Analytic methods for modeling stochastic regulatory networks

Methods in Molecular Biology

Volumn 880, Issue , 2012, Pages 273-322

  Walczak, Aleksandra M ^a   Mugler, Andrew ^b   Wiggins, Chris H ^c  

^a LABORATOIRE DE PHYSIQUE STATISTIQUE   (France)

^b FOM INSTITUTE AMOLF   (Netherlands)

^c Department of Earth and Environmental Sciences   (United States)

Author keywords

Analytical methods; Birth death process; Bursts; Feedback; Fokker Planck approximation; Gene regulation; Generating function; Langevin equation; Linear noise approximation; Master equation; Spectral method; Stochastic gene regulation

Indexed keywords

ANALYTIC METHOD; DEATH; GENE CONTROL; NOISE; PROBABILITY; STOCHASTIC MODEL; BIOLOGICAL MODEL; COMPUTER SIMULATION; METHODOLOGY; MONTE CARLO METHOD; PHYSIOLOGY; REVIEW; SIGNAL TRANSDUCTION; SINGLE CELL ANALYSIS; STATISTICAL MODEL; STATISTICS;

COMPUTER SIMULATION; MODELS, BIOLOGICAL; MODELS, STATISTICAL; MONTE CARLO METHOD; PROBABILITY; SIGNAL TRANSDUCTION; SINGLE-CELL ANALYSIS; STOCHASTIC PROCESSES;

EID: 84886686382     PISSN: 10643745     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-1-61779-833-7_13     Document Type: Chapter

References (49)

1. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–6
2. Ozbudak EM, Thattai M, Kurtser I, Grossman AD, van Oudenaarden A (2002) Regulation of noise in the expression of a single gene. Nat Genet 31(1):69–73
3. Raj A, Peskin CS, Tranchina DA, Vargas DY, Tyagi S (2006) Stochastic mrna synthesis in mammalian cells. Plos Biol 4(10):e309
4. Pedraza JM, van Oudenaarden A (2005) Noise propagation in gene networks. Science 307 (5717):1965–9
5. van Zon JS, ten Wolde PR (2005) Simulating biochemical networks at the particle level and in time and space: Green’s function reaction dynamic. Phys Rev Lett 94:128103
6. van Zon JS, ten Wolde PR (2005) Green’s function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space. J Chem Phys 123:234910
7. Allen RJ, Frenkel D, ten Wolde PR (2006) Forward flux sampling-type schemes for simulating rare events: efficiency analysis. J Chem Phys 124:194111
8. Valeriani C, Allen R, Morelli M, Frenkel D, ten Wolde PR (2007) Computing stationary distributions in equilibrium and non-equilibrium systems with Forward Flux Sampling. J Chem Phys 127:114109
9. Morelli MJ, Allen RJ, Tanase-Nicola S, ten Wolde PR (2008) Eliminating fast reactions in stochastic simulations of biochemical networks: a bistable genetic switch. J Chem Phys 128:045105
10. Munsky B, Khammash M (2006) The finite state projection algorithm for the solution of the chemical master equation. J Chem Phys 124:044104
11. Munsky B, Khammash M (2007) A multiple time interval finite state projection algorithm for the solution to the chemical master equation. J Comput Phys 226:818–835
12. El-Samad H, Khammash M, Petzold L, Gillespie D (2005) Stochastic modeling of gene regulatory networks. Int J Robust Nonlinear Control 15:691–711
13. Lampoudi S, Gillespie DT, Petzold LR (2009) The multinomial simulation algorithm for discrete stochastic simulation of reaction-diffusion systems. J Chem Phys 130:094104–16
14. Gillespie DT, Roh M, Petzold LR (2009) Refining the weighted stochastic simulation algorithm. J Chem Phys 130:174103
15. Chevalier M, El-Samad H (2009) A rigorous framework for multi-scale simulation of stochastic cellular networks. J Chem Phys 131:054102
16. Didier F, Henzinger TA, Mateescu M, Wolf V (2009) Fast adaptive uniformization of the chemical master equation. Proceedings of the High Performance Computational Systems Biology Workshop, IEEE Computer Society, pp 118–127
17. van Kampen NG (1992) Stochastic processes in physics and chemistry. North-Holland, Amsterdam
18. Gardiner CW (2004) Handbook of stochastic methods: for physics, chemistry and the natural sciences, 3rd edn. Springer, New York
19. Zwanzig R (2001) Nonequilibrium statistical mechanics, 1st edn. Oxford University Press, Oxford, USA
20. Kepler TB, Elston TC (2001) Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J 81:3116
21. Swain PS, Elowitz MB, Siggia ED (2002) Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc Natl Acad Sci USA 99(20):12795–800
22. Hasty J, Issacs F, Dolnik M, McMillen D, Collins JJ (2001) Designer gene networks: towards fundamental cellular control. Chaos 11:207
23. Hasty J, Pradines J, Dolnik M, Collins JJ (2000) Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci USA 97:2075
24. Bialek W (2001) Stability and noise in biochemical switches. In: Leen TK, Dietterich TG, Tresp V (eds) Advances in neural information processing 13, 13th edn. MIT Press, Cambridge, pp 103–109
25. Mehta P, Mukhopadhyay R, Wingreen NS (2008) Exponential sensitivity of noise-driven switching in genetic networks. Phys Biol 5:026005
26. Thattai M, van Oudenaarden A (2001) Intrinsic noise in gene regulatory networks. Proc Natl Acad Sci USA 98(15):8614–9
27. Hornos JEM, Schultz D, Innocentini GCP, Wang J, Walczak AM, Onuchic JN, Wolynes PG (2005) Self-regulating gene: an exact solution. Phys Rev E Stat Nonlin Soft Matter Phys 72:051907
28. Walczak AM, Mugler A, Wiggins CH (2009) A stochastic spectral analysis of transcriptional regulatory cascades. Proc Natl Acad Sci USA 106(16):6529
29. Mugler A, Walczak AM, Wiggins CH (2009) Spectral solutions to stochastic models of gene expression with bursts and regulation. Phys Rev E Stat Nonlin Soft Matter Phys 80 (4):041921
30. Mugler A, Ziv E, Nemenman I, Wiggins CH (2008) Quantifying evolvability in small biological networks. IET Syst Biol 3 (5):379–387
31. Bialek W, Setayeshgar S (2005) Physical limits to biochemical signaling. Proc Natl Acad Sci USA 102(29):10040–5
32. Tkacik G, Walczak AM, Bialek W (2009) Optimizing information flow in small genetic networks. Phys Rev E Stat Nonlin Soft Matter Phys 80:031920
33. Walczak AM, Tkacik G, Bialek W (2010) Optimizing information flow in small genetic networks II: feed forward networks. Phys Rev E Stat Nonlin Soft Matter Phys 81:041905
34. Iyer-Biswas S, Hayot F, Jayaprakash C (2009) Stochasticity of gene products from transcriptional pulsing. Phys Rev E Stat Nonlin Soft Matter Phys 79:31911
35. Warren PB, Tanase-Nicola S, ten Wolde PR (2006) Exact results for noise power spectra in linear biochemical reaction networks. J Chem Phys 125:1449041–11
36. Tanase-Nicola S, Warren PB, ten Wolde PR (2006) Signal detection, modularity, and the correlation between extrinsic and intrinsic noise in biochemical networks. Phys Rev Lett 97(6):068102
37. Paulsson J (2004) Summing up the noise in gene networks. Nature 427(6973):415–8
38. Elf J, Ehrenberg M (2003) Fast evaluation of fluctuations in biochemical networks with the linear noise approximation. Genome Res 13:2475–2484
39. Doi M (1976) Second quantization representation for classical many-particle system. J Physics A Math Gen 9:1465
40. ZelDovich YB, Ovchinnikov AA (1978) The mass action law and the kinetics of chemical reactions with allowance for thermodynamic fluctuations of the density. Sov J Exp Theor Phys 47:829
41. Peliti L (1986) Renormalisation of fluctuation effects in the a+a to a reaction. J Phys A Math Gen 19:L365
42. Sakurai JJ (1985) Modern quantum mechanics. Pearson Education India, Delhi
43. Bintu L, Buchler NE, Garcia HG et al (2005) Transcriptional regulation by the numbers: models. Curr Opin Genet Dev 15:116
44. Bintu L, Buchler NE, Garcia HG et al (2005) Transcriptional regulation by the numbers: applications. Curr Opin Genet Dev 15:125
45. Raj A, van Oudenaarden A (2008) Nature, nurture, or chance: stochastic gene expression and its consequences. Cell 135(2):216–226
46. Golding I, Paulsson J, Zawilski SM, Cox EC (2005) Real-time kinetics of gene activity in individual bacteria. Cell 123(6):1025–36
47. Walczak AM, Sasai M, Wolynes PG (2005) Self-consistent proteomic field theory of stochastic gene switches. Biophys J 88:828
48. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361
49. Koepf W (1998) Hypergeometric summation: an algorithmic approach to summation and special function identities. Vieweg, Braunschweig, Germany