Parameterization of a nonlinear genotype to phenotype map using molecular networks

Mathematical models of networks of molecular interactions controlling the expression of traits could theoretically be used as genotype to phenotype (GP) maps. Such maps are nonlinear functions of the environment and the genotype. It is possible to use nonlinear least square minimization methods to fit a model to a set of phenotypic data but the convergence of these methods is not automatic and may lead to a multiplicity of solutions. Both factors raise a number of questions with respect to using molecular networks as nonlinear maps. A method to fit a molecular network representing a bistable switch to various types of phenotypic data is introduced. This method relies on the identification of the model stable steady states and the estimation of the proportion of cells in each of them. