Abstract
In biological systems, regulation plays an important role in keeping metabolite concentrations within physiological ranges. To study the dynamical implications of self-regulation, we consider a functional form used in genetic networks and couple it to a mechanism associated with chemical self-replication. For the two-variable minimal model, we find that activation can yield chemical toggles similar to those reported for gene repression in E. coli as well as more complex dynamics.
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References
Latchman, D.S.: Gene Regulation, 5th edn. Taylor and Francis, New York (2005)
Ptashne, M.: A Genetic Switch. Cold Spring Harbor Laboratory, Cold Spring Harbor (2004)
Ptashne M., Gann, A.: Genes and Signals. Cold Spring Harbor Laboratory, Cold Spring Harbor (2002)
Alon, U.: An Introduction to Systems Biology. Chapman and Hall, Boca Raton (2007)
Aguda, B.D., Friedman, A.: Models of Cellular Regulation. Oxford University Press, Oxford (2008)
Goldbeter, A.: Biological rhythms as temporal dissipative structures. Adv. Chem. Phys. 135, 253–295 (2007)
Rosenfeld, N., Elowitz, M.B., Alon, U.: Negative autoregulation speeds the response times of transcription networks. J. Mol. Biol. 323, 785–793 (2002)
Smolen, P., Baxter, D.A., Byrne, J.H.: Mathematical modeling of gene networks. Neuron 26, 567–580 (2000)
Ingolla, N.T., Murray, A.W.: Positive-feedback loops as a flexible biological module. Curr. Biol. 17, 668–677 (2007)
Guido, N.J., Wang, X., Adalsteinsson, D., McMillen, D., Hasty, J., Cantor, C.R.: A bottom-up approach to gene regulation. Nature 439, 856–860 (2006)
Atkinson, M.R., Savageau, M.A., Myers, J.T., Ninfa, A.J.: Development of genetic circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli. Cell 113, 597–607 (2003)
Cherry, J.L., Adler, F.R.: How to make a biological switch. J. Theor. Biol. 203, 117–133 (2000)
Suel, G.M., Garcia-Ojalvo, J., Liberman, L.M., Elowitz, M.B.: An excitable gene regulatory circuit induces transient cellular differentiation. Nature 440, 545–550 (2006)
Ferrell Jr., J.R.: Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Chem. Biol. 6, 140–148 (2002)
Goodwin, B.C.: Oscillatory behavior in enzymatic control processes. In: Weber, G. (ed.) Advances in Enzyme Regulation, vol. 3, pp. 425–438 (1965)
Tyson, J.J.: Periodic enzyme synthesis: reconsideration of the theory of oscillatory repression. J. Theor. Biol. 80, 27–38 (1979)
Tyson, J.J.: Periodic enzyme synthesis and oscillatory repression: why is the period of oscillation close to the cell cycle time?. J. Theor. Biol. 103, 313–328 (1983)
Tyson, J.J., Othmer, H.G.: The dynamics of feedback control circuits in biochemical pathways. Prog. Theor. Biol. 5, 1–62 (1978)
Gardner, T.S., Cantor, C.R., Collins, J.J.: Construction of a genetic toggle switch in Escherichia coli. Science 403, 339–342 (2000)
Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Science 403, 335–338 (2000)
Rebek Jr., J.J.: Synthetic self-replicating molecules. Sci. Am. 271, 48–55 (1994)
Tsai, L.L., Hutchison, G.H., Peacock-López, E.: Turing patterns in a self-replicating mechanism with self-complementary template. J. Chem. Phys. 113, 2003–2006 (2000)
Peacock-López, E., Radov, D.B., Flesner, C.: Mixed-mode oscillations in a template mechanism. Biophys. Chem. 65, 171–178 (1997)
