bind to the mRNA with high affinity to specific sites and of proteins that bind with low affinity nonspecifically to multiple sites along the transcript. The final mRNP is therefore the result of a stochastic process and may vary in stoichiometry from one instance to the next.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{BS2019,
  author       = {Rakefet Ben-Yishay and Yaron Shav-Tal},
  journal      = {Curr. Opin. Cell Biol.},
  title        = {The Dynamic Lifecycle of {mRNA} in the Nucleus},
  year         = {2019},
  pages        = {69-75},
  volume       = {58},
  abstract     = {The mRNA molecule roams through the nucleus on its way out to the cytoplasm. mRNA encounters and is bound by many protein factors, from the moment it begins to emerge from RNA polymerase II and during its travel in the nucleoplasm, where it will come upon chromatin and nuclear bodies. Some of the protein factors that engage with the mRNA can process it, until finally reaching a mature state fit for export through the nuclear pore complex (NPC). Examining the lifecycle of mRNAs in living cells using mRNA tagging techniques opens a window into our understanding of the rules that drive the dynamics of gene expression from transcription to mRNA export.},
  annote       = {This paper discusses the entire life cycle of mRNA in the nucleus. One interesting section reviews evidence that transcription is either ``on'' or ``off'' for any given copy of a gene, i.e.\ either a gene is transcribed at the maximum rate of which it is capable, or it is not being transcribed at all. Graded responses then are population-level phenomena rather than a reflection of single-cell behavior. There is a brief discussion of ``polymerase convoys'', although it is not clear from this review how widespread this phenomenon is. One can imagine that mechanical factors having to do with the DNA conformation (e.g.) would slow a leading polymerase relative to trailing polymerases, leading to the formation of convoys. Some mRNAs seem to be retained in the nucleus for a significant period of time post-transcription (tens of minutes). One paper is cited that presents evidence for length-dependent export kinetics.},
  creationdate = {2023-10-17T17:13:07},
  doi          = {10.1016/j.ceb.2019.02.007},
  owner        = {marcroussel},
}

@Article{CDD2020,
  author       = {Anusha Chaudhuri and Subhadeep Das and Biswadip Das},
  journal      = {WIREs RNA},
  title        = {Localization Elements and Zip Codes in the Intracellular Transport and Localization of Messenger {RNAs} in \emph{Saccharomyces cerevisiae}},
  year         = {2020},
  pages          = {e1591},
  volume       = {11},
  abstract     = {Intracellular trafficking and localization of mRNAs provide a mechanism of regulation of expression of genes with excellent spatial control. mRNA localization followed by localized translation appears to be a mechanism of targeted protein sorting to a specific cell-compartment, which is linked to the establishment of cell polarity, cell asymmetry, embryonic axis determination, and neuronal plasticity in metazoans. However, the complexity of the mechanism and the components of mRNA localization in higher organisms prompted the use of the unicellular organism Saccharomyces cerevisiae as a simplified model organism to study this vital process. Current knowledge indicates that a variety of mRNAs are asymmetrically and selectively localized to the tip of the bud of the daughter cells, to the vicinity of endoplasmic reticulum, mitochondria, and nucleus in this organism, which are connected to diverse cellular processes. Interestingly, specific cis-acting RNA localization elements (LEs) or RNA zip codes play a crucial role in the localization and trafficking of these localized mRNAs by providing critical binding sites for the specific RNA-binding proteins (RBPs). In this review, we present a comprehensive account of mRNA localization in S. cerevisiae, various types of localization elements influencing the mRNA localization, and the RBPs, which bind to these LEs to implement a number of vital physiological processes. Finally, we emphasize the significance of this process by highlighting their connection to several neuropathological disorders and cancers.},
  annote       = {This review paper discusses the mechanisms of mRNA localization to various parts of the cell. This generally involves an RNA-binding protein, often one that recognizes a particular structure rather than a sequence. Some diseases associated with defects in mRNA localization are also discussed.},
  creationdate = {2023-11-06T20:09:30},
  doi          = {10.1002/wrna.1591},
  keywords     = {cis-acting element, localization element (LE), mRNA localization, RNA binding proteins (RBP), RNA zip code},
  owner        = {marcroussel},
}

@Article{SS2013,
  author       = {Jonathan Sheinberger and Shav-Tal, Yaron},
  journal      = {Nucleus},
  title        = {The Dynamic Pathway of Nuclear {RNA} in Eukaryotes},
  year         = {2013},
  pages        = {195-205},
  volume       = {4},
  abstract     = {The passage of mRNA molecules from the site of synthesis, through the nucleoplasm and the nuclear pore, en route to the cytoplasm, might appear straightforward. Nonetheless, several decades of detailed examination of this pathway, from high resolution electron microscopy in fixed specimens, through the development of immuno-detection techniques and fluorescence toolkits, to the current era of live-cell imaging, show this to be an eventful journey. In addition to mRNAs, several species of noncoding RNAs travel and function in the nucleus, some being retained within throughout their lifetime. This review will highlight the nucleoplasmic paths taken by mRNAs and noncoding RNAs in eukaryotic cells with special focus on live-cell data and in concurrence with the biophysical nature of the nucleus.},
  annote       = {Much of this review paper focuses on measurements of RNA diffusion coefficients in the nucleus and on what can be inferred from them. Additional topics include retention of certain transcripts in the nucleus, nuclear export, and the effects of the packing of components in the nucleus on RNA diffusive transport.},
  creationdate = {2023-11-07T20:08:05},
  doi          = {10.4161/nucl.24434},
  keywords     = {mRNA export, RNA dynamics, inter-chromatin, live-cell imaging, nucleoplasm},
  owner        = {marcroussel},
}

@Article{BPM82,
  author       = {Richard D. Bliss and Page R. Painter and Allen G. Marr},
  journal      = {J. Theor. Biol.},
  title        = {Role of feedback inhibition in stabilizing the classical operon},
  year         = {1982},
  pages        = {177-193},
  volume       = {97},
  annote       = {A two-delay model of the tryptophan operon is presented. The two delays correspond respectively to the time between initiation of transcription and initiation of translation and to the time between initiation of transcription and the appearance of a functional enzyme. In the linear stability analysis, only the total delay appears. The operon is stable for normal values of the parameters, but mutations which decrease the enzyme inhibition can destabilize the operon.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{BS1987,
  author       = {F. Buchholtz and F. W. Schneider},
  journal      = {Biophys. Chem.},
  title        = {Computer Simulation of {T3}/{T7} Phage Infection Using Lag Times},
  year         = {1987},
  pages        = {171-179},
  volume       = {26},
  annote       = {A mechanism for the transcriptional and translational processes of four key phage genes (RNA polymerase, DNase, primase and DNA polymerase) is proposed. The model involves multiple delays, mostly related to the time required to read the phage genes. The model is tuned using experimental data and replicates the kinetics of the process very well.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1016/0301-4622(87)80020-0},
  owner        = {roussel},
}

@Article{BM1988,
  author       = {S. N. Busenberg and J. M. Mahaffy},
  journal      = {SIAM J. Appl. Math.},
  title        = {The effects of dimension and size for a compartmental model of repression},
  year         = {1988},
  pages        = {882-903},
  volume       = {48},
  annote       = {A eukaryotic operon model with transcriptional and translational delays is studied. The effect of cell size on the stability of solutions is of particular interest. For a range of cell sizes, oscillatory solutions arise which the authors speculate may be involved in cell cycle control.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{Lewis2003,
  author       = {Julian Lewis},
  journal      = {Curr. Biol.},
  title        = {Autoinhibition with Transcriptional Delay: A Simple Mechanism for the Zebrafish Somitogenesis Oscillator},
  year         = {2003},
  pages        = {1398-1408},
  volume       = {13},
  annote       = {Lewis proposes a simple mRNA/protein model with transcriptional and translational delays for the somitogenesis oscillator based on the her1/her7 dynamics in zebrafish. The paper includes a very useful set of parameter estimates, with a rich set of references to the literature which could be useful in other modeling studies of gene expression. This model displays a classic delay-induced oscillation whose period is largely controlled by the sum of the delays. The solutions are remarkably insensitive to the transcription rate due to negative feedback. He also studies a noisy version of this model, although it's not clear how he carries out the simulations. Noise-sustained oscillations are observed. When Delta-Notch signalling is added, adjacent cells can become synchronized. As the signalling delays increase, a predictable phase difference emerges. It is also possible to tweak this model such that the signalling subsystem rather than the cell-autonomous her1/her7 oscillator sets the oscillatory waveform. The paper concludes with some thoughts on the relationship between the zebrafish and mouse somitogenesis oscillators, the latter having a much longer period. Throughout the paper, he emphasizes that the behavior of these models is not easily intuited and that mathematical analysis is invaluable in establishing whether biochemical hypotheses in fact explain particular phenomena.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1016/S0960-9822(03)00534-7},
  owner        = {roussel},
}

@Article{Monk2003,
  author       = {Nicholas A. M. Monk},
  journal      = {Curr. Biol.},
  title        = {Oscillatory Expression of {Hes1}, p53, and {NF}-$\kappa${B} Driven by Transcriptional Time Delays},
  year         = {2003},
  pages        = {1409-1413},
  volume       = {13},
  annote       = {Very simple oscillatory models based on delayed negative feedback are presented for the systems listed in the title. Each of these has a period of two to three hours.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1016/S0960-9822(03)00494-9},
  owner        = {roussel},
}

@Article{CLW2022,
  author       = {Lin-Jie Chiu and Ming-Yang Ling and En-Hsuan Wu and Chao-Xuan You and Ssu-Ting Lin and Che-Chi Shu},
  journal      = {J. Taiwan Inst. Chem. Eng.},
  title        = {The Distributed Delay Rearranges the Bimodal Distribution at Protein Level},
  year         = {2022},
  pages          = {104436},
  volume       = {137},
  abstract     = {Background
In bimodal distribution, we refer ON to the mode with a higher protein level and OFF to a lower protein level. The traditional wisdom of manipulating the population in each mode is done by adding an inducer or inhibitor to change the protein number.

Methods
By delay stochastic simulation algorithm, we applied transcriptional or translational delay to the gene expression system of toggle switches. We also incorporated distributed delay in the model. From a deterministic aspect, reaction delay does NOT alter the steady-state value. Thus, our approach is different from the conventional method.

Significant Findings
The transcriptional delay rearranged the bimodal distribution at the protein level and the influence of the translational delay is even higher. The increment of delay time pushes more cells to have the protein in the ON mode. Remarkably, the distributed delay of translation guides 98\% of cells to have protein in the ON mode. We then displayed the time-course trajectories and discovered the cause leading to the rearrangement of bimodal distribution. We also exclude the possibility that rearrangement of bimodal distribution simply comes from the trivial reason, the change of the input distribution, and concluded that the change of dynamic stochastic processes is crucial.},
  annote       = {The authors study a model of a genetic toggle switch by stochastic simulation, either with or without transcription and translation delays, and with either fixed or Gaussian distributed delays with various standard deviations. None of the results are too surprising.},
  creationdate = {2022-07-25T21:36:37},
  doi          = {10.1016/j.jtice.2022.104436},
  keywords     = {Bistable steady states; Bistability; Mathematic model; Transition probability; Bimodality; Noise intensity},
  owner        = {marcroussel},
}

@Article{RW2007,
  author       = {Katja Rateitschak and Olaf Wolkenhauer},
  journal      = {Math. Biosci.},
  title        = {Intracellular Delay Limits Cyclic Changes in Gene Expression},
  year         = {2007},
  pages        = {163-179},
  volume       = {205},
  annote       = {This is a very interesting paper on the differences between gene expression models with fixed and distributed delays. Two models are examined, one an oscillatory model of the Hes1--p53--NF-$\kappa$B system, and the other a model for repression of Hes1 by the Gro/TLE1/Hes1 complex. Stability switches from a stable steady state to oscillations and back to a stable steady state are observed as the average delay is increased. The reverse Hopf bifurcation to stability is not seen in the models with fixed delays. There is also an interesting discussion of the relevance of sustained vs damped oscillations in the natural system, where the response only depends on sampling of the oscillatory state over a short period of time.},
  creationdate = {2022-08-03T13:20:08},
  keywords     = {Gene expression with negative feedback; Distributed time delay; Limit cycle oscillations},
}

@Article{JP2015,
  author       = {Martin Jansen and Peter Pfaffelhuber},
  journal      = {J. Theor. Biol.},
  title        = {Stochastic Gene Expression with Delay},
  year         = {2015},
  pages        = {355-363},
  volume       = {364},
  annote       = {The authors study a simple model of gene expression with delays very similar to those we pioneered \cite{RZ2006b}. They find that distributed delays decrease the variance of the protein population relative to a model with a fixed delay, or one without any delays.},
  creationdate = {2017-10-30T00:00:00},
  doi          = {10.1016/j.jtbi.2014.09.031},
  keywords     = {Chemical reaction network, Poisson process},
  owner        = {marcroussel},
}

@Article{KFC2013,
  author       = {Hojoong Kwak and Nicholas J. Fuda and Leighton J. Core and John T. Lis},
  journal      = {Science},
  title        = {Precise Maps of {RNA} Polymerase Reveal How Promoters Direct Initiation and Pausing},
  year         = {2013},
  pages        = {950-953},
  volume       = {339},
  abstract     = {Transcription regulation occurs frequently through promoter-associated pausing of RNA polymerase II (Pol II). We developed a precision nuclear run-on and sequencing (PRO-seq) assay to map the genome-wide distribution of transcriptionally engaged Pol II at base pair resolution. Pol II accumulates immediately downstream of promoters, at intron-exon junctions that are efficiently used for splicing, and over 3' polyadenylation sites. Focused analyses of promoters reveal that pausing is not fixed relative to initiation sites, nor is it specified directly by the position of a particular core promoter element or the first nucleosome. Core promoter elements function beyond initiation, and when optimally positioned they act collectively to dictate the position and strength of pausing. This ``complex interaction'' model was tested with insertional mutagenesis of the Drosophila Hsp70 core promoter.},
  annote       = {Using high-resolution maps of RNA polymerase II occupancy on a gene, the authors study the factors that may affect pausing. They detect both promoter-proximal pausing and pausing at 3' intron-exon junctions. Promoter-proximal pauses (PPPs) are divided into two classes: a class that is more proximal to the start site, 25 to 50 bp downstream, which they call `Prox', and one that is more distal, 55 to 75 bp downstream, labeled `Dist'. The Prox class is more focused, occurring within 3 or 4 bp of the same location each time. The Dist class is more dispersed, occurring within 10 or so bp of the average location. Prox-class PPPs don't seem to involve nucleosomes, while Dist PPPs do. Inserting small spacers of up to 5 bp between the Inr (initiator) and MTE (motif 10 element) promoter elements had little effect on the Prox pattern, while larger spacers converted a Prox PPP into something more like a Dist PPP.},
  creationdate = {2022-09-10T15:11:59},
  doi          = {10.1126/science.1229386},
  owner        = {marcroussel},
}

@Article{HBG+2006,
  author       = {Aaron R Hieb and Sean Baran and James A Goodrich and Jennifer F. Kugel},
  journal      = {EMBO J.},
  title        = {An 8nt {RNA} Triggers a Rate-Limiting Shift of {RNA} Polymerase {II} Complexes into Elongation},
  year         = {2006},
  pages        = {3100-3109},
  volume       = {25},
  annote       = {Several experiments are used to show that there is a rate-limiting step in early transcription by eukaryotic RNA polymerase II following which the polymerase shifts into a rapid elongation state. This step occurs after an 8\,nt transcript has been synthesized, and either before or concurrently with translocation to the +9 position. Negative DNA superhelicity or the activity of TFIIE or TFIIH are required at this step. This paper contains several useful summaries of the early events of transcription (with kinetic data) in the form of kinetic schemes.},
  creationdate = {2018-06-15T00:00:00},
  owner        = {Marc},
}

@Article{SHS+2014,
  author       = {Timothy J. Stasevich and Yoko Hayashi-Takanaka and Yuko Sato and Kazumitsu Maehara and Yasuyuki Ohkawa and Kumiko Sakata-Sogawa and Makio Tokunaga and Takahiro Nagase and Naohito Nozaki and James G. McNally and Hiroshi Kimura},
  journal      = {Nature},
  title        = {Regulation of {RNA} Polymerase {II} Activation by Histone Acetylation in Single Living Cells},
  year         = {2014},
  pages        = {272-275},
  volume       = {516},
  annote       = {Acetylation of lysine-27 of histone H3 accelerates the search kinetics of transcriptional activators \emph{and} accelerates the transition from transcriptional initiation to elongation (i.e.\ promoter escape). The authors use a model in part of their analysis (the model of Darzacq and coworkers \cite{Darzacq-etal2007}), which yields estimates of various kinetic parameters for their experimental system, including initiation rate constants, rates of promoter escape, and abortion probability.},
  creationdate = {2015-02-04T00:00:00},
  doi          = {10.1038/nature13714},
  owner        = {roussel},
}

@Article{SJG+2018,
  author       = {Barbara Steurer and Roel C. Janssens and Bart Geverts and Marit E. Geijer and Franziska Wienholz and Arjan F. Theil and Jiang Chang and Shannon Dealy and Joris Pothof and Wiggert A. van Cappellen and Adriaan B. Houtsmuller and Jurgen A. Marteijn},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {Live-Cell Analysis of Endogeneous {GFP-RPB1} Uncovers Rapid Turnover of Initiating and Promoter-Paused {RNA} Polymerase {II}},
  year         = {2018},
  pages        = {E4368-E4376},
  volume       = {115},
  abstract     = {Initiation and promoter-proximal pausing are key regulatory steps of RNA Polymerase II (Pol II) transcription. To study the in vivo dynamics of endogenous Pol II during these steps, we generated fully functional GFP-RPB1 knockin cells. GFP-RPB1 photobleaching combined with computational modeling revealed four kinetically distinct Pol II fractions and showed that on average 7\% of Pol II are freely diffusing, while 10\% are chromatin-bound for 2.4 seconds during initiation, and 23\% are promoter-paused for only 42 seconds. This unexpectedly high turnover of Pol II at promoters is most likely caused by premature termination of initiating and promoter-paused Pol II and is in sharp contrast to the 23 minutes that elongating Pol II resides on chromatin. Our live-cell-imaging approach provides insights into Pol II dynamics and suggests that the continuous release and reinitiation of promoter-bound Pol II is an important component of transcriptional regulation.},
  annote       = {RPB1 is a subunit of RNA polymerase II. A GFP-RPB1 fusion protein was created and shown to be fully functional in a human fibroblast cell line. A series of FRAP experiments with and without various blocking agents was undertaken. The take-home message is summarized in Fig.\ 3 of the paper. It shows that cells spend a relatively small amount of time in initiation, but that most (87\%) initiation events end in abortion; that cells pause for approximately 42\,s in the promoter-proximal region, but that approximately 92\% of paused complexes abort; and that only about 7\% of the RNAPII molecules are freely diffusing at any given time. As a side-effect of these experiments, the authors obtain a nuclear RNAPII concentration of $0.18\,\mu\mathrm{M}$ and a nuclear volume of $734\,\mu\mathrm{m^3}$.},
  creationdate = {2019-03-03T00:00:00},
  doi          = {10.1073/pnas.1717920115},
  keywords     = {RNA Polymerase II, transcription, transcription dynamics, promoter-proximal pausing, live-cell imaging},
  owner        = {marcroussel},
}

@Article{JIM1998,
  author       = {Dean A. Jackson and Franciso J. Iborra and Erik M. M. Manders and Peter R. Cook},
  journal      = {Mol. Biol. Cell},
  title        = {Numbers and Organization of {RNA} Polymerases, Nascent Transcripts, and Transcription Units in {HeLa} Nuclei},
  year         = {1998},
  pages        = {1523-1536},
  volume       = {9},
  annote       = {The authors report on a set of experiments to determine how many RNA polymerases are transcribing from how many initiation sites in eukaryotic (HeLa) cells. They find that approximately 15\,000 copies of RNA polymerase I and 75\,000 copies of RNA polymerases II and III are active at any given time. (They have no easy way to distinguish RNA polymerase II from III.) Outside of the nucleolus, one or a very small number of polymerases are transcribing most genes. When more than one polymerase is transcribing a gene, they are typically spaced by 1.8\,kb. The spatial arrangement of polymerases suggests the existence of transcription factories, each containing approximately 30 polymerases.},
  creationdate = {2023-01-24T12:39:18},
}

@Article{BRE2011,
  author       = {Alistair N. Boettiger and Peter L. Ralph and Steven N. Evans},
  journal      = {PLoS Comput. Biol.},
  title        = {Transcriptional Regulation: Effects of Promoter Proximal Pausing on Speed, Synchrony and Reliability},
  year         = {2011},
  pages          = {e1001136},
  volume       = {7},
  abstract     = {Recent whole genome polymerase binding assays in the Drosophila embryo have shown that a substantial proportion of uninduced genes have pre-assembled RNA polymerase-II transcription initiation complex (PIC) bound to their promoters. These constitute a subset of promoter proximally paused genes for which mRNA elongation instead of promoter access is regulated. This difference can be described as a rearrangement of the regulatory topology to control the downstream transcriptional process of elongation rather than the upstream transcriptional initiation event. It has been shown experimentally that genes with the former mode of regulation tend to induce faster and more synchronously, and that promoter-proximal pausing is observed mainly in metazoans, in accord with a posited impact on synchrony. However, it has not been shown whether or not it is the change in the regulated step per se that is causal. We investigate this question by proposing and analyzing a continuous-time Markov chain model of PIC assembly regulated at one of two steps: initial polymerase association with DNA, or release from a paused, transcribing state. Our analysis demonstrates that, over a wide range of physical parameters, increased speed and synchrony are functional consequences of elongation control. Further, we make new predictions about the effect of elongation regulation on the consistent control of total transcript number between cells. We also identify which elements in the transcription induction pathway are most sensitive to molecular noise and thus possibly the most evolutionarily constrained. Our methods produce symbolic expressions for quantities of interest with reasonable computational effort and they can be used to explore the interplay between interaction topology and molecular noise in a broader class of biochemical networks. We provide general-purpose code implementing these methods.},
  annote       = {The authors consider stochastic models of transcription initiation in which regulation either occurs at the PIC assembly step or at the promoter-proximal pause. Simulating a family},
  creationdate = {2023-11-17T12:27:36},
  doi          = {10.1371/journal.pcbi.1001136},
  owner        = {roussel},
}

@Article{KSC2002,
  author       = {Kimura, Hiroshi and Kimihiko Sugaya and Cook, Peter R.},
  journal      = {J. Cell Biol.},
  title        = {The Transcription Cycle of {RNA} Polymerase {II} in Living Cells},
  year         = {2002},
  pages        = {777-782},
  volume       = {159},
  annote       = {The authors tagged the catalytic subunit of RNA polymerase II, and expressed this tagged protein in Chinese hamster ovary (CHO) cells with a temperature-sensitive mutation in this unit. The tagged protein complements the mutation, and so it is functional. They they studied the dynamics of the polymerase by FRAP. Their data is consistent with 20 to 25\% of the polymerase being engaged at any given time. Binding of the polymerase to any other factors must be highly transient. The transcription cycle takes an average of 28 to 40 minutes to complete. This is about twice as long as would be expected based on typical elongation rates. I would suggest that the difference reflects splicing.},
  creationdate = {2019-10-25T00:00:00},
  keywords     = {green fluorescent protein; photobleaching; actinomycin D; DRB; kinetics},
  owner        = {roussel},
}

@Article{TR2020,
  author       = {Elizabeth A. M. Trofimenkoff and Roussel, Marc R.},
  journal      = {Math. Biosci.},
  title        = {Small Binding-Site Clearance Delays Are Not Negligible in Gene Expression Modeling},
  year         = {2020},
  pages        = {108376},
  volume       = {325},
  creationdate = {2020-07-30T00:00:00},
  doi          = {10.1016/j.mbs.2020.108376},
  owner        = {marcroussel},
}

@Article{Epstein90,
  author       = {Irving R. Epstein},
  journal      = {J. Chem. Phys.},
  title        = {Differential delay equations in chemical kinetics: Some simple linear model systems},
  year         = {1990},
  pages        = {1702-1712},
  volume       = {92},
  abstract     = {The reasons for and the effects of incorporating time lags into the differential equations of chemical kinetics are investigated for some simple model systems. Complex networks of first-order reactions may, in the limit of long times, be described by relatively simple systems of differential delay (differential difference) equations, in which the effects of intermediates are replaced by time lags. Explicit inclusion of time lags affords a more physically realistic description of nucleation in certain solid state reactions. An electrochemical cell with lagged feedback gives rise to a particularly simple and instructive delay equation. A two-chamber system in which molecules diffuse with a time lag through a membrane shows unexpected oscillatory, and seemingly nonconservative behavior, which is explained in terms of the number of molecules in passage through the membrane.},
  annote       = {Several linear delay models are studied. The first is a system modeling the kinetics of linearly coupled sequential reactions; a proof of the validity of the reduction is offered. Another is the so-called fundamental delay equation, arising in this case from an electrochemical cell model. Finally, a reduction of diffusion to a delay equation is presented and analyzed. Several methods of solving delay-differential equations are suggested.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1063/1.458052},
  keywords     = {Network theory, Electrochemistry, First-order reactions, Chemical kinetics and dynamics},
  owner        = {roussel},
}

@Article{HCC2023,
  author       = {Hyukpro Hong and Mark Jayson Cortez and Cheng, Yu-Yu and Hang Joon Kim and Choi, Boseung and Josi{\'c}, Kre\v{s}imir and Kim, Jae Kyoung},
  journal      = {Bioinformatics},
  title        = {Inferring Delays in Partially Observed Gene Regulation Processes},
  year         = {2023},
  pages          = {btad670},
  volume       = {39},
  abstract     = {Motivation
Cell function is regulated by gene regulatory networks (GRNs) defined by protein-mediated interaction between constituent genes. Despite advances in experimental techniques, we can still measure only a fraction of the processes that govern GRN dynamics. To infer the properties of GRNs using partial observation, unobserved sequential processes can be replaced with distributed time delays, yielding non-Markovian models. Inference methods based on the resulting model suffer from the curse of dimensionality.

