The dynamics of hybrid metabolic-genetic oscillators
Kaper, Tasso J.
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Citation (published version)Ed Reznik, Tasso J Kaper, Daniel Segre. 2013. "The dynamics of hybrid metabolic-genetic oscillators." CHAOS, Volume 23, Issue 1, 013132. https://doi.org/10.1063/1.4793573
The synthetic construction of intracellular circuits is frequently hindered by a poor knowledge of appropriate kinetics and precise rate parameters. Here, we use generalized modeling (GM) to study the dynamical behavior of topological models of a family of hybrid metabolic-genetic circuits known as "metabolators." Under mild assumptions on the kinetics, we use GM to analytically prove that all explicit kinetic models which are topologically analogous to one such circuit, the "core metabolator," cannot undergo Hopf bifurcations. Then, we examine more detailed models of the metabolator. Inspired by the experimental observation of a Hopf bifurcation in a synthetically constructed circuit related to the core metabolator, we apply GM to identify the critical components of the synthetically constructed metabolator which must be reintroduced in order to recover the Hopf bifurcation. Next, we study the dynamics of a re-wired version of the core metabolator, dubbed the "reverse" metabolator, and show that it exhibits a substantially richer set of dynamical behaviors, including both local and global oscillations. Prompted by the observation of relaxation oscillations in the reverse metabolator, we study the role that a separation of genetic and metabolic time scales may play in its dynamics, and find that widely separated time scales promote stability in the circuit. Our results illustrate a generic pipeline for vetting the potential success of a circuit design, simply by studying the dynamics of the corresponding generalized model.
Rights© 2013 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Ed Reznik, Tasso J Kaper, Daniel Segre. 2013. "The dynamics of hybrid metabolic-genetic oscillators." Chaos, Volume 23, Issue 1, 013132 and may be found at https://doi.org/10.1063/1.4793573.
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