Control design for sustained oscillation in a two-gene regulatory network

Abstract

Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior.

Numerical simulation of piecewise-linear models of gene regulatory networks using complementarity systems

“…While a qualitative analysis is appropriate for certain problems, the absence of precise quantitative predictions is not desirable in others, such as the analysis of a limit cycle [9] or the design of a controller for a synthetic network [11]. The quantitative study of PWL models of gene regulatory networks is hindered by the fact that, as of now, no general and efficient tool for the numerical simulation of Filippov extensions is available.…”

“…The fact that not all cells oscillate, and that the periods and amplitudes vary between oscillating cells, can be attributed to stochastic effects that are not accounted for in deterministic ODE or PWL models [69]. The occurrence of limit cycles in repressilator models has been an active subject of research for ODE models (see [69,70] for reviews) and PWL models [11,[14][15][16].…”

“…Second, the simplified mathematical form of the models makes them easier to analyze. Among other things, this makes it possible to single out the precise role of specific subnetworks [9,10] and to analyze the feasibility of control schemes [11].…”

Structural Principles for Complex Dynamics in Glass Networks

“…Several studies have previously dealt with control of piecewise-linear systems to create (or destroy) fixed points or periodic solutions (see [Farcot & Gouzé, 2008;Edwards et al, 2010] and references therein). The procedures we propose for designing parameters to generate desired behaviors are interpretable in the context of rate constants in gene networks, although the manipulation of individual focal points is more difficult in an experimental setting than a change in a single parameter in the original differential equation system, which would affect the positions of multiple focal points.…”

Qualitative control of undesired oscillations in a genetic negative feedback loop with uncertain measurements

“…This system was also controlled in [26] in order to stabilize its unstable fixed point, and real biological implementations were performed in order to support the analytical results. A similar idea is presented in [9], where the production rate of a two-dimensional PWA genetic feedback loop is controlled in order to create a periodic orbit. More theoretically, a general framework has been developed in [12] in order to control PWA gene regulatory networks.…”