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The mean and noise of FPT modulated by promoter architecture in gene networks
a. | Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China |
b. | School of Mathematics, Jiaying University, Meizhou 514015, China |
c. | School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China |
d. | College of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China |
Increasing experimental evidences suggest that cell phenotypic variation often depends on the accumulation of some special proteins. Recently, a lot of studies have shown that the complexity of promoter architecture plays a major role in regulating transcription and controlling expression dynamics and further phenotype. One unanswered question is why the organism chooses such a complex promoter architecture and how the promoter architecture affects the timing of proteins amount up to a given threshold. To address this issue, we study the effect of promoter architecture on the first-passage time (FPT) by formulating a multi-state gene model, that may reflect the complexity of promoter architecture. We derive analytical formulae for FPT moments in each case of irreversible promoter and reversible promoter regulation, which is the first time to give these analytical results in the existing literature. We show that the mean and noise of FPT increase with the state number of promoter architecture if the mean residence time at $ off$ states is not fixed. Inversely, if the mean residence time at $ off$ states is fixed, then complex promoter architecture will not vary the mean of FPT but will tend to decrease the noise of FPT. Our results show that, in the same inactive promoter states, the noise of FPT with promoters in irreversible case is always less than that in reversible case. In conclusion, our results reveal the effect of the promoter architecture on FPT and enhance understanding of the regulation mechanism of gene expression.
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doi: 10.1016/j.jtbi.2013.12.006. |
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Stochastic switching in biology: from genotype to phenotype, J. Phys. A: Math. Theor., 50 (2017), 133001,136pp.
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G. H. Lin, J. S. Yu, Z. Zhou, Q. W. Sun and F. Jiao, Fluctuations of mRNA distributions in multiple pathway activated transcription, Discrete Contin. Dyn. Syst. Ser. B, (2018), Accepted for publication, 26 pp. Google Scholar |
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show all references
References:
[1] |
A. Amir, O. Kobiler, A. Rokney, A. B. Oppenheim and J. Stavans, Noise in timing and precision of gene activities in a genetic cascade, Molec. Syst. Biol., 3 (2007), 71. Google Scholar |
[2] |
J. M. Bean, E. D. Siggia and F. R. Cross, Coherence and timing of cell cycle start examined at single-cell resolution, Mol. Cell., 21 (2006), 3-14. Google Scholar |
[3] |
A. Becskei, B. B. Kaufmann and A. V. Oudenaarden, Contributions of low molecule number and chromosomal positioning to stochastic gene expression, Nat. Gen., 37 (2005), 937-944. Google Scholar |
[4] |
W. J. Blake, M. Kærn, C. R. Cantor and J. J. Collins, Noise in eukaryotic gene expression, Nature, 422 (2003), 633-637. Google Scholar |
[5] |
W. J. Blake, G. Balazsi and M. A. Kohanski, et al., Phenotypic consequences of promotermediated transcriptional noise, Mol. Cell, 24 (2006), 853-865. Google Scholar |
[6] |
J. A. Bonachela and S. A. Levin,
Evolutionary comparison between viral lysis rate and latent period, J. Theor. Biol., 345 (2014), 32-42.
doi: 10.1016/j.jtbi.2013.12.006. |
[7] |
P. C. Bressloff,
Stochastic switching in biology: from genotype to phenotype, J. Phys. A: Math. Theor., 50 (2017), 133001,136pp.
