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Propagation of Extrinsic Fluctuations in Biochemical Birth–Death Processes

  • P. C. Bressloff
  • E. Levien
Article
  • 31 Downloads

Abstract

Biochemical reactions are often subject to a complex fluctuating environment, which means that the corresponding reaction rates may themselves be time-varying and stochastic. If the environmental noise is common to a population of downstream processes, then the resulting rate fluctuations will induce statistical correlations between them. In this paper we investigate how such correlations depend on the form of environmental noise by considering a simple birth–death process with dynamical disorder in the birth rate. In particular, we derive expressions for the second-order statistics of two birth–death processes evolving in the same noisy environment. We find that these statistics not only depend on the second-order statistics of the environment, but the full generator of the process describing it, thus providing useful information about the environment. We illustrate our theory by considering applications to stochastic gene transcription and cell sensing.

Keywords

Birth–death processes Gene expression Cell signaling Intrinsic and extrinsic noise Correlations 

Notes

Acknowledgements

PCB was supported by the National Science Foundation (DMS-1613048). EL was supported by the National Science Foundation (DMS-RTG 1148230).

References

  1. Anderson DF, Kurtz TG (2015) Stochastic analysis of biochemical systems, vol 1. Stochastics in biological systems. Springer, BerlinCrossRefzbMATHGoogle Scholar
  2. Aymoz D, Wosika V, Durandau E, Pelet S (2016) Real-time quantification of protein expression at the single-cell level via dynamic protein synthesis translocation reporters. Nat Commun 7:11304CrossRefGoogle Scholar
  3. Balaban NQ, Merrin J, Chait R, Kowalik L, Leibler S (2004) Bacterial persistence as a phenotypic switch. Science 205:1578–1579Google Scholar
  4. Brémaud P (2013) Markov chains: Gibbs fields, Monte Carlo simulation, and queues, vol 31. Springer, BerlinzbMATHGoogle Scholar
  5. Bressloff PC (2017) Stochastic switching in biology: from genotype to phenotype. J Phys A 50:133001MathSciNetCrossRefzbMATHGoogle Scholar
  6. Chen L, Wang R, Zhou T, Aihara K (2005) Noise-induced cooperative behavior in a multicell system. Bioinformatics 21:2722–2729CrossRefGoogle Scholar
  7. Cookson NA, Mather WH, Danino T, Mondragon-Palomino O, Williams RJ, Tsimring LS, Hasty J (2014) Queueing up for enzymatic processing: correlated signaling through coupled degradation. Mol Syst Biol 7:561–561CrossRefGoogle Scholar
  8. Dattani J, Barahona M (2017) Stochastic models of gene transcription with upstream drives: exact solution and sample path characterization. J R Soc Interface 14:20160833CrossRefGoogle Scholar
  9. Davis MHA (1984) Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J R Soc B 46:353–388zbMATHGoogle Scholar
  10. Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297:1183–1186CrossRefGoogle Scholar
  11. Gardiner CW (2009) Handbook of stochastic methods, 4th edn. Springer, BerlinzbMATHGoogle Scholar
  12. Gupta A, Milias-Argeitis A, Khammash M (2017) Dynamic disorder in simple enzymatic reactions induces stochastic amplification of substrate. J R Soc Interface 14:20170311CrossRefGoogle Scholar
  13. Hilfinger A, Paulsson J (2011) Separating intrinsic from extrinsic fluctuations in dynamic biological systems. Proc Natl Acad Sci USA 108:12167–12172CrossRefGoogle Scholar
  14. Hilfinger A, Norman TM, Vinnicombe G, Paulsson J (2016a) Constraints on fluctuations in sparsely characterized biological systems. Phys Rev Lett 116:058101CrossRefzbMATHGoogle Scholar
  15. Hilfinger A, Norman T, Paulsson J (2016b) Exploiting natural fluctuations to identify kinetic mechanisms in sparsely characterized systems. Cell Syst 2:251–259CrossRefGoogle Scholar
  16. Hufton PG, Lin YT, Galla T, McKane AJ (2016) Intrinsic noise in systems with switching environments. Phys Rev E 93:052119CrossRefGoogle Scholar
  17. Kepler TB, Elston TC (2001) Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys J 81:3116–3136CrossRefGoogle Scholar
  18. Kifer Y (2009) Large deviations and adiabatic transitions for dynamical systems and Markov processes in fully coupled averaging. In: Memoirs of the AMS 201 (944)Google Scholar
  19. Kreyszig E (1989) Introductory functional analysis with applications, vol 81. Wiley, New YorkzbMATHGoogle Scholar
  20. Kurtz TG (1976) Limit theorems and diffusion approximations for density dependent Markov chains. Math Prog Stud 5:67–78MathSciNetCrossRefzbMATHGoogle Scholar
  21. Levien E, Bressloff PC (2016) A stochastic hybrid framework for obtaining statistics of many random walkers in a switching environment. Multiscale Model Simul 14:1417–1433MathSciNetCrossRefzbMATHGoogle Scholar
  22. Norman TM, Lord ND, Paulsson J, Losick R (2015) Stochastic switching of cell fate in microbes. Annu Rev Microbiol 69:381–403CrossRefGoogle Scholar
  23. Ohno M, Karagiannis P, Taniguchi Y (2014) Protein expression analyses at the single cell level. Molecules 19:13932–13947CrossRefGoogle Scholar
  24. Rhee A, Cheong R, Levchenko A (2014) Noise decomposition of intracellular biochemical signaling networks using nonequivalent reporters. Proc Natl Acad Sci 11:17330–17335CrossRefGoogle Scholar
  25. Sánchez A, Garcia HG, Jones D, Phillips R, Kondev J (2011) Effect of promoter architecture on the cell-to-cell variability in gene expression. PLoS Comp Biol 7(3):e1001100CrossRefGoogle Scholar
  26. Seger J, Brockman H (1987) What is bet-hedging? In: Harvey PH, Partridge L (eds) Oxford surveys in evolutionary biology, vol 4. Oxford University Press, Oxford, pp 182–211Google Scholar
  27. Thattai M, Van Oudenaarden A (2004) Stochastic gene expression in fluctuating environments. Genetics 167:523–530CrossRefGoogle Scholar
  28. van Kampen NG (1992) Stochastic processes in physics and chemistry. North-Holland, AmsterdamzbMATHGoogle Scholar
  29. Waters CM, Basser BL (2005) Quorum sensing: cell-to-cell communication in bacteria. Annu Rev Cell Dev 21:319–346CrossRefGoogle Scholar
  30. Weiss R, Knight TF (2000) Engineered communications for microbial robotics. DNA 6:13–17zbMATHGoogle Scholar
  31. Zhou T, Chen L, Aihara K (2015) Molecular communication through stochastic synchronization induced by extracellular fluctuations. Phys Rev Lett 95:178103CrossRefGoogle Scholar
  32. Zwanzig R (1990) Rate processes with dynamical disorder. Acc Chem Res 23:148–152CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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