Research article Special Issues

A comparative analysis of noise properties of stochastic binary models for a self-repressing and for an externally regulating gene

  • Correction on: Mathematical Biosciences and Engineering 18: 300-304
  • Received: 02 July 2020 Accepted: 05 August 2020 Published: 13 August 2020
  • This manuscript presents a comparison of noise properties exhibited by two stochastic binary models for: (ⅰ) a self-repressing gene; (ⅱ) a repressed or activated externally regulating one. The stochastic models describe the dynamics of probability distributions governing two random variables, namely, protein numbers and the gene state as ON or OFF. In a previous work, we quantify noise in protein numbers by means of its Fano factor and write this quantity as a function of the covariance between the two random variables. Then we show that distributions governing the number of gene products can be super-Fano, Fano or sub-Fano if the covariance is, respectively, positive, null or negative. The latter condition is exclusive for the self-repressing gene and our analysis shows the conditions for which the Fano factor is a sufficient classifier of fluctuations in gene expression. In this work, we present the conditions for which the noise on the number of gene products generated from a self-repressing gene or an externally regulating one are quantitatively similar. That is important for inference of gene regulation from noise in gene expression quantitative data. Our results contribute to a classification of noise function in biological systems by theoretically demonstrating the mechanisms underpinning the higher precision in expression of a self-repressing gene in comparison with an externally regulated one.

    Citation: Guilherme Giovanini, Alan U. Sabino, Luciana R. C. Barros, Alexandre F. Ramos. A comparative analysis of noise properties of stochastic binary models for a self-repressing and for an externally regulating gene[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5477-5503. doi: 10.3934/mbe.2020295

    Related Papers:

  • This manuscript presents a comparison of noise properties exhibited by two stochastic binary models for: (ⅰ) a self-repressing gene; (ⅱ) a repressed or activated externally regulating one. The stochastic models describe the dynamics of probability distributions governing two random variables, namely, protein numbers and the gene state as ON or OFF. In a previous work, we quantify noise in protein numbers by means of its Fano factor and write this quantity as a function of the covariance between the two random variables. Then we show that distributions governing the number of gene products can be super-Fano, Fano or sub-Fano if the covariance is, respectively, positive, null or negative. The latter condition is exclusive for the self-repressing gene and our analysis shows the conditions for which the Fano factor is a sufficient classifier of fluctuations in gene expression. In this work, we present the conditions for which the noise on the number of gene products generated from a self-repressing gene or an externally regulating one are quantitatively similar. That is important for inference of gene regulation from noise in gene expression quantitative data. Our results contribute to a classification of noise function in biological systems by theoretically demonstrating the mechanisms underpinning the higher precision in expression of a self-repressing gene in comparison with an externally regulated one.


