Advertisement

First-passage time statistics of stochastic transcription process for time-dependent reaction rates

  • Kuheli Biswas
  • Mayank Shreshtha
  • Anudeep Surendran
  • Anandamohan GhoshEmail author
Regular Article
  • 47 Downloads

Abstract.

Transcription in gene expression is an intrinsically noisy process which involves production and degradation of mRNAs. An important quantity to describe this stochastic process is the first-passage time (FPT), i.e., the time taken by mRNAs to reach a particular threshold. The process of transcription can be modelled as a simple birth-death process, assuming that the promoter is always in an active state and to encode the stochastic environment we consider the transcription rate to be time dependent. This generalization is suitable to capture bursty mRNA dynamics usually modelled as an ON-Off model and simplifies the calculation of FPT statistics for a cell population. We study the role of periodic modulation of the transcription rate on different moments of FPT distribution of a population of cells. Our calculation shows that for sinusoidal modulation there exists an extremal value of mean FPT as a function of the time period and phase of the transcription signal. However, for the square wave modulation of transcription rates simulation results show that the extremal value of the MFPT behaves monotonically with the variation of the phase.

Graphical abstract

Keywords

Living systems: Biological networks 

References

  1. 1.
    M. Thattai, A. Van Oudenaarden, Proc. Natl. Acad. Sci. U.S.A. 98, 8614 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    M.B. Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Science 297, 1183 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    W.J. Blake, M. Kærn, C.R. Cantor, J.J. Collins, Nature 422, 633 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    J.M. Raser, E.K. O’Shea, Science 304, 1811 (2004)ADSCrossRefGoogle Scholar
  5. 5.
    J. Paulsson, Nature 427, 415 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    A. Raj, C.S. Peskin, D. Tranchina, D.Y. Vargas, S. Tyagi, PLoS Biol. 4, e309 (2006)CrossRefGoogle Scholar
  7. 7.
    I. Golding, J. Paulsson, S.M. Zawilski, E.C. Cox, Cell 123, 1025 (2005)CrossRefGoogle Scholar
  8. 8.
    D.R. Larson, R.H. Singer, D. Zenklusen, Trends Cell Biol. 19, 630 (2009)CrossRefGoogle Scholar
  9. 9.
    J.R. Chubb, T. Trcek, S.M. Shenoy, R.H. Singer, Curr. Biol. 16, 1018 (2006)CrossRefGoogle Scholar
  10. 10.
    M.S.H. Ko, J. Theor. Biol. 153, 181 (1991)CrossRefGoogle Scholar
  11. 11.
    J.W. Young, J.C.W. Locke, A. Altinok, N. Rosenfeld, T. Bacarian, P.S. Swain, E. Mjolsness, M.B. Elowitz, Nat. Protoc. 7, 80 (2012)CrossRefGoogle Scholar
  12. 12.
    H.Y. Park, H. Lim, Y.J. Yoon, A. Follenzi, C. Nwokafor, M. Lopez-Jones, X. Meng, R.H. Singer, Science 343, 422 (2014)ADSCrossRefGoogle Scholar
  13. 13.
    N. Crosetto, M. Bienko, A. Van Oudenaarden, Nat. Rev. Genet. 16, 57 (2015)CrossRefGoogle Scholar
  14. 14.
    N.D.L. Owens, I.L. Blitz, M.A. Lane, I. Patrushev, J.D. Overton, M.J. Gilchrist, K.W.Y. Cho, M.K. Khokha, Cell Rep. 14, 632 (2016)CrossRefGoogle Scholar
  15. 15.
    P.S. Swain, M.B. Elowitz, E.D. Siggia, Proc. Natl. Acad. Sci. U.S.A. 99, 12795 (2002)ADSCrossRefGoogle Scholar
  16. 16.
    V. Shahrezaei, P.S. Swain, Proc. Natl. Acad. Sci. U.S.A. 105, 17256 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science B.V., Amsterdam, Netherlands, 1992)Google Scholar
  18. 18.
    L. So, A. Ghosh, C. Zong, L.A. Sepúlveda, R. Segev, I. Golding, Nat. Genet. 43, 554 (2011)CrossRefGoogle Scholar
  19. 19.
    J. Peccoud, B. Ycart, Theor. Popul. Biol. 48, 222 (1995)CrossRefGoogle Scholar
  20. 20.
    R. Murugan, Biophys. Chem. 121, 51 (2006)CrossRefGoogle Scholar
  21. 21.
    S. Nandi, A. Ghosh, Phys. Biol. 12, 016015 (2015)ADSCrossRefGoogle Scholar
  22. 22.
    J. Dattani, M. Barahona, J. R. Soc. Interface 4, 20160833 (2017)CrossRefGoogle Scholar
  23. 23.