Results
We develop a simulation-based Bayesian MCMC method employing an approximate likelihood for the efficient and accurate inference of GRN parameters when only some of their products are observed. We illustrate our approach using a two-step activation model: An activation signal leads to the accumulation of an unobserved regulatory protein, which triggers the expression of observed fluorescent proteins. With prior information about observed fluorescent protein synthesis, our method successfully infers the dynamics of the unobserved regulatory protein. We can estimate the delay and kinetic parameters characterizing target regulation including transcription, translation, and target searching of an unobserved protein from experimental measurements of the products of its target gene. Our method is scalable and can be used to analyze non-Markovian models with hidden components.

Availability and Implementation
Our code is implemented in R and is freely available with a simple example data at https://github.com/Mathbiomed/SimMCMC.},
  annote       = {The authors develop a statistical method for inferring kinetic parameters, including gene expression delays, from time series of protein concentrations in single cells. Depending on what is observed, some parameters may not be identifiable. If estimates of the ``missing'' parameters are available from other experiments however, excellent estimates of the remaining parameters are obtained.},
  creationdate = {2023-11-19T19:55:18},
  doi          = {10.1093/bioinformatics/btad670},
  owner        = {marcroussel},
}

@Article{CCC2020,
  author       = {Boseung Choi and Yu-Yu Cheng and Selahattin Cinar and William Ott and Bennett, Matthew R. and Josi\'c, Kre\v{s}imir and Kim, Jae Kyoung},
  journal      = {Bioinformatics},
  title        = {Bayesian Inference of Distributed Time Delay in Transcriptional and Translational Regulation},
  year         = {2020},
  pages        = {586-593},
  volume       = {36},
  abstract     = {Motivation: Advances in experimental and imaging techniques have allowed for unprecedented insights into the dynamical processes within individual cells. However, many facets of intracellular dynamics remain hidden, or can be measured only indirectly. This makes it challenging to reconstruct the regulatory networks that govern the biochemical processes underlying various cell functions. Current estimation techniques for inferring reaction rates frequently rely on marginalization over unobserved processes and states. Even in simple systems this approach can be computationally challenging, and can lead to large uncertainties and lack of robustness in parameter estimates. Therefore we will require alternative approaches to efficiently uncover the interactions in complex biochemical networks.
Results: We propose a Bayesian inference framework based on replacing uninteresting or unobserved reactions with time delays. Although the resulting models are non-Markovian, recent results on stochastic systems with random delays allow us to rigorously obtain expressions for the likelihoods of model parameters. In turn, this allows us to extend MCMC methods to efficiently estimate reaction rates, and delay distribution parameters, from single-cell assays. We illustrate the advantages, and potential pitfalls, of the approach using a birth-death model with both synthetic and experimental data, and show that we can robustly infer model parameters using a relatively small number of measurements. We demonstrate how to do so even when only the relative molecule count within the cell is measured, as in the case of fluorescence microscopy.
Availability and implementation: Accompanying code in R is available at https://github.com/cbskust/DDE_BD.},
  annote       = {An algorithm for estimating the parameters of a stochastic chemical system with a distributed delay is presented. A functional form must be assumed for the delay distribution, and an incorrect assumption leads to systematically incorrect estimates of the delay variance, although the mean delay is correctly recovered. If absolute measurements of populations are unavailable, the independent estimate of one kinetic parameter (in the case treated here, the dilution rate) allows the recovery of all of the parameters of the model.},
  creationdate = {2022-05-30T11:52:14},
  doi          = {10.1093/bioinformatics/btz574},
  owner        = {marcroussel},
}

@Article{MacDonald1976,
  author       = {N. MacDonald},
  journal      = {Math. Biosci.},
  title        = {Time Delay in Prey-Predator Models},
  year         = {1976},
  pages        = {321-330},
  volume       = {28},
  annote       = {Simple examples of gamma-distributed delays in a Lotka-Volterra model are treated. The delay terms are exactly represented as additional ODEs. It is shown that such delays can lead to limit-cycle behavior.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1016/0025-5564(76)90130-9},
  owner        = {roussel},
}

@Article{MacDonald1977a,
  author       = {N. MacDonald},
  journal      = {J. Theor. Biol.},
  title        = {Time Lag in a Model of a Biochemical Reaction Sequence with End Product Inhibition},
  year         = {1977},
  pages        = {549-556},
  volume       = {67},
  annote       = {The author studies a Goodwin model using the equivalence between linear decay chains and gamma-distributed delays. If the Hill coefficient in the feedback term $\rho=1$, no oscillations are possible. However, oscillations are possible for any $\rho\ge 2$.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1016/0022-5193(77)90056-X},
  owner        = {roussel},
}

@Book{MacDonald89,
  author       = {N. MacDonald},
  publisher    = {Cambridge},
  title        = {Biological Delay Systems: Linear Stability Theory},
  year         = {1989},
  address      = {Cambridge},
  annote       = {The main focus of this book is the classification of the roots of quasi-polynomials arising in the linearized stability analysis of delay-differential equations. The author also describes quite thoroughly the stability analysis of ordinary differential equations. Both discrete and distributed delays are considered. Many methods are presented, some of which reduce quasi-polynomial questions to ordinary polynomial problems.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{BLM2013,
  author       = {Manual Barrio and Leier, Andr{\'e} and Marquez-Lago, Tatiana T.},
  journal      = {J. Chem. Phys.},
  title        = {Reduction of Chemical Reaction Networks through Delay Distributions},
  year         = {2013},
  pages          = {104114},
  volume       = {138},
  abstract     = {Accurate modelling and simulation of dynamic cellular events require two main ingredients: an adequate description of key chemical reactions and simulation of such chemical events in reasonable time spans. Quite logically, posing the right model is a crucial step for any endeavour in Computational Biology. However, more often than not, it is the associated computational costs which actually limit our capabilities of representing complex cellular behaviour. In this paper, we propose a methodology aimed at representing chains of chemical reactions by much simpler, reduced models. The abridgement is achieved by generation of model-specific delay distribution functions, consecutively fed to a delay stochastic simulation algorithm. We show how such delay distributions can be analytically described whenever the system is solely composed of consecutive first-order reactions, with or without additional ``backward'' bypass reactions, yielding an exact reduction. For models including other types of monomolecular reactions (constitutive synthesis, degradation, or ``forward'' bypass reactions), we discuss why one must adopt a numerical approach for its accurate stochastic representation, and propose two alternatives for this. In these cases, the accuracy depends on the respective numerical sample size. Our model reduction methodology yields significantly lower computational costs while retaining accuracy. Quite naturally, computational costs increase alongside network size and separation of time scales. Thus, we expect our model reduction methodologies to significantly decrease computational costs in these instances. We anticipate the use of delays in model reduction will greatly alleviate some of the current restrictions in simulating large sets of chemical reactions, largely applicable in pharmaceutical and biological research.},
  annote       = {Methods for deriving delay distributions for sequences of reactions, whether they are partially reversible or all irreversible, are presented. One interesting method relies on the matrix exponential since the solution of a linear system, in this case, a master equation, can be written in terms of the matrix exponential. The authors consider additions such as bypass reactions, i.e. reactions that skip over some species in the chain, whether in the forward or backward direction, sinks (degradation, probability leaks), as well as additional incoming reactions, i.e. reactions that inject material at some midpoint in the chain. In the latter case, the chain is separated into two distinct chains, each with its own delay, one that goes the length of the chain, and the other that starts at the injection point. They also consider converting the Michaelis-Menten mechanism into a Brown mechanism, but they limit their solution to the case $e_0\ll s_0$.},
  creationdate = {2024-02-08T20:16:17},
  doi          = {10.1063/1.4793982},
  file         = {:BLM2013.pdf:PDF},
  owner        = {marcroussel},
}

@Article{LBM2014,
  author       = {Andre Leier and Barrio, Manuel and Marquez-Lago, Tatiana T.},
  journal      = {J. R. Soc. Interface},
  title        = {Exact Model Reduction with Delays: Closed-Form Distributions and Extensions to Fully Bi-Directional Monomolecular Reactions},
  year         = {2014},
  pages          = {20140108},
  volume       = {11},
  abstract     = {In order to systematically understand the qualitative and quantitative behaviour of chemical reaction networks, scientists must derive and analyse associated mathematical models. However, biochemical systems are often very large, with reactions occurring at multiple time scales, as evidenced by signalling pathways and gene expression kinetics. Owing to the associated computational costs, it is then many times impractical, if not impossible, to solve or simulate these systems with an appropriate level of detail. By consequence, there is a growing interest in developing techniques for the simplification or reduction of complex biochemical systems. Here, we extend our recently presented methodology on exact reduction of linear chains of reactions with delay distributions in two ways. First, we report that it is now possible to deal with fully bi-directional monomolecular systems, including degradations, synthesis and generalized bypass reactions. Second, we provide all derivations of associated delays in analytical, closed form. Both advances have a major impact on further reducing computational costs,while still retaining full accuracy. Thus, we expect our new methodology to respond to current simulation needs in pharmaceutical, chemical and biological research.},
  annote       = {The authors derive delay distributions for reversible linear subsystems, which may include `jumps' between non-adjacent states (which they call `bypass reactions').},
  creationdate = {2023-11-05T22:33:24},
  doi          = {10.1098/rsif.2014.0108},
  keywords     = {chemical reaction networks, exact model reduction, distributed delays},
  owner        = {marcroussel},
}

@Article{KKS2015,
  author       = {Alon Kalo and Itamar Kanter and Amit Shraga and Jonathan Sheinberger and Hadar Tzemach and Noa Kinor and Singer, Robert H. and Timoth{\'e}e Lionnet and Shav-Tal, Yaron},
  journal      = {Cell Rep.},
  title        = {Cellular Levels of Signaling Factors Are Sensed by $\beta$-actin Alleles to Modulate Transcriptional Pulse Intensity},
  year         = {2015},
  pages        = {419-432},
  volume       = {11},
  abstract     = {The transcriptional response of $\beta$-actin to extracellular
stimuli is a paradigm for transcription factor
complex assembly and regulation. Serum induction
leads to a precisely timed pulse of $\beta$-actin transcription
in the cell population. Actin protein is proposed
to be involved in this response, but it is not known
whether cellular actin levels affect nuclear $\beta$-actin
transcription. We perturbed the levels of key
signaling factors and examined the effect on the
induced transcriptional pulse by following endogenous
$\beta$-actin alleles in single living cells. Lowering
serum response factor (SRF) protein levels leads to
loss of pulse integrity, whereas reducing actin protein
levels reveals positive feedback regulation, resulting
in elevated gene activation and a prolonged
transcriptional response. Thus, transcriptional pulse
fidelity requires regulated amounts of signaling proteins,
and perturbations in factor levels eliminate
the physiological response, resulting in either tuning
down or exaggeration of the transcriptional pulse.},
  annote      = {This paper contains a great deal of interesting quantitative data on transcription of the $\beta$-actin gene following various experimental manipulations. The authors used the now-standard MS2 system to track mRNAs in the cell. They find that serum induction results in clearly defined pulses of $\beta$-actin transcription. As many as 50 RNA polymerases can transcribe each allele at any given time, and about three of four alleles are active under these conditions. The response is surprisingly fast: transcription can start within a couple of minutes of serum induction. The elongation rate was found to be about 2 kb/min. Nuclear export of mRNA was found to take 10 to 20 minutes.},
  creationdate = {2023-10-31T12:45:53},
  doi          = {10.1016/j.celrep.2015.03.039},
  owner        = {roussel},
}

@Article{KG2000,
  author       = {Jennifer F. Kugel and James A. Goodrich},
  journal      = {J. Biol. Chem.},
  title        = {A Kinetic Model for the Early Steps of {RNA} Synthesis by Human {RNA} Polymerase {II}},
  year         = {2000},
  pages        = {40483-40491},
  volume       = {275},
  annote       = {Through a series of competition experiments coupled with some rapid kinetics, it is discovered that there is an early, rapid event in transcription in which the stability of the ternary transcription complex increases greatly. The term escape commitment is coined by the authors to describe this event, which occurs around the 4-nt stage. The authors also fit a kinetic model for transcription, reporting rate constants for the rate-limiting step (under their experimental conditions), namely promoter escape (the step following escape commitment and continuing to the 15-nt stage), and constraints on the other rate constants.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1074/jbc.M006401200},
  owner        = {roussel},
}

@Article{MP2013,
  author       = {Namiko Mitarai and Steen Pedersen},
  journal      = {Phys. Biol.},
  title        = {Control of Ribosome Traffic by Position-Dependent Choice of Synonymous Codons},
  year         = {2013},
  pages          = {056011},
  volume       = {10},
  abstract     = {Messenger RNA (mRNA) encodes a sequence of amino acids by using codons. For most amino acids, there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the mRNA but also might have an effect on nearby ribosomes by affecting the appearance of `traffic jams' where multiple ribosomes collide and form queues. To test this `context effect' further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild-type (WT) sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the WT sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.},
  annote       = {The authors use a simple model of translation consisting of initiation in a single step, followed by stepwise codon translation, to study the effect of variations in codon translation speed (and thus of synonymous codon substitutions) on traffic and overall translation rate. They find that early slow codons tend to reduce traffic jams, whereas slow codons later in the gene can slow translation significantly at high initiation rates.},
  creationdate = {2017-07-13T00:00:00},
  doi          = {10.1088/1478-3975/10/5/056011},
  owner        = {roussel},
}

