Impact of cross-correlated sine-Wiener noises in the gene transcriptional regulatory system

Guanghui Cheng; Yuangen Yao; Rong Gui; Ming Yi; Guanghui Cheng; Yuangen Yao; Rong Gui; Ming Yi

doi:10.3934/mbe.2019328

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 6587-6601. doi: 10.3934/mbe.2019328

Previous Article Next Article

Research article Special Issues

Impact of cross-correlated sine-Wiener noises in the gene transcriptional regulatory system

1.
Department of Electrical and Electronic Engineering, Wuhan Polytechnic University, Wuhan, P.R. China
2.
Department of Physics, College of Science, Huazhong Agricultural University, Wuhan, P.R. China
3.
School of Mathematics and Physics, China University of Geosciences, Wuhan, P.R. China

Received: 28 January 2019 Accepted: 28 June 2019 Published: 16 July 2019

We studied fluctuation-induced switching processes in the gene transcriptional regulatory system under cross-correlated sine-Wiener (CCSW) noises. It is numerically demonstrated that the increase of the multiplicative noise intensity A and cross-correlation time τ in CCSW noises can reduce the concentration of the TF-A monomer and switch to an "off" state. In addition, when the cross-correlation time τ is small, the increase of the additive noise intensity B leads to a switch of the process from "off"→"on". Simultaneously, the increase of the cross-correlation intensity λ of CCSW noises contributes to maintaining the current state. When the cross-correlation time is large, the high concentration state has two peaks and the stationary probability distribution presents a three-peak structure.
- bistable system,
- cross-correlated sine-Wiener noises,
- switch process,
- three-peak structure,
- stationary probability distribution,
- mean first passage time
Citation: Guanghui Cheng, Yuangen Yao, Rong Gui, Ming Yi. Impact of cross-correlated sine-Wiener noises in the gene transcriptional regulatory system[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 6587-6601. doi: 10.3934/mbe.2019328

Related Papers:

Abstract

We studied fluctuation-induced switching processes in the gene transcriptional regulatory system under cross-correlated sine-Wiener (CCSW) noises. It is numerically demonstrated that the increase of the multiplicative noise intensity A and cross-correlation time τ in CCSW noises can reduce the concentration of the TF-A monomer and switch to an "off" state. In addition, when the cross-correlation time τ is small, the increase of the additive noise intensity B leads to a switch of the process from "off"→"on". Simultaneously, the increase of the cross-correlation intensity λ of CCSW noises contributes to maintaining the current state. When the cross-correlation time is large, the high concentration state has two peaks and the stationary probability distribution presents a three-peak structure.

