Elimination of Fast Variables in Chemical Langevin Equations

Overview

Journal J Chem Phys

Publisher American Institute of Physics

Specialties Biophysics
Chemistry

Date 2008 Dec 10

PMID 19063552

Citations 4

Authors

Yueheng Lan

Timothy C Elston

Garegin A Papoian

Affiliations

Soon will be listed here.

Abstract

Internal and external fluctuations are ubiquitous in cellular signaling processes. Because biochemical reactions often evolve on disparate time scales, mathematical perturbation techniques can be invoked to reduce the complexity of stochastic models. Previous work in this area has focused on direct treatment of the master equation. However, eliminating fast variables in the chemical Langevin equation is also an important problem. We show how to solve this problem by utilizing a partial equilibrium assumption. Our technique is applied to a simple birth-death-dimerization process and a more involved gene regulation network, demonstrating great computational efficiency. Excellent agreement is found with results computed from exact stochastic simulations. We compare our approach with existing reduction schemes and discuss avenues for future improvement.

Citing Articles

Channel based generating function approach to the stochastic Hodgkin-Huxley neuronal system.

Ling A, Huang Y, Shuai J, Lan Y Sci Rep. 2016; 6:22662.

PMID: 26940002 PMC: 4778126. DOI: 10.1038/srep22662.

Equilibrium distributions of simple biochemical reaction systems for time-scale separation in stochastic reaction networks.

Melykuti B, Hespanha J, Khammash M J R Soc Interface. 2014; 11(97):20140054.

PMID: 24920118 PMC: 4208355. DOI: 10.1098/rsif.2014.0054.

Stochastic delay accelerates signaling in gene networks.

Josic K, Lopez J, Ott W, Shiau L, Bennett M PLoS Comput Biol. 2011; 7(11):e1002264.

PMID: 22102802 PMC: 3213172. DOI: 10.1371/journal.pcbi.1002264.

Adiabatic coarse-graining and simulations of stochastic biochemical networks.

Sinitsyn N, Hengartner N, Nemenman I Proc Natl Acad Sci U S A. 2009; 106(26):10546-51.

PMID: 19525397 PMC: 2705573. DOI: 10.1073/pnas.0809340106.

References

Barkai N, Leibler S . Robustness in simple biochemical networks. Nature. 1997; 387(6636):913-7. DOI: 10.1038/43199. View

Walczak A, Onuchic J, Wolynes P . Absolute rate theories of epigenetic stability. Proc Natl Acad Sci U S A. 2005; 102(52):18926-31. PMC: 1323203. DOI: 10.1073/pnas.0509547102. View

Salis H, Kaznessis Y . Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J Chem Phys. 2005; 122(5):54103. DOI: 10.1063/1.1835951. View

Kaern M, Blake W, Collins J . The engineering of gene regulatory networks. Annu Rev Biomed Eng. 2003; 5:179-206. DOI: 10.1146/annurev.bioeng.5.040202.121553. View

Blake W, Kaern M, Cantor C, Collins J . Noise in eukaryotic gene expression. Nature. 2003; 422(6932):633-7. DOI: 10.1038/nature01546. View

Erban R, Kevrekidis I, Adalsteinsson D, Elston T . Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation. J Chem Phys. 2006; 124(8):084106. DOI: 10.1063/1.2149854. View

Rieke F, Baylor D . Origin of reproducibility in the responses of retinal rods to single photons. Biophys J. 1998; 75(4):1836-57. PMC: 1299855. DOI: 10.1016/S0006-3495(98)77625-8. View

Puchalka J, Kierzek A . Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J. 2004; 86(3):1357-72. PMC: 1303974. DOI: 10.1016/S0006-3495(04)74207-1. View

Swain P . Efficient attenuation of stochasticity in gene expression through post-transcriptional control. J Mol Biol. 2004; 344(4):965-76. DOI: 10.1016/j.jmb.2004.09.073. View

10.

Kepler T, Elston T . Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J. 2001; 81(6):3116-36. PMC: 1301773. DOI: 10.1016/S0006-3495(01)75949-8. View

11.

Honeycutt . Stochastic Runge-Kutta algorithms. I. White noise. Phys Rev A. 1992; 45(2):600-603. DOI: 10.1103/physreva.45.600. View

12.

Ross J, Vlad M . Nonlinear kinetics and new approaches to complex reaction mechanisms. Annu Rev Phys Chem. 2004; 50:51-78. DOI: 10.1146/annurev.physchem.50.1.51. View

13.

Meng T, Somani S, Dhar P . Modeling and simulation of biological systems with stochasticity. In Silico Biol. 2005; 4(3):293-309. View

14.

Hornberg J, Binder B, Bruggeman F, Schoeberl B, Heinrich R, Westerhoff H . Control of MAPK signalling: from complexity to what really matters. Oncogene. 2005; 24(36):5533-42. DOI: 10.1038/sj.onc.1208817. View

15.

Kiehl T, Mattheyses R, Simmons M . Hybrid simulation of cellular behavior. Bioinformatics. 2004; 20(3):316-22. DOI: 10.1093/bioinformatics/btg409. View

16.

Morelli M, Allen R, Tanase-Nicola S, Wolde P . Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch. J Chem Phys. 2008; 128(4):045105. DOI: 10.1063/1.2821957. View

17.

Suel G, Garcia-Ojalvo J, Liberman L, Elowitz M . An excitable gene regulatory circuit induces transient cellular differentiation. Nature. 2006; 440(7083):545-50. DOI: 10.1038/nature04588. View

18.

Vilar J, Kueh H, Barkai N, Leibler S . Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci U S A. 2002; 99(9):5988-92. PMC: 122889. DOI: 10.1073/pnas.092133899. View

19.

Ozbudak E, Thattai M, Kurtser I, Grossman A, van Oudenaarden A . Regulation of noise in the expression of a single gene. Nat Genet. 2002; 31(1):69-73. DOI: 10.1038/ng869. View

20.

Weinberger L, Burnett J, Toettcher J, Arkin A, Schaffer D . Stochastic gene expression in a lentiviral positive-feedback loop: HIV-1 Tat fluctuations drive phenotypic diversity. Cell. 2005; 122(2):169-82. DOI: 10.1016/j.cell.2005.06.006. View