An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions

Abstract

Abstract. A specific class of ODEs has been shown to be adequate to describe the essential features of the complex dynamics of Gene-Regulatory Networks (GRN). But, the effective exploitation of such models to predict the dynamics of specific GRNs by classical numerical schemes is greatly hampered by the current lack of precise and quantitative information on regulation mechanisms and kinetic parameters. Due to the size and complexity of large GRNs, classical qualitative analysis could be very hard, or even impracticable, to be carried out by hand, and conventional qualitative simulation approaches rapidly lead to an exponential growth of the generated behavior tree that, besides all possible sound behaviors, may also contain spurious ones. This paper discusses the work-in-progress of a research effort aiming at the design and implementation of a computational framework for qualitative simulation of the dynamics of a class of ODE models of GRNs. The algorithm we propose results from a set of symbolic computation algorithms that carry out the integration of qualitative reasoning techniques with singular perturbation analysis methods. The former techniques allow us to cope with uncertain and incomplete knowledge whereas the latter ones lay the mathematical groundwork for a sound and complete algorithm capable to deal with regulation processes that occur at different time scales.

Dynamics of actively regulated gene networks

“…Also, from Eqs. (23) and (24) it follows that if q < q r = 2 √ |αβ|/|γ 1 − γ 2 |, then ρ = −q(γ 1 + γ 2 )/2 = −qγ , whereγ is the average of the switching degradation rates. As actual values of q are mostly much smaller than q r , we can safely let ρ = −qγ .…”

“…A switching domain is a narrow domain around thresholds or threshold intersections. Some problems remain unsolved after earlier papers on this model framework [10,19,20,22,23]. One problem concerns the stability analysis of so-called singular stationary points.…”