@Article{Kremling2007,
  author       = {A. Kremling},
  journal      = {Biotech. Bioeng.},
  title        = {Comment on Mathematical Models Which Describe Transcription and Calculate the Relationship Between mRNA and Protein Expression Ratio},
  year         = {2007},
  pages        = {815-819},
  volume       = {96},
  abstract     = {Mathematical models to describe transcription (Arnold et al. (2001); Biotech Bioeng 72:548--561) and translation (Mehra et al. (2003); Biotech Bioeng 84:822--841) in bacteria are modified in order to improve reaction kinetics and to include the number of polymerase molecules that are active on the DNA, as well as to include the number of ribosomes that are active on the nascent and on the completed mRNA, respectively.},
  annote       = {The steady-state approximation is applied to transcription and translation models. The models consider promoter/ribosome binding site clearance, as well as the stepwise addition of nucleotides.},
  creationdate = {2020-05-05T00:00:00},
  doi          = {10.1002/bit.21065},
  keywords     = {transcription; translation; mathematical modeling},
  owner        = {marcroussel},
}

@Article{PWB1995,
  author       = {Gina M. Perez-Howard and P. Anthony Weil and Joseph M. Beechem},
  journal      = {Biochemistry},
  title        = {Yeast {TATA} Binding Protein Interaction with {DNA}: Fluorescence Determination of Oligomeric State, Equilibrium Binding, On-Rate, and Dissociation Kinetics},
  year         = {1995},
  pages        = {8005-8017},
  volume       = {34},
  annote       = {The authors carry out a number of equilibrium and kinetic measurements for the binding of TBP to DNA, and dissociation of this complex. Their equilibrium and kinetic measurements are found to be consistent with each other. Their results also suggest that TBP oligomerizes in solution.},
  creationdate = {2014-08-26T00:00:00},
  doi          = {10.1021/bi00025a006},
  owner        = {roussel},
}

@Article{CP1995,
  author       = {Robert A. Coleman and B. Franklin Pugh},
  journal      = {J. Biol. Chem.},
  title        = {Evidence for Functional Binding and Stable Sliding of the {TATA} Binding Protein on Nonspecific {DNA}},
  year         = {1995},
  pages        = {13850-13859},
  volume       = {270},
  abstract     = {The TATA binding protein (TBP) is required at RNA polymerase I, II, and III promoters that either contain or lack a TATA box. In an effort to understand how TBP might function at such a wide variety of promoters, we have investigated the specific and nonspecific DNA binding properties of human TBP. We show that TBP has less than a 103-fold preference for binding a TATA box (TATAAAAG) than for an average nonspecific site. In contrast to TBP, which binds to the minor groove of DNA, major groove binding proteins typically display binding specificities in the range of 106. Once TBP is bound to DNA, whether it be a TATA box or nonspecific DNA, binding is quite stable with a t of dissociation in the range of 20-60 min for a 300-base pair DNA fragment. In this binding state, TBP appears to be capable of stable one-dimensional sliding along the DNA. Sequence-specific binding can be accounted for, in part, by different rates of sliding. Additional findings demonstrate that specific and nonspecific DNA impart upon TBP an enormous and equivalent degree of thermal stability, suggesting that the TBP$\cdot$DNA interface on nonspecific DNA is not radically different from that on TATA. Consistent with this notion, we find that nonspecifically bound TBP is competent in establishing pol II transcription complexes on DNA. Together, these finding provide a plausible mechanistic explanation for the ability of TBP to function at TATA-containing and TATA-less promoters.},
  annote       = {The authors study the binding of human TBP to DNA, both to the TATA box and to nonspecific DNA. TBP binds to the minor groove of DNA, where there are few sequence-specific features. Not surprisingly then, the binding of TBP to nonspecific sites is only about 1000 times less stable than the binding to a TATA box. The authors find a $K_D$ for binding to a TATA box of $4.6\times 10^{-10}\,\mathrm{M}$. The $K_D$ for binding to a nonspecific DNA site was found to be $3.4\times 10^{-7}\,\mathrm{M}$. Dissociation rate constants of the complex were measured at different temperatures. The dissociation from a TATA sequence and from nonspecific sites proceeds with very similar rate constants (of order $10^{-4}\,\mathrm{s}^{-1}$). At higher temperatures, TBP is rapidly inactivated. Here, the authors show that TBP bound to DNA, whether to a TATA box or to a nonspecific site, is much more thermostable than free (dimerized) TBP. The thermostabilization of both TATA-bound and nonspecifically bound TBP shows that there are no dramatic differences in the way TBP binds to both types of sites. The authors also show that transcription can be initiated from TBP bound to nonspecific sites.},
  creationdate = {2015-02-22T00:00:00},
  doi          = {10.1074/jbc.270.23.13850},
  owner        = {marcroussel},
}

@Article{DJS+2005,
  author       = {Arindam Dasgupta and Sarah A Juedes and Rebekka O Sprouse and David T Auble},
  journal      = {EMBO J.},
  title        = {Mot1-mediated Control of Transcription Complex Assembly and Activity},
  year         = {2005},
  pages        = {1717-1729},
  volume       = {24},
  abstract     = {Mot1 is an essential Snf2/Swi2-related ATPase and TATA-binding protein (TBP)-associated factor (TAF). In vitro, Mot1 utilizes ATP hydrolysis to disrupt TBP-DNA complexes, but the relationship of this activity to Mot1's in vivo function is unclear. Chromatin immunoprecipitation was used to determine how Mot1 affects the assembly of preinitiation complexes (PICs) at Mot1-controlled promoters in vivo. We find that the Mot1-repressed HSP26 and INO1 promoters are both regulated by TBP recruitment; inactivation of Mot1 leads to increased PIC formation coincident with derepression of transcription. For the Mot1-activated genes BNA1 and URA1, inactivation of Mot1 also leads, remarkably, to increased TBP binding to the promoters, despite the fact that transcription of these genes is obliterated in mot1 cells. In contrast, levels of Taf1, TFIIB, and RNA polymerase II are reduced at Mot1-activated promoters in mot1 cells. These results suggest that Mot1-mediated displacement of TBP underlies its mechanism of repression and activation at these genes. We suggest that at activated promoters, Mot1 disassembles transcriptionally inactive TBP, thereby facilitating the formation of a TBP complex that supports functional PIC assembly.},
  annote       = {The authors study the function of Mot1 at both Mot1-activated and -inactivated promoters. In both cases, they find that their results are consistent with Mot1 playing a role in dissociating TBP from the promoter, ensuring its recycling. As part of their study, they looked at the lifetime of the TBP-promoter complex by an indirect method (monitoring mRNA levels), estimating a half-life for this complex of 5 to 8 minutes under normal conditions.},
  creationdate = {2019-08-19T00:00:00},
  doi          = {10.1038/sj.emboj.7600646},
  keywords     = {ATPase; Mot1; Snf2; TAF; TBP},
  owner        = {Marc},
}

@Article{SKM+2008,
  author       = {Rebekka O. Sprouse and Tatiana S. Karpova and Florian Mueller and Arindam Dasgupta and McNally, James G. and David T. Auble},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {Regulation of {TATA}-Binding Protein Dynamics in Living Yeast Cells},
  year         = {2008},
  pages        = {13304-13308},
  volume       = {105},
  abstract     = {Although pathways for assembly of RNA polymerase (Pol) II transcription preinitiation complexes (PICs) have been well established in vitro, relatively little is known about the dynamic behavior of Pol II general transcription factors in vivo. In vitro, a subset of Pol II factors facilitates reinitiation by remaining very stably bound to the promoter. This behavior contrasts markedly with the highly dynamic behavior of RNA Pol I transcription complexes in vivo, which undergo cycles of disassembly/reassembly at the promoter for each round of transcription. To determine whether the dynamic behavior of the Pol II machinery in vivo is fundamentally different from that of Pol I and whether the static behavior of Pol II factors in vitro fully recapitulates their behavior in vivo, we used fluorescence recovery after photobleaching (FRAP). Surprisingly, we found that all or nearly all of the TATA-binding protein (TBP) population is highly mobile in vivo, displaying FRAP recovery rates of <15 s. These high rates require the activity of the TBP-associated factor Mot1, suggesting that TBP/chromatin interactions are destabilized by active cellular processes. Furthermore, the distinguishable FRAP behavior of TBP and TBP-associated factor 1 indicates that there are populations of these molecules that are independent of one another. The distinct FRAP behavior of most Pol II factors that we tested suggests that transcription complexes assemble via stochastic multistep pathways. Our data indicate that active Pol II PICs can be much more dynamic than previously considered.},
  annote       = {From FRAP experiments it appears that the lifetime of TBP at the promoter once transcription initiation has occurred is less than 15~s in yeast. Rapid dissociation of TBP from the promoter depends on Mot1.},
  creationdate = {2019-04-07T00:00:00},
  doi          = {10.1073pnas.0801901105},
  owner        = {marcroussel},
}

@Article{LHE2021,
  author       = {Jonathan Liu and Donald Hansen and Elizabeth Eck and Yang Joon Kim and Meghan Turner and Simon Alamos and Hernan G. Garcia},
  journal      = {PLoS Comput. Biol.},
  title        = {Real-Time Single-Cell Characterization of the Eukaryotic Transcription Cycle Reveals Correlations between {RNA} Initiation, Elongation, and Cleavage},
  year         = {2021},
  pages          = {e1008999},
  volume       = {17},
  abstract     = {The eukaryotic transcription cycle consists of three main steps: initiation, elongation, and cleavage of the nascent RNA transcript. Although each of these steps can be regulated as well as coupled with each other, their in vivo dissection has remained challenging because available experimental readouts lack sufficient spatiotemporal resolution to separate the contributions from each of these steps. Here, we describe a novel application of Bayesian inference techniques to simultaneously infer the effective parameters of the transcription cycle in real time and at the single-cell level using a two-color MS2/PP7 reporter gene and the developing fruit fly embryo as a case study. Our method enables detailed investigations into cell-to-cell variability in transcription-cycle parameters as well as single-cell correlations between these parameters. These measurements, combined with theoretical modeling, suggest a substantial variability in the elongation rate of individual RNA polymerase molecules. We further illustrate the power of this technique by uncovering a novel mechanistic connection between RNA polymerase density and nascent RNA cleavage efficiency. Thus, our approach makes it possible to shed light on the regulatory mechanisms in play during each step of the transcription cycle in individual, living cells at high spatiotemporal resolution.},
  annote       = {A simple model of transcription that includes initiation, elongation and cleavage is fit to data from MS2/PP7 fluorescence reporting of nascent RNA experiments for the \emph{hunchback} gene in \emph{Drosophila}. A wealth of insights and quantitative data are obtained, among which the following stand out: For this particular gene, bursting is rare. Rather, it appears that transcription initiation proceeds at a roughly constant rate for extended periods of time. The mean elongation rate is 1.7\,kb/min. However, the data are only well fit by the model if the authors assume that different polymerases elongate at different rates, with a distribution supported over an interval from about 0.5 to more than 5\,kb/min. Once elongation is complete, the cleavage time is in the range of 1.5 to 3\,min. The model parameters display correlations, which the authors interpret as indicating that elongation rate affects other processes. For example, slow elongation appears to favor more rapid cleavage of the transcript. The authors find that, for this gene, there is a steady state RNAPII density of about 20 molecules/kb, which would imply that polymerases occupy approximately 80\% of the transcript. The \emph{hunchback} gene therefore operates in a high density regime. Traffic might therefore explain at least some of the variation in elongation rates.},
  creationdate = {2024-02-23T20:44:30},
  doi          = {10.1371/journal.pcbi.1008999},
  owner        = {marcroussel},
}

@Article{GTL2013,
  author       = {Garcia, Hernan G. and Mikhail Tikhonov and Albert Lin and Thomas Gregor},
  journal      = {Curr. Biol.},
  title        = {Quantitative Imaging of Transcription in Living \emph{Drosophila} Embryos Links Polymerase Activity to Patterning},
  year         = {2013},
  pages        = {2140-2145},
  volume       = {23},
  abstract     = {Spatiotemporal patterns of gene expression are fundamental to every developmental program. The resulting macroscopic domains have been mainly characterized by their levels of gene products. However, the establishment of such patterns results from differences in the dynamics of microscopic events in individual cells such as transcription. It is unclear how these microscopic decisions lead to macroscopic patterns, as measurements in fixed tissue cannot access the underlying transcriptional dynamics. In vivo transcriptional dynamics have long been approached in single-celled organisms, but never in a multicellular developmental context. Here, we directly address how boundaries of gene expression emerge in the Drosophila embryo by measuring the absolute number of actively transcribing polymerases in real time in individual nuclei. Specifically, we show that the formation of a boundary cannot be quantitatively explained by the rate of mRNA production in each cell, but instead requires amplification of the dynamic range of the expression boundary. This amplification is accomplished by nuclei randomly adopting active or inactive states of transcription, leading to a collective effect where the fraction of active nuclei is modulated in space. Thus, developmental patterns are not just the consequence of reproducible transcriptional dynamics in individual nuclei, but are the result of averaging expression over space and time.},
  annote       = {The authors develop a method based on the MS2 fluorescent reporter system for studying the expression of genes in vivo. Specifically, they look at expression from the \emph{hunchback} P2 enhancer and promoter in \emph{Drosophila} embryos. They find that patterning involves the gene being expressed in more cells in the anterior region, and then fewer cells expressing the gene through the transition region, i.e.\ on a cellular level, the gene can be on or off, and developmental signals modulate the likelihood that the gene is turned on. The authors obtain a variety of quantitative data on transcription, including a rate of elongation of 1.5\,kb/min, a very high processivity once the polymerase has initiated transcription, RNAPII loading rates of up to 20 molecules per minute, and average spacing between polymerases of 150\,nt.},
  creationdate = {2024-02-24T12:01:19},
  doi          = {10.1016/j.cub.2013.08.054},
  owner        = {marcroussel},
}

