Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

Modulation of first-passage time for bursty gene expression via random signals

a. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
b. Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China

The stochastic nature of cell-specific signal molecules (such as transcription factor, ribosome, etc.) and the intrinsic stochastic nature of gene expression process result in cell-to-cell variations at protein levels. Increasing experimental evidences suggest that cell phenotypic variations often depend on the accumulation of some special proteins. Hence, a natural and fundamental question is: How does input signal affect the timing of protein count up to a given threshold? To this end, we study effects of input signal on the first-passage time (FPT), the time at which the number of proteins crosses a given threshold. Input signal is distinguished into two types: constant input signal and random input signal, regulating only burst frequency (or burst size) of gene expression. Firstly, we derive analytical formulae for FPT moments in each case of constant signal regulation and random signal regulation. Then, we find that random input signal tends to increases the mean and noise of FPT compared with constant input signal. Finally, we observe that different regulation ways of random signal have different effects on FPT, that is, burst size modulation tends to decrease the mean of FPT and increase the noise of FPT compared with burst frequency modulation. Our findings imply a fundamental mechanism that random fluctuating environment may prolong FPT. This can provide theoretical guidance for studies of some cellular key events such as latency of HIV and lysis time of bacteriophage $λ.$ In conclusion, our results reveal impacts of external signal on FPT and aid understanding the regulation mechanism of gene expression.

  Figure/Table
  Supplementary
  Article Metrics

Keywords First-passage time; gene expression; random input signal; burst frequency; burst size; regulation

Citation: Qiuying Li, Lifang Huang, Jianshe Yu. Modulation of first-passage time for bursty gene expression via random signals. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1261-1277. doi: 10.3934/mbe.2017065

