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2014, 11(6): 1431-1448. doi: 10.3934/mbe.2014.11.1431

Effects of elongation delay in transcription dynamics

1. 

School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

2. 

Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

3. 

School of Mathematics and System Sciences and LMIB, Beihang University, Beijing, 100191, China

4. 

Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084

Received  June 2014 Revised  August 2014 Published  September 2014

In the transcription process, elongation delay is induced by the movement of RNA polymerases (RNAP) along the DNA sequence, and can result in changes in the transcription dynamics. This paper studies the transcription dynamics that involved the elongation delay and effects of cell division and DNA replication. The stochastic process of gene expression is modeled with delay chemical master equation with periodic coefficients, and is studied numerically through the stochastic simulation algorithm with delay. We show that the average transcription level approaches to a periodic dynamics over cell cycles at homeostasis, and the elongation delay can reduce the transcription level and increase the transcription noise. Moreover, the transcription elongation can induce bimodal distribution of mRNA levels that can be measured by the techniques of flow cytometry.
Citation: Xuan Zhang, Huiqin Jin, Zhuoqin Yang, Jinzhi Lei. Effects of elongation delay in transcription dynamics. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1431-1448. doi: 10.3934/mbe.2014.11.1431
References:
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U. Alon, An Introduction to Systems Biology, Chapman & Hall/RCR, New York, 2006.

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I. Artsimovitch and R. Landick, The transcriptional regulator rfah stimulates RNA chain synthesis after recruitment to elongation complexes by the exposed on template DNA strand, Cell, 109 (2002), 193-203.

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M. J. Bailey, C. Hughes and V. Koronakis, Rfah and the ops element, components of a novel system controlling bacterial transcription elongation, Mol. Microbiol., 26 (1997), 845-851.

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W. J. Blake, C. R. Cantor Mads Kærn and J. J. Collins, Noise in eukaryotic gene expression, Nature, 422 (2003), 633-637. doi: 10.1038/nature01546.

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D. Bratsun, D. Volfson, L. S. Tsimring, and J. Hasty, Delay-induced stochastic oscillations in gene regulation, Proc. Natl. Acad. Sci. USA, 102 (2005), 14593-14598. doi: 10.1073/pnas.0503858102.

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L. Cai, N. Friedman and X. S. Xie, Stochastic protein expression in individual cells at the single molecule level, Nature, 440 (2006), 358-362. doi: 10.1038/nature04599.

[8]

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), 442-446. doi: 10.1126/science.1161427.

[9]

D. L. Cook, A. N. Gerber and S. J. Tapscott, Modeling stochastic gene expression: Implications for haploinsufficiency, Proc. Natl. Acad. Sci. USA, 95 (1998), 15641-15646. doi: 10.1073/pnas.95.26.15641.

[10]

X. Darzacq, Y. Shav-Tal, V. de Turris, Y. Brody, S. M. Shenoy, R. D. Phair and R. H. Singer, In vivo dynamics of RNA polymerase II transcription, Nat. Struct. Mol. Biol., 14 (2007), 796-806. doi: 10.1038/nsmb1280.

[11]

M. Dobrzyński and F. J. Bruggeman, Elongation dynamics shape bursty transcription and translation, Proc. Natl. Acad. Sci. USA, 106 (2009), 2583-2588. doi: 10.1073/pnas.0803507106.

[12]

A. Dvir, Promoter escape by RNA polymerase II, Biochim. Biophys. Acta., 1577 (2002), 208-223. doi: 10.1016/S0167-4781(02)00453-0.

[13]

M. B. Elowitz, A. J. Levine, E. D. Siggia and P. S. Swain, Stochastic gene expression in a single cell, Science, 297 (2002), 1183-1186. doi: 10.1126/science.1070919.

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J. Lei, Stochasticity in single gene expression with both intrinsic noise and fluctuation in kinetic parameters, J. Theor. Biol., 256 (2009), 485-492. doi: 10.1016/j.jtbi.2008.10.028.

