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Bistability and switching in the lysis/lysogeny genetic regulatory network of bacteriophage \(\lambda\). (English) Zbl 1439.92096
Summary: Bistability and switching are two important aspects of the genetic regulatory network of \(\lambda\) phage. Positive and negative feedbacks are key regulatory mechanisms in this network. By the introduction of threshold values, the developmental pathway of \(\lambda\) phage is divided into different stages. If the protein level reaches a threshold value, positive or negative feedback will be effective and regulate the process of development. Using this regulatory mechanism, we present a quantitative model to realize bistability and switching of \(\lambda\) phage based on experimental data. This model gives descriptions of decisive mechanisms for different pathways in induction. A stochastic model is also introduced for describing statistical properties of switching in induction. A stochastic degradation rate is used to represent intrinsic noise in induction for switching the system from the lysogenic pathway to the lysis pathway. The approach in this paper represents an attempt to describe the regulatory mechanism in genetic regulatory network under the influence of intrinsic noise in the framework of continuous models.

MSC:
92C42 Systems biology, networks
92D10 Genetics and epigenetics
92C70 Microbiology
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[1] Ackers, G. K.; Johnson, A. D.; Shea, M. A., Quantitative model for gene regulation by λ phage repressor, Proc. Natl. Acad. Sci. USA, 79, 1129-1133 (1982)
[2] Alon, U.; Surette, M. G.; Barkai, N.; Leibler, S., Robustness in bacterial chemotaxis, Nature (London), 397, 168-171 (1999)
[3] Arkin, A.; Ross, J.; McAdams, H. H., Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected Escherichia coli cells, Genetics, 149, 1633-1648 (1998)
[4] Barkai, N.; Leibler, S., Robustness in simple biochemical networks, Nature (London), 387, 913-917 (1997)
[5] Becskei, A.; Serrano, L., Engineering stability in gene networks by autoregulation, Nature (London), 405, 590-593 (2000)
[6] Cherry, J. L.; Adler, F. R., How to make a biological switch, J. Theor. Biol., 203, 117-133 (2000)
[7] Darling, P. J.; Holt, J. M.; Ackers, G. K., Coupled energetics of λcro repressor self-assembly and site-specific DNA operator binding II: cooperative interactions of cro dimers, J. Mol. Biol., 302, 625-638 (2000)
[8] Dodd, I. B.; Perkins, A. J.; Tsemitsidis, D.; Egan, J. B., Octamerization of λ cI repressor is needed for effective repression of P_RM and efficient switching from lysogeny, Genes Dev., 15, 3013-3022 (2001)
[9] Gardner, T. S.; Collins, J. J., Neutralizing noise in gene networks, Nature (London), 405, 520-521 (2000)
[10] Gardner, T. S.; Cantor, C. R.; Collins, J. J., Construction of a genetic toggle switch in Escherichia coli, Nature (London), 403, 339-342 (2000)
[11] Gillespie, D. T., Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81, 2340-2361 (1977)
[12] Gillespie, D. T., Approximate accelerated stochastic simulation of chemically reacting systems, J. Chem. Phys., 115, 1716-1733 (2001)
[13] Gonze, D.; Halloy, J.; Goldbeter, A., Robustness of circadian rhythms with respect to molecular noise, Proc. Natl Acad. Sci. USA, 99, 673-678 (2002)
[14] Hasty, J.; Collins, J. J., Translating the noise, Nature Genet., 31, 13-14 (2002)
[15] Hasty, J.; Pradines, J.; Dolnik, M.; Collins, J. J., Noise-based switches and amplifiers for gene expression, Proc. Natl Acad. Sci. USA, 97, 2075-2080 (2000)
[16] Hasty, J.; Issacs, F.; Dolnik, M.; McMillen, D.; Collins, J. J., Design gene networktowards fundamental cellular control, Chaos, 11, 207-220 (2001) · Zbl 1029.92011
[17] Hasty, J.; McMillen, D.; Isaacs, F.; Collins, J. J., Computational studies of gene regulatory networksin numero molecular biology, Nat. Rev. Genet., 2, 268-279 (2001)
[18] Johnson, A. D.; Poteete, A. R.; Lauer, G.; Sauer, R. T.; Ackers, G. K.; Ptashne, M., λ repressor and cro-components of an efficient molecular switch, Nature (London), 294, 217-223 (1981)
[19] Van Kampen, N. G., Stochastic Processes in Physics and Chemistry (1992), North-Holland: North-Holland Amsterdam · Zbl 0974.60020
[20] Maurer, R.; Meyer, B. J.; Ptashne, M., Gene regulation at the right operator O_P of bacteriophage λ, I. O_R3 and autogenous negative control by repressor, J. Mol. Biol., 139, 147-161 (1980)
[21] McAdams, H. H.; Arkin, A., Stochastic mechanism in gene expression, Proc. Natl Acad. Sci. USA, 94, 814-819 (1997)
[22] Meyer, B. J.; Maurer, R.; Ptashne, M., Gene regulation at the right operator O_P of bacteriophage λ, II O_R1, O_R2 and O_R3their roles in mediating the effects of repressor and cro, J. Mol. Biol., 139, 163-194 (1980)
[23] Ptashne, M., A Genetic Switch: Phage λ and Higher Organisms (1992), Cell Press: Cell Press Cambridge, MA
[24] Ptashne, M.; Jeffrey, A.; Johnson, A. D.; Maurer, R.; Meyer, B. J.; Pabo, C. O.; Roberts, T. M.; Sauer, R. T., How the λ repressor and cro work, Cell, 19, 1-11 (1980)
[25] Reinitz, J.; Vaisnys, J. R., Theoretical and experimental analysis of the phage lambda genetic switch missing levels of co-operativity, J. Theor. Biol., 145, 295-318 (1990)
[26] Shea, M. A.; Ackers, G. K., The O_R control system of bacteriophage Lambdaa physical-chemical model for gene regulation, J. Mol. Biol., 181, 211-230 (1985)
[27] Smolen, P.; Baxter, D. A.; Byrne, J. H., Mathematical modelling of gene networks, Neuron, 26, 567-580 (2000)
[28] Thattai, M.; van Oudenaarden, A., Intrinsic noise in gene regulatory networks, Proc. Natl Acad. Sci. USA, 98, 8614-8619 (2001)
[29] Tian, T.; Burrage, K., Implicit Taylor methods for stiff stochastic differential equations, Appl. Numer. Math., 38, 167-185 (2001) · Zbl 0983.65007
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