Modeling stochastic noise in gene regulatory systems

详细信息    查看全文

• 作者：Arwen Meister (1)
  Chao Du (1)
  Ye Henry Li (1)
  Wing Hung Wong (1)
  
• 关键词：gene regulation ; stochastic modeling ; simulation ; Master equation ; Gillespie algorithm ; Langevin equation
• 刊名：Quantitative Biology
• 出版年：2014
• 出版时间：March 2014
• 年：2014
• 卷：2
• 期：1
• 页码：1-29
• 全文大小：3,968 KB
• 参考文献：1. Swain, P. S., Elowitz, M. B. and Siggia, E. D. (2002) Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. U.S.A., 99, 12795鈥?2800. CrossRef
  2. Paulsson, J. (2004) Summing up the noise in gene networks. Nature, 427, 415鈥?18. CrossRef
  3. Elowitz, M. B., Levine, A. J., Siggia, E. D. and Swain, P. S. (2002) Stochastic gene expression in a single cell. Sci. Signal., 297, 1183.
  4. Ozbudak, E. M., Thattai, M., Kurtser, I., Grossman, A. D. and van Oudenaarden, A. (2002) Regulation of noise in the expression of a single gene. Nat. Genet., 31, 69鈥?3. CrossRef
  5. Blake, W. J., Kaern, M., Cantor, C. R. and Collins, J. J. (2003) Noise in eukaryotic gene expression. Nature, 422, 633鈥?37 CrossRef
  6. Rao, C. V., Wolf, D. M. and Arkin, A. P. (2002) Control, exploitation and tolerance of intracellular noise. Nature, 420, 231鈥?37. CrossRef
  7. Kaern, M., Elston, T. C., Blake, W. J. and Collins, J. J. (2005) Stochasticity in gene expression: from theories to phenotypes. Nat. Rev. Genet., 6, 451鈥?64. CrossRef
  8. Raj, A. and van Oudenaarden, A. (2008) Nature, nurture, or chance: stochastic gene expression and its consequences. Cell, 135, 216鈥?26. CrossRef
  9. Munsky, B., Neuert, G. and van Oudenaarden, A. (2012) Using gene expression noise to understand gene regulation. Science, 336, 183鈥?87. CrossRef
  10. Hager, G. L., McNally, J. G. and Misteli, T. (2009) Transcription dynamics. Mol. Cell, 35, 741鈥?53. CrossRef
  11. Kittisopikul, M. and S眉el, G. M. (2010) Biological role of noise encoded in a genetic network motif. Proc. Natl. Acad. Sci. U.S.A., 107, 13300鈥?3305. CrossRef
  12. Pedraza, J. M. and van Oudenaarden, A. (2005) Noise propagation in gene networks. Science, 307, 1965鈥?969. CrossRef
  13. Kepler, T. B. and Elston, T. C. (2001) Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J., 81, 3116鈥?136. CrossRef
  14. Ma, R., Wang, J., Hou, Z. and Liu, H. (2012) Small-number effects: a third stable state in a genetic bistable toggle switch. Phys. Rev. Lett., 109, 248107. CrossRef
  15. Elowitz, M. B. and Leibler, S. (2000) A synthetic oscillatory network of transcriptional regulators. Nature, 403, 335鈥?38. CrossRef
  16. Gardner, T., Cantor, C. and Collins, J. (2000) Construction of a genetic toggle switch in / Escherichia coli. Nature, 403, 339鈥?42. CrossRef
  17. Hasty, J., McMillen, D. and Collins, J. J. (2002) Engineered gene circuits. Nature, 420, 224鈥?30. CrossRef
  18. Ozbudak, E. M., Thattai, M., Lim, H. N., Shraiman, B. I. and Van Oudenaarden, A. (2004) Multistability in the lactose utilization network of / Escherichia coli. Nature, 427, 737鈥?40. CrossRef
  19. Frigola, D., Casanellas, L., Sancho, J. M. and Iba帽es, M. (2012) Asymmetric stochastic switching driven by intrinsic molecular noise. PLoS ONE, 7, e31407. CrossRef
  20. Novak, B. and Tyson, J. J. (1997) Modeling the control of DNA replication in fission yeast. Proc. Natl. Acad. Sci. U.S.A., 94, 9147鈥?152. CrossRef
  21. Arkin, A., Ross, J. and McAdams, H. H. (1998) Stochastic kinetic analysis of developmental pathway bifurcation in phage lambdainfected / Escherichia coli cells. Genetics, 149, 1633鈥?648.
  22. Thattai, M. and van Oudenaarden, A. (2001) Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. U.S.A., 98, 8614鈥?619. CrossRef
  23. Tao, Y. (2004) Intrinsic noise, gene regulation and steady-state statistics in a two gene network. J. Theor. Biol., 231, 563鈥?68. CrossRef
  24. Rosenfeld, N., Young, J. W., Alon, U., Swain, P. S. and Elowitz, M. B. (2005) Gene regulation at the single-cell level. Sci. Signal., 307, 1962.
  25. Krishnamurthy, S., Smith, E., Krakauer, D., Fontana, W. (2007) The stochastic behavior of a molecular switching circuit with feedback. Biol. Direct, 2, 1鈥?7. CrossRef
  26. Munsky, B., Trinh, B. and Khammash, M. (2009) Listening to the noise: random fluctuations reveal gene network parameters. Mol. Syst. Biol., 5, 318. CrossRef
  27. Dunlop, M. J., Cox, R. S. 3rd, Levine, J. H., Murray, R.M. and Elowitz, M. B. (2008) Regulatory activity revealed by dynamic correlations in gene expression noise. Nat. Genet., 40, 1493鈥?498. CrossRef
  28. Stewart-Ornstein, J., Weissman, J. S. and El-Samad, H. (2012) Cellular noise regulons underlie fluctuations in / Saccharomyces cerevisiae. Mol. Cell, 45, 483鈥?93. CrossRef
  29. Van Kampen, N. G. Stochastic Processes in Physics and Chemistry. (3rd, Ed). North Holland, 2007.
  30. Peles, S., Munsky, B. and Khammash, M. (2006) Reduction and solution of the chemical Master equation using time scale separation and finite state projection. J. Chem. Phys., 125, 204104. CrossRef
  31. Hegland, M., Burden, C., Santoso, L., MacNamara, S. and Booth, H. (2007) A solver for the stochastic master equation applied to gene regulatory networks. J. Comput. Appl. Math., 205, 708鈥?24. CrossRef