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J. Lei, G. He, H. Liu and Q. Nie, A delay model for noise-induced bi-directional switching, Nonlinearity, 22 (2009), 2845-2859. doi: 10.1088/0951-7715/22/12/003.

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B. Munsky, G. Neuert and A. van Oudenaarden, Using gene expression noise to understand gene regulation, Science, 336 (2012), 183-187. doi: 10.1126/science.1216379.

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T. O'Brien and J. T. Lis, Rapid changes in drosophila transcription after an instantaneous heat shock, Mol. Cell. Biol., 13 (1993), 3456-3463.

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G. Orphanides and D. Reinberg, A unified theory of gene expression, Cell, 108 (2002), 439-451. doi: 10.1016/S0092-8674(02)00655-4.

[28]

E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman and A. van Oudenaarden, Regulation of noise in the expression of a single gene, Nat. Genet., 31 (2002), 69-73. doi: 10.1038/ng869.

[29]

J. Paulsson, Summing up the noise in gene networks, Nature, 427 (2004), 415-418. doi: 10.1038/nature02257.

[30]

J. Paulsson, Models of stochastic gene expression, Phys. Life Rev., 2 (2005), 157-175. doi: 10.1016/j.plrev.2005.03.003.

[31]

J. M. Pedraza and J. Paulsson, Effects of molecular memory and bursting on fluctuations in gene expression, Science, 319 (2008), 339-343. doi: 10.1126/science.1144331.

[32]

S. Proshkin, A. R. Rahmouni, A. Mironov and E. Nudler, Cooperation between translating ribosomes and RNA polymerase in transcription elongation, Science, 328 (2010), 504-508. doi: 10.1126/science.1184939.

[33]

N. J. Proudfoot, A. Furger and M. J. Dye, Integrating mRNA processing with transcription, Cell, 108 (2002), 501-572. doi: 10.1016/S0092-8674(02)00617-7.

[34]

T. Rajala, A. Häkkinen, S. Healy, O. Yli-Harja and A. S. Ribeiro, Effects of transcriptional pausing on gene expression dynamics, PLoS Comp. Biol., 6 (2010), e1000704. doi: 10.1371/journal.pcbi.1000704.

[35]

D. B. Renner, Y. Yamaguchi, T. Wada, H. Handa and D. H. Price, A highly purified RNA polymerase II elongation control system, J. Biol. Chem., 276 (2001), 42601-42609. doi: 10.1074/jbc.M104967200.

[36]

A. S. Ribeiro, Stochastic and delayed stochastic models of gene expression and regulation, Math. Biosci., 223 (2010), 1-11. doi: 10.1016/j.mbs.2009.10.007.

[37]

A. S. Ribeiro, O-P. Smolander, T. Rajala, A. Häkkinen and O. Yli-Harja, Delayed stochastic model of transcription at the single nucleotide level, J. Comput. Biol., 16 (2009), 539-553. doi: 10.1089/cmb.2008.0153.

[38]

M. R. Roussel and R. Zhu, Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression, Phys. Biol., 3 (2006), 274-284. doi: 10.1088/1478-3975/3/4/005.

[39]

V. Shahrezaei, J. F. Ollivier and P. S. Swain, Colored extrinsic fluctuations and stochastic gene expression, Mol. Syst. Biol., 4 (2008), 196. doi: 10.1038/msb.2008.31.

[40]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256-17261. doi: 10.1073/pnas.0803850105.

[41]

A. Shundrovsky, T. J. Santangelo, J. W. Roberts and M. D. Wang, A single-molecule technique to study sequence-dependent transcription pausing, Biophy. J., 87 (2004), 3945-3953. doi: 10.1529/biophysj.104.044081.

[42]

J. Sticker, S. Cookson, M. R. Bennett, W. H. Mather, L. S. Tsimring and J. Hasty, A fast, robust and tunable synthetic gene oscillator, Nature, 456 (2008), 516-519.