    加载中


    [1] M. Delbrück, Statistical fluctuations in autocatalytic reactions, J. Chem. Phys., 8 (1940), 120-124. doi: 10.1063/1.1750549
    [2] M. B. Elowitz, A. J. Levine, E. D. Siggia, P. S. Swain, Stochastic gene expression in a single cell, Science, 297 (2002), 1183-1186. doi: 10.1126/science.1070919
    [3] W. J. Blake, M. K?rn, C. R. Cantor, J. J. Collins, Noise in eukaryotic gene expression, Nature, 422 (2003), 633-637.
    [4] A. Raj, C. S. Peskin, D. Tranchina, D. Y. Vargas, S. Tyagi, Stochastic mrna synthesis in mammalian cells, PLOS Biol., 4 (2006), e309.
    [5] D. M. Suter, N. Molina, D. Gatfield, K. Schneider, U. Schibler, F. Naef, Mammalian genes are transcribed with widely different bursting kinetics, Science, 332 (2011), 472-474. doi: 10.1126/science.1198817
    [6] B. Munsky, G. Neuert, A. van Oudenaarden, Using gene expression noise to understand gene regulation, Science, 336 (2012), 183-187.
    [7] J. M. Raser, E. K. O'Shea, Noise in gene expression: origins, consequences, and control, Science, 309 (2005), 2010-2013.
    [8] A. M. Arias, P. Hayward, Filtering transcriptional noise during development: concepts and mechanisms, Nat. Rev. Genet., 7 (2006), 34-44. doi: 10.1038/nrg1750
    [9] G. Chalancon, C. N. Ravarani, S. Balaji, A. Martinez-Arias, L. Aravind, R. Jothi, et al., Interplay between gene expression noise and regulatory network architecture, Trends Genet., 28 (2012), 221-232.
    [10] A. Sanchez, I. Golding, Genetic determinants and cellular constraints in noisy gene expression, Science, 342 (2013), 1188-1193. doi: 10.1126/science.1242975
    [11] J. Ansel, H. Bottin, C. Rodriguez-Beltran, C. Damon, M. Nagarajan, S. Fehrmann, et al., Cellto-cell stochastic variation in gene expression is a complex genetic trait, PLoS Genet., 4 (2008), e1000049.
    [12] A. Brock, S. Krause, D. E. Ingber, Control of cancer formation by intrinsic genetic noise and microenvironmental cues, Nat. Rev. Cancer, 15 (2015), 499-509. doi: 10.1038/nrc3959
    [13] S. S. Shen-Orr, R. Milo, S. Mangan, U. Alon, Network motifs in the transcriptional regulation network of escherichia coli, Nat. Genet., 31 (2002), 64-68. doi: 10.1038/ng881
    [14] G. T. Reeves, The engineering principles of combining a transcriptional incoherent feedforward loop with negative feedback, J. Biol. Eng., 13 (2019).
    [15] N. Rosenfeld, M. B. Elowitz, U. Alon, Negative autoregulation speeds the response times of transcription networks, J. Mol. Biol., 323 (2002), 785-793. doi: 10.1016/S0022-2836(02)00994-4
    [16] A. Sancar, L. A. Lindsey-Boltz, T.-H. Kang, J. T. Reardon, J. H. Lee, N. Ozturk, Circadian clock control of the cellular response to DNA damage, FEBS Lett., 584 (2010), 2618-2625. doi: 10.1016/j.febslet.2010.03.017
    [17] M. A. Savageau, Comparison of classical and autogenous systems of regulations in inducible operons, Nature, 252 (1974), 546-549. doi: 10.1038/252546a0
    [18] S. Hooshangi, R. Weiss, The effect of negative feedback on noise propagation in transcriptional gene networks, Chaos, 16 (2006), 026108.
    [19] D. Nevozhay, R. M. Adams, K. F. Murphy, K. Josic, G. Balázsi, Negative autoregulation linearizes the dose-response and suppresses the heterogeneity of gene expression., Proc. Natl. Acad. Sci. U.S.A., 106 (2009), 5123-5128. doi: 10.1073/pnas.0809901106
    [20] A. Becskei, L. Serrano, Engineering stability in gene networks by autoregulation., Nature, 405 (2000), 590-593. doi: 10.1038/35014651
    [21] A. F. Ramos, J. E. M. Hornos, J. Reinitz, Gene regulation and noise reduction by coupling of stochastic processes, Phys. Rev. E, 91 (2015), 020701(R).
    [22] A. F. Ramos, J. E. M. Hornos, Symmetry and stochastic gene regulation., Phys. Rev. Lett., 99 (2007), 108103.
    [23] A. F. Ramos, J. Reinitz, Physical implications of so(2, 1) symmetry in exact solutions for a selfrepressing gene, J. Chem. Phys., 151 (2019), 041101.
    [24] J. N. Anastas, R. T. Moon, Wnt signalling pathways as therapeutic targets in cancer, Nat. Rev. Cancer, 13 (2013), 11-26. doi: 10.1038/nrc3419
    [25] C. K. Mirabelli, R. Nusse, D. A. Tuveson, B. O. Williams, Perspectives on the role of wnt biology in cancer, Sci. Signal., 12 (2019), eaay4494.
    [26] G. Balázsi, A. van Oudenaarden, J. J. Collins, Cellular decision making and biological noise: from microbes to mammals, Cell, 144 (2011), 910-925. doi: 10.1016/j.cell.2011.01.030
    [27] L. S. Tsimring, Noise in biology, Rep. Prog. Phys., 77 (2014), 026601.
    [28] K. Sneppen, Models of life: epigenetics, diversity and cycles, Rep. Prog. Phys., 80 (2017), 042601.