@Article{HK2019,
  author       = {Paul J. Hurtado and Adam S. Kirosingh},
  journal      = {J. Math. Biol.},
  title        = {Generalizations of the `Linear Chain Trick': Incorporating More Flexible Dwell Time Distributions into Mean Field {ODE} Models},
  year         = {2019},
  pages        = {1831-1883},
  volume       = {79},
  abstract     = {In this paper we generalize the Linear Chain Trick (LCT; aka the Gamma Chain Trick) to help provide modelers more flexibility to incorporate appropriate dwell time assumptions into mean field ODEs, and help clarify connections between individual-level stochastic model assumptions and the structure of corresponding mean field ODEs. The LCT is a technique used to construct mean field ODE models from continuous-time stochastic state transition models where the time an individual spends in a given state (i.e., the dwell time) is Erlang distributed (i.e., gamma distributed with integer shape parameter). Despite the LCT's widespread use, we lack general theory to facilitate the easy application of this technique, especially for complex models. Modelers must therefore choose between constructing ODE models using heuristics with oversimplified dwell time assumptions, using time consuming derivations from first principles, or to instead use non-ODE models (like integro-differential or delay differential equations) which can be cumbersome to derive and analyze. Here, we provide analytical results that enable modelers to more efficiently construct ODE models using the LCT or related extensions. Specifically, we provide (1) novel LCT extensions for various scenarios found in applications, including conditional dwell time distributions; (2) formulations of these LCT extensions that bypass the need to derive ODEs from integral equations; and (3) a novel Generalized Linear Chain Trick (GLCT) framework that extends the LCT to a much broader set of possible dwell time distribution assumptions, including the flexible phase-type distributions which can approximate distributions on R+ and can be fit to data.},
  annote       = {The authors pick apart the linear chain trick as a means of generating ODE representations of distributed-delay systems. They consider a number of generalizations that amount to using a more complex linear network than a simple chain.},
  creationdate = {2024-02-11T15:30:55},
  doi          = {10.1007/s00285-019-01412-w},
  keywords     = {Gamma chain trick; Linear Chain Trick; Distributed delay; Mean field model; Phase-type distributions; Time lag},
  owner        = {marcroussel},
}

@Article{BMN2010,
  author       = {Golan Bel and Brian Munsky and Ilya Nemenman},
  journal      = {Phys. Biol.},
  title        = {The Simplicity of Completion Time Distributions for Common Complex Biochemical Processes},
  year         = {2010},
  pages          = {016003},
  volume       = {7},
  abstract     = {Biochemical processes typically involve huge numbers of individual reversible steps, each with its own dynamical rate constants. For example, kinetic proofreading processes rely upon numerous sequential reactions in order to guarantee the precise construction of specific macromolecules. In this work, we study the transient properties of such systems and fully characterize their first passage (completion) time distributions. In particular, we provide explicit expressions for the mean and the variance of the completion time for a kinetic proofreading process and computational analyses for more complicated biochemical systems. We find that, for a wide range of parameters, as the system size grows, the completion time behavior simplifies: it becomes either deterministic or exponentially distributed, with a very narrow transition between the two regimes. In both regimes, the dynamical complexity of the full system is trivial compared to its apparent structural complexity. Similar simplicity is likely to arise in the dynamics of many complex multistep biochemical processes. In particular, these findings suggest not only that one may not be able to understand individual elementary reactions from macroscopic observations, but also that such an understanding may be unnecessary.},
  annote       = {The authors analyze a stochastic model of kinetic proofreading or, as it might be more aptly described, a model of a set of sequential reversible reactions that can be aborted. This class of processes would include elongation in templated polymerization (transcription, translation). They find that for large numbers of steps, the distribution of completion times converges either to a gamma distribution (and in the limit to a $\delta$ function), or to an exponential distribution. The transition between these two regimes is relatively sharp.},
  creationdate = {2018-04-12T00:00:00},
  doi          = {10.1088/1478-3975/7/1/016003},
  owner        = {roussel},
}

@Article{BCH2013,
  author       = {H. T. Banks and Jared Catenacci and Shuhua Hu},
  journal      = {Stoch. Anal. Appl.},
  title        = {A Comparison of Stochastic Systems with Different Types of Delays},
  year         = {2013},
  pages        = {913-955},
  volume       = {31},
  abstract     = {In this article, we investigate the effects of different types of delays, a fixed delay and a random delay, on the dynamics of stochastic systems as well as their relationship with each other in the context of a just-in-time network model. The specific example on which we focus is a pork production network model. We numerically explore the corresponding deterministic approximations for the stochastic systems with these two different types of delays. Numerical results reveal that the agreement of stochastic systems with fixed and random delays depend on the population size and the variance of the random delay, even when the mean value of the random delay is chosen the same as the value of the fixed delay. When the variance of the random delay is sufficiently small, the histograms of state solutions to the stochastic system with a random delay are similar to those of the stochastic model with a fixed delay regardless of the population size. We also compared the stochastic system with a Gamma distributed random delay to the stochastic system constructed based on the Kurtz's limit theorem from a system of deterministic delay differential equations with a Gamma distributed delay. We found that with the same population size the histogram plots for the solution to the second system appear more dispersed than the corresponding ones obtained for the first case. In addition, we found that there is more agreement between the histograms of these two stochastic systems as the variance of the Gamma distributed random delay decreases.},
  annote       = {Using a pork production model, the authors study the effects of fixed and random delays in a stochastic model. They also consider the limiting differential equation obtained by the Kurtz approach, with delays inserted afterwards. For the variable delays, and integrodifferential equation is obtained, which is then approximated using the ``linear chain trick''. A brief summary of the results is that there are cases where all of these model formulations give different mean behavior. Accordingly, one needs to be very careful in introducing fixed delays or in reducing a stochastic system to differential equations for the mean.},
  creationdate = {2017-10-02T00:00:00},
  doi          = {10.1080/07362994.2013.806217},
  keywords     = {Fixed vs. random delays; Gamma distribution and the linear chain trick; Kurtz limit theorem; Markov Chain stochastic vs. deterministic approximations; Systems with delays},
  owner        = {marcroussel},
}

@Article{JKL2014,
  author       = {Iris Jonkers and Kwak, Hojoong and John T Lis},
  journal      = {eLife},
  title        = {Genome-Wide Dynamics of {Pol II} Elongation and its Interplay with Promoter Proximal Pausing, Chromatin, and Exons},
  year         = {2014},
  pages          = {e02407},
  volume       = {3},
  abstract     = {Production of mRNA depends critically on the rate of RNA polymerase II (Pol II)
elongation. To dissect Pol II dynamics in mouse ES cells, we inhibited Pol II transcription at either
initiation or promoter-proximal pause escape with Triptolide or Flavopiridol, and tracked Pol II
kinetically using GRO-seq. Both inhibitors block transcription of more than 95\% of genes, showing
that pause escape, like initiation, is a ubiquitous and crucial step within the transcription cycle.
Moreover, paused Pol II is relatively stable, as evidenced from half-life measurements at $\sim 3200$ genes.
Finally, tracking the progression of Pol II after drug treatment establishes Pol II elongation rates at
over 1000 genes. Notably, Pol II accelerates dramatically while transcribing through genes, but slows
at exons. Furthermore, intergenic variance in elongation rates is substantial, and is influenced by a
positive effect of H3K79me2 and negative effects of exon density and CG content within genes.},
  annote       = {Extensive measurements of transcription kinetics were carried out for more than 3000 genes in mouse embryonic stem cells. Promoter-proximal pausing occurs in almost all of the genes studied, with half lives of the paused complexes ranging from about 2 to more than 20 minutes (mean 7 minutes). P-TEFb is required to exit promoter-proximal pausing. Polymerases display a range of transcription elongation rates, from about 0.5 to 4 kb/min, depending on the gene. As a general rule, the polymerase accelerates as it moves through a gene, which results in larger average spacing between polymerases the further down the gene it travels. The polymerase seems to slow down while transcribing exons, but speed gained moving through early introns seems to be at least partially retained. It's also possible that polymerases ``push'' each other, as it was found that elongation is faster when polymerases are tightly packed on the template DNA.},
  creationdate = {2024-02-16T21:50:55},
  doi          = {10.7554/eLife.02407},
}

@Article{SG2023,
  author       = {Juraj Szavits-Nossan and Grima, Ramon},
  journal      = {Phys. Rev. E},
  title        = {Uncovering the Effect of {RNA} Polymerase Steric Interactions on Gene Expression Noise: Analytical Distributions of Nascent and Mature {RNA} Numbers},
  year         = {2023},
  pages          = {034405},
  volume       = {108},
  abstract     = {The telegraph model is the standard model of stochastic gene expression, which can be solved exactly to obtain the distribution of mature RNA numbers per cell. A modification of this model also leads to an analytical distribution of nascent RNA numbers. These solutions are routinely used for the analysis of single-cell data, including the inference of transcriptional parameters. However, these models neglect important mechanistic features of transcription elongation, such as the stochastic movement of RNA polymerases and their steric (excluded-volume) interactions. Here we construct a model of gene expression describing promoter switching between inactive and active states, binding of RNA polymerases in the active state, their stochastic movement including steric interactions along the gene, and their unbinding leading to a mature transcript that subsequently decays. We derive the steady-state distributions of the nascent and mature RNA numbers in two important limiting cases: constitutive expression and slow promoter switching. We show that RNA fluctuations are suppressed by steric interactions between RNA polymerases, and that this suppression can in some instances even lead to sub-Poissonian fluctuations; these effects are most pronounced for nascent RNA and less prominent for mature RNA, since the latter is not a direct sensor of transcription. We find a relationship between the parameters of our microscopic mechanistic model and those of the standard models that ensures excellent consistency in their prediction of the first and second RNA number moments over vast regions of parameter space, encompassing slow, intermediate, and rapid promoter switching, provided the RNA number distributions are Poissonian or super-Poissonian. Furthermore, we identify the limitations of inference from mature RNA data, specifically showing that it cannot differentiate between highly distinct RNA polymerase traffic patterns on a gene.},
  annote       = {The authors study a family of TASEP-like models of transcription in both constitutive expression and telegrapher's noise situations. Initiation and termination are each modeled as single steps, and the polymerase is assumed to ``jump'' by its own length at each step of elongation. In some variations, the stochastic nature of elongation as well as exclusion are considered, while in others the polymerase is assumed to move at a constant rate. A variety of results are obtained on the distributions of RNAs on the template strand and on the number distribution of transcripts (nascent or completed).},
  creationdate = {2024-02-25T21:44:45},
  doi          = {10.1103/PhysRevE.108.034405},
  owner        = {marcroussel},
}

@Article{DB2009,
  author       = {Maciej Dobrzy{\'n}ski and Frank J. Bruggeman},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {Elongation Dynamics Shape Bursty Transcription and Translation},
  year         = {2009},
  pages        = {2583-2588},
  volume       = {106},
  abstract     = {Cells in isogenic populations may differ substantially in their molecular make up because of the stochastic nature of molecular processes. Stochastic bursts in process activity have a great potential for generating molecular noise. They are characterized by (short) periods of high process activity followed by (long) periods of process silence causing different cells to experience activity periods varying in size, duration, and timing. We present an analytically solvable model of bursts in molecular networks, originally developed for the analysis of telecommunication networks. We define general measures for model-independent characterization of bursts (burst size, significance, and duration) from stochastic time series. Inspired by the discovery of bursts in mRNA and protein production by others, we use those indices to investigate the role of stochastic motion of motor proteins along biopolymer chains in determining burst properties. Collisions between neighboring motor proteins can attenuate bursts introduced at the initiation site on the chain. Pausing of motor proteins can give rise to bursts. We investigate how these effects are modulated by the length of the biopolymer chain and the kinetic properties of motion. We discuss the consequences of those results for transcription and translation.},
  annote       = {The authors start by analyzing a simple model in which an on/off Poisson process controls a Poisson production process. This is called an interrupted Poisson process. They introduce statistical procedures to determine the burst size, burst duration, and burst significance (a measure of the extent to which the system is bursty). These are then used to characterize the bursting properties of a set of simple models that could describe either transcription or translation. Initiation is modeled using their simple initial model with on/off switching. If the parameters are set such that there are few collisions during elongation, then the bursts are preserved. On the other hand, if collisions are frequent, then the bursts become weaker (lower significance) as the chain becomes longer. Rare but lengthy pauses can create bursts by accumulating polymerases behind the paused polymerase (or ribosome). On the other hand, frequent pauses disrupt bursts. The authors describe the mechanism as breaking a burst train in two when one of the polymerases inside a burst pauses.},
  creationdate = {2017-10-13T00:00:00},
  doi          = {10.1073/pnas.0803507106},
  keywords     = {bursts, interrupted Poisson process, transcriptional pausing, waiting times},
  owner        = {roussel},
}

@Article{BKW+2013,
  author       = {Pavol Bokes and John R. King and Andrew T. A. Wood and Matthew Loose},
  journal      = {Bull. Math. Biol.},
  title        = {Transcriptional Bursting Diversifies the Behaviour of a Toggle Switch: Hybrid Simulation of Stochastic Gene Expression},
  year         = {2013},
  pages        = {351-371},
  volume       = {75},
  annote       = {In the modeling approach used here, the distribution of transcriptional burst times and burst sizes is derived from a model, or these distributions could be assumed. Protein numbers are updated at the discrete times generated from the appropriate burst time distribution. The protein dynamics between bursts is similarly obtained from a solvable deterministic model, e.g.\ simple decay. The protein population at the time of the next burst can therefore be computed. A simple autoregulatory model and a genetic toggle switch are studied by this method.},
  creationdate = {2019-10-24T00:00:00},
  keywords     = {Gene expression; Stochastic hybrid models},
  owner        = {roussel},
}

@Article{Suter-etal2011,
  author       = {David M. Suter and Nacho Molina and David Gatfield and Kim Schneider and Ueli Schibler and Felix Naef},
  journal      = {Science},
  title        = {Mammalian Genes Are Transcribed with Widely Different Bursting Kinetics},
  year         = {2011},
  pages        = {472-474},
  volume       = {332},
  annote       = {A system with a rapidly decaying luciferase encoded by a short-lived mRNA is used to study fluctuations in transcription by RNA polymerase II \emph{in vivo}. A couple of results in this paper particularly caught my eye: First, they were able to measure rate constants for activation and inactivation of a gene. Second, they found that the distribution of activation times of a gene is consistent with a model in which activation proceeds in two steps, while inactivation occurs in a single step.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {DOI:10.1126/science.1198817},
  owner        = {roussel},
}

@Article{WAR2021,
  author       = {Yihan Wan and Dimitrios G. Anastasakis and Joseph Rodriguez and Palangat, Murali and Prabhakar Gudla and George Zaki and Mayank Tandon and Gianluca Pegoraro and Chow, Carson C. and Markus Hafner and Larson, Daniel R.},
  journal      = {Cell},
  title        = {Dynamic Imaging of Nascent {RNA} Reveals General Principles of Transcription Dynamics and Stochastic Splice Site Selection},
  year         = {2021},
  pages        = {2878-2895},
  volume       = {184},
  abstract     = {The activities of RNA polymerase and the spliceosome are responsible for the heterogeneity in the abundance and isoform composition of mRNA in human cells. However, the dynamics of these megadalton enzymatic complexes working in concert on endogenous genes have not been described. Here, we establish a quasi-genome-scale platform for observing synthesis and processing kinetics of single nascent RNA molecules in real time.We find that all observed genes show transcriptional bursting. We also observe large kinetic variation in intron removal for single introns in single cells, which is inconsistent with deterministic splice site selection. Transcriptome-wide footprinting of the U2AF complex, nascent RNA profiling, long-read sequencing, and lariat sequencing further reveal widespread stochastic recursive splicing within introns. We propose and validate a unified theoretical model to explain the general features of transcription and pervasive stochastic splice site selection.},
  annote       = {Most of our thinking about splicing revolves around the idea that the spliceosome detects a single 5' splice site and a single branch point, and cuts out the intron in a single process. However, it has been known for some time that recursive splicing, in which introns are removed in pieces via the use of internal 5' splice sites and branch points, is also possible. This paper shows that about 30\% of mRNAs are subject to recursive splicing. In the model proposed by the authors, the 5' splice site and branch point are selected stochastically, and splicing events continue until the entire intron has been removed. The paper contains a large number of useful quantitative measurements of the splicing and transcription processes, including the durations of times that genes are actively transcribing and not, the mean time required to complete one splicing event (which is \emph{not} the same as the time required to remove an intron according to the authors' model), and the mean transcription rate. The splicing time in particular is found to be about 8\,min.},
  creationdate = {2022-09-19T09:26:39},
  doi          = {10.1016/j.cell.2021.04.012},
  owner        = {marcroussel},
}

@Article{CFX2006,
  author       = {Cai, Long and Friedman, Nir and Xie, X. Sunney},
  journal      = {Nature},
  title        = {Stochastic Protein Expression in Individual Cells at the Single Molecule Level},
  year         = {2006},
  pages        = {358-362},
  volume       = {440},
  abstract     = {In a living cell, gene expression---the transcription of DNA to messenger RNA followed by translation to protein---occurs stochastically, as a consequence of the low copy number of DNA and mRNA molecules involved These stochastic events of protein production are difficult to observe directly with measurements on large ensembles of cells owing to lack of synchronization among cells. Measurements so far on single cells lack the sensitivity to resolve individual events of protein production. Here we demonstrate a microfluidic-based assay that allows real-time observation of the expression of $\beta$-galactosidase in living Escherichia coli cells with single molecule sensitivity. We observe that protein production occurs in bursts, with the number of molecules per burst following an exponential distribution. We show that the two key parameters of protein expression---the burst size and frequency---can be either determined directly from real-time monitoring of protein production or extracted from a measurement of the steady-state copy number distribution in a population of cells. Application of this assay to probe gene expression in individual budding yeast and mouse embryonic stem cells demonstrates its generality. Many important proteins are expressed at low levels, and are thus inaccessible by current genomic and proteomic techniques. This microfluidic single cell assay opens up possibilities for system-wide characterization of the expression of these low copy number proteins.},
  annote       = {This paper describes a microfluidic decide that allows a small number of cells to be trapped in a volume of about 100\,pL. This allows for very sensitive single-cell studies, in this case performed using a relatively simple setup with a fluorescence microscope. The authors study the distribution of $\beta$-galactosidase in uninduced \emph{Escherichia coli} cells. They find that, due to random dissociation of the Lac repressor, the cells generate 0.16 bursts of synthesis per cell cycle, with about 8 enzymes produced per burst.},
  creationdate = {2024-02-14T10:59:01},
  doi          = {10.1038/nature04599},
  owner        = {marcroussel},
}

@inbook{LMB1978LLN,
    author = {B. W. Lindgren and G. W. McElrath and D. A. Berry},
    title = {Introduction to Probability and Statistics},   edition={fourth},
    publisher = {Macmillan},    address={New York},
    year = 1978,
    pages={154-156}
}

@article {Janisch2021,
    AUTHOR = {Janisch, M.},
     TITLE = {Kolmogorov's strong law of large numbers holds for pairwise
              uncorrelated random variables},
   JOURNAL = {Theory Probab. Appl.},
    VOLUME = {66},
      YEAR = {2021},
     PAGES = {263--275},
    doi={10.1137/S0040585X97T990381}
}

@Article{LJH2019,
  author       = {Anton J. M. Larsson and Per Johnsson and Michael Hagemann-Jensen and Leonard Hartmanis and Omid R. Faridani and Bj{\"o}rn Reinius and {\AA}sa Segerstolpe and Chloe M. Rivera and Ren, Bing and Rickard Sandberg},
  journal      = {Nature},
  title        = {Genomic Encoding of Transcriptional Burst Kinetics},
  year         = {2019},
  pages        = {251-254},
  volume       = {565},
  abstract     = {Mammalian gene expression is inherently stochastic and results in discrete bursts of RNA molecules that are synthesized from each allele. Although transcription is known to be regulated by promoters and enhancers, it is unclear how cis-regulatory sequences encode transcriptional burst kinetics. Characterization of transcriptional bursting, including the burst size and frequency, has mainly relied on live-cell or single-molecule RNA fluorescence in situ hybridization recordings of selected loci. Here we determine transcriptome-wide burst frequencies and sizes for endogenous mouse and human genes using allele-sensitive single-cell RNA sequencing. We show that core promoter elements affect burst size and uncover synergistic effects between TATA and initiator elements, which were masked at mean expression levels. Notably, we provide transcriptome-wide evidence that enhancers control burst frequencies, and demonstrate that cell-type-specific gene expression is primarily shaped by changes in burst frequencies. Together, our data show that burst frequency is primarily encoded in enhancers and burst size in core promoters, and that allelic single-cell RNA sequencing is a powerful model for investigating transcriptional kinetics.},
  annote       = {The authors measure the distributions of burst sizes and frequencies in mouse and human cells. They find that the burst sizes are largely controlled by the promoter while enhancers control burst frequencies.},
  creationdate = {2024-02-27T23:21:13},
  doi          = {10.1038/s41586-018-0836-1},
  owner        = {marcroussel},
}

@Article{FPG2021,
  author       = {Tatiana Filatova and Nikola Popovic and Grima, Ramon},
  journal      = {Bull. Math. Biol.},
  title        = {Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination},
  year         = {2021},
  pages          = {3},
  volume       = {83},
  abstract     = {Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.},
  annote       = {The authors study a stochastic model of RNA synthesis that includes gene activation/deactivation, initiation (in a single step), elongation, dropoff, pausing and decay. Much of their work focuses on the derivation of distributions of numbers of nascent RNA in various cases, although they also compute distributions of RNAs along the template and distributions of numbers of mature RNAs, model fluorescence intensity measurements in smFISH experiments (which are proportional not only to the number of nascent mRNAs but to their lengths), and briefly consider the distribution of elongation times. They consider both bursty and constitutive expression. One interesting factor is that the stochastic kinetics of elongation tends to disperse polymerases, i.e.\ it introduces a diffusive component to the inter-polymerase distances. An appendix gives an introduction to geometric singular perturbation theory.},
  creationdate = {2024-02-10T15:22:35},
  doi          = {10.1007/s11538-020-00827-7},
  keywords     = {Stochastic gene expression; Master equation; RNA fluctuations; Singular perturbation theory; Distributions of RNA molecules; Stochastic simulations},
  owner        = {marcroussel},
}

@Article{Hamano2016,
  author       = {Masahiro Hamano},
  journal      = {Electron. Notes Theor. Comput. Sci.},
  title        = {Stochastic Transcription Elongation via Rule Based Modelling},
  year         = {2016},
  pages        = {73-88},
  volume       = {326},
  abstract     = {Transcription elongation is the mechanism by which RNA polymerase (RNAP) moves along template unzipped DNA and synthesizes a complementary single-stranded RNA. During the elongation, RNAP forms a stable transcription elongation complex (TEC) with the template DNA and the nascent RNA. The mechanism involves back-tracked and forward-tracked modes of TEC and the polymerisation and depolymerisation of RNA. To capture the stochasticity of the elongation, we describe the mechanism in terms of rule-based modelling through the TEC's local window frame of adjacent active sites. In this way, we can uniformly derive the variations of known kinetic pathways for various interaction combinations of TEC's active sites. From the compact interactions at local sites, we find abstracted rules for the elongation. As the semantic counterpart, we derive quasi-steady state approximations to the chemical master equations. The stochastic models are thermodynamically interpreted as the free energy distributions of agents with variant configurations.},
  annote       = {This paper describes a rule-based modeling approach to elongation in transcription. The model is roughly equivalent to that of Voliotis and coworkers \cite{Voliotis-etal2008}. Various limits are considered, including one that looks like our model \cite{RZ2006c}. It is shown that, assuming that back- and forward-translocation are in equilibrium, an elongation step has a Michaelis-Menten dependence on the NTP concentration.},
  creationdate = {2023-11-05T17:00:57},
  doi          = {10.1016/j.entcs.2016.09.019},
  keywords     = {RNA polymerase, Transcription Elongation Complex, Master Equation, Rule-Based Modelling, Brownian Ratchet Model, Equilibrium Kinetics, Chemical Equilibrium, Steady State Dynamics, Quasi-Steady State, Michaelis-Menten Kinetics, Free Energy, Boltzmann Distribution},
  owner        = {marcroussel},
}

@Article{PMY+2012,
  author       = {Ilya Potapov and Jarno M{\"a}kel{\"a} and Olli Yli-Harja and Andre S. Ribeiro},
  journal      = {J. Theor. Biol.},
  title        = {Effects of Codon Sequence on the Dynamics of Genetic Networks},
  year         = {2012},
  pages        = {17-25},
  volume       = {315},
  annote       = {Using Ribeiro's single-nucleotide resolution transcription/translation model, the authors study the effect of codon sequence on the dynamics of small genetic networks. As might be expected, codon usage has a significant effect on the distribution of protein number in a cell. On the other hand, the fluctuations in protein numbers, measured by the coefficient of variation (CV), are negligible. Many genes start with slowly-translated codons, known as a slow ramp, or end with such a ramp. A slow ramp at the end of a gene seems to have much less effect on gene expression dynamics than a slow ramp at the beginning, perhaps because a slow ramp at the beginning spaces out the ribosomes. The effect of slow ramps was studied in a model of a genetic toggle switch and in a repressilator genetic oscillator model. In the genetic toggle switch, a ramp at the beginning of one of the two genes involved in the toggle strongly biases the toggle towards the gene without a ramp. In the repressilator, the inclusion of slow ramps at the beginning of each gene makes oscillations less distinct.},
  creationdate = {2012-11-12T00:00:00},
  doi          = {10.1016/j.jtbi.2012.08.029},
  owner        = {marcroussel},
}

@Article{SN2010,
  author       = {Maria J. Schilstra and Chrystopher L. Nehaniv},
  journal      = {BioSystems},
  title        = {Stochastic Model of Template-Directed Elongation Processes in Biology},
  year         = {2010},
  pages        = {55-60},
  volume       = {102},
  annote       = {A Petri-net is a bipartite graph very closely analogous to those we have used in qualitative stability analysis, with ``places'' nodes (roughly speaking, reactants) and ``transitions'' nodes (roughly, reactions). The authors construct a Petri-net for an elongation process, which could be transcription or translation. The authors use this Petri-net to study issues around the effect of the size of the polymerase, and the effect of different balances of initiation rates vs elongation rates.},
  creationdate = {2018-07-10T00:00:00},
  keywords     = {Replication, Transcription, Translation, Initiation, Elongation, Termination, Template-directed, Petri-net, Semaphore, Stochastic, Congestion, Kinetics},
  owner        = {roussel},
}

@Article{Hsu2002,
  author       = {Hsu, Lilian M.},
  journal      = {Biochim. Biophys. Acta},
  title        = {Promoter Clearance and Escape in Prokaryotes},
  year         = {2002},
  pages        = {191-207},
  volume       = {1577},
  abstract     = {Promoter escape is the last stage of transcription initiation when RNA polymerase, having initiated de novo phosphodiester bond synthesis, must begin to relinquish its hold on promoter DNA and advance to downstream regions (DSRs) of the template. In vitro, this process is marked by the release of high levels of abortive transcripts at most promoters, reflecting the high instability of initial transcribing complexes (ITCs) and indicative of the existence of barriers to the escape process. The high abortive initiation level is the result of the existence of unproductive ITCs that carry out repeated initiation and abortive release without escaping the promoter. The formation of unproductive ITCs is a widespread phenomenon, but it occurs to different extent on different promoters. Quantitative analysis of promoter mutations suggests that the extent and pattern of abortive initiation and promoter escape is determined by the sequence of promoter elements, both in the promoter recognition region (PRR) and the initial transcribed sequence (ITS). A general correlation has been found that the stronger the promoter DNA-polymerase interaction, the poorer the ability of RNA polymerase to escape the promoter. In gene regulation, promoter escape can be the rate-limiting step for transcription initiation. An increasing number of regulatory proteins are known to exert their control at this step. Examples are discussed with an emphasis on the diverse mechanisms involved. At the molecular level, the X-ray crystal structures of RNA polymerase and its various transcription complexes provide the framework for understanding the functional data on abortive initiation and promoter escape. Based on structural and biochemical evidence, a mechanism for abortive initiation and promoter escape is described.},
  annote       = {This is a thorough review of what was known about promoter escape in prokaryotes as of its writing. Despite the title, the author makes no distinction between promoter escape and promoter clearance. The discussion is centered around a detailed mechanism for promoter escape. One key question which had been unresolved at the time of this review was whether sigma factor was released concurrently with promoter escape. Measured promoter escape times fall in the range of 5\,s to 10\,min. The author also mentions the inverse relationship between promoter binding strength and the rate of escape: escape from stronger promoters is slower.},
  creationdate = {2019-12-20T00:00:00},
  doi          = {10.1016/S0167-4781(02)00452-9},
  keywords     = {Promoter escape; Abortive initiation; Sigma release/displacement; Scrunching/translocation; Stressed intermediate},
  owner        = {marcroussel},
}

@Article{RPT+2006,
  author       = {Arjun Raj and Charles S. Peskin and Daniel Tranchina and Diana Y. Vargas and Sanjay Tyagi},
  journal      = {PLoS Biol.},
  title        = {Stochastic {mRNA} Synthesis in Mammalian Cells},
  year         = {2006},
  pages          = {e309},
  volume       = {4},
  abstract     = {Individual cells in genetically homogeneous populations have been found to express different numbers of molecules of specific proteins. We investigated the origins of these variations in mammalian cells by counting individual molecules of mRNA produced from a reporter gene that was stably integrated into the cell's genome. We found that there are massive variations in the number of mRNA molecules present in each cell. These variations occur because mRNAs are synthesized in short but intense bursts of transcription beginning when the gene transitions from an inactive to an active state and ending when they transition back to the inactive state. We show that these transitions are intrinsically random and not due to global, extrinsic factors such as the levels of transcriptional activators. Moreover, the gene activation causes burst-like expression of all genes within a wider genomic locus. We further found that bursts are also exhibited in the synthesis of natural genes. The bursts of mRNA expression can be buffered at the protein level by slow protein degradation rates. A stochastic model of gene activation and inactivation was developed to explain the statistical properties of the bursts. The model showed that increasing the level of transcription factors increases the average size of the bursts rather than their frequency. These results demonstrate that gene expression in mammalian cells is subject to large, intrinsically random fluctuations and raise questions about how cells are able to function in the face of such noise.},
  annote       = {The authors use FISH in transfected Chinese hamster ovary (CHO) cells to study the dynamics of mRNA, and particularly its synthesis. Their main finding is that mRNA is produced in bursts. These bursts are due to a local, random event in the chromatin, perhaps chromatin remodelling, so that two genes in the same region of the genome are likely to have coordinated bursts. Transcriptional activators apparently function by extending the length of a burst rather than by increasing the frequency of the bursts, i.e.\ the random chromatin event that allows for transcription to start is independent of transcription factors, but the transcription factors may sustain the transcriptionally productive state. In addition to artificial constructs, the authors find the same kind of bursty dynamics for the mRNA encoding the large subunit of RNA polymerase II. They also look at protein levels corresponding to their mRNAs. For proteins with short half-lives, the protein level more or less follows the mRNA level, i.e.\ it's bursty. However, the bursts just ``top up'' the levels of proteins with long half-lives.},
  creationdate = {2015-07-30T00:00:00},
  doi          = {10.1371/journal.pbio.0040309},
  owner        = {marcroussel},
}

@Article{MCG2012,
  author       = {Tetsuya Muramoto and Danielle Cannon and Marek Gierli{\'n}ski and Adam Corrigan and Geoffrey J. Barton and Chubb, Jonathan R.},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {Live Imaging of Nascent {RNA} Dynamics Reveals Distinct Types of Transcriptional Pulse Regulation},
  year         = {2012},
  pages        = {7350-7355},
  volume       = {109},
  abstract     = {Transcription of genes can be discontinuous, occurring in pulses or bursts. It is not clear how properties of transcriptional pulses vary between different genes. We compared the pulsing of five housekeeping and five developmentally induced genes by direct imaging of single gene transcriptional events in individual living Dictyostelium cells. Each gene displayed its own transcriptional signature, differing in probability of firing and pulse duration, frequency, and intensity. In contrast to the prevailing view from both prokaryotes and eukaryotes that transcription displays binary behavior, strongly expressed housekeeping genes altered the magnitude of their transcriptional pulses during development. These nonbinary ``tunable'' responses may be better suited than stochastic switch behavior for housekeeping functions. Analysis of RNA synthesis kinetics using fluorescence recovery after photobleaching implied modulation of housekeeping-gene pulse strength occurs at the level of transcription initiation rather than elongation. In addition, disparities between single cell and population measures of transcript production suggested differences in RNA stability between gene classes. Analysis of stability using RNAseq revealed no major global differences in stability between developmental and housekeeping transcripts, although strongly induced RNAs showed unusually rapid decay, indicating tight regulation of expression.},
  annote       = {The authors analyzed the transcription kinetics of several genes in \emph{Dictyostelium}, which they separated into two sets: housekeeping genes, and genes involved in ``development'' (including sensing extracellular cAMP and cell adhesion). The housekeeping genes, which are downregulated during aggregation and differentiation, are expressed in bursts of decreasing frequency and magnitude once the starvation response is triggered. For the developmental genes on the other hand, only the frequency of pulses changes according to the growth conditions. The authors were able to use their data to estimate the transcription elongation rate in \emph{Dictyostelium} to be 1.3\,kb/min.},
  creationdate = {2022-06-14T15:17:51},
  doi          = {10.1073/pnas.1117603109},
  keywords     = {transcriptional bursting; RNA turnover; stochastic gene expression},
  owner        = {marcroussel},
}

@InProceedings{XKK2013,
  author       = {Xiaohua Xu and Niraj Kumar and Arjun Krishnan and Rahul V. Kulkarni},
  booktitle    = {52nd IEEE Conference on Decision and Control},
  title        = {Stochastic Modeling of Dwell-time Distributions During Transcriptional Pausing and Initiation},
  year         = {2013},
  pages        = {4068-4073},
  abstract     = {The process of transcription has been intensively
studied for several decades, however there is still much to learn
about the underlying biochemcial processes. Recent advances
in single-molecule techniques have provided new experimental
data that highlights the role of transcriptional pausing in
the regulation of gene expression. In some cases, it has been
shown that transcriptional pauses are rate-limiting stochastic
processes, thus a quantitative understanding requires stochastic
modeling of the underlying processes. We propose a coarsegrained
stochastic model to analyze the dwell-time distribution
for transcriptional pausing. The proposed kinetic scheme can
also be used to model transcriptional initiation and to analyze
the corresponding noise in gene expression. We obtain analytical
solutions which can provide useful insights into current and
future experiments focusing on time-resolved single-molecule
studies of transcriptional pausing and noise in gene expression.},
  annote       = {This paper briefly studies two models. The first is a model of the transit through a given template site by RNA polymerase that incorporates pausing, including both short pauses and a long-lived paused state that is accessed from the short-paused state. For this model, the dwell time distribution is obtained analytically. The second model is a three-step pseudo-first-order model of initiation with instantaneous production of protein in bursts. The Fano factor of the protein distribution is obtained for this model.},
  creationdate = {2023-09-25T12:56:30},
  file         = {:XKK2013.pdf:PDF},
  owner        = {roussel},
}

@Article{PBS+2018,
  author       = {Pabitra K. Parua and Gregory T. Booth and Miriam Sans{\'o} and Bradley Benjamin and Jason C. Tanny and Lis, John T. and Fisher, Robert P.},
  journal      = {Nature},
  title        = {A {Cdk9}-{PP1} Switch Regulates the Elongation-Termination Transition of {RNA} Polymerase {II}},
  year         = {2018},
  pages        = {460-464},
  volume       = {558},
  annote       = {Spt5 is an elongation factor of RNA polymerase II. Cdk9 phosphorylates both Spt5 and a PP1 isoform called Dis2. Dis2 phosphorylation is inhibitory. During elongation, Spt5 is phosphorylated and accelerates elongation. As the polymerase passes the cleavage and polyadenylation site, Cdk9 becomes inactive. Dis2 consequently becomes dephosphorylated, in turn dephosphorylating Spt5. This slows the polymerase, and facilitates removal of the polymerase from the template by the XRN2/Rat1 exoribonuclease.},
  creationdate = {2019-06-24T00:00:00},
  owner        = {roussel},
}

@Article{FXF2021,
  author       = {Peiyuan Feng and An Xiao and Meng Fang and Fangping Wan and Shuya Li and Peng Lang and Dan Zhao and Jianyang Zeng},
  journal      = {Proc. Natl. Acad. Sci. U.S.A.},
  title        = {A Machine Learning-Based Framework for Modeling Transcription Elongation},
  year         = {2021},
  pages          = {e2007450118},
  volume       = {118},
  abstract     = {RNA polymerase II (Pol II) generally pauses at certain positions along gene bodies, thereby interrupting the transcription elongation process, which is often coupled with various important biological functions, such as precursor mRNA splicing and gene expression regulation. Characterizing the transcriptional elongation dynamics can thus help us understand many essential biological processes in eukaryotic cells. However, experimentally measuring Pol II elongation rates is generally time and resource consuming. We developed PEPMAN (polymerase II elongation pausing modeling through attention-based deep neural network), a deep learning-based model that accurately predicts Pol II pausing sites based on the native elongating transcript sequencing (NET-seq) data. Through fully taking advantage of the attention mechanism, PEPMAN is able to decipher important sequence features underlying Pol II pausing. More importantly, we demonstrated that the analyses of the PEPMAN-predicted results around various types of alternative splicing sites can provide useful clues into understanding the cotranscriptional splicing events. In addition, associating the PEPMAN prediction results with different epigenetic features can help reveal important factors related to the transcription elongation process. All these results demonstrated that PEPMAN can provide a useful and effective tool for modeling transcription elongation and understanding the related biological factors from available high-throughput sequencing data.},
  annote       = {The authors developed a machine-learning algorithm for predicting RNA polymerase II pausing sites. Their algorithm recognizes pausing sites due to various sequence features, including splice sites, sites that are epigenetically modified, and binding sites for various transcription factors. Interestingly, a persistent false positive prediction arises at binding sites for a particular type of basic helix-loop-helix transcription factors.},
  creationdate = {2024-02-06T22:08:15},
  doi          = {10.1073/pnas.2007450118},
  keywords     = {Pol II pausing; deep learning; alternative splicing},
  owner        = {marcroussel},
}

@book{Billingsley1995,
    author = {Patrick Billingsley},
    title = {Probability and Measure},
    publisher = {Wiley},    address = {New York},
    year = 1995
}

