Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling

Expand
  • 1 Center for Mathematical Sciences and School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
    2 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA

Received date: 2019-01-24

  Revised date: 2019-07-02

  Online published: 2020-02-19

Abstract

The aim of this article is to review our recent work on nonlocal dynamics of non-Gaussian systems arising in a gene regulatory network. We have used the mean exit time, escape probability and maximal likely trajectory to quantify dynamical behaviors of a stochastic diferential system with non-Gaussian α-stable Lévy motions, to examine how the nonGaussianity index and noise intensity afect the gene transcription processes.

Cite this article

Xiaoli Chen, Jinqiao Duan . Nonlocal Dynamics for Non-Gaussian Systems Arising in Biophysical Modeling[J]. Communications on Applied Mathematics and Computation, 2020 , 2(2) : 201 -213 . DOI: 10.1007/s42967-019-00046-5

References

1. Duan, J.:An Introduction to Stochastic Dynamics. Cambridge University Press, New York (2015)
2. Øksendal, B.K.:Stochastic Diferential Equations:an Introduction with Applications. Springer, Berlin (2005)
3. Wu, F., Chen, X., Zheng, Y., Duan, J., Kurths, J., Li, X.:Lévy noise-induced transition and enhanced stability in a gene regulatory network. Chaos 28, 075510 (2018)
4. Chen, X., Wu, F., Zheng, Y., Duan, J., Kurths, J., Li, X.:Most probable dynamics of a genetic regulatory network under stable Lévy noise. Appl. Math. Comput. 348, 425-436 (2019)
5. Sel, G.M., Jordi, G., Louisa, M.L., Michael, B.E.:An excitable gene regulatory circuit induces transient cellular diferentiation. Nature 440(7083), 545 (2006)
6. Grossman, A.D.:Genetic networks controlling the initiation of sporulation and the development of genetic competence in Bacillus subtilis. Annu. Rev. Genet. 29(1), 477-508 (1995)
7. Cagătay, T., Turcotte, M., Elowitz, M., Süel, G.:Architecture-dependent noise discriminates functionally analogous diferentiation circuits. Cell 139, 512-522 (2009)
8. Mugler, A., Kittisopikul, M., Hayden, L., Liu, J., Wiggins, C.H., Süel, G.M., Walczak, A.M.:Noise expands the response range of the Bacillus subtilis competence circuit. PLoS Comput. Biol. 12(3), e1004793 (2016)
9. Dubnau, D.:DNA uptake in bacteria. Annu. Rev. Microbiol. 53(1), 217-244 (1999)
10. Samoilov, M., Price, G., Arkin, A.:From fuctuations to phenotypes:the physiology of noise. Sci. Stke 2006, re17 (2006)
11. Veening, J., Smits, W., Kuipers, O.:Bistability, epigenetics, and bet-hedging in bacteria. Annu. Rev. Microbiol. 62, 193-210 (2008)
12. Zheng, Y., Serdukova, L., Duan, J., Kurths, J.:Transitions in a genetic transcriptional regulatory system under Lévy motion. Sci. Rep. 6, 29274 (2016)
13. Wang, H., Cheng, X., Duan, J., Kurths, J., Li, X.:Likelihood for transcriptions in a genetic regulatory system under asymmetric stable Lévy noise. Chaos 28, 013121 (2018)
14. Raj, A., Peskin, C., Tranchina, D., Vargas, D., Tyagi, S.:Stochastic mRNA synthesis in mammalian cells. PLoS Biol. 4, E309-E309 (2013)
15. Golding, I., Paulsson, J., Zawilski, S., Cox, E.:Real-time kinetics of gene activity in individual bacteria. Cell 123, 1025-1036 (2005)
16. Muramotoa, T., Cannona, D., Gierli, M., Corrigana, A., Bartonb, G.J., Chubba, J.R.:Live imaging of nascent RNA dynamics reveals distinct types of transcriptional pulse regulation. Proc. Nat. Acad. Sci. 109, 7350-7355 (2012)
17. Sun, X., Li, X., Zheng, Y.:Fokker-Planck equations for Marcus stochastic diferential equations driven by Lévy processes. (2016). arXiv:1605.06365 (arXiv preprint)
18. Applebaum, D.:Lévy Processes and Stochastic Calculus, 2nd edn. Cambridge University Press, Cambridge (2009)
19. Cai, R., Chen, X., Duan, J., Kurths, J., Li, X.:Lévy noise-induced escape in an excitable system. J. Stat. Mech Theory Exp. 6, 063503 (2017)
20. Gao, T., Duan, J., Li, X., Song, R.:Mean exit time and escape probability for dynamical systems driven by Lévy noise. SIAM J. Sci. Comput. 36, A887-A906 (2014)
21. Gao, T., Duan, J., Li, X.:Fokker-Planck equations for stochastic dynamical systems with symmetric Lévy motions. Appl. Math. Comput. 278, 1-20 (2016)
22. Cheng, Z., Duan, J., Wang, L.:Most probable dynamics of some nonlinear systems under noisy fuctuations. Commun. Nonlinear Sci. Numer. Simul. 30(1-3), 108-114 (2016)
23. Wang, H., Chen, X., Duan, J.:A stochastic Pitchfork bifurcation in most probable phase portraits. Int. J. Bifurc. Chaos 28(01), 1850017 (2018)
24. Jiang, G., Shu, C.W.:Efcient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202-228 (1996)
25. Shu, C.W., Osher, S.:Efcient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77, 439-471 (1988)
26. Xu, Y., Feng, J., Li, J., Zhang, H.:Lévy noise induced switch in the gene transcriptional regulatory system. Chaos 23, 013110 (2013)
27. Mehta, P., Mukhopadhyay, R., Wingreen, N.S.:Exponential sensitivity of noise-driven switching in genetic networks. Phys. Biol. 5(2), 026005 (2008)
28. Zhdanov, V.P.:Transient stochastic bistable kinetics of gene transcription during the cellular growth. Chem. Phys. Lett. 424(4-6), 394-398 (2006)
29. Schultz, D., Wolynes, P.G., Jacob, E.B., Onuchic, J.N.:Deciding fate in adverse times:sporulation and competence in Bacillus subtilis. Proc. Nat. Acad. Sci. 106(50), 21027-21034 (2009)
Options
Outlines

/