Journal of Statistical Physics

, Volume 131, Issue 1, pp 153–165 | Cite as

Multiple Stochastic Point Processes in Gene Expression

  • Rajamanickam MuruganEmail author


We generalize the idea of multiple-stochasticity in chemical reaction systems to gene expression. Using Chemical Langevin Equation approach we investigate how this multiple-stochasticity can influence the overall molecular number fluctuations. We show that the main sources of this multiple-stochasticity in gene expression could be the randomness in transcription and translation initiation times which in turn originates from the underlying bio-macromolecular recognition processes such as the site-specific DNA-protein interactions and therefore can be internally regulated by the supra-molecular structural factors such as the condensation/super-coiling of DNA. Our theory predicts that (1) in case of gene expression system, the variances (φ) introduced by the randomness in transcription and translation initiation-times approximately scales with the degree of condensation (s) of DNA or mRNA as φ s −6. From the theoretical analysis of the Fano factor as well as coefficient of variation associated with the protein number fluctuations we predict that (2) unlike the singly-stochastic case where the Fano factor has been shown to be a monotonous function of translation rate, in case of multiple-stochastic gene expression the Fano factor is a turn over function with a definite minimum. This in turn suggests that the multiple-stochastic processes can also be well tuned to behave like a singly-stochastic point processes by adjusting the rate parameters.


Multiple stochastic point processes Gene expression Time dependent rates 


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  1. 1.
    Teich, M.C.: Fractal character of the auditory neural spike train. IEEE Trans. Biomed. Eng. 36, 150–160 (1989) CrossRefGoogle Scholar
  2. 2.
    Turcott, R.G., Lowen, S.B., Li, E., Johnson, D.H., Tsuchitani, C., Teich, M.C.: A nonstationary Poisson point process describes the sequence of action potentials over long time scales in lateral-superior-olive auditory neurons. Biol. Cybern. 70, 209–217 (1994) zbMATHCrossRefGoogle Scholar
  3. 3.
    Lowen, S.B., Teich, M.C.: Doubly stochastic Poisson point process driven by fractal shot noise. Phys. Rev. A. 43, 4192 (1991) CrossRefADSGoogle Scholar
  4. 4.
    Lowen, S.B., Teich, M.C.: The periodogram and Allan variance reveal fractal exponents greater than unity in auditory-nerve spike trains. J. Acoust. Soc. Am. 99, 3585–3591 (1996) CrossRefADSGoogle Scholar
  5. 5.
    Lowen, S.B., Teich, M.C.: Fractal-Based Point Processes. Wiley-Interscience, New York (2005) zbMATHGoogle Scholar
  6. 6.
    Murugan, R.: Critical jump sizes in DNA protein interactions. Biophys. Chem. 120, 143–148 (2006) CrossRefGoogle Scholar
  7. 7.
    Murugan, R.: DNA-protein interactions under random jump conditions. Phys. Rev. E 69, 011911 (2004) CrossRefADSGoogle Scholar
  8. 8.
    Murugan, R.: Effect of external fluctuations on the affinity-specificity negative correlation in DNA probe interactions. Phys. Rev. E 73, 051915 (2006) CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Murugan, R.: Generalized theory of site-specific DNA-protein interactions. Phys. Rev. E 76, 011901 (2007) CrossRefADSGoogle Scholar
  10. 10.
    Murugan, R.: Stochastic transcription initiation: time dependent transcription rates. Biophys. Chem. 121, 51–56 (2006) CrossRefGoogle Scholar
  11. 11.
    Zwanzig, R.: Rate processes with dynamical disorder. Acc. Chem. Res. 23, 148–152 (1990) CrossRefGoogle Scholar
  12. 12.
    Raser, J.M., O’Shea, E.K.: Noise in gene expression: origins, consequences, and control. Nature 309, 2010–2013 (2005) Google Scholar
  13. 13.
    Berg, O.G.: A model for the statistical fluctuations of protein numbers in a microbial population. J. Theor. Biol. 71, 587–603 (1978) CrossRefGoogle Scholar
  14. 14.
    Risken, H.: Fokker–Plank Equations. Springer, Berlin (1992) Google Scholar
  15. 15.
    Gardiner, C.W.: Handbook of Stochastic Methods. Springer, Berlin (2002) Google Scholar
  16. 16.
    Lewin, B.: Genes VIII. Oxford University Press, London (2004) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Kreiman Lab, Department of Ophthalmology and NeurologyChildren’s Hospital Boston Harvard Medical SchoolBostonUSA
  2. 2.Department of Chemical SciencesTata Institute of Fundamental ResearchMumbaiIndia

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