Peacock-López, E.: Chemical oscillations: the Templator Model. Chem. Educ. 6, 202–209 (2001)
Beutel, K.M., Peacock-López, E.: Chemical oscillations and Turing patterns in a generalized two-variable model of chemical self-replication. J. Chem. Phys. 125, 024908 (2006)
Chung, J.M., Peacock-López, E.: Bifurcation diagrams and Turing patterns in a chemical self-replicating reaction-diffusion system with cross-diffusion. J. Chem. Phys. 127, 174003 (2007)
Chung, J.M., Peacock-López, E.: Cross-diffusion in the Templator model of chemical self-replication. Phys. Lett A. 371, 41–47 (2007)
Beutel, K.M., Peacock-López, E.: Complex dynamics in a cross-catalytic self-replication mechanism. J. Chem. Phys. 126, 125104 (2007)
Beutel, K.M., Peacock-López, E.: Chemical oscillations: two-variable chemical models. Chem. Educ. 12, 224–235 (2007)
McGhee, E.A., Peacock-López, E.: An introduction to Turing patterns in nonlinear chemical kinetics. Chem. Educ. 10, 84–94 (2005)
Gray, P., Scott, S.K.: Chemical Oscillations and Instabilities. Oxford University Press, Oxford (1990)
Widder, S., Schicho, J., Schuster, P.: Dynamic patterns of gene regulation I: simple two-gene system. J. Theor. Biol. 246, 395–419 (2007)
Hasty, J., McMillen, D., Isaacs, F., Collins, J.J.: Computational studies of gene regulatory networks: in numero molecular biology. Nature Rev. Gen. 2, 268–279 (2001)
Hasty, J., Issacs, F., Dolnik, M., McMillen, D., Collins, J.J.: Designer gene networks: towards fundamental cellular control. Chaos 11, 207–220 (2001)
van Riel, N.A.W.: Dynamic modelling and analysis of biochemical networks: mechanism-based models and model-based experiments. Brief. Bioinform. 7, 364–374 (2006)
Ferrell, J.E., Pomeranian, J.R., Kim, S.Y., Tunnel, N.B., Xing, W., Huang, C-Y.F., Machete, E.M.: Simple, realistic models of complex biological processes: positive feedback and bistability in a cell fate switch and a cell cycle oscillator. EBS Lett. 583, 3999-4005 (2009)
Kobayashi, T., Chen, L., Sahara, K.: Modeling genetic switches with positive feedback loops. J. Theor. Biol. 221, 379–399 (2003)
Zhdanov, V.P.: Kinetic models of gene regulation including non-coding RNAs. Phys. Rep. 500, 1–42 (2011)
Goh, K.-I.I., Kahng, B., Cho, K.-H.: Sustained oscillations in extended genetic oscillatory systems. Biophys. J. 94, 4270–4276 (2008)
Isaacs, F.J., Hasty, J., Cantor, C.R., Collins, J.J.: Prediction and measurement of autoregulatory genetic module. Proc. Natl. Acad. Sci. U.S.A. 100, 7714–7719 (2003)
Goldbeter, A., Gonze, D., Houart, G., Leloup, J.-C., Halloy, J., Dupont, G.: From simple to complex oscillatory behavior in metabolic and genetic control networks. Chaos 11, 247–250 (2001)
Ichinose, N., Yada, T., Gotoh, O., Aihara, K.: Reconstruction of transcription-translation dynamics with a model of gene networks. J. Theor. Biol. 255, 378–386 (2008)
Mileyko, Y., Joh, R.I., Weitz, J.S.: Small-scale copy number variation and large-scale changes in gene expression. Proc. Natl. Acad. Sci. U.S.A. 105, 16659–16664 (2008)
Muller, S., Hofbauer, J., Endler, L.: A generalized model of the repressilator. J. Math. Biol. 53, 905–937 (2006)
Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovaskii, D., Alon, U.: Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002)
