Optimal robust search for parameter values of qualitative models of gene regulatory networks

Computational and mathematical models are a must for the in silico analysis or design of Gene Regulatory Networks (GRN) as they offer a theoretical context to deeply address biological regulation. We have proposed a framework where models of network dynamics are expressed through a class of nonlinear and temporal multiscale Ordinary Differential Equations (ODE). To find out models that disclose network structures underlying an observed or desired network behavior, and parameter values that enable the candidate models to reproduce such behavior, we follow a reasoning cycle that alternates procedures for model selection and parameter refinement. Plausible network models are first selected via qualitative simulation, and next their parameters are given quantitative values such that the ODE model solution reproduces the specified behavior. This paper gives algorithms to tackle the parameter refinement problem formulated as an optimization problem. We search, within the parameter space symbolically expressed, for the largest hypersphere whose points correspond to parameter values such that the ODE solution gives an instance of the given qualitative trajectory. Our approach overcomes the limitation of a previously proposed stochastic approach, namely computational load and very reduced scalability. Its applicability and effectiveness are demonstrated through two benchmark synthetic networks with different complexity.