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

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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.

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References

  1. M. Thattai, A. Van Oudenaarden, Proc. Natl. Acad. Sci. U.S.A. 98, 8614 (2001)

    Article  ADS  Google Scholar 

  2. M.B. Elowitz, A.J. Levine, E.D. Siggia, P.S. Swain, Science 297, 1183 (2002)

    Article  ADS  Google Scholar 

  3. W.J. Blake, M. Kærn, C.R. Cantor, J.J. Collins, Nature 422, 633 (2003)

    Article  ADS  Google Scholar 

  4. J.M. Raser, E.K. O’Shea, Science 304, 1811 (2004)

    Article  ADS  Google Scholar 

  5. J. Paulsson, Nature 427, 415 (2004)

    Article  ADS  Google Scholar 

  6. A. Raj, C.S. Peskin, D. Tranchina, D.Y. Vargas, S. Tyagi, PLoS Biol. 4, e309 (2006)

    Article  Google Scholar 

  7. I. Golding, J. Paulsson, S.M. Zawilski, E.C. Cox, Cell 123, 1025 (2005)

    Article  Google Scholar 

  8. D.R. Larson, R.H. Singer, D. Zenklusen, Trends Cell Biol. 19, 630 (2009)

    Article  Google Scholar 

  9. J.R. Chubb, T. Trcek, S.M. Shenoy, R.H. Singer, Curr. Biol. 16, 1018 (2006)

    Article  Google Scholar 

  10. M.S.H. Ko, J. Theor. Biol. 153, 181 (1991)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  13. N. Crosetto, M. Bienko, A. Van Oudenaarden, Nat. Rev. Genet. 16, 57 (2015)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  15. P.S. Swain, M.B. Elowitz, E.D. Siggia, Proc. Natl. Acad. Sci. U.S.A. 99, 12795 (2002)

    Article  ADS  Google Scholar 

  16. V. Shahrezaei, P.S. Swain, Proc. Natl. Acad. Sci. U.S.A. 105, 17256 (2008)

    Article  ADS  Google Scholar 

  17. N.G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier Science B.V., Amsterdam, Netherlands, 1992)

  18. L. So, A. Ghosh, C. Zong, L.A. Sepúlveda, R. Segev, I. Golding, Nat. Genet. 43, 554 (2011)

    Article  Google Scholar 

  19. J. Peccoud, B. Ycart, Theor. Popul. Biol. 48, 222 (1995)

    Article  Google Scholar 

  20. R. Murugan, Biophys. Chem. 121, 51 (2006)

    Article  Google Scholar 

  21. S. Nandi, A. Ghosh, Phys. Biol. 12, 016015 (2015)

    Article  ADS  Google Scholar 

  22. J. Dattani, M. Barahona, J. R. Soc. Interface 4, 20160833 (2017)

    Article  Google Scholar 

  23. P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)

    Article  ADS  Google Scholar 

  24. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, 2001)

