Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth-death process

Physical Biology

Volumn 9, Issue 5, 2012, Pages

  Zuk, Pawel J ^a,b   Kochańczyk, Marek ^a   Jaruszewicz, Joanna ^a   Bednorz, Witold ^b   Lipniacki, Tomasz ^a,c  

^a INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

^b UNIVERSITY OF WARSAW   (Poland)

^c Rice University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PHOSPHATASE; PHOSPHOTRANSFERASE;

ARTICLE; BIOLOGICAL MODEL; ENZYME ACTIVATION; METABOLISM; MONTE CARLO METHOD; PROBABILITY; STATISTICS; TEMPERATURE; THERMODYNAMICS;

ENZYME ACTIVATION; MARKOV CHAINS; MODELS, BIOLOGICAL; MONTE CARLO METHOD; PHOSPHORIC MONOESTER HYDROLASES; PHOSPHOTRANSFERASES; STOCHASTIC PROCESSES; TEMPERATURE; THERMODYNAMICS;

EID: 84867238454     PISSN: 14783967     EISSN: 14783975     Source Type: Journal    
DOI: 10.1088/1478-3975/9/5/055002     Document Type: Article

References (41)

1. Becskei A, Séraphin B and Serrano L 2001 Positive feedback in eukaryotic gene networks: cell differentiation by graded to binary response conversion EMBO J. 20 2528-35 (Pubitemid 32452871)
2. Ferrell J E Jr 2002 Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability Curr. Opin. Cell. Biol. 14 140-8 (Pubitemid 34219501)
3. Ptashne M 2004 A Genetic Switch: Phage Lambda Revisited (Cold Spring Harbor, NY: Cold Spring Harbor Laboratory Press)
4. Chatterjee A, Kaznessis Y N and Hu W S 2008 Tweaking biological switches through a better understanding of bistability behavior Curr. Opin. Biotechnol. 19 475-81
5. Sprinzak D, Lakhanpal A, LeBon L, Santat L A, Fontes M E, Anderson G A, Garcia-Ojalvo J and Elowitz M B 2010 Cis-interactions between Notch and Delta generate mutually exclusive signalling states Nature 465 86-90
6. Acar M, Becskei A and van Oudenaarden A 2005 Enhancement of cellular memory by reducing stochastic transitions Nature 435 228-32 (Pubitemid 40685951)
7. Lu T, Hasty J and Wolynes P G 2006 Effective temperature in stochastic kinetics and gene networks Biophys. J. 91 84-94 (Pubitemid 44015310)
8. Zhang Q, Bhattacharya S, Kline D E, Crawford R B, Conolly R B, Thomas R S, Kaminski N E and Andersen M E 2010 Stochastic modeling of B lymphocyte terminal differentiation and its suppression by dioxin BMC Syst. Biol. 4 40
9. Ogasawara H and Kawato M 2010 The protein kinase Mζ network as a bistable switch to store neuronal memory BMC Syst. Biol. 4 181
10. Lipniacki T, Hat B, Faeder J R and Hlavacek W S 2008 Stochastic effects and bistability in T cell receptor signaling J. Theor. Biol. 254 110-22
11. Puszyski K, Hat B and Lipniacki T 2008 Oscillations and bistability in the stochastic model of p53 regulation J. Theor. Biol. 254 452-65
12. Hat B, Kazmierczak B and Lipniacki T 2011 B cell activation triggered by the formation of the small receptor cluster: a computational study PLoS Comput. Biol. 7 e1002197
13. Song C, Phenix H, Abedi V, Scott M, Ingalls B P, Kærn M and Perkins T J 2010 Estimating the stochastic bifurcation structure of cellular networks PLoS Comput. Biol. 6 e1000699
14. Keizer J 1978 Maxwell-type constructions for multiple nonequilibrium steady states Proc. Natl Acad. Sci. USA 75 3023-6 (Pubitemid 8395111)
15. Vellela M and Qian H 2009 Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the Schlögl model revisited J. R. Soc. Interface 6 925-40 PMID: 19095615
16. Ross J, Hunt K L C and Hunt P M 1988 Thermodynamics far from equilibrium: reactions with multiple stationary states J. Chem. Phys. 88 2719-29
