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Immunosuppressant treatment dynamics in renal transplant recipients: an iterative modeling approach
Distribution profiles in gene transcription activated by the cross-talking pathway
1. | Center for Applied Mathematics, Guangzhou University, Guangzhou 510006, China |
2. | School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China |
Gene transcription is a stochastic process, manifested by the heterogeneous mRNA distribution in an isogenic cell population. Bimodal distribution has been observed in the transcription of stress responsive genes which have evolved to be easily turned on and easily turned off. This is against the conclusion in the classical two-state model that bimodality occurs only when the gene is hardly turned on and hardly turned off. In this paper, we extend the gene activation process in the two-state model by introducing the cross-talking pathway that involves the random selection between a spontaneous weak basal pathway and a stress-induced strong signaling pathway. By deriving exact forms of mRNA distribution at steady-state, we find that the cross-talking pathway is much more likely to trigger the bimodal distribution. Our further analysis reveals an observed transition among the decaying, bimodal and unimodal mRNA distribution for stress gene upon enhanced stimulations. Especially, the bimodality occurs when the stress-induced signalling pathway is more frequently selected, reinforcing the assertion that bimodal transcription is a general feature of stress genes in response to environmental change.
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F. Jiao, M. Tang and J. Yu,
Distribution profiles and their dynamic transition in stochastic gene transcription, J. Differential Equations, 254 (2013), 3307-3328.
doi: 10.1016/j.jde.2013.01.019. |
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D. L. Jones, R. C. Brewster and R. Phillips,
Promoter architecture dictates cell-to-cell variability in gene expression, Science, 346 (2014), 1533-1536.
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J. Kuang, M. Tang and J. Yu,
The mean and noise of protein numbers in stochastic gene expression, J. Math. Biol., 67 (2013), 261-291.
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D. R. Larson, C. Fritzsch, L. Sun, X. Meng, D. S. Lawrence and R. H. Singer, Direct observation of frequency modulated transcription in single cells using light activation,
eLife, 2 (2013), e00750.
doi: 10.7554/eLife.00750. |
[11] |
Q. Li, L. Huang and J. 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. |
[12] |
Y. Li, M. Tang and J. Yu,
Transcription dynamics of inducible genes modulated by negative regulations, Math. Med. Biol., 32 (2015), 115-136.
doi: 10.1093/imammb/dqt019. |
[13] |
G. Lin, J. Yu, Z. Zhou, Q. Sun and F. Jiao, Fluctuations of mRNA distributions in multiple pathway activated transcription,
Discrete Contin. Dyn. Syst. B, (2018), in press.
doi: 10.3934/dcdsb.2018219. |
[14] |
J. Macia, S. Regot, T. Peeters, N. Conde, R. Sol$\acute{e}$ and F. Posas, Dynamic signaling in the Hog1 MAPK pathway relies on high basal signal transduction,
Sci. Signal, 2 (2009), ra13.
doi: 10.1126/scisignal.2000056. |
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C. Miller et al., Dynamic transcriptome analysis measures rates of mRNA synthesis and decay in yeast,
Mol. Syst. Biol., 7 (2011), 458. |
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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.
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[17] |
E. Nadal, G. Ammerer and F. Posas,
Controlling gene expression in response to stress, Nat. Rev. Genet., 12 (2011), 833-845.
doi: 10.1038/nrg3055. |
[18] |
S. Paliwal,
MAPK-mediated bimodal gene expression and adaptive gradient sensing in yeast, Nature, 446 (2007), 46-51.
|
[19] |
R. B. Paris,
A Kummer-type transformation for a 2F2 hypergeometric function, J. Comput. Appl. Math., 173 (2005), 379-382.
doi: 10.1016/j.cam.2004.05.005. |
[20] |
J. Peccoud and B. Ycart,
Markovian modelling of gene-product synthesis, Theor. Popul. Biol., 48 (1995), 222-234.
|
[21] |
V. Pelechano, S. Chávez and J.E. Pérez-Ortín, A complete set of nascent transcription rates for yeast genes,
Plos One, 5 (2010), e15442. |
[22] |
S. Pelet,
Transient activation of the HOG MAPK pathway regulates bimodal Gene expression, Science, 332 (2011), 732-735.
|
[23] |
A. Raj, C.S. Peskin, D. Tranchina, D.Y. Vargas and S. Tyagi, Stochastic mRNA synthesis in mammalian cells,
PLoS Biol., 4 (2006), e309.
