Parameter Identification of Stochastic Gene Regulation Models by Indicator-Based Evolutionary Level Set Approximation

Abstract

Continuous level set approximation seeks to find a set of points (parameter vectors) that approximates the set of sets of parameters that for a given function map to a given output value. In this work we will look at a class of difficult to solve level set problems with innumerably many solutions and show how their solution sets can be approximated by robust evolutionary search methods.

In particular, this paper seeks to solve noisy parameter identification problem from biology where the task is to find the set of parameter settings of a stochastic gene regulatory network, simulated by Gillespie’s algorithm with delays, that match existing observations. In this context the necessity of active diversity maintenance and adaptation of search operators to find all feasible subspaces is studied. As a result a robust implementation and default setting of evolutionary level set approximation (ELSA) for noisy parameter identification problems will be developed and validated. The validation uses two classical gene regulatory networks and it is demonstrated that a larger set of reaction parameters can be found that potentially could explain the observed stochastic dynamics.