References

  • [1] D. W. Adams,J. Errington, Bacterial cell division: Assembly, maintenance and disassembly of the Z ring, Nat. Rev. Microbiol., 7 (2009): 642-653.
  • [2] W. J. Blake,M. KAErn,C. R. Cantor,J. J. Collins, Noise in eukaryotic gene expression, Nature, 422 (2003): 633-637.
  • [3] H. Boeger,J. Griesenbeck,R. D. Kornberg, Nucleosome retention and the stochastic nature of promoter chromatin remodeling for transcription, Cell, 133 (2008): 716-726.
  • [4] L. Cai,N. Friedman,X. S. Xie, Stochastic protein expression in individual cells at the single molecule level, Nature, 440 (2006): 358-362.
  • [5] A. K. Chavali, V. C. Wong and K. Miller-Jensen, Distinct promoter activation mechanisms modulate noise-driven HIV gene expression, Sci. Rep., 5 (2015), 17661.
  • [6] S. Chong,C. Y. Chen,H. Ge,X. S. Xie, Mechanism of transcriptional bursting in bacteria, Cell, 158 (2014): 314-326.
  • [7] J. R. Chubb,T. B. Liverpool, Bursts and pulses: insights from single cell studies into transcriptional mechanisms, Curr. Opin. Genet. Dev., 20 (2010): 478-484.
  • [8] R. D. Dar,N. N. Hosmane,M. R. Arkin, Screening for noise in gene expression identifies drug synergies, Science, 344 (2014): 1392-1396.
  • [9] R. D. Dar, B. S. Razooky and A. Singh, etc., Transcriptional burst frequency and burst size are equally modulated across the human genome, Proc. Natl. Acad. Sci. USA., 109 (2012), 17454–17459.
  • [10] J. J. Dennehy and I. N. Wang, Factors influencing lysis time stochasticity in bacteriophage $λ$, BMC Microbiol., 11 (2011), 174.
  • [11] R. E. Dolmetsch,K. Xu,R. S. Lewis, Calcium oscillations increase the efficiency and specificity of gene expression, Nature, 392 (1998): 933-936.
  • [12] V. Elgart, T. Jia, A. T. Fenley and R. Kulkarni, Connecting protein and mRNA burst distributions for stochastic models of gene expression, Phys. Biol., 8 (2011), 046001.
  • [13] M. B. Elowitz,A. J. Levine,E. D. Siggia,P. S. Swaim, Stochastic gene expression in a single cell, Science, 297 (2002): 1183-1186.
  • [14] N. Geva-zatorsky,E. Dekel,E. Batchelor,G. Lahav,U. Alon, Fourier analysis and systems identification of the p53 feedback loop, Proc. Natl. Acad. Sci. USA., 107 (2010): 13550-13555.
  • [15] K. R. Ghusinga, C. A. Vargas-Garcia and A. Singh, A mechanistic stochastic framework for regulating bacterial cell division, Sci. Rep., 6 (2016), 30229.
  • [16] T. Gregor,D. W. Tank,E. F. Wieschaus,W. Bialek, Probing the limits to positional information, Cell, 130 (2007): 153-164.
  • [17] A. Gründing,M. D. Manson,R. Yong, Holins kill without warning, Proc. Natl. Acad. Sci. USA., 98 (2001): 9348-9352.
  • [18] N. K. Grzimek,D. Dreis,S. Schmalz,M. J. Reddehase, Random, asynchronous, and asymmetric transcriptional activity of enhancer-flanking major immediate-early genes ie1/3 and ie2 during murine cytomegalovirus latency in the lungs, J. Virol, 75 (2001): 2692-2705.
  • [19] T. Günther and A. Grundhoff, The epigenetic landscape of latent kaposi sarcoma-associated herpesvirus genomes, PLoS Pathog., 6 (2010), e1000935.
  • [20] P. Guptasarma, Does replication-induced transcription regulate synthesis of the myriad low copy number proteins of Escherichia coli?, Bioessays, 17 (1995): 987-997.
  • [21] P. Hänggi,P. Talkner,M. Borkovec, Reaction-rate theory: Fifty years after Kramers, Rev. Mod. Phys., 62 (1990): 251-341.
  • [22] B Hu, D. A. Kessler, W. J. Rappel and H. Levine, Effects of Input noise on a simple biochemical switch, Phy. Rev. Lett., 107 (2011), 148101.
  • [23] L. Huang, Z. Yuan, P. Liu and T. Zhou, Feedback-induced counterintuitive correlations of gene expression noise with bursting kinetics, Phys. Rev. E, 90 (2014), 052702.
  • [24] P. J. Ingram, M. P. H. Stumpf and J. Stark, Nonidentifiability of the source of intrinsic noise in gene expression from single-burst data, PLoS Comput. Biol., 4 (2008), e1000192.
  • [25] F. Jiao,M. Tang,J. Yu, Distribution profiles and their dynamic transition in stochastic gene transcription, J. Differential Equations, 254 (2013): 3307-3328.
  • [26] I. G. Johnston, B. Gaal and R. P. Neves, et al., Mitochondrial variability as a source of extrinsic cellular noise, PloS Comput. Biol., 8 (2011), e1002416.
  • [27] T. B. Kepler,T. C. Elston, Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations, Biophys. J., 81 (2001): 3116-3136.
  • [28] T. K. Kim,R. Shiekhattar, Architectural and functional commonalities between enhancers and promoters, Cell, 162 (2015): 948-959.
  • [29] D. M. Knipe and A. Cliffe, Chromatin control of herpes simplex virus lytic and latent infection, Nat. Rev. Microbiol., 6 (2008), 211-221,
  • [30] J. Kuang,M. Tang,J. Yu, The mean and noise of protein numbers in stochastic gene expression, J. Math. Biol., 67 (2013): 261-291.
  • [31] D. R. Larson, What do expression dynamics tell us about the mechanism of transcription?, Curr. Opin. Genet. Dev., 21 (2011): 591-599.
  • [32] J. H. Levine,Y. Lin,M. B. Elowitz, Functional roles of pulsing in genetic circuits, Science, 342 (2013): 1193-1200.
  • [33] W. Li,D. Notani,M. G. Rosenfeld, Enhancers as non-coding RNA transcription units: Recent insights and future perspectives, Nat. Rev. Genet., 17 (2016): 207-223.
  • [34] Y. Li,M. Tang,J. Yu, Transcription dynamics of inducible genes modulated by negative regulations, Mathematical Medicine and Biology, 32 (2015): 115-136.
  • [35] H. Maamar,A. Raj,D. Dubnau, Noise in gene expression determines cell fate in Bacillus subtilis, Science, 317 (2007): 526-529.
  • [36] H. H. McAdams,A. Arkin, Stochastic mechanisms in gene expression, Proc. Natl. Acad. Sci. USA., 94 (1997): 814-819.
  • [37] K. Miller-Jensen,S. S. Dey,D. V. Schaffer,A. P. Arkin, Varying virulence: Epigenetic control of expression noise and disease processes, Trends Biotechnol., 29 (2011): 517-525.
  • [38] T. Morisaki,K. Lyon,K. F. DeLuca, Real-time quantification of single RNA translation dynamics in living cells, Science, 352 (2016): 1425-1429.
  • [39] A. Ochab-marcinek,M. Tabaka, Bimodal gene expression in noncooperative regulatory systems, Proc. Natl. Acad. Sci. USA., 107 (2010): 22096-22101.
  • [40] U. A. Orom,T. Derrien,M. Beringer,K. Gumireddy, Long noncoding RNAs with enhancer-like function in human cells, Cell, 143 (2010): 46-58.
  • [41] M. Osella and M. C. Lagomarsino, Growthrate-dependent dynamics of a bacterial genetic oscillator, Phys. Rev. E, 87 (2013), 012726.
  • [42] J. Pahle, A. K. Green, C. J. Dixon and U. Kummer, Information transfer in signaling pathways: A study using coupled simulated and experimental data, BMC Bioinformatics, 9 (2008), 139.
  • [43] J. Paulsson,O. G. Berg,M. Ehrenberg, Stochastic focusing: fluctuation-enhanced sensitivity of intracellular regulation, Proc. Natl. Acad. Sci. USA., 97 (2000): 7148-7153.
  • [44] J. M. Pedraza,J. Paulsson, Effects of molecular memory and bursting on fluctuations in gene expression, Science, 319 (2008): 339-343.
  • [45] N. Petrenko,R. V. Chereji,M. N. McClean, Noise and interlocking signaling pathways promote distinct transcription factor dynamics in repond to different stresses, Mol. Biol. Cell, 24 (2013): 45-57.
  • [46] A. Raj,A. V. Oudenaarden, Nature, nurture, or chance: Stochastic gene expression and its consequences, Cell, 135 (2008): 216-226.
  • [47] J. M. Raser,E. K. O'Shea, Control of stochasticity in eukaryotic gene expression, Science, 304 (2004): 1811-1814.
  • [48] L. Salmena,L. Poliseno,Y. Tay,L. Kats,P. P. Pandolfi, A ceRNA hypothesis: The Rosetta stone of a hidden RNA language, Cell, 146 (2011): 353-358.
  • [49] A. Sanchez,S. Choubey,J. Kondev, Regulation of noise in gene expression, Annu. Rev. Biophys., 42 (2013): 469-491.