    [29] J. Peccoud, B. Ycart, Markovian modelling of gene product synthesis, Theor. Popul. Biol., 48 (1995), 222-234. doi: 10.1006/tpbi.1995.1027
    [30] J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, et al., Self-regulating gene: an exact solution., Phys. Rev. E, 72 (2005), 051907.
    [31] S. Iyer-Biswas, F. Hayot, C. Jayaprakash, Stochasticity of gene products from transcriptional pulsing, Phys. Rev. E, 79 (2009), 031911. doi: 10.1103/PhysRevE.79.031911
    [32] A. F. Ramos, G. C. P. Innocentini, J. E. M. Hornos, Exact time-dependent solutions for a selfregulating gene, Phys. Rev. E, 83 (2011), 062902.
    [33] A. F. Ramos, L. R. Gama, M. C. C. Morais, P. C. M. Martins, Chapter 14: Stochastic modeling for investigation of regulation of transcription of RKIP gene, Prognostic and Therapeutic Applications of RKIP in Cancer, Academic Press, (2020), 257-276.
    [34] A. Subramanian, P. Tamayo, V. K. Mootha, S. Mukherjee, B. L. Ebert, M. A. Gillette, et al., Gene set enrichment analysis: A knowledge-based approach for interpreting genome-wide expression profiles, Proc. Natl. Acad. Sci. U.S.A., 102 (2005), 15545-15550.
    [35] K. Park, T. Prüstel, Y. Lu, J. S. Tsang, Machine learning of stochastic gene network phenotypes, preprint, bioRxiv: 825943.
    [36] L. R. Gama, G. Giovanini, G. Balázsi, A. F. Ramos, Binary expression enhances reliability of messaging in gene networks, Entropy, 22 (2020), 479.
    [37] A. Bakk, R. Metzler, K. Sneppen, Sensitivity of OR in phage λ, Biophys. J., 86 (2004), 58-66.
    [38] A. Grönlund, P. Lötstedt, J. Elf, Transcription factor binding kinetics constrain noise suppression via negative feedback, Nat. Commun., 4 (2013), 1864.
    [39] D. C. Marciano, R. C. Lua, C. Herman, O. Lichtarge, Cooperativity of negative autoregulation confers increased mutational robustness, Phys. Rev. Lett., 116 (2016), 258104. doi: 10.1103/PhysRevLett.116.258104
    [40] K. S. Farquhar, D. A. Charlebois, M. Szenk, J. Cohen, D. Nevozhay, G. Balázsi, Role of network-mediated stochasticity in mammalian drug resistance, Nat. Commun., 10 (2019), 2766.
    [41] G. M. Cooper, The Cell: A Molecular Approach, 2nd edition, Sinauer Associates Inc, Sunderland (MA), 2000.
    [42] D. K. Hawley, W. R. McClure, Mechanism of activation of transcription initiation from the lambda-PRM promoter, J. Mol. Biol., 157 (1982), 493-525. doi: 10.1016/0022-2836(82)90473-9
    [43] A. R. Kim, C. Martinez, J. Ionides, A. F. Ramos, M. Z. Ludwig, N. Ogawa, et al., Rearrangements of 2.5 kilobases of noncoding dna from the drosophila even-skipped locus define predictive rules of genomic cis-regulatory logic, PLoS Genet., 9 (2013), e1003243.
    [44] M. R. Fabian, N. Sonenberg, W. Filipowicz, Regulation of mrna translation and stability by micrornas, Annu. Rev. Biochem., 79 (2010), 351-79. doi: 10.1146/annurev-biochem-060308-103103
    [45] R. Grima, D. R. Schmidt, T. J. Newman, Steady-state fluctuations of a genetic feedback loop: An exact solution, J. Chem. Phys., 137 (2012), 035104.
    [46] G. C. P. Innocentini, A. F. Ramos, J. E. M. Hornos, Comment on "steady-state fluctuations of a genetic feedback loop: an exact solution" [J. Chem. Phys. 137, 035104 (2012)], J. Chem. Phys., 142 (2015), 027101.
    [47] J. Holehouse, Z. Cao, R. Grima, Stochastic modeling of autoregulatory genetic feedback loops: A review and comparative study, Biophys. J., 118 (2020), 1517-1525. doi: 10.1016/j.bpj.2020.02.016
    [48] C. Jia, R. Grima, Small protein number effects in stochastic models of autoregulated bursty gene expression, J. Chem. Phys., 152 (2020), 084115.
    [49] Z. Cao, R. Grima, Analytical distributions for detailed models of stochastic gene expression in eukaryotic cells, Proc. Natl. Acad. Sci. U.S.A., 117 (2020), 4682-4692. doi: 10.1073/pnas.1910888117
    [50] R. Yvinec, L. G. S. da Silva, G. N. Prata, J. Reinitz, A. F. Ramos, Bursting on a two state stochastic model for gene transcription in drosophila embryos, preprint, bioRxiv: 107979.
    [51] N. Kumar, T. Platini, R. V. Kulkarni, Exact distributions for stochastic gene expression models with bursting and feedback, Phys. Rev. Lett., 113 (2014), 268105.
    [52] T. Tripathi, D. Chowdhury, Interacting RNA polymerase motors on a DNA track: Effects of traffic congestion and intrinsic noise on RNA synthesis, Phys. Rev. E, 77 (2008), 011921.
    [53] S. Choubey, J. Kondev, A. Sanchez, Deciphering transcriptional dynamics in vivo by counting nascent rna molecules, PLoS Comput. Biol., 11 (2015), e1004345.