[43]

G. M. Süel, J. Garcia-Ojalvo, L. M. Liberman and M. B. Elowitz, An excitable gene regulatory circuit induces transient cellular differentiation, Nature, 440 (2006), 545-550.

[44]

P. S. Swain, M. B. Elowitz and E. D. Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Natl. Acad. Sci. USA, 99 (2002), 12795-12800. doi: 10.1073/pnas.162041399.

[45]

I. A. Swinburne and P. A. Silver, Intron delays and transcriptional timing during development, Dev. Cell, 14 (2008), 324-330. doi: 10.1016/j.devcel.2008.02.002.

[46]

C. N. Tennyson, H. J. Klamut and R. G. Worton, The human dystrophin gene requires 16 hours to be transcribed and is cotranscriptionally spliced, Nat. Genet., 9 (1995), 184-190. doi: 10.1038/ng0295-184.

[47]

T. Tian, K. Burrage, P. M. Burrage and M. Carletti, Stochastic delay differential equation for genetic regulatory networks, J. Comput. Appl. Math., 205 (2007), 696-707. doi: 10.1016/j.cam.2006.02.063.

[48]

M. Tigges, T. T. Marquez-Lago, J. Stelling, and M. Fussenegger, A tunable synthetic mammalian oscillator, Nature, 457 (2009), 309-312. doi: 10.1038/nature07616.

[49]

T-L. To and N. Maheshri, Noise can induce bimodality in positive transcriptional feedback loops without bistability, Science, 327 (2010), 1142-1145. doi: 10.1126/science.1178962.

[50]

S. X. Xie, Paul J. Choi, G-W. Li, N. K. Lee and G. Lia, Single-molecule approach to molecular biology in living bacterial cells, Ann. Rev. Biophy., 37 (2008), 417-444. doi: 10.1146/annurev.biophys.37.092607.174640.

[51]

M. Yonaha and N. J. Proudfoot, Specific transcriptional pausing activates polyadenylation in a coupled in vitro system, Mol. Cell, 3 (1999), 593-600. doi: 10.1016/S1097-2765(00)80352-4.

[52]

R. Yvinec, C. j. Zhuge, J. Lei and M. C. Mackey, Adiabatic reduction of a model of stochastic gene expression with jump markov process, J. Math. Biol., 68 (2014), 1051-1070. doi: 10.1007/s00285-013-0661-y.

[53]

E. Zavala and T. T. Marquez-Lago, Delays induce novel stochastic effects in negative feedback gene circuits, Biophy. J., 106 (2014), 467-478. doi: 10.1016/j.bpj.2013.12.010.

[54]

J. Zhang, L. Chen and T. Zhou, Analytical distribution and tunability of noise in a model of promoter progress, Biophy. J., 102 (2012), 1247-1257. doi: 10.1016/j.bpj.2012.02.001.

[55]

J. Zhang and T. Zhou, Promoter-mediated transcriptional dynamics, Biophy. J., 106 (2014), 479-488. doi: 10.1016/j.bpj.2013.12.011.

[56]

L. Zhang, K. Radtke, L. Zheng, A. Q. Cai, T. F. Schilling and Q. Nie, Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain, Mol. Syst. Biol., 8 (2012), 613. doi: 10.1038/msb.2012.45.

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R. Zhu, A. S. Ribeiro, D. Salahub and S. A. Kauffman, Studying genetic regulatory networks at the molecular level: Delayed reaction stochastic models, J. Theor. Biol., 246 (2007), 725-745. doi: 10.1016/j.jtbi.2007.01.021.

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show all references

References:
[1]

M. Acar, J. T. Mettetal and A. van Oudenaarden, Stochastic switching as a survival strategy in fluctuating environments, Nat. Genet., 40 (2008), 71-475. doi: 10.1038/ng.110.

[2]

U. Alon, An Introduction to Systems Biology, Chapman & Hall/RCR, New York, 2006.

[3]

I. Artsimovitch and R. Landick, The transcriptional regulator rfah stimulates RNA chain synthesis after recruitment to elongation complexes by the exposed on template DNA strand, Cell, 109 (2002), 193-203.

[4]

M. J. Bailey, C. Hughes and V. Koronakis, Rfah and the ops element, components of a novel system controlling bacterial transcription elongation, Mol. Microbiol., 26 (1997), 845-851.

[5]

W. J. Blake, C. R. Cantor Mads Kærn and J. J. Collins, Noise in eukaryotic gene expression, Nature, 422 (2003), 633-637. doi: 10.1038/nature01546.

[6]

D. Bratsun, D. Volfson, L. S. Tsimring, and J. Hasty, Delay-induced stochastic oscillations in gene regulation, Proc. Natl. Acad. Sci. USA, 102 (2005), 14593-14598. doi: 10.1073/pnas.0503858102.

[7]

L. Cai, N. Friedman and X. S. Xie, Stochastic protein expression in individual cells at the single molecule level, Nature, 440 (2006), 358-362. doi: 10.1038/nature04599.

[8]

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), 442-446. doi: 10.1126/science.1161427.

[9]

D. L. Cook, A. N. Gerber and S. J. Tapscott, Modeling stochastic gene expression: Implications for haploinsufficiency, Proc. Natl. Acad. Sci. USA, 95 (1998), 15641-15646. doi: 10.1073/pnas.95.26.15641.

[10]

X. Darzacq, Y. Shav-Tal, V. de Turris, Y. Brody, S. M. Shenoy, R. D. Phair and R. H. Singer, In vivo dynamics of RNA polymerase II transcription, Nat. Struct. Mol. Biol., 14 (2007), 796-806. doi: 10.1038/nsmb1280.

[11]

M. Dobrzyński and F. J. Bruggeman, Elongation dynamics shape bursty transcription and translation, Proc. Natl. Acad. Sci. USA, 106 (2009), 2583-2588. doi: 10.1073/pnas.0803507106.

[12]

A. Dvir, Promoter escape by RNA polymerase II, Biochim. Biophys. Acta., 1577 (2002), 208-223. doi: 10.1016/S0167-4781(02)00453-0.

[13]

M. B. Elowitz, A. J. Levine, E. D. Siggia and P. S. Swain, Stochastic gene expression in a single cell, Science, 297 (2002), 1183-1186. doi: 10.1126/science.1070919.

[14]

A. M. Femino, F. S. Fay, K. Fogarty and R. H. Singer, Visualization of single RNA transcripts in situ, Science, 280 (1998), 585-590. doi: 10.1126/science.280.5363.585.

[15]

N. Friedman, L. Cai and X. S. Xie, Linking stochastic dynamics to population distribution: an analytical framework of gene expression, Phys. Rev. Lett., 97 (2006), 168302. doi: 10.1103/PhysRevLett.97.168302.

[16]

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. doi: 10.1016/j.cell.2005.09.031.

[17]

S. R. Goldman, R. H. Ebright and B. E. Nickels, Direct detection of abortive RNA transcripts in vivo, Science, 324 (2009), 927-928. doi: 10.1126/science.1169237.

[18]

T. Hearn, C. Haurie and M. C. Mackey, Cyclical neutropenia and the peripheral control of white blood cell production, J. Theor. Biol., 192 (1998), 167-187. doi: 10.1006/jtbi.1997.0589.

[19]

K. M. Herbert, A. La Porta, B. J. Wong, R. A. Mooney, K. C. Neuman, R. Landick and S. M. Block, Sequence-resolved detection of pausing by single RNA polymerase molecules, Cell, 125 (2006), 1083-1094. doi: 10.1016/j.cell.2006.04.032.

[20]

M. Kærn, T. C. Elston, W. J. Blake and J. J. Collins, Stochasticity in gene expression expression: From theories to phenotypes, Nat. Rev. Genet., 6 (2005), 451-464.

[21]

M. Kerszberg, Noise, delays, robustness, canalization and all that, Curr. Opin. Genet. Dev., 14 (2004), 440-445. doi: 10.1016/j.gde.2004.06.001.

[22]

M. L. Kireeva, B. Hancock, G. H. Cremona, W. Walter, V. M. Studitsky and M. Kashlev, Nature of the nucleosomal barrier to RNA polymerase II, Mol. Cell, 18 (2005), 97-108. doi: 10.1016/j.molcel.2005.02.027.

[23]

J. Lei, Stochasticity in single gene expression with both intrinsic noise and fluctuation in kinetic parameters, J. Theor. Biol., 256 (2009), 485-492. doi: 10.1016/j.jtbi.2008.10.028.

[24]

J. Lei, G. He, H. Liu and Q. Nie, A delay model for noise-induced bi-directional switching, Nonlinearity, 22 (2009), 2845-2859. doi: 10.1088/0951-7715/22/12/003.

[25]

B. Munsky, G. Neuert and A. van Oudenaarden, Using gene expression noise to understand gene regulation, Science, 336 (2012), 183-187. doi: 10.1126/science.1216379.

[26]

T. O'Brien and J. T. Lis, Rapid changes in drosophila transcription after an instantaneous heat shock, Mol. Cell. Biol., 13 (1993), 3456-3463.

[27]

G. Orphanides and D. Reinberg, A unified theory of gene expression, Cell, 108 (2002), 439-451. doi: 10.1016/S0092-8674(02)00655-4.

[28]

E. M. Ozbudak, M. Thattai, I. Kurtser, A. D. Grossman and A. van Oudenaarden, Regulation of noise in the expression of a single gene, Nat. Genet., 31 (2002), 69-73. doi: 10.1038/ng869.

[29]

J. Paulsson, Summing up the noise in gene networks, Nature, 427 (2004), 415-418. doi: 10.1038/nature02257.

[30]

J. Paulsson, Models of stochastic gene expression, Phys. Life Rev., 2 (2005), 157-175. doi: 10.1016/j.plrev.2005.03.003.

[31]

J. M. Pedraza and J. Paulsson, Effects of molecular memory and bursting on fluctuations in gene expression, Science, 319 (2008), 339-343. doi: 10.1126/science.1144331.

[32]

S. Proshkin, A. R. Rahmouni, A. Mironov and E. Nudler, Cooperation between translating ribosomes and RNA polymerase in transcription elongation, Science, 328 (2010), 504-508. doi: 10.1126/science.1184939.

[33]

N. J. Proudfoot, A. Furger and M. J. Dye, Integrating mRNA processing with transcription, Cell, 108 (2002), 501-572. doi: 10.1016/S0092-8674(02)00617-7.

[34]

T. Rajala, A. Häkkinen, S. Healy, O. Yli-Harja and A. S. Ribeiro, Effects of transcriptional pausing on gene expression dynamics, PLoS Comp. Biol., 6 (2010), e1000704. doi: 10.1371/journal.pcbi.1000704.

[35]

D. B. Renner, Y. Yamaguchi, T. Wada, H. Handa and D. H. Price, A highly purified RNA polymerase II elongation control system, J. Biol. Chem., 276 (2001), 42601-42609. doi: 10.1074/jbc.M104967200.

[36]

A. S. Ribeiro, Stochastic and delayed stochastic models of gene expression and regulation, Math. Biosci., 223 (2010), 1-11. doi: 10.1016/j.mbs.2009.10.007.

[37]

A. S. Ribeiro, O-P. Smolander, T. Rajala, A. Häkkinen and O. Yli-Harja, Delayed stochastic model of transcription at the single nucleotide level, J. Comput. Biol., 16 (2009), 539-553. doi: 10.1089/cmb.2008.0153.

[38]

M. R. Roussel and R. Zhu, Validation of an algorithm for delay stochastic simulation of transcription and translation in prokaryotic gene expression, Phys. Biol., 3 (2006), 274-284. doi: 10.1088/1478-3975/3/4/005.

[39]

V. Shahrezaei, J. F. Ollivier and P. S. Swain, Colored extrinsic fluctuations and stochastic gene expression, Mol. Syst. Biol., 4 (2008), 196. doi: 10.1038/msb.2008.31.

[40]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256-17261. doi: 10.1073/pnas.0803850105.

[41]

A. Shundrovsky, T. J. Santangelo, J. W. Roberts and M. D. Wang, A single-molecule technique to study sequence-dependent transcription pausing, Biophy. J., 87 (2004), 3945-3953. doi: 10.1529/biophysj.104.044081.

[42]

J. Sticker, S. Cookson, M. R. Bennett, W. H. Mather, L. S. Tsimring and J. Hasty, A fast, robust and tunable synthetic gene oscillator, Nature, 456 (2008), 516-519.

[43]

G. M. Süel, J. Garcia-Ojalvo, L. M. Liberman and M. B. Elowitz, An excitable gene regulatory circuit induces transient cellular differentiation, Nature, 440 (2006), 545-550.

[44]

P. S. Swain, M. B. Elowitz and E. D. Siggia, Intrinsic and extrinsic contributions to stochasticity in gene expression, Proc. Natl. Acad. Sci. USA, 99 (2002), 12795-12800. doi: 10.1073/pnas.162041399.

[45]

I. A. Swinburne and P. A. Silver, Intron delays and transcriptional timing during development, Dev. Cell, 14 (2008), 324-330. doi: 10.1016/j.devcel.2008.02.002.

[46]

C. N. Tennyson, H. J. Klamut and R. G. Worton, The human dystrophin gene requires 16 hours to be transcribed and is cotranscriptionally spliced, Nat. Genet., 9 (1995), 184-190. doi: 10.1038/ng0295-184.

[47]

T. Tian, K. Burrage, P. M. Burrage and M. Carletti, Stochastic delay differential equation for genetic regulatory networks, J. Comput. Appl. Math., 205 (2007), 696-707. doi: 10.1016/j.cam.2006.02.063.

[48]

M. Tigges, T. T. Marquez-Lago, J. Stelling, and M. Fussenegger, A tunable synthetic mammalian oscillator, Nature, 457 (2009), 309-312. doi: 10.1038/nature07616.

[49]

T-L. To and N. Maheshri, Noise can induce bimodality in positive transcriptional feedback loops without bistability, Science, 327 (2010), 1142-1145. doi: 10.1126/science.1178962.

[50]

S. X. Xie, Paul J. Choi, G-W. Li, N. K. Lee and G. Lia, Single-molecule approach to molecular biology in living bacterial cells, Ann. Rev. Biophy., 37 (2008), 417-444. doi: 10.1146/annurev.biophys.37.092607.174640.

[51]

M. Yonaha and N. J. Proudfoot, Specific transcriptional pausing activates polyadenylation in a coupled in vitro system, Mol. Cell, 3 (1999), 593-600. doi: 10.1016/S1097-2765(00)80352-4.

[52]

R. Yvinec, C. j. Zhuge, J. Lei and M. C. Mackey, Adiabatic reduction of a model of stochastic gene expression with jump markov process, J. Math. Biol., 68 (2014), 1051-1070. doi: 10.1007/s00285-013-0661-y.

[53]

E. Zavala and T. T. Marquez-Lago, Delays induce novel stochastic effects in negative feedback gene circuits, Biophy. J., 106 (2014), 467-478. doi: 10.1016/j.bpj.2013.12.010.

[54]

J. Zhang, L. Chen and T. Zhou, Analytical distribution and tunability of noise in a model of promoter progress, Biophy. J., 102 (2012), 1247-1257. doi: 10.1016/j.bpj.2012.02.001.

[55]

J. Zhang and T. Zhou, Promoter-mediated transcriptional dynamics, Biophy. J., 106 (2014), 479-488. doi: 10.1016/j.bpj.2013.12.011.

[56]

L. Zhang, K. Radtke, L. Zheng, A. Q. Cai, T. F. Schilling and Q. Nie, Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain, Mol. Syst. Biol., 8 (2012), 613. doi: 10.1038/msb.2012.45.

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