@Article{BarNahum-etal2005,
  author       = {Gil Bar-Nahum and Vitaly Epshtein and Andrei E Ruckenstein and Ruslan Rafikov and Arkady Mustaev and Evgeny Nudler},
  journal      = {Cell},
  title        = {A Ratchet Mechanism of Transcription Elongation and Its Control},
  year         = {2005},
  pages        = {183-193},
  volume       = {120},
  annote       = {The authors study two lethal RNA polymerase (RNAP) II mutations, both in the G loop of the enzyme. The G loop controls the motion of the F bridge. The F bridge in turn has a ratcheting action that, on average, keeps the polymerase moving in the right direction when the appropriate contacts are made between the incoming RNA nucleotide and the DNA nucleotide, but that actually favors backtracking when the two don't match. Of the two mutants, one is fast and error-prone, while the other is slow, to the point of being stall-prone, but even more accurate than the wild type. A simple kinetic model, to be found in the supplementary materials, is used to support some of the claims made about the system.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{Shaevitz-etal2003,
  author       = {Joshua W. Shaevitz and Ello A. Abbondanzieri and Robert Landick and Steven M. Block},
  journal      = {Nature},
  title        = {Backtracking by Single {RNA} Polymerase Molecules Observed at Near-Base-Pair Resolution},
  year         = {2003},
  pages        = {684-687},
  volume       = {426},
  annote       = {Using DNA tethered at one end to a bead and an RNA polymerase also tethered to a bead, both held by optical trapping under slight tension, the motion of the polymerase during transcription is studied. Under these experimental conditions, both short and long pauses are observed. The long pauses are associated with backtracking, presumably as part of the proofreading pathway in which misincorporated RNA bases are cut off prior to the resumption of transcription. The long pauses are also said to have a ``broad, non-exponential'' distribution, but no additional information is provided about this distribution. Quite a bit of statistical data about these pauses and about backtracking is provided under various conditions.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1038/nature02191},
  owner        = {roussel},
}

@Article{GB2000,
  author       = {Michael A. Gibson and Jehoshua Bruck},
  journal      = {J. Phys. Chem. A},
  title        = {Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels},
  year         = {2000},
  pages        = {1876-1889},
  volume       = {104},
  abstract     = {There are two fundamental ways to view coupled systems of chemical equations:  as continuous, represented
by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes
whose variables are numbers of molecules. Although the former is by far more common, systems with very
small numbers of molecules are important in some applications (e.g., in small biological cells or in surface
processes). In both views, most complicated systems with multiple reaction channels and multiple chemical
species cannot be solved analytically. There are exact
numerical simulation methods to simulate trajectories
of discrete, stochastic systems, (methods that are rigorously equivalent to the Master Equation approach) but
these  do  not  scale  well  to  systems  with  many  reaction  pathways.  This  paper  presents  the  Next  Reaction
Method, an exact algorithm to simulate coupled chemical reactions that is also
efficient:  it (a) uses only a
single random number per simulation event, and (b) takes time proportional to the
logarithm of the number
of reactions, not to the number of reactions itself. The Next Reaction Method is extended to include time-dependent rate constants and non-Markov processes and is applied to a sample application in biology (the
lysis/lysogeny  decision  circuit  of  lambda  phage).  The  performance  of  the  Next  Reaction  Method  on  this
application is compared with one standard method and an optimized version of that standard method.},
  annote       = {A highly efficient variant of Gillespie's stochastic simulation algorithm called the next reaction method is proposed and proven to be equivalent to the classical method. This method relies on the use of a dependency graph to determine which propensities need to be updated, on an indexed priority queue to determine which reaction event occurs next, and on some clever statistics to avoid generating more than one new random number at every update. Extensions to time-dependent Markov processes, i.e.\ to processes in which the rate constants, volume, or other parameters change with time, and to non-Markovian (delayed) processes are also considered.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1021/jp993732q},
  owner        = {roussel},
}

@Article{FDT2016,
  author       = {Yan-Ling Feng and Jian-Min Dong and Xu-Lei Tang},
  journal      = {Chin. Phys. Lett.},
  title        = {Non-{Markovian} Effect on Gene Transcriptional Systems},
  year         = {2016},
  eid          = {108701},
  volume       = {33},
  abstract     = {The time delays in both synthesis and degradation reactions, reflecting the non-Markovian behavior, are introduced in the stochastic gene transcriptional dynamics. The effects of the time delays on the stationary probability distribution, mean first passage time and stochastic resonance are discussed in detail based on the delayed stochastic differential equation and the corresponding delay Fokker-Planck equation. The time delays in synthesis reactions and in degradation reactions play a completely opposite role. The time delay in synthesis (degradation) reaction enhances (reduces) the mean first passage time, and tends to reduce (enhance) the signal-to-noise ratio. Finally, the effect of Gauss-distributed time delays on the transcriptional system is explored to test whether the previous approximation of employing a certain delay time works well or not.},
  annote       = {This paper looks at a very simple production-destruction system with time delays in both the production and destruction terms. The latter means that positive solutions cannot be guaranteed. They add multiplicative noise to the production term, as well as an additive noise term. The authors display the solution of a delay Fokker-Planck equation, which is bimodal. They examine the effects of the delays on the mean first passage times between the two modes. They also observe ``stochastic resonance'' with respect to the delays (although I don't quite see this as SR in the classical sense). They briefly look at the effect of noise in the delays themselves, and find that this has very little effect. Thus, fixed delays are an excellent approximation, at least for delays with a Gaussian ditribution in their model.},
  creationdate = {2020-09-15T00:00:00},
  doi          = {10.1088/0256-307X/33/10/108701},
  owner        = {marcroussel},
}

@Article{JL2023,
  author       = {Chen Jia and Youming Li},
  journal      = {SIAM J. Appl. Math.},
  title        = {Analytical Time-Dependent Distributions for Gene Expression Models with Complex Promoter Switching Mechanisms},
  year         = {2023},
  pages        = {1572-1602},
  volume       = {83},
  abstract     = {Classical gene expression models assume exponential switching time distributions between the active and inactive promoter states. However, recent experiments have shown that many genes in mammalian cells may produce nonexponential switching time distributions, implying the existence of multiple promoter states and molecular memory in the promoter switching dynamics. Here we analytically solve a gene expression model with random bursting and complex promoter switching, and derive the time-dependent distributions of the mRNA and protein copy numbers, generalizing the steady-state solution obtained in [T. Zhou and J. Zhang, SIAM J. Appl. Math., 72 (2012), pp. 789--818] and [U. Herbach, SIAM J. Appl. Math., 79 (2019), pp. 1007--1029]. Using multiscale simplification techniques, we find that molecular memory has no influence on the time-dependent distribution when promoter switching is very fast or very slow, while it significantly affects the distribution when promoter switching is neither too fast nor too slow. By analyzing the dynamical phase diagram of the system, we also find that molecular memory in the inactive gene state weakens transient and stationary bimodality of the copy number distribution, while molecular memory in the active gene state enhances such bimodality.},
  annote       = {The authors study a class of models in which there are multiple promoter states. In the most general case, arbitrary transitions are allowed between states and transcription can proceed, albeit at different rates, from any state. They also study the situation where the promoter states are visited sequentially, with the last promoter state leading back to the first. Two cases of this arrangement are considered, one in which all but one of the states is transcriptionally active, and one in which only one of the states is active. The authors obtain a large number of analytic results for this model, and a close reading of this paper would be rewarding to someone who wanted to learn how to study such models. Depending on the parameters, the distribution of protein numbers can be unimodal or bimodal. In some cases, the bimodality is only transient and gives way to unimodality in time. In others, stationary bimodality is obtained.},
  creationdate = {2024-05-04T16:48:20},
  doi          = {10.1137/22M147219X},
  file         = {:JL2023.pdf:PDF},
  keywords     = {transient distribution, bursting, molecular memory, multiscale simplification},
  owner        = {marcroussel},
}

@Article{JWY2019,
  author       = {Chen Jia and Le Yi Wang and George G. Yin and Zhang, Michael Q.},
  journal      = {Phys. Rev. E},
  title        = {Single-Cell Stochastic Gene Expression Kinetics with Coupled Positive-Plus-Negative Feedback},
  year         = {2019},
  eid          = {052406},
  volume       = {100},
  abstract     = {Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with
positive-plus-negative feedback. A triphasic stochastic bifurcation is observed upon increasing the ratio of the
positive and negative feedback strengths, which reveals a strong synergistic interaction between positive and
negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression
mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is
relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of
macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with
large burst frequencies and the Lévy limit applies to proteins with large burst sizes. We derive the analytic
steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and
its two macroscopic limits, generalizing the results obtained by Liu et al. [Chaos 26, 043108 (2016)]. We
also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting
model [Friedman, Cai, and Xie, Phys. Rev. Lett. 97, 168302 (2006)]. Our analytic results are further applied to
study the structure of gene expression noise in a coupled gene circuit, and a complete decomposition of noise in
terms of five different biophysical origins is provided.},
  annote       = {The authors study a stochastic model in which a protein enhances the transitions of the promoter both to the active and to the inactive state, hence the ``positive-plus-negative feedback'' of the title. They find a pair of stochastic bifurcation curves in the positive/negative feedback parameter plane, one of which separates regions where the mean is amplified from one where it is reduced, and the other of which separates regions where noise is amplified vs reduced. Between these two curves lies a region where the mean is amplified while noise is reduced, i.e.\ a ``goldilocks'' region for control of gene expression. The most interesting part of the paper may be the one where they look at macroscopic limits of their model. They study two extremes: high burst frequence at constant burst size and large burst size at constant burst frequency. They name the first of these two regimes the ``Kurtz limit'' due to its similarity to the Kurtz approach to the conversion from the mesoscopic to the macroscopic limits. The second is regime is called the ``L{\'e}vy limit'' as it results in behavior ressembling a L{\'e}vy flight, i.e. sudden large excursions. If one wanted to use the results in this paper, one would have to be careful because I've found one significant error. In their treatment of the Kurtz limit, the authors define $p_i(x)$ as the steady-state continuum limit of the conditional probability density for (continuous) protein level $x$ when the gene is in state $i$, with $i=0$ for the inactive gene and $i=1$ for the active gene. They then define the probability density of protein level $x$ as $p(x)=p_0(x)+p_1(x)$, which is clearly wrong. They get away with this mistake partly because their figures only includes examples where the probabilities of being in the two states of the gene are equal. It's possible that they have a correct equation somewhere, because the definition of $p(x)$ would also be missing a factor of $1/2$ even if we limit ourselves to the case they studied.},
  creationdate = {2024-05-23T23:36:07},
  doi          = {10.1103/PhysRevE.100.052406},
  file         = {:C\:/Users/mrous/OneDrive - University of Lethbridge/bib_database/JWY2019.pdf:PDF},
}

@inbook{Goldstein-wave-eq,
    author = {Herbert Golstein},
    title = {Classical Mechanics},
    publisher = {Addison-Wesley},
    year = 1980,    address={Reading, Massachusetts},
    chapter = 12
}

@Article{Othmer1983,
  author       = {H. G. Othmer},
  journal      = {J. Math. Biol.},
  title        = {A Continuum Model for Coupled Cells},
  year         = {1983},
  pages        = {351-369},
  volume       = {17},
  abstract     = {A continuum model of diffusion-coupled cells that more accurately reflects the presence of low-permeability gap junctions between cells is analyzed. It is shown by a multi-scale analysis that to lowest order the slow evolution of the mean concentration is described by the usual ordinary differential equations for a discrete model. Furthermore, stable non-uniform steady solutions are shown to exist in the continuum model of a one component system, whereas this is impossible for the standard reaction-diffusion model of this system. It is also shown how to average the equations in this continuum model to obtain a system of reaction-diffusion equations with constant coefficients. Among other things, the authors provide an equation that provides estimates of the diffusion coefficient through cell-cell junctions given the diffusion coefficient in the cytoplasm and measured apparent diffusion coefficients in a tissue.},
  annote       = {There are some differences between the solutions of reaction-diffusion equations and of conceptually equivalent discrete multicellular models which are different to reconcile. For instance, the discrete model has solutions which vanish as the mesh size of the equivalent PDE discretization goes to zero. Also, the discrete models may have nonuniform solutions in models with just one chemical, but this is impossible for PDEs with Neumann boundary conditions. A reaction-diffusion model of two coupled cells separated by a gap junction is studied. A perturbation treatment is applied in which the discrete model solution reappears to lowest order. The key is apparently the consideration of the inherently inhomogeneous nature of cell-cell junctions. The possibility of inhomogeneous solutions, in which the two cells have different concentration profiles of the diffusible chemical, is also recovered and an example is given for a piecewise linear reaction term. Finally, and perhaps most interestingly, an averaging procedure is carried out in which the rapidly varying diffusion coefficients due to the alternation over small spatial scales of cells and gap junctions yields an equivalent reaction-diffusion model with constant diffusion coefficients which is valid over large length scales.},
  creationdate = {2012-07-25T00:00:00},
  doi          = {10.1007/BF00276521},
  keywords     = {Reaction-diffusion equations, Coupled cells, Averaging},
  owner        = {roussel},
}

@Article{SVN89,
  author       = {Deborah Sulsky and Richard R. Vance and William I. Newman},
  journal      = {J. Theor. Biol.},
  title        = {Time Delays in Age-Structured Populations},
  year         = {1989},
  pages        = {403-422},
  volume       = {141},
  annote       = {Age-structured population (PDE) models can be reformulated as delay-differential equation systems. A few simple examples are studied. An elegant stability analysis method is used.},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}

@Article{RR2004,
  author       = {Catharine J. Roussel and Marc R. Roussel},
  journal      = {Prog. Biophys. Mol. Biol.},
  title        = {Reaction-Diffusion Models of Development With State-Dependent Chemical Diffusion Coefficients},
  year         = {2004},
  pages        = {113-160},
  volume       = {86},
  creationdate = {2012-07-25T00:00:00},
  owner        = {roussel},
}