References

[1]	L.S. Tsimring, Noise in biology, Rep. Prog. Phys., 77(2014), 026601.
[2]	Y. Harada, T. Funatsu, K. Murakami, et al., Single-molecule imaging of RNA polymerase-DNA interactions in real time, Biophys. J., 76 (1999), 709–715.
[3]	J. Hasty, J. Pradines, M. Dolnik, et al., Noise-based switches and amplifiers for gene expression, Proc. Natl. Acad. Sci. U. S. A., 97 (2000), 2075–2080.
[4]	P. S. Swain, M. B. Elowitz and E. D. Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Natl. Acad. Sci. U. S. A., 99 (2002), 12795–12800.
[5]	C. V. Rao, D. M. Wolf and A. P. Arkin, Control, exploitation and tolerance of intracellular noise, Nature, 420 (2002), 231–237.
[6]	L. Bandiera, A. Pasini, L. Pasotti, et al., Experimental measurements and mathematical modeling of biological noise arising from transcriptional and translational regulation of basic synthetic gene circuits, J. Theor. Biol., 395 (2016), 153–160.
[7]	S. Rulands and B. D. Simons, Tracing cellular dynamics in tissue development, maintenance and disease, Curr. Opin. Cell Biol., 43 (2016), 38–45.
[8]	M. A. Nowak and B. Waclaw, Genes, environment, and "bad luck", Science, 355 (2017), 1266–1267.
[9]	L. Gammaitoni, P. Hänggi, P. Jung, et al., Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223–287.
[10]	A. S. Pikovsky and J. Kurths, Coherence resonance in a noise-driven excitable system, Phys. Rev. Lett., 78 (1997), 775–778.
[11]	C. Van den Broeck, J. M. Parrondo, and R. Toral, Noise-induced nonequilibrium phase transition, Phys. Rev. Lett., 73 (1994), 3395–3398.
[12]	J. Hasty, F. Isaacs, M. Dolnik, et al., Designer gene networks: Towards fundamental cellular control, Chaos, 11 (2001), 207–220.
[13]	H. Chen, K. Shiroguchi, H. Ge, et al., Genome-wide study of mRNA degradation and transcript elongation in Escherichia coli, Mol. Syst. Biol., 11 (2015), 781.
[14]	G. W. Li and X. S. Xie, Central dogma at the single-molecule level in living cells, Nature, 475 (2011), 308–315.
[15]	A. Sanchez, S. Choubey and J. Kondev, Regulation of noise in gene expression, Annu. Rev. Biophys., 42 (2013), 469–491.
[16]	P. Smolen, D. A. Baxter and J. H. Byrne, Frequency selectivity, multistability, and oscillations emerge from models of genetic regulatory systems, Am. J. Physiol., 274 (1998), 531–542.
[17]	Q. Liu and Y. Jia, Fluctuations-induced switch in the gene transcriptional regulatory system, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 70 (2004), 041907.
[18]	Y. Sharma, P. S. Dutta and A. K. Gupta, Anticipating regime shifts in gene expression: The case of an autoactivating positive feedback loop, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 93 (2016), 032404.
[19]	C. Wang, M. Yi, K. Yang, et al., Time delay induced transition of gene switch and stochastic resonance in a genetic transcriptional regulatory model, BMC Syst. Biol., 6 (2012), S9.
[20]	C. J. Wang and K. L. Yang, Correlated noise-based switches and stochastic resonance in a bistable genetic regulation system, Eur. Phys. J. B, 89 (2016), 173.
[21]	X. Chen, Y. M. Kang and Y. X. Fu, Switches in a genetic regulatory system under multiplicative non-Gaussian noise, J. Theor. Biol., 435 (2017), 134–144.
[22]	C. Zhang, L. P. Du, Q. S. Xie, et al., Emergent bimodality and switch induced by time delays and noises in a synthetic gene circuit, Physica A, 484 (2017), 253–266.
[23]	X. Fang, Q. Liu, C. Bohrer, et al., Cell fate potentials and switching kinetics uncovered in a classic bistable genetic switch, Nat. Commun., 9 (2018), 2787.
[24]	C. Li, Z. L. Jia and D. C. Mei, Effects of correlation time between noises on the noise enhanced stability phenomenon in an asymmetric bistable system, Front. Phys., 10 (2015), 95–101.
[25]	A. d'Onofrio and A. Gandolfi, Resistance to antitumor chemotherapy due to bounded-noise-induced transitions, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 82 (2010), 061901.
[26]	A. d'Onofrio, Bounded-noise-induced transitions in a tumor-immune system interplay, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 81 (2010), 021923.
[27]	A. D'Onofrio, Bounded noises in physics, biology, and engineering, Birkhäuser Basel, 2013.
[28]	G.Q. Cai and C. Wu, Modeling of bounded stochastic processes, Probabilist. Eng. Mech., 19 (2004), 197–203.
[29]	C.-J. Wang, Q.-F. Lin, Y.-G. Yao, et al., Dynamics of a stochastic system driven by cross-correlated sine-Wiener bounded noises, Nonlinear Dyn., 95 (2018), 1941–1956.
[30]	W. Guo and D.-C. Mei, Stochastic resonance in a tumor–immune system subject to bounded noises and time delay, Physica A, 416 (2014), 90–98.
[31]	Y. G. Yao, W. Cao, Q. M. Pei, et al., Breakup of Spiral Wave and Order-Disorder Spatial Pattern Transition Induced by Spatially Uniform Cross-Correlated Sine-Wiener Noises in a Regular Network of Hodgkin-Huxley Neurons, Complexity, 2018 (2018), 1–10.
[32]	Y. Yao, C. Ma, C. Wang, et al., Detection of sub-threshold periodic signal by multiplicative and additive cross-correlated sine-Wiener noises in the FitzHugh–Nagumo neuron, Physica A, 492 (2018), 1247–1256.
[33]	Y. Yao, M. Yi and D. Hou, Coherence resonance induced by cross-correlated sine-Wiener noises in the FitzHugh–Nagumo neurons, Int. J. Mod. Phys. B, 31 (2017), 1750204.
[34]	G. H. Cheng, R. Gui, Y. G. Yao, et al., Enhancement of temporal regularity and degradation of spatial synchronization induced by cross-correlated sine-Wiener noises in regular and small-world neuronal networks, Physica A, 520 (2019), 361–369.
[35]	W. Guo, L.-C. Du and D.-C. Mei, Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor–immune system interplay, Physica A, 391 (2012), 1270–1280.
[36]	S. Q. Zhu, Steady-State Analysis of a Single-Mode Laser with Correlations Between Additive and Multiplicative Noise, Phys. Rev. A, 47 (1993), 2405–2408.
[37]	P. Liu and L. J. Ning, Transitions induced by cross-correlated bounded noises and time delay in a genotype selection model, Physica A, 441 (2016), 32–39.
[38]	R. Ma, J. Wang, Z. Hou, et al., Small-number effects: a third stable state in a genetic bistable toggle switch, Phys. Rev. Lett., 109 (2012), 248107.
[39]	J. E. Ferrell, Jr., Bistability, bifurcations, and Waddington's epigenetic landscape, Curr Biol, 22 (2012), R458–R466.
[40]	Y. Jia and J. R. Li, Transient properties of a bistable kinetic model with correlations between additive and multiplicative noises: Mean first-passage time, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 53 (1996), 5764–5768.

Reader Comments

Your name:*

Email:*
© 2019 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)