Paul, N., Joyce, G.F.: A self-replicating ligase ribozyme. Proc. Natl. Acad. Sci. U.S.A. 99, 12733–12740 (2002)
Lincoln, T.A., Joyce, G.F.: Self-sustained replication of an RNA enzyme. Science 323, 1229–1232 (2009)
Murray, J.D.: Mathematical Biology II, 3rd. edn. Springer, Berlin (2003)
Epstein, I.R., Pojman, J.A.: Introduction to Nonlinear Chemical Dynamics, Oscillations, Waves, Patterns, and Chaos. Oxford University Press, New York (1998)
Edelstein-Keshet, L.: Mathematical Models in Biology. Random House, New York (1988)
Strogatz, S.H.: Nonlinear Dynamics and Chaos. Addison Wesley, Reading (1994)
Ermentrout, B.: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. SIAM, Philadelphia (2002)
Portle, S., Iadevaia, S., San, K.-Y., Bennett, G.N., Mantzaris, N.: Environmentally-modulated changes in fluorescence distribution in cells with oscillatory genetic network dynamics. J. Biotechnol. 140, 203–217 (2009)
Poincaré, H.: Le Méthodes Nouvelles de la Mécanique Céleste, vol. I. Gauthier-Villars, Paris (1892)
Andronov, A.A., Witt, A.: Sur la theorie mathematique des autooscillations. C. R. Acad. Sci. Paris 190, 256–258 (1930)
Hopf, E.: Abzweigung einer periodischen Losung von einer stationaren Losung eines Differetialsystems. Ber. Math.-Phys. Kl. Sachs, Acad. Wiss. Leipzig 94, 1–22 (1942)
Guckenheimer, J.: Numerical analysis of dynamical systems. In: Hasselblatt, B., Katok, A. (eds.) Handbook of Dynamical Systems, vol. 2, pp. 345–390. Elsevier, New York (2002)
Fung, E., Wong, W.W., Suen, J.K., Butlter, T., Lee, S.-G., Liao, J.C.: A synthetic gene-metabolic oscillator. Nature 435, 118–122 (2005)
Schõffl, F., Prãndl, R., Reindl, A.: Regulation of the heat-shock response. Plant Physiol. 117, 1135–1141 (1998)
Morimoto, R.I.: Cells in stress: transcriptional activation of heat shock genes. Science 259, 1409–1410 (1993)
Morimoto, R.I., Sarge, K.D., Abravaya, K.: Transcriptional regulation of heat shock genes. J. Biol. Chem. 267, 21987–21990 (1992)
Joyce, G.F.: A glimpse of biology’s first enzyme. Science 315, 1507–1508 (2007)
Kim, D.-E., Joyce, G.F.: Cross-catalytic replication of an RNA ligase ribozyme. Chem. Biol. 11, 1505–1512 (2004)
Tang, M.: The mean frequency of transcriptional bursting and its variation in single cells. J. Math. Biol. 98, 27–58 (2010)
Singh, A., Razooky, B., Cox, C., Simpson, M.L., Weinberget, L.S.: Transcriptional bursting from the HIV-1 promoter is a significant source of stochastic noise in HIV-1 gene expression. Biophys. J. 98, L32–L34 (2010)
Pedroza, J.M., Paulson, J.: Effects of molecular memory and bursting on fluctuations in gene expression. Science 319, 339–343 (2008)
Acknowledgements
One of us (EPL) would like to thank Professor Allen Rodgers, and the Chemistry Department of the University of Cape Town for their hospitality during my sabbatical leave. The authors would also like to thank Paola P. Freidrich and Alex Y. Peacock-Villada for helpful comments, and Williams College and the National Science Foundation (CHE-0911380) for their financial support.
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Lou, S.J., Peacock-López, E. Self-regulation in a minimal model of chemical self-replication. J Biol Phys 38, 349–364 (2012). https://doi.org/10.1007/s10867-011-9252-6
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DOI: https://doi.org/10.1007/s10867-011-9252-6