  32. Macnamara, S., Bersani, A. M., Burrage, K. and Sidje, R. B. (2008) Stochastic chemical kinetics and the total quasi-steady-state assumption: application to the stochastic simulation algorithm and chemical master equation. J. Chem. Phys., 129, 095105. CrossRef
  33. Smadbeck, P. and Kaznessis, Y. (2012) Stochastic model reduction using a modified Hill-type kinetic rate law. J. Chem. Phys., 137, 234109. CrossRef
  34. Waldherr, S., Wu, J. and Allg枚wer, F. (2010) Bridging time scales in cellular decision making with a stochastic bistable switch. BMC Syst. Biol., 4, 108. CrossRef
  35. Liang, J. and Qian, H. (2010) Computational cellular dynamics based on the chemical master equation: A challenge for understanding complexity. Journal of Computer Science and Technology, 25, 154鈥?68. CrossRef
  36. Gutierrez, P. S., Monteoliva, D. and Diambra, L. (2012) Cooperative binding of transcription factors promotes bimodal gene expression response. PLoS ONE, 7, e44812. CrossRef
  37. Khanin, R. and Higham, D. J. (2008) Chemical Master Equation and Langevin regimes for a gene transcription model. Theor. Comput. Sci., 408, 31鈥?0. CrossRef
  38. Meister, A., Li, Y. H., Choi, B. and Wong, W. H. (2013) Learning a nonlinear dynamical system model of gene regulation: A perturbed steady-state approach. Ann. Appl. Stat., 7, 1311鈥?333. CrossRef
  39. Faith, J. J., Hayete, B., Thaden, J. T., Mogno, I., Wierzbowski, J., Cottarel, G., Kasif, S., Collins, J. J. and Gardner, T. S. (2007) Largescale mapping and validation of / Escherichia coli transcriptional regulation from a compendium of expression profiles. PLoS Biol., 5, e8. CrossRef
  40. Bansal, M., Belcastro, V., Ambesi-Impiombato, A. and di Bernardo, D. (2007) How to infer gene networks from expression profiles. Mol. Syst. Biol., 3, 78. CrossRef
  41. Gardner, T. S., di Bernardo, D., Lorenz, D. and Collins, J. J. (2003) Inferring genetic networks and identifying compound mode of action via expression profiling. Science, 301, 102鈥?05. CrossRef
  42. di Bernardo, D., Thompson, M. J., Gardner, T. S., Chobot, S. E., Eastwood, E. L., Wojtovich, A. P., Elliott, S. J., Schaus, S. E. and Collins, J. J. (2005) Chemogenomic profiling on a genome-wide scale using reverse-engineered gene networks. Nat. Biotechnol., 23, 377鈥?83. CrossRef
  43. Michaelis, L. and Menten, M. L. (1913) Die kinetik der invertinwirkung. Biochem. Z., 49, 333鈥?69.
  44. Hill, A. V. (1913) The combinations of haemoglobin with oxygen and with carbon monoxide. Biochem. J., 7, 471鈥?80.
  45. Ackers, G. K., Johnson, A. D. and Shea, M. A. (1982) Quantitative model for gene regulation by lambda phage repressor. Proc. Natl. Acad. Sci. U.S.A., 79, 1129鈥?133. CrossRef
  46. Shea, M. A. and Ackers, G. K. (1985) The OR control system of bacteriophage lambda: A physicalchemical model for gene regulation. J. Mol. Biol., 181, 211鈥?30. CrossRef
  47. Bintu, L., Buchler, N. E., Garcia, H. G., Gerland, U., Hwa, T., Kondev, J. and Phillips, R. (2005) Transcriptional regulation by the numbers: models. Curr. Opin. Genet. Dev., 15, 116鈥?24. CrossRef
  48. Bintu, L., Buchler, N. E., Garcia, H. G., Gerland, U., Hwa, T., Kondev, J., Kuhlman, T. and Phillips, R. (2005) Transcriptional regulation by the numbers: applications. Curr. Opin. Genet. Dev., 15, 125鈥?35. CrossRef
  49. Rao, C. V. and Arkin, A. P.(2003) Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys., 118, 4999鈥?010. CrossRef
  50. Walker, J. A. Dynamical Systems and Evolution Equations. New York: Plenum Press, 1939.
  51. Kubo, R., Matsuo, K. and Kitahara, K. (1973) Fluctuation and relaxation of macrovariables. J. Stat. Phys., 9, 51鈥?6. CrossRef
  52. Gillespie, D. T. (1977) Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81, 2340鈥?361. CrossRef
  53. Gillespie, D. T. (2000) The chemical Langevin equation. J. Chem. Phys., 113, 297. CrossRef
  54. Komorowski, M., Finkenst盲dt, B., Harper, C. V. and Rand, D. A. (2009) Bayesian inference of biochemical kinetic parameters using the linear noise approximation. BMC Bioinformatics, 10, 343. CrossRef
  55. Choi, B. Learning networks in biological systems, Ph.D. thesis, Department of Applied Physics, Stanford University, Stanford, 2012.
  56. Planck, M. and Verband Deutscher Physikalischer Gesellschaften. Physikalische abhandlungen und vortr盲ge. 1958.
  57. Lord Rayleigh. (1891) Liii. Dynamical problems in illustration of the theory of gases. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 32, 424鈥?45. CrossRef
  58. Einstein, A. (1906) Eine neue bestimmung der molek uldimensionen. Annalen der Physik, 324, 289鈥?06. CrossRef
  59. Von Smoluchowski, M. (1906). Zur kinetischen theorie der brownschen molekularbewegung und der suspensionen. Annalen der physik, 326, 756鈥?80. CrossRef
  60. Van Kampen, N. G. Fluctuations in Nonlinear Systems. Fluctuation Phenomena in Solids, New York: Academic Press, 1965.
  61. Bar-Haim, A. and Klafter, J. (1998) Geometric versus energetic competition in light harvesting by dendrimers. J. Phys. Chem. B, 102, 1662鈥?664. CrossRef
  62. Chickarmane, V. and Peterson, C. (2008) A computational model for understanding stem cell, trophectoderm and endoderm lineage determination. PLoS ONE, 3, e3478. CrossRef
  63. Zavlanos, M. M., Julius, A. A., Boyd, S. P. and Pappas, G. J. (2011) Inferring stable genetic networks from steady-state data. Automatica, 47, 1113鈥?122. CrossRef
  
• 作者单位：Arwen Meister (1)
  Chao Du (1)
  Ye Henry Li (1)
  Wing Hung Wong (1)
  
  1. Computational Biology Lab, Bio-X Program, Stanford University, Stanford, CA, 94305, USA
  
• ISSN：2095-4697

文摘

The Master equation is considered the gold standard for modeling the stochastic mechanisms of gene regulation in molecular detail, but it is too complex to solve exactly in most cases, so approximation and simulation methods are essential. However, there is still a lack of consensus about the best way to carry these out. To help clarify the situation, we review Master equation models of gene regulation, theoretical approximations based on an expansion method due to N.G. van Kampen and R. Kubo, and simulation algorithms due to D.T. Gillespie and P. Langevin. Expansion of the Master equation shows that for systems with a single stable steady-state, the stochastic model reduces to a deterministic model in a first-order approximation. Additional theory, also due to van Kampen, describes the asymptotic behavior of multistable systems. To support and illustrate the theory and provide further insight into the complex behavior of multistable systems, we perform a detailed simulation study comparing the various approximation and simulation methods applied to synthetic gene regulatory systems with various qualitative characteristics. The simulation studies show that for large stochastic systems with a single steady-state, deterministic models are quite accurate, since the probability distribution of the solution has a single peak tracking the deterministic trajectory whose variance is inversely proportional to the system size. In multistable stochastic systems, large fluctuations can cause individual trajectories to escape from the domain of attraction of one steady-state and be attracted to another, so the system eventually reaches a multimodal probability distribution in which all stable steadystates are represented proportional to their relative stability. However, since the escape time scales exponentially with system size, this process can take a very long time in large systems.