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Gene expression in self-repressing system with multiple gene copies. (English) Zbl 1273.92021

Summary: We analyze a simple model of a self-repressing system with multiple gene copies. Protein molecules may bound to DNA promoters and block their own transcription. We derive analytical expressions for the variance of the number of protein molecules in the stationary state in the self-consistent mean-field approximation. We show that the Fano factor (the variance divided by the mean value) is bigger for the one-gene case than for two gene copies and the difference decreases to zero as frequencies of binding and unbinding increase to infinity.

MSC:

92C40 Biochemistry, molecular biology
92D10 Genetics and epigenetics
37N25 Dynamical systems in biology
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[1] Barzel, B., & Biham, O. (2011). Binomial moment equations for stochastic reaction systems. Phys. Rev. Lett., 106, 150602. · doi:10.1103/PhysRevLett.106.150602
[2] Barzel, B., Biham, O., & Kupferman, R. (2011). Analysis of the multiplane method for stochastic simulations of reaction networks with fluctuations. Multiscale Model. Simul., 6, 963–982. · Zbl 1149.60318 · doi:10.1137/070685245
[3] Becskei, A., & Serrano, L. (2000). Engineering stability in gene networks by autoregulation. Nature, 405, 590–593. · doi:10.1038/35014651
[4] Hat, B., Paszek, P., Kimmel, M., Piechór, K., & Lipniacki, T. (2007). How the number of alleles influences gene expression. J. Stat. Phys., 128, 511–533. · Zbl 1115.92028 · doi:10.1007/s10955-006-9218-4
[5] Hornos, J. E., Schultz, D., Innocentini, G. C., Wang, J., Walczak, A. M., Onuchic, J. N., & Wolynes, P. G. (2005). Self-regulating gene: an exact solution. Phys. Rev. E, 72, 051907. · doi:10.1103/PhysRevE.72.051907
[6] Huang, K. (1963). Statistical mechanics. New York: Wiley.
[7] Kepler, T., & Elston, T. (2001). Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations. Biophys. J., 81, 3116–3136. · doi:10.1016/S0006-3495(01)75949-8
[8] Komorowski, M., Miekisz, J., & Kierzek, A. (2009). Translational repression contributes greater noise to gene expression than transcriptional repression. Biophys. J., 96, 372–384. · doi:10.1016/j.bpj.2008.09.052
[9] Lipniacki, T., Paszek, P., Marciniak-Czochra, A., Brasier, A. R., & Kimmel, M. (2006). Transcriptional stochasticity in gene expression. J. Theor. Biol., 238, 348–367. · doi:10.1016/j.jtbi.2005.05.032
[10] Lipshtat, A., Perets, H., Balaban, N., & Biham, O. (2005). Modeling of negative autoregulated genetic networks in single cells. Gene, 347, 265–271. · doi:10.1016/j.gene.2004.12.016
[11] Loinger, A., & Biham, O. (2009). Analysis of genetic toggle switch systems encoded on plasmids. Phys. Rev. Lett., 103, 068104. · doi:10.1103/PhysRevLett.103.068104
[12] Ma, S.-K. (1985). Statistical mechanics. Singapore: World Scientific. · Zbl 0952.82500
[13] Miekisz, J., & Szymańska, P. (2012). On spins and genes. Math. Appl., 40(1), 15–25. · Zbl 1320.00038
[14] Nasell, I. (2003). An extension of the moment closure method. Theor. Popul. Biol., 64, 233–239. · Zbl 1104.92051 · doi:10.1016/S0040-5809(03)00074-1
[15] Ohkubo, J. (2010). Approximation scheme based on effective interactions for stochastic gene regulation. Phys. Rev. E, 83, 041915.
[16] Paszek, P. (2007). Modeling stochasticity in gene regulation: characterization in the terms of the underlying distribution function. Bull. Math. Biol., 69, 1597–1601. · Zbl 1298.92068 · doi:10.1007/s11538-006-9176-7
[17] Paulsson, J. (2004). Summing up the noise in gene networks. Nature, 427, 415–418. · doi:10.1038/nature02257
[18] Paulsson, J. (2005). Models of stochastic gene expression. Phys. Life Rev., 2, 157–175. · doi:10.1016/j.plrev.2005.03.003
[19] Qian, H., Shi, P.-Z., & Xing, J. (2009). Stochastic bifurcation, slow fluctuations, and bistability as an origin of biochemical complexity. Phys. Chem. Chem. Phys., 11, 4861–4870. · doi:10.1039/b900335p
[20] Ramos, A. F., Innocentini, G. P., & Hornos, J. E. (2011). Exact time dependent solutions for a self-regulating gene. Phys. Rev. E, 83, 062902. · doi:10.1103/PhysRevE.83.062902
[21] Simpson, M., Cox, L. C. D., & Sayler, G. S. (2003). Frequency domain analysis of noise in autoregulated gene circuits. Proc. Natl. Acad. Sci. USA, 100, 4551–4556. · doi:10.1073/pnas.0736140100
[22] Swain, P. S., Elowitz, M. B., & Siggia, E. D. (2002). Intrinsic and extrinsic contributions to stochasticity in gene expression. Proc. Natl. Acad. Sci. USA, 99, 12795–12800. · doi:10.1073/pnas.162041399
[23] Thattai, M., & van Oudenaarden, A. (2001). Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. USA, 98, 8614–8619. · doi:10.1073/pnas.151588598
[24] Van Kampen, N. (1997). Stochastic processes in physics and chemistry (2nd ed.). Amsterdam: Elsevier. · Zbl 0511.60038
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