doi: 10.1088/1751-8121/aa5db4. |
[8] |
C. R. Brown, C. Mao, F. Elena, M. S. Jurica and H. Boeger, Linking stochastic fluctuations in chromatin structure and gene expression, PLoS Biol., 11 (2013), e1001621. Google Scholar |
[9] |
L. Cai, N. Friedman and X. S. Xie, Stochastic protein expression in individual cells at the single molecule level, Nature, 440 (2006), 358-362. Google Scholar |
[10] |
L. B. Carey, D. V. Dijk, P. M. A. Sloot, J. A. Kaandorp and E. Segal, Promoter sequence determines the relationship between expression level and noise, PLoS Biol., 11 (2013), e1001528. Google Scholar |
[11] |
L. Chantranupong and R. H. Heineman, A common, non-optimal phenotypic endpoint in experimental adaptations of bacteriophage lysis time, BMC Evolut. Biol., 12 (2012), 37. Google Scholar |
[12] |
P. J. Choi, L. Cai, K. Frieda and X. S. Xie, A stochastic single molecule event triggers phenotype switching of a bacterial cell, Science, 322 (2008), 442-445. Google Scholar |
[13] |
A. Coulon, O. Gandrillon and G. Beslon, On the spontaneous stochastic dynamics of a single gene: Complexity of the molecular interplay at the promoter, BMC Syst. Biol., 4 (2010), 2. Google Scholar |
[14] |
M. H. DeGroot and M. J. Schervish, Probability and Statistics, 4th ed. Pearson, 2012. Google Scholar |
[15] |
J. J. Dennehy and N. I. Wang, Factors influencing lysis time stochasticity in bacteriophage $\lambda$, BMC Microbiol, 11 (2011), 1-12. Google Scholar |
[16] |
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. Google Scholar |
[17] |
P. L. Felmer, A. Quaas, M. X. Tang and J. S. Yu,
Random dynamics of gene transcription activation in single cells, J. Differ. Equ., 247 (2009), 1796-1816.
doi: 10.1016/j.jde.2009.06.006. |
[18] |
H. B. Fraser, A. E. Hirsh, G. Giaever, J. Kumm and M. B. Eisen, Noise minimization in eukaryotic gene expression, PLoS Biol., 6 (2004), 835-838. Google Scholar |
[19] |
K. R. Ghusinga, C. A. Vargas-Garcia and A. Singh, A mechanistic stochastic framework for regulating bacterial cell division, Sci. Rep., 6 (2016), 30229. Google Scholar |
[20] |
I. Golding, J. Paulsson, S. M. Zawilski and E. C. Cox, Real-time kinetics of gene activity in individual bacteria, Cell, 123 (2005), 1025-1036. Google Scholar |
[21] |
R. Heineman and J. Bull, Testing optimality with experimental evolution: Lysis time in a bacteriophage, Evolution, 61 (2007), 1695-1709. Google Scholar |
[22] |
G. Hornung, R. Bar-Ziv and D. Rosin, et al., Noise-mean relationship in mutated promoters, Genome. Res., 22 (2012), 2409-2417. Google Scholar |
[23] |
L. F. Huang, J. J. Zhang, P. J. Liu and T. S. Zhou, Effects of promoter leakage on dynamics of gene expression, BMC Syst. Biol., 9 (2015), 16. Google Scholar |
[24] |
L. F. Huang, Z. J. Yuan, J. S. Yu and T. S. Zhou,
Fundamental principles of energy consumption for gene expression, Chaos, 25 (2015), 123101, 10pp..
doi: 10.1063/1.4936670. |
[25] |
L. F. Huang, P. J. Liu, Z. J. Yuan, T. S. Zhou and J. S. Yu, The free-energy cost of interaction between DNA loops, Sci. Rep., 7 (2017), 12610. Google Scholar |
[26] |
F. Jiao, M. X. Tang and J. S. Yu,
Distribution profiles and their dynamic transition in stochastic gene transcription, J. Diff. Equat., 254 (2013), 3307-3328.
doi: 10.1016/j.jde.2013.01.019. |
[27] |
M. Kærn, T. C. Elston, W. J. Blake and J. J. Collins, Stochasticity in gene expression: From theories to phenotypes, Nat. Rev. Genet., 6 (2005), 451-464. Google Scholar |
[28] |
O. Kobiler, A. Rokney and N. Friedman, et al., Quantitative kinetic analysis of the bacteriophage λ genetic network, Proc. Natl. Acad. Sci. U. S. A., 102 (2005), 4470-4475. Google Scholar |
[29] |
J. H. Kuang, M. X. Tang and J. S. Yu,
The mean and noise of protein numbers in stochastic gene expression, J. Math. Biol., 67 (2013), 261-291.
doi: 10.1007/s00285-012-0551-8. |
[30] |
N. Kumar, A. Singh and R. V. Kulkarni, Transcriptional Bursting in Gene Expression: Analytical Results for General Stochastic Models, PLoS Comput. Biol., 11 (2015), e1004292. Google Scholar |
[31] |
W. Li, D. Notani and M.G. Rosenfeld, Enhancers as non-coding RNA transcription units: Recent insights and future perspectives, Nat. Rev. Genet., 17 (2016), 207-223. Google Scholar |
[32] |
Q. Y. Li, L. F. Huang and J. S. Yu,
Modulation of first-passage time for bursty gene expression via random signals, Math. Biosci. Eng., 14 (2017), 1261-1277.
doi: 10.3934/mbe.2017065. |
[33] |
Y. Y. Li, M. X. Tang and J. S. Yu,
Transcription dynamics of inducible genes modulated by negative regulations, Math. Med. Biol., 32 (2015), 115-136.
doi: 10.1093/imammb/dqt019. |
[34] |
G. H. Lin, J. S. Yu, Z. Zhou, Q. W. Sun and F. Jiao, Fluctuations of mRNA distributions in multiple pathway activated transcription, Discrete Contin. Dyn. Syst. Ser. B, (2018), Accepted for publication, 26 pp. Google Scholar |
[35] |
H. H. McAdams and A. Arkin, Stochastic mechanisms in gene expression, Proc. Natl. Acad. Sci. U. S. A., 94 (1997), 814-819. Google Scholar |
[36] |
B. Munsky, G. Neuert and A. V. Oudenaarden,
Using gene expression noise to understand gene regulation, Science, 336 (2012), 183-187.
doi: 10.1126/science.1216379. |
[37] |
K. F. Murphy, G. Balazsi and J. J. Collins, Combinatorial promoter design for engineering noisy gene expression, Proc. Natl. Acad. Sci. U. S. A., 104 (2007), 12726-12731. Google Scholar |
[38] |
R. Murugan and G. Kreiman, On the minimization of fluctuations in the response times of autoregulatory gene networks, Biophys. J., 101 (2011), 1297-1306. Google Scholar |
[39] |
A. Ochab-Marcinek and M. Tabaka, Bimodal gene expression in noncooperative regulatory systems, Proc. Natl. Acad. Sci. U. S. A., 107 (2010), 22096-22101. Google Scholar |
[40] |
M. Osella and M. C. Lagomarsino, Growthrate-dependent dynamics of a bacterial genetic oscillator, Phys. Rev. E., 87 (2013), 012726. Google Scholar |
[41] |
E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman and A. Oudenaarden, Regulation of noise in the expression of a single gene, Nat. Gen., 31 (2002), 69-73. Google Scholar |
[42] | A. Papoulis and S. U. Pillai, Probability, random variables and stochastic processes, 4th ed, McGraw Hill, McGraw Hill. Google Scholar |
[43] |
J. Paulsson, Models of stochastic gene expression, Phys. Lif. Rev., 2 (2005), 157-175. Google Scholar |
[44] |
J. M. Pedraza and J. Paulsson, Effects of Molecular Memory and Bursting on Fluctuations in Gene Expression, Science, 319 (2008), 1144331. Google Scholar |
[45] |
J. M. Raser and E. K. O Shea, Noise in gene expression: Origins, consequences, and control, Science, 309 (2005), 2010-2013. Google Scholar |
[46] |
J. M. Raser and E. K. O Shea, Control of stochasticity in eukaryotic gene expression, Science, 304 (2004), 1811-1814. Google Scholar |
[47] |
S. Redner, A Guide to First-Passage Processes, Cambridge University Press, 2001.
doi: 10.1017/CBO9780511606014.![]() ![]() |
[48] |
J. Ren, F. Jiao, Q. W. Sun, M. X. Tang and J. S. Yu,
The dynamics of gene transcription in random environments, Discrete Contin. Dyn. Syst. Ser. B, 23 (2018), 3167-3194.
doi: 10.3934/dcdsb.2018224. |
[49] | S. K. Ross, Introduction to Probability Models, 10th ed, Academic Press, 2010. Google Scholar |
[50] |
F. M. V. Rossi, A. M. Kringstein, A. Spicher, O. M. Guicherit and H. M. Blau, Transcriptional control: Rheostat converted to on/off switch, Mol. Cell, 6 (2000), 723-728. Google Scholar |
[51] |
A. Sanchez and J. Kondev, Transcriptional control of noise in gene expression, Proc. Natl. Acad. Sci. U. S. A., 105 (2008), 5081-5086. Google Scholar |
[52] |
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