17. Ge H and Qian H 2009 Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a bistable biochemical system Phys. Rev. Lett. 103 148103
18. Ross J, Hunt K L C and Hunt P M 1992 Thermodynamic and stochastic theory for nonequilibrium systems with multiple reactive intermediates: the concept and role of excess work J. Chem. Phys. 96 618-29
19. Chu X, Ross J, Hunt P M and Hunt K L C 1993 Thermodynamic and stochastic theory of reaction-diffusion systems with multiple stationary states J. Chem. Phys. 99 3444-54
20. Bialek W 2000 Stability and noise in biochemical switches arXiv:cond-mat/0005235
21. Murray J D 2003 Mathematical Biology (New York: Springer)
22. Matheson I, Walls D F and Gardiner C W 1975 Stochastic models of first-order nonequilibrium phase transitions in chemical reactions J. Stat. Phys. 12 21-34
23. Nicolis G and Lefever R 1977 Comment on the kinetic potential and the Maxwell construction in non-equilibrium chemical phase transitions Phys. Lett. A 62 469-71
24. Barndorff-Nielsen O E and Cox D R 1989 Asymptotic Techniques for Use in Statistics (London: Chapman and Hall)
25. Schlögl F 1971 On thermodynamics near a steady state Z. Phys. A 248 446-58
26. Hornos E M, Schultz D, Innocentini G C P, Wang J, Walczak A M, Onuchic J N and Wolynes PG 2005 Self-regulating gene: an exact solution Phys. Rev. E 72 051907 (Pubitemid 41777717)
27. Feng H, Han B and Wang J 2011 Adiabatic and non-adiabatic non-equilibrium stochastic dynamics of single regulating genes J. Phys. Chem. B 115 1254-61
28. Morelli M J, Allen R J, Tanase-Nicola S and ten Wolde P R 2008 Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch J. Chem. Phys. 128 045105 (Pubitemid 351200455)
29. Frigola D, Casanellas L, Sancho J M and Ibaes M 2012 Asymmetric stochastic switching driven by intrinsic molecular noise PLoS ONE 7 E31407
30. Van Kampen N G 2007 Stochastic Processes in Physics and Chemistry (Elsevier: Amsterdam)
31. Groot S R and Mazur P 1962 Non-Equilibrium Thermodynamics (Amsterdam: North-Holland)
32. Walczak A M, Mugler A and Wiggins C H 2012 Analytic methods for modeling stochastic regulatory networks Computational Modeling of Signaling Networks (Methods in Molecular Biology vol 880) ed M Betterton and X Liu (New York: Humana)
33. Feng H D and Wang J 2011 Correlation function, response function and effective temperature of gene networks Chem. Phys. Lett. 510 267-72
34. Wilhelm T 2009 The smallest chemical reaction system with bistability BMC Syst. Biol. 3 90
35. Roskoski R Jr 2005 Src kinase regulation by phosphorylation and dephosphorylation Biochem. Biophys. Res. Commun. 331 1-14 (Pubitemid 40545134)
36. Bradshaw J M 2010 The Src, Syk, and Tec family kinases: distinct types of molecular switches Cell. Signal. 22 1175-84
37. Markevich N I, Hoek J B and Kholodenko B N 2004 Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades J. Cell. Biol. 164 353-9 (Pubitemid 38174763)
38. Gilfillan A M and Rivera J 2009 The tyrosine kinase network regulating mast cell activation Immunol. Rev. 228 149-69
39. Stamatakis M and Vlachos D G 2011 Equivalence of on-lattice stochastic chemical kinetics with the well-mixed chemical master equation in the limit of fast diffusion Comput. Chem. Eng. 35 2602-10
40. Hänggi P, Grabert H, Talker P and Thomas H 1984 Bistable systems: master equation versus Fokker-Planck modeling Phys. Rev. A 29 371-378
41. Miekisz J 2005 Equilibrium selection in evolutionary games with random matching of players J. Theor. Biol. 232 47-53 (Pubitemid 39388374)