doi: 10.1371/journal.pbio.0040309. |
[24] |
J. Ren, F. Jiao, Q. Sun, M. Tang and J. Yu,
The dynamics of gene transcription in random environments, AIMS, 23 (2018), 3167-3194.
doi: 10.3934/dcdsb.2018224. |
[25] |
A. Sanchez and I. Golding,
Genetic determinants and cellular constraints in noisy gene expression, Science, 342 (2013), 1188-1193.
doi: 10.1126/science.1242975. |
[26] |
Q. Sun, M. Tang and J. Yu,
Modulation of gene transcription noise by competing transcription factors, J. Math. Biol., 64 (2012), 469-494.
doi: 10.1007/s00285-011-0420-x. |
[27] |
Q. Sun, M. Tang and J. Yu,
Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways, Bull. Math. Biol., 74 (2012), 375-398.
doi: 10.1007/s11538-011-9683-z. |
[28] |
M. Tang,
The mean and noise of stochastic gene transcription, J. Theor. Biol., 253 (2008), 271-280.
doi: 10.1016/j.jtbi.2008.03.023. |
[29] |
Q. Wang, L. Huang, K. Wen and J. Yu,
The mean and noise of stochastic gene transcription with cell division, Math. Biosci. Eng., 15 (2018), 1255-1270.
|
[30] |
J. Yu and X. Liu,
Monotonic dynamics of mRNA degradation by two pathways, J. Appl. Anal. Comput., 7 (2017), 1598-1612.
|
[31] |
J. Yu, Q. Sun and M. Tang,
The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway activated transcription, J. Theor. Biol., 363 (2014), 223-234.
doi: 10.1016/j.jtbi.2014.08.024. |
[32] |
D. Zenklusen, D. R. Larson and R. H. Singer,
Single-RNA counting reveals alternative modes of gene expression in yeast, Nat. Struct. Mol. Biol., 15 (2008), 1263-1271.
|
[33] |
T. Zhou and J. Zhang,
Analytical results for a multistate gene model, SIAM J. Appl. Math., 72 (2012), 789-818.
doi: 10.1137/110852887. |
show all references
References:
[1] |
W. Chu and W. Zhang,
Transformations of Kummer-type for 2F2-series and their q-analogues, J. Comput. Appl. Math., 216 (2008), 467-473.
doi: 10.1016/j.cam.2007.05.024. |
[2] |
P. L. Felmer,
Random dynamics of gene transcription activation in single cells, J. Differential Equations, 247 (2009), 1796-1816.
doi: 10.1016/j.jde.2009.06.006. |
[3] |
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. |
[4] |
S. Iyer-Biswas, F. Hayot and C. Jayaprakash, Stochasticity of gene products from transcriptional pulsing,
Phys. Rev. E, 79 (2009), 031911.
doi: 10.1103/PhysRevE.79.031911. |
[5] |
F. Jiao, Q. Sun, M. Tang, J. Yu and B. Zheng,
Distribution modes and their corresponding parameter regions in stochastic gene transcription, SIAM J. Appl. Math., 75 (2015), 2396-2420.
doi: 10.1137/151005567. |
[6] |
F. Jiao, M. Tang and J. Yu,
Distribution profiles and their dynamic transition in stochastic gene transcription, J. Differential Equations, 254 (2013), 3307-3328.
doi: 10.1016/j.jde.2013.01.019. |
[7] |
D. L. Jones, R. C. Brewster and R. Phillips,
Promoter architecture dictates cell-to-cell variability in gene expression, Science, 346 (2014), 1533-1536.
doi: 10.1126/science.1255301. |
[8] |
M. Kaern, 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.
doi: 10.1038/nrg1615. |
[9] |
J. Kuang, M. Tang and J. 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. |
[10] |
D. R. Larson, C. Fritzsch, L. Sun, X. Meng, D. S. Lawrence and R. H. Singer, Direct observation of frequency modulated transcription in single cells using light activation,
eLife, 2 (2013), e00750.
doi: 10.7554/eLife.00750. |
[11] |
Q. Li, L. Huang and J. 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. |
[12] |
Y. Li, M. Tang and J. Yu,
Transcription dynamics of inducible genes modulated by negative regulations, Math. Med. Biol., 32 (2015), 115-136.
