Abstract
We develop and analyze a model of a minimal synthetic gene circuit, that describes part of the gene expression machinery in Escherichia coli, and enables the control of the growth rate of the cells during the exponential phase. This model is a piecewise non-linear system with two variables (the concentrations of two gene products) and an input (an inducer). We study the qualitative dynamics of the model and the bifurcation diagram with respect to the input. Moreover, an analytic expression of the growth rate during the exponential phase as function of the input is derived. A relevant problem is that of identifiability of the parameters of this expression supposing noisy measurements of exponential growth rate. We present such an identifiability study that we validate in silico with synthetic measurements.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andrianantoandro, E., Basu, S., Karig, D., Weiss, R.: Synthetic biology: new engineering rules for an emerging discipline. Molecular Systems Biology 2(1) (2006)
Khalil, A., Collins, J.: Synthetic biology: applications come of age. Nature Reviews Genetics 11(5), 367–379 (2010)
Mukherji, S., Van Oudenaarden, A.: Synthetic biology: understanding biological design from synthetic circuits. Nature Reviews Genetics 10(12), 859–871 (2009)
Elowitz, M., Leibler, S., et al.: A synthetic oscillatory network of transcriptional regulators. Nature 403(6767), 335–338 (2000)
Gardner, T., Cantor, C., Collins, J.: Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000)
Tigges, M., Marquez-Lago, T., Stelling, J., Fussenegger, M.: A tunable synthetic mammalian oscillator. Nature 457(7227), 309–312 (2009)
Monod, J.: The growth of bacterial cultures. Annual Review of Microbiology 3(1), 371–394 (1949)
Marr, A.G.: Growth rate of Escherichia coli. Microbiological Reviews 55(2), 316–333 (1991)
Kaern, M., Blake, W., Collins, J.: The engineering of gene regulatory networks. Annual Review of Biomedical Engineering 5(1), 179–206 (2003)
Tan, C., Marguet, P., You, L.: Emergent bistability by a growth-modulating positive feedback circuit. Nature Chemical Biology 5(11), 842–848 (2009)
Bettenbrock, K., Sauter, T., Jahreis, K., Kremling, A., Lengeler, J.W., Gilles, E.D.: Correlation between growth rates, EIIACrr phosphorylation, and Intracellular Cyclic AMP levels in Escherichia coli K-12. J. Bacteriol. 189(19), 6891–6900 (2007)
Ropers, D., de Jong, H., Page, M., Schneider, D., Geiselmann, J.: Qualitative simulation of the carbon starvation response in Escherichia coli. Biosystems 84(2), 124–152 (2006)
de Jong, H., Geiselmann, J., Hernandez, C., Page, M.: Genetic network analyzer: qualitative simulation of genetic regulatory networks. Bioinformatics 19(3), 336–344 (2003)
Casey, R., Jong, H., Gouzé, J.: Piecewise-linear models of genetic regulatory networks: Equilibria and their stability. Journal of Mathematical Biology 52(1), 27–56 (2006)
Chaves, M., Gouzé, J.-L.: Piecewise Affine Models of Regulatory Genetic Networks: Review and Probabilistic Interpretation. In: Lévine, J., Müllhaupt, P. (eds.) Advances in the Theory of Control, Signals and Systems with Physical Modeling. LNCIS, vol. 407, pp. 241–253. Springer, Heidelberg (2010)
De Jong, H., Gouzé, J., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology 66(2), 301–340 (2004)
Gouzé, J., Sari, T.: A class of piecewise linear differential equations arising in biological models. Dynamical Systems 17(4), 299–316 (2002)
Grognard, F., De Jong, H., Gouzé, J.: Piecewise-linear models of genetic regulatory networks: theory and example. Biology and Control Theory: Current Challenges, 137–159 (2007)
Yagil, G., Yagil, E.: On the relation between effector concentration and the rate of induced enzyme synthesis. Biophysical Journal 11(1), 11–27 (1971)
Filippov, A., Arscott, F.: Differential equations with discontinuous righthand sides. In: Mathematics and its Applications Series. Kluwer Academic Publishers (1988)
Klumpp, S., Zhang, Z., Hwa, T.: Growth rate-dependent global effects on gene expression in bacteria. Cell 139(7), 1366–1375 (2010)
Scott, M., Gunderson, C.W., Mateescu, E.M., Zhang, Z., Hwa, T.: Interdependence of cell growth and gene expression: Origins and consequences. Science 330(6007), 1099–1102 (2010)
Eden, E., Geva-Zatorsky, N., Issaeva, I., Cohen, A., Dekel, E., Danon, T., Cohen, L., Mayo, A., Alon, U.: Proteome half-life dynamics in living human cells. Science 331(6018), 764–768 (2011)
Krin, E., Sismeiro, O., Danchin, A., Bertin, P.N.: The regulation of Enzyme IIAGlc expression controls adenylate cyclase activity in Escherichia coli. Microbiology 148(5), 1553–1559 (2002)
Notley-McRobb, L., Death, A., Ferenci, T.: The relationship between external glucose concentration and cAMP levels inside Escherichia coli: implications for models of phosphotransferase-mediated regulation of adenylate cyclase. Microbiology 143(6), 1909–1918 (1997)
Vajda, S., Rabitz, H., Walter, E., Lecourtier, Y.: Qualitative and quantitative identifiability analysis of nonlinear chemical kinetic models. Chemical Engineering Communications 83(1), 191–219 (1989)
Chis, O., Banga, J., Balsa-Canto, E.: Structural identifiability of systems biology models: A critical comparison of methods. PloS one 6(11), e27755 (2011)
Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., Timmer, J.: Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15), 1923–1929 (2009)
Walter, É., Pronzato, L.: Identification of parametric models from experimental data. Communications and Control Engineering, Springer (1997)
Dochain, D., Vanrolleghem, P.: Dynamical Modelling and Estimation in Wastewater Treatment Processes. IWA Publishing (2001)
Seber, G., Wild, C.: Nonlinear regression, vol. 503. Libre Digital (2003)
Gallant, A.: Nonlinear regression. The American Statistician 29(2), 73–81 (1975)
Bremer, H., Dennis, P., et al.: Modulation of chemical composition and other parameters of the cell by growth rate. Escherichia Coli and Salmonella: Cellular and Molecular Biology 2, 1553–1569 (1996)
Goldberg, D.: Genetic algorithms in search, optimization, and machine learning. Addison-Wesley (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Carta, A., Chaves, M., Gouzé, JL. (2012). A Simple Model to Control Growth Rate of Synthetic E. coli during the Exponential Phase: Model Analysis and Parameter Estimation. In: Gilbert, D., Heiner, M. (eds) Computational Methods in Systems Biology. CMSB 2012. Lecture Notes in Computer Science(), vol 7605. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33636-2_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-33636-2_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33635-5
Online ISBN: 978-3-642-33636-2
eBook Packages: Computer ScienceComputer Science (R0)