  25. S. Mukherji, M.S. Ebert, G.X.Y. Zheng, J.S. Tsang, P.A. Sharp, A. Van Oudenaarden, Nat. Genet. 43, 854 (2011)

    Article  Google Scholar 

  26. S. Bagga, J. Bracht, S. Hunter, K. Massirer, J. Holtz, R. Eachus, A.E. Pasquinelli, Cell 122, 553 (2005)

    Article  Google Scholar 

  27. A. Raj, A. Van Oudenaarden, Cell 135, 216 (2008)

    Article  Google Scholar 

  28. A. Singh, J.J. Dennehy, J. R. Soc. Interface 11, 20140140 (2014)

    Article  Google Scholar 

  29. A. Sanchez, I. Golding, Science 342, 1188 (2013)

    Article  ADS  Google Scholar 

  30. T. Lionnet, R.H. Singer, EMBO Rep. 13, 313 (2012)

    Article  Google Scholar 

  31. D.M. Suter, N. Molina, D. Gatfield, K. Schneider, U. Schibler, F. Naef, Science 332, 472 (2011)

    Article  ADS  Google Scholar 

  32. M. Shreshtha, A. Surendran, A. Ghosh, Phys. Biol. 13, 036004 (2016)

    Article  ADS  Google Scholar 

  33. A.M. Corrigan, J.R. Chubb, Curr. Biol. 24, 205 (2014)

    Article  Google Scholar 

  34. I. Mihalcescu, W. Hsing, S. Leibler, Nature 430, 81 (2004)

    Article  ADS  Google Scholar 

  35. J. Bieler, R. Cannavo, K. Gustafson, C. Gobet, D. Gatfield, F. Naef, Mol. Syst. Biol. 10, 739 (2014)

    Article  Google Scholar 

  36. S. Lück, P. Westermark, Cell. Mol. Life Sci. 73, 497 (2016)

    Article  Google Scholar 

  37. D.R. Larson, C. Fritzsch, L. Sun, X. Meng, D.S. Lawrence, R.H. Singer, Elife 2, e00750 (2013)

    Article  Google Scholar 

  38. E.J. Olson, L.A. Hartsough, B.P. Landry, R. Shroff, J.J. Tabor, Nat. Methods 11, 449 (2014)

    Article  Google Scholar 

  39. A. Mugler, A.M. Walczak, C.H. Wiggins, Phys. Rev. Lett. 105, 058101 (2010)

    Article  ADS  Google Scholar 

  40. J. Jedrak, A. Ochab-Marcinek, Phys. Rev. E 94, 032401 (2016)

    Article  ADS  Google Scholar 

  41. D.T. Gillespie, Annu. Rev. Phys. Chem. 58, 35 (2007)

    Article  ADS  Google Scholar 

  42. D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)

    Article  ADS  Google Scholar 

  43. B.D. Gomperts, I.M. Kramer, P.E.R. Tatham, Signal Transduction (Academic Press, New York, 2002) Chapt. 18

  44. O. Hobert, Science 319, 1785 (2008)

    Article  ADS  Google Scholar 

  45. P. Hanggi, H. Grabert, P. Talkner, H. Thomas, Phys. Rev. A 29, 371 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  46. R. Grima, P. Thomas, A.V. Straube, J. Chem. Phys. 135, 084103 (2011)

    Article  ADS  Google Scholar 

  47. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences (Springer, 2004)

  48. S. Dev, S. Chatterjee, Phys. Rev. E 99, 012402 (2019)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  50. A. Singh, B. Razooky, C.D. Cox, M.L. Simpson, L.S. Weinberger, Biophys. J. 98, L32 (2010)

    Article  Google Scholar 

  51. S. Hooshangi, S. Thiberge, R. Weiss, Proc. Natl. Acad. Sci. U.S.A. 102, 3581 (2005)

    Article  ADS  Google Scholar 

  52. M.R. Bennett, W.L. Pang, N.A. Ostroff, B.L. Baumgartner, S. Nayak, L.S. Tsimring, J. Hasty, Nature 454, 1119 (2008)

    Article  ADS  Google Scholar 

  53. S. Nouaille, S. Mondeil, A.L. Finoux, C. Moulis, L. Girbal, M. Cocaign-Bousquet, Nucl. Acids Res. 45, 11711 (2017)

    Article  Google Scholar 

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Authors and Affiliations

  1. Indian Institute of Science Education and Research Kolkata, 741246, Mohanpur, Nadia, India

    Kuheli Biswas, Mayank Shreshtha, Anudeep Surendran & Anandamohan Ghosh

  2. School of Mathematical Sciences, Queen Mary University of London, London, UK

    Mayank Shreshtha

  3. School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia

    Anudeep Surendran

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  1. Kuheli Biswas
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  2. Mayank Shreshtha
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  3. Anudeep Surendran
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  4. Anandamohan Ghosh
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Correspondence to Anandamohan Ghosh.

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Biswas, K., Shreshtha, M., Surendran, A. et al. First-passage time statistics of stochastic transcription process for time-dependent reaction rates. Eur. Phys. J. E 42, 24 (2019). https://doi.org/10.1140/epje/i2019-11788-8

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