doi: 10.1093/imammb/dqt019. |
[13] |
G. Lin, J. Yu, Z. Zhou, Q. Sun and F. Jiao, Fluctuations of mRNA distributions in multiple pathway activated transcription,
Discrete Contin. Dyn. Syst. B, (2018), in press.
doi: 10.3934/dcdsb.2018219. |
[14] |
J. Macia, S. Regot, T. Peeters, N. Conde, R. Sol$\acute{e}$ and F. Posas, Dynamic signaling in the Hog1 MAPK pathway relies on high basal signal transduction,
Sci. Signal, 2 (2009), ra13.
doi: 10.1126/scisignal.2000056. |
[15] |
C. Miller et al., Dynamic transcriptome analysis measures rates of mRNA synthesis and decay in yeast,
Mol. Syst. Biol., 7 (2011), 458. |
[16] |
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. |
[17] |
E. Nadal, G. Ammerer and F. Posas,
Controlling gene expression in response to stress, Nat. Rev. Genet., 12 (2011), 833-845.
doi: 10.1038/nrg3055. |
[18] |
S. Paliwal,
MAPK-mediated bimodal gene expression and adaptive gradient sensing in yeast, Nature, 446 (2007), 46-51.
|
[19] |
R. B. Paris,
A Kummer-type transformation for a 2F2 hypergeometric function, J. Comput. Appl. Math., 173 (2005), 379-382.
doi: 10.1016/j.cam.2004.05.005. |
[20] |
J. Peccoud and B. Ycart,
Markovian modelling of gene-product synthesis, Theor. Popul. Biol., 48 (1995), 222-234.
|
[21] |
V. Pelechano, S. Chávez and J.E. Pérez-Ortín, A complete set of nascent transcription rates for yeast genes,
Plos One, 5 (2010), e15442. |
[22] |
S. Pelet,
Transient activation of the HOG MAPK pathway regulates bimodal Gene expression, Science, 332 (2011), 732-735.
|
[23] |
A. Raj, C.S. Peskin, D. Tranchina, D.Y. Vargas and S. Tyagi, Stochastic mRNA synthesis in mammalian cells,
PLoS Biol., 4 (2006), e309.
doi: 10.1371/journal.pbio.0040309. |
[24] |
J. Ren, F. Jiao, Q. Sun, M. Tang and J. Yu,
The dynamics of gene transcription in random environments, AIMS, 23 (2018), 3167-3194.
doi: 10.3934/dcdsb.2018224. |
[25] |
A. Sanchez and I. Golding,
Genetic determinants and cellular constraints in noisy gene expression, Science, 342 (2013), 1188-1193.
doi: 10.1126/science.1242975. |
[26] |
Q. Sun, M. Tang and J. Yu,
Modulation of gene transcription noise by competing transcription factors, J. Math. Biol., 64 (2012), 469-494.
doi: 10.1007/s00285-011-0420-x. |
[27] |
Q. Sun, M. Tang and J. Yu,
Temporal profile of gene transcription noise modulated by cross-talking signal transduction pathways, Bull. Math. Biol., 74 (2012), 375-398.
doi: 10.1007/s11538-011-9683-z. |
[28] |
M. Tang,
The mean and noise of stochastic gene transcription, J. Theor. Biol., 253 (2008), 271-280.
doi: 10.1016/j.jtbi.2008.03.023. |
[29] |
Q. Wang, L. Huang, K. Wen and J. Yu,
The mean and noise of stochastic gene transcription with cell division, Math. Biosci. Eng., 15 (2018), 1255-1270.
|
[30] |
J. Yu and X. Liu,
Monotonic dynamics of mRNA degradation by two pathways, J. Appl. Anal. Comput., 7 (2017), 1598-1612.
|
[31] |
J. Yu, Q. Sun and M. Tang,
The nonlinear dynamics and fluctuations of mRNA levels in cross-talking pathway activated transcription, J. Theor. Biol., 363 (2014), 223-234.
doi: 10.1016/j.jtbi.2014.08.024. |
[32] |
D. Zenklusen, D. R. Larson and R. H. Singer,
Single-RNA counting reveals alternative modes of gene expression in yeast, Nat. Struct. Mol. Biol., 15 (2008), 1263-1271.
|
[33] |
T. Zhou and J. Zhang,
Analytical results for a multistate gene model, SIAM J. Appl. Math., 72 (2012), 789-818.
doi: 10.1137/110852887. |



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