Effect of Rate Constants in TF Regulated Gene Expression

Enakshi Guru¹, Sanghamitra Chatterjee²

¹Department of Physics, Camellia Institute of Technology, Kolkata, India.
²Department of Electronics, Camellia Institute of Technology, Kolkata, India.

DOI: 10.4236/oalib.1101147                

Abstract

Simple mathematical model of gene expression has been studied thoroughly in this paper. We assume that protein synthesis and protein decay are deterministic in nature whereas transition from active to inactive state is totally stochastic. The probability distribution function of transcript number is calculated and evidence of binary and graded response has been observed for different reaction rates. Slow and fast kinetics have been studied explicitly. Different rate constants play a significant role in calculating distribution function (PDF) and mean value of TF regulated gene expression. It is seen that rate constants control the variance as well. A small change in the value of the rate constant gives a significant change in average protein value. The randomness of gene expression is reduced with increasing value of one of the rate constants. The main focus of this paper is to observe the effect of rate constants in transcription factor regulated gene expression.

Keywords

Transcription Factor Regulation, Binary and Graded Response, Rate of Protein Activation, Fast and Slow Kinetics, Probability Distribution Function

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Alberts, B., Bray, D., Lewis, J., Ruff, M. and Roberts, K. (1989) Molecular Biology of the Cell. Garland Publishing, New York.
[2]	Andrianantoandro, E., Basu, S., Karig, D.K. and Weiss, R. (2006) Synthetic Biology: New Engineering Rules for an Emerging Discipline. Molecular Synthetic Biology, 2, 1-4.
[3]	Hasty, J., McMillen, D., Isaacs, F. and Collins, J.J. (2001) Computational Studies of Gene Regulatory Network: In Numeromolecular Biology. Nature Reviews Genetics, 2, 268. http://dx.doi.org/10.1038/35066056
[4]	Hasty, J., McMillen, D. and Collins, J.J. (2002) Engineered Genetic Circuits. Nature, 420, 224-230. http://dx.doi.org/10.1038/nature01257
[5]	Alon, U. (2006) An Introduction to System Biology: Design Principles of Biological Circuits. Chapman and Hall, London.
[6]	Karmakar, R. and Bose, I. (2006) Stochastic Model of Transcription Factor-Regulated Gene Expression. Physical Biology, 3, 200. http://dx.doi.org/10.1088/1478-3975/3/3/005
[7]	Gutierrez, P.S., Monteoliva, D. and Diambra, L. (2012) Cooperative Binding of Transcription Factors Promotes Bimodal Gene Expression Response. PLoS One, 7, e44812. http://dx.doi.org/10.1371/journal.pone.0044812
[8]	Gutierrez, P.S., Monteoliva, D. and Diambra, L. (2009) Role of Cooperative Binding on Noise Expression. Physical Review E, 80, Article ID: 011914. http://dx.doi.org/10.1103/PhysRevE.80.011914
[9]	Pirone, J.R. and Elston, T.C. (2004) Fluctuation in Transcription Factor Binding Can Explain the Graded and Binary Response Observed in Inducible Gene Expression. Journal of Theoretical Biology, 226, 111-121. http://dx.doi.org/10.1016/j.jtbi.2003.08.008
[10]	Karmakar, R. and Bose, I. (2004) Graded and Binary Response in Stochastic Gene Expression. Physical Biology, 1, 197. http://dx.doi.org/10.1088/1478-3967/1/4/001
[11]	Novick, A. and Weiner, M. (1957) Enzyme Induction as an All-or-None Phenomenon. Proceedings of the National Academy of Sciences of the United States of America, 43, 553-566. http://dx.doi.org/10.1073/pnas.43.7.553
[12]	Blake, W.J., Kaern, M., Cantor, C.R. and Collins, J.J. (2003) Noise in Eukaryotic Gene Expression. Nature, 422, 633-637. http://dx.doi.org/10.1038/nature01546
[13]	Blake, W.J., Kaern, M., Cantor, C.R. and Collins, J.J. (2005) Stochasticity in Gene Expression: From the Theories of Phenotypes. Nature Reviews Genetics, 6, 451-464. http://dx.doi.org/10.1038/nrg1615
[14]	McAdams, H.H. and Arkin, A. (1997) Stochastic Mechanism in Gene Expression. Proceedings of the National Academy of Sciences of the United States of America, 94, 814-819. http://dx.doi.org/10.1073/pnas.94.3.814
[15]	Elowitz, M.B., Liebler, S., Siggia, A.J. and Swain, E.D. (2002) Stochastic Gene Expression in a Single Cell. Science, 297, 1183-1186.
[16]	Guru, E. and Chatterjee, S. (2013) Study of Synthetic Biomolecular Network in Escherichia Coli. International Journal of Biophysics, 3, 38-50.
[17]	Rosenfeld, N., Young, J.W., Alon, U., Swain, P.S. and Elowitz, M.B. (2005) Gene Regulation at the Single Cell Level. Science, 307, 1962-1965. http://dx.doi.org/10.1126/science.1106914
[18]	Thattai, M. and Van Oudenaarden, A. (2001) Intrinsic Noise in Gene Regulatory Network. Proceedings of the National Academy of Sciences of the United States of America, 98, 8614-8619. http://dx.doi.org/10.1073/pnas.151588598
[19]	Ozbudak, E.M., Thattai, M., Kurlser, I., Grossman, A.D. and Van Qudenaarden, A. (2002) Regulation of Noise in the Expression of a Single Gene. Nature Genetics, 31, 69-73. http://dx.doi.org/10.1038/ng869
[20]	Swain, P.S., Elowitz, M.B. and Siggia, E.D. (2002) Intrinsic and Extrinsic Contribution to Stochasticity in Gene Expression. Proceedings of the National Academy of Sciences of the United States of America, 99, 12795-12800. http://dx.doi.org/10.1073/pnas.162041399
[21]	Thattai, V. and Qudenaarden, A. (2001) Intrinsic Noise in Gene Regulatory Networks. Proceedings of the National Academy of Sciences of the United States of America, 98, 8614-8619. http://dx.doi.org/10.1073/pnas.151588598
[22]	Cook, D.L., Gerber, A.N. and Tapscott, S.J. (1998) Stochastic Gene Expression: Implications for Haploinsufficiency. Proceedings of the National Academy of Sciences of the United States of America, 95, 15641-15647. http://dx.doi.org/10.1073/pnas.95.26.15641
[23]	Gillespie, D.T. (1977) Exact Stochastic Simulation of Coupled Chemical Reaction. The Journal of Physical Chemistry, 81, 2340-2361. http://dx.doi.org/10.1021/j100540a008