  • [50] A. Sanchez,I. Golding, Genetic determinants and cellular constraints in noisy gene expression, Science, 342 (2013): 1188-1193.
  • [51] V. Shahrezaei,P. S. Swain, Analytical distribution for stochastic gene expression, Proc. Natl. Acad. Sci. USA., 105 (2008): 17256-17261.
  • [52] M. Shreshtha, A. Surendran and A. Ghosh, Estimation of mean first passage time for bursty gene expression, Phys. Biol., 13 (2016), 036004.
  • [53] A. Singh and J. J. Dennehy, Stochastic holin expression can account for lysis time variation in the bacteriophage $λ$, J. R. Soc. Interface, 11 (2014), 20140140.
  • [54] A. Singh and M. Soltani, Quantifying intrinsic and extrinsic variability in stochastic gene expression models, PLoS ONE, 8 (2013), e84301.
  • [55] R. Skupsky, J. C. Burnett and J. E. Foley, et al., HIV promoter integration site primarily modulates transcriptional burst size rather than frequency, PLoS Comput. Biol., 6 (2010), e1000952.
  • [56] M. Soltani, C. A. Vargas-Garcia, D. Antunes and A. Singh, Intercellular variability in protein levels from stochastic expression and noisy cell cycle processes, PLoS Comput. Biol. 12 (2016), e1004972.
  • [57] G. M. Süel, R. P. Kulkarni and J. Dworkin, et al., Tunability and noise dependence in differentiation dynamics, Science, 315 (2007), 1137455.
  • [58] Q. Sun,M. Tang,J. Yu, Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways, Bull. Math. Biol., 74 (2012): 375-398.
  • [59] Q. Sun,M. Tang,J. Yu, Modulation of gene transcription noise by competing transcription factors, J. Math. Biol., 64 (2012): 469-494.
  • [60] D. M. Suter,N. Molina,D. Gatfield,K. Schneider,U. Schibler,F. Naef, Mammalian genes are transcribed with widely different bursting kinetics, Science, 332 (2011): 472-474.
  • [61] P. S. Swain,M. B. Elowitz,E. D. Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Natl. Acad. Sci. USA., 99 (2002): 12795-12800.
  • [62] M. Thattai,O.A. Van, Intrinsic noise in gene regulatory networks, Proc. Natl. Acad. Sci. USA., 98 (2001): 8614-8619.
  • [63] R. L. Thompson, C. M. Preston and N. M. Sawtell, De novo synthesis of vp16 coordinates the exit from hsv latency in vivo,PLoS Pathog., 5 (2009), e1000352.
  • [64] F. Tostevin, R. W. De and P. R. Ten Wolde, Reliability of frequency and amplitude decoding in gene regulation, Phys. Rev. Lett., 108 (2012), 108104.
  • [65] Z. Toth, D. T. Maglinte, S. H. Lee, H. R. Lee and L. Y. Wong, Epigenetic analysis of kshv latent and lytic genomes, PLoS Pathog. , 6 (2010), e1001013.
  • [66] H. Wang, Z. Yuan, P. Liu and T. Zhou, Mechanisms of information decoding in a cascade system of gene expression, Phys. Rev. E, 93 (2016), 052411.
  • [67] K. B. Wee,W. K. Yio,U. Surana,K. H. Chiam, Transcription factor oscillations induce differential gene expressions, Biophys. J., 102 (2012): 2413-2423.
  • [68] S. L. Werner,D. Barken,A. Hoffmann, Stimulus specificity of gene expression programs determined by temporal control of IKK activity, Science, 309 (2005): 1857-1861.
  • [69] J. Yu,Q. Sun,M. Tang, The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway activated transcription, Journal Theoretical Biology, 363 (2014): 223-234.
  • [70] J. Yu,J. Xiao,X. Ren,K. Lao,X. S. Xie, Probing gene expression in live cells, one protein molecule at a time, Science, 311 (2006): 1600-1603.
  • [71] J. Zhang,L. Chen,T. Zhou, Analytical distribution and tunability of noise in a model of promoter progress, Biophys. J., 102 (2012): 1247-1257.

 

This article has been cited by

  • 1. Kunwen Wen, Lifang Huang, Qi Wang, Jianshe Yu, Modulation of first-passage time for gene expression via asymmetric cell division, International Journal of Biomathematics, 2019, 10.1142/S1793524519500529

Reader Comments

your name: *   your email: *  

Copyright Info: 2017, Jianshe Yu, licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved