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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:
[1]

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

[2]

U. Alon, An Introduction to Systems Biology,, Chapman & Hall/RCR, (2006).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[5]

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

[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.  doi: 10.1073/pnas.0503858102.  Google Scholar

[7]

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

[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.  doi: 10.1126/science.1161427.  Google Scholar

[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.  doi: 10.1073/pnas.95.26.15641.  Google Scholar

[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.  doi: 10.1038/nsmb1280.  Google Scholar

[11]

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

[12]

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

[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.  doi: 10.1126/science.1070919.  Google Scholar

[14]

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

[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).  doi: 10.1103/PhysRevLett.97.168302.  Google Scholar

[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.  doi: 10.1016/j.cell.2005.09.031.  Google Scholar

[17]

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

[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.  doi: 10.1006/jtbi.1997.0589.  Google Scholar

[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.  doi: 10.1016/j.cell.2006.04.032.  Google Scholar

[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.   Google Scholar

[21]

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

[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.  doi: 10.1016/j.molcel.2005.02.027.  Google Scholar

[23]

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

[24]

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

[25]

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

[26]

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

[27]

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

[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.  doi: 10.1038/ng869.  Google Scholar

[29]

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

[30]

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

[31]

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

[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.  doi: 10.1126/science.1184939.  Google Scholar

[33]

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

[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).  doi: 10.1371/journal.pcbi.1000704.  Google Scholar

[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.  doi: 10.1074/jbc.M104967200.  Google Scholar

[36]

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

[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.  doi: 10.1089/cmb.2008.0153.  Google Scholar

[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.  doi: 10.1088/1478-3975/3/4/005.  Google Scholar

[39]

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

[40]

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

[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.  doi: 10.1529/biophysj.104.044081.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.1073/pnas.162041399.  Google Scholar

[45]

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

[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.  doi: 10.1038/ng0295-184.  Google Scholar

[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.  doi: 10.1016/j.cam.2006.02.063.  Google Scholar

[48]

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

[49]

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

[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.  doi: 10.1146/annurev.biophys.37.092607.174640.  Google Scholar

[51]

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

[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.  doi: 10.1007/s00285-013-0661-y.  Google Scholar

[53]

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

[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.  doi: 10.1016/j.bpj.2012.02.001.  Google Scholar

[55]

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

[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).  doi: 10.1038/msb.2012.45.  Google Scholar

[57]

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.  doi: 10.1016/j.jtbi.2007.01.021.  Google Scholar

[58]

R. Zhu and D. Salahub, Delay stochastic simulation of sinlge-gene expression reveals a detailed relationship between protein noise and mean abundance,, FEBS Lett., 582 (2008), 2905.   Google Scholar

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.  doi: 10.1038/ng.110.  Google Scholar

[2]

U. Alon, An Introduction to Systems Biology,, Chapman & Hall/RCR, (2006).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[5]

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

[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.  doi: 10.1073/pnas.0503858102.  Google Scholar

[7]

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

[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.  doi: 10.1126/science.1161427.  Google Scholar

[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.  doi: 10.1073/pnas.95.26.15641.  Google Scholar

[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.  doi: 10.1038/nsmb1280.  Google Scholar

[11]

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

[12]

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

[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.  doi: 10.1126/science.1070919.  Google Scholar

[14]

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

[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).  doi: 10.1103/PhysRevLett.97.168302.  Google Scholar

[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.  doi: 10.1016/j.cell.2005.09.031.  Google Scholar

[17]

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

[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.  doi: 10.1006/jtbi.1997.0589.  Google Scholar

[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.  doi: 10.1016/j.cell.2006.04.032.  Google Scholar

[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.   Google Scholar

[21]

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

[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.  doi: 10.1016/j.molcel.2005.02.027.  Google Scholar

[23]

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

[24]

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

[25]

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

[26]

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

[27]

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

[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.  doi: 10.1038/ng869.  Google Scholar

[29]

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

[30]

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

[31]

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

[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.  doi: 10.1126/science.1184939.  Google Scholar

[33]

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

[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).  doi: 10.1371/journal.pcbi.1000704.  Google Scholar

[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.  doi: 10.1074/jbc.M104967200.  Google Scholar

[36]

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

[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.  doi: 10.1089/cmb.2008.0153.  Google Scholar

[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.  doi: 10.1088/1478-3975/3/4/005.  Google Scholar

[39]

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

[40]

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

[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.  doi: 10.1529/biophysj.104.044081.  Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[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.  doi: 10.1073/pnas.162041399.  Google Scholar

[45]

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

[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.  doi: 10.1038/ng0295-184.  Google Scholar

[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.  doi: 10.1016/j.cam.2006.02.063.  Google Scholar

[48]

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

[49]

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

[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.  doi: 10.1146/annurev.biophys.37.092607.174640.  Google Scholar

[51]

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

[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.  doi: 10.1007/s00285-013-0661-y.  Google Scholar

[53]

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

[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.  doi: 10.1016/j.bpj.2012.02.001.  Google Scholar

[55]

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

[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).  doi: 10.1038/msb.2012.45.  Google Scholar

[57]

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.  doi: 10.1016/j.jtbi.2007.01.021.  Google Scholar

[58]

R. Zhu and D. Salahub, Delay stochastic simulation of sinlge-gene expression reveals a detailed relationship between protein noise and mean abundance,, FEBS Lett., 582 (2008), 2905.   Google Scholar

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