    P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)ADSCrossRefGoogle Scholar
  24. 24.
    S. Redner, A Guide to First-Passage Processes (Cambridge University Press, 2001)Google Scholar
  25. 25.
    S. Mukherji, M.S. Ebert, G.X.Y. Zheng, J.S. Tsang, P.A. Sharp, A. Van Oudenaarden, Nat. Genet. 43, 854 (2011)CrossRefGoogle Scholar
  26. 26.
    S. Bagga, J. Bracht, S. Hunter, K. Massirer, J. Holtz, R. Eachus, A.E. Pasquinelli, Cell 122, 553 (2005)CrossRefGoogle Scholar
  27. 27.
    A. Raj, A. Van Oudenaarden, Cell 135, 216 (2008)CrossRefGoogle Scholar
  28. 28.
    A. Singh, J.J. Dennehy, J. R. Soc. Interface 11, 20140140 (2014)CrossRefGoogle Scholar
  29. 29.
    A. Sanchez, I. Golding, Science 342, 1188 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    T. Lionnet, R.H. Singer, EMBO Rep. 13, 313 (2012)CrossRefGoogle Scholar
  31. 31.
    D.M. Suter, N. Molina, D. Gatfield, K. Schneider, U. Schibler, F. Naef, Science 332, 472 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    M. Shreshtha, A. Surendran, A. Ghosh, Phys. Biol. 13, 036004 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    A.M. Corrigan, J.R. Chubb, Curr. Biol. 24, 205 (2014)CrossRefGoogle Scholar
  34. 34.
    I. Mihalcescu, W. Hsing, S. Leibler, Nature 430, 81 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    J. Bieler, R. Cannavo, K. Gustafson, C. Gobet, D. Gatfield, F. Naef, Mol. Syst. Biol. 10, 739 (2014)CrossRefGoogle Scholar
  36. 36.
    S. Lück, P. Westermark, Cell. Mol. Life Sci. 73, 497 (2016)CrossRefGoogle Scholar
  37. 37.
    D.R. Larson, C. Fritzsch, L. Sun, X. Meng, D.S. Lawrence, R.H. Singer, Elife 2, e00750 (2013)CrossRefGoogle Scholar
  38. 38.
    E.J. Olson, L.A. Hartsough, B.P. Landry, R. Shroff, J.J. Tabor, Nat. Methods 11, 449 (2014)CrossRefGoogle Scholar
  39. 39.
    A. Mugler, A.M. Walczak, C.H. Wiggins, Phys. Rev. Lett. 105, 058101 (2010)ADSCrossRefGoogle Scholar
  40. 40.
    J. Jedrak, A. Ochab-Marcinek, Phys. Rev. E 94, 032401 (2016)ADSCrossRefGoogle Scholar
  41. 41.
    D.T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007)ADSCrossRefGoogle Scholar
  42. 42.
    D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)ADSCrossRefGoogle Scholar
  43. 43.
    B.D. Gomperts, I.M. Kramer, P.E.R. Tatham, Signal Transduction (Academic Press, New York, 2002) Chapt. 18Google Scholar
  44. 44.
    O. Hobert, Science 319, 1785 (2008)ADSCrossRefGoogle Scholar
  45. 45.
    P. Hanggi, H. Grabert, P. Talkner, H. Thomas, Phys. Rev. A 29, 371 (1984)ADSMathSciNetCrossRefGoogle Scholar
  46. 46.
    R. Grima, P. Thomas, A.V. Straube, J. Chem. Phys. 135, 084103 (2011)ADSCrossRefGoogle Scholar
  47. 47.
    C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, 2004)Google Scholar
  48. 48.
    S. Dev, S. Chatterjee, Phys. Rev. E 99, 012402 (2019)ADSCrossRefGoogle Scholar
  49. 49.
    R.D. Dar, B.S. Razooky, A. Singh, T.V. Trimeloni, J.M. McCollum, C.D. Cox, M.L. Simpson, L.S. Weinberger, Proc. Natl. Acad. Sci. U.S.A. 109, 17454 (2012)ADSCrossRefGoogle Scholar
  50. 50.
    A. Singh, B. Razooky, C.D. Cox, M.L. Simpson, L.S. Weinberger, Biophys. J. 98, L32 (2010)CrossRefGoogle Scholar
  51. 51.
    S. Hooshangi, S. Thiberge, R. Weiss, Proc. Natl. Acad. Sci. U.S.A. 102, 3581 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    M.R. Bennett, W.L. Pang, N.A. Ostroff, B.L. Baumgartner, S. Nayak, L.S. Tsimring, J. Hasty, Nature 454, 1119 (2008)ADSCrossRefGoogle Scholar
  53. 53.
    S. Nouaille, S. Mondeil, A.L. Finoux, C. Moulis, L. Girbal, M. Cocaign-Bousquet, Nucl. Acids Res. 45, 11711 (2017)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Kuheli Biswas
    • 1
  • Mayank Shreshtha
    • 1
    • 2
  • Anudeep Surendran
    • 1
    • 3
  • Anandamohan Ghosh
    • 1
    Email author
  1. 1.Indian Institute of Science Education and Research KolkataMohanpur, NadiaIndia
  2. 2.School of Mathematical SciencesQueen Mary University of LondonLondonUK
  3. 3.School of Mathematical SciencesQueensland University of TechnologyBrisbaneAustralia

Personalised recommendations