    [54] H. Xu, S. O. Skinner, A. M. Sokac, I. Golding, Stochastic kinetics of nascent rna, Phys. Rev. Lett., 117 (2016), 128101.
    [55] M. Thattai, A. van Oudenaarden, Intrinsic noise in gene regulatory networks, Proc. Natl. Acad. Sci. USA, 98 (2001), 8614-8619.
    [56] G. C. P. Innocentini, J. E. M. Hornos, Modeling stochastic gene expression under repression., J. Math. Biol., 55 (2007), 413-431. doi: 10.1007/s00285-007-0090-x
    [57] V. Shahrezaei, P. S. Swain, Analytical distributions for stochastic gene expression, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256-17261. doi: 10.1073/pnas.0803850105
    [58] Z. Cao, R. Grima, Linear mapping approximation of gene regulatory networks with stochastic dynamics, Nat. Commun., 9 (2018), 3305.
    [59] A. F. Ramos, G. C. P. Innocentini, F. M. Forger, J. E. M. Hornos, Symmetry in biology: from genetic code to stochastic gene regulation, IET Syst. Biol., 4 (2010), 311-329. doi: 10.1049/iet-syb.2010.0058
    [60] R. Andersson, A. Sandelin, Determinants of enhancer and promoter activities of regulatory elements, Nat. Rev. Genet., 21 (2019), 71-87.
    [61] N. Rosenfeld, T. J. Perkins, U. Alon, M. B. Elowitz, P. S. Swain, A fluctuation method to quantify in vivo fluorescence data, Biophys. J., 91 (2006), 759-766. doi: 10.1529/biophysj.105.073098
    [62] G. N. Prata, J. E. M. Hornos, A. F. Ramos, Stochastic model for gene transcription on drosophila melanogaster embryos, Phys. Rev. E, 93 (2016), 022403.
    [63] M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series vol. 55, 10th edition, U.S. Department of Commerce, Washington (DC), 1972.
    [64] O. Hallikas, K. Palin, N. Sinjushina, R. Rautiainen, J. Partanen, E. Ukkonen, et al., Genome-wide prediction of mammalian enhancers based on analysis of transcription-factor binding affinity, Cell, 124 (2006), 47-59.
    [65] C. P. Fulco, J. Nasser, T. R. Jones, G. Munson, D. T. Bergman, V. Subramanian, et al., Activityby-contact model of enhancer-promoter regulation from thousands of CRISPR perturbations, Nat. Genet., 51 (2019), 1664-1669.
    [66] I. Heemskerk, K. Burt, M. Miller, S. Chhabra, M. C. Guerra, L. Liu, et al., Rapid changes in morphogen concentration control self-organized patterning in human embryonic stem cells, eLife, 8 (2019), e40526.
    [67] A. Paré, D. Lemons, D. Kosman, W. Beaver, Y. Freund, W. McGinnis, Visualization of individual scr mrnas during drosophila embryogenesis yields evidence for transcriptional bursting, Curr. Biol., 19 (2009), 2037-2042. doi: 10.1016/j.cub.2009.10.028
    [68] A. Crudu, A. Debussche, O. Radulescu, Hybrid stochastic simplifications for multiscale gene networks, BMC Syst. Biol., 3 (2009), 89: 1-89: 25.
    [69] H. Kuwahara, S. T. Arold, X. Gao, Beyond initiation-limited translational bursting: the effects of burst size distributions on the stability of gene expression, Integr. Biol., 7 (2015), 1622-1632. doi: 10.1039/c5ib00107b
    [70] J. M. Pedraza, A. van Oudenaarden, Noise propagation in gene networks, Science, 307 (2005), 1965-1969.
    [71] L. A. Sepúlveda, H. Xu, J. Zhang, M. Wang, I. Golding, Measurement of gene regulation in individual cells reveals rapid switching between promoter states, Science, 351 (2016), 1218-1222. doi: 10.1126/science.aad0635
    [72] D. Chetverina, M. Fujioka, M. Erokhin, P. Georgiev, J. B. Jaynes, P. Schedl, Boundaries of loop domains (insulators): Determinants of chromosome form and function in multicellular eukaryotes, BioEssays, 39 (2017), 1600233.
    [73] J. Mozziconacci, M. Merle, A. Lesne, The 3d genome shapes the regulatory code of developmental genes, J. Mol. Biol., 432 (2020), 712-723. doi: 10.1016/j.jmb.2019.10.017
    [74] P. P. Fiziev, The heun functions as a modern powerful tool for research in different scientific domains, preprint, arXiv: 1512.04025.
    [75] T. Fournier, J. Gabriel, C. Mazza, J. Pasquier, J. Galbete, N. Mermod, Steady-state expression of self-regulated genes, Bioinformatics, 23 (2007), 3185-3192. doi: 10.1093/bioinformatics/btm490
    [76] D. Lepzelter, H. Feng, J. Wang, Oscillation, cooperativity, and intermediates in the self-repressing gene, Chem. Phys. Lett., 490 (2010), 216-220.
    [77] E. S. Cheb-Terrab, A. D. Roche, Hypergeometric solutions for third order linear odes, preprint, arXiv: 0803.3474.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3882) PDF downloads(152) Cited by(4)

Article outline

Figures and Tables

Figures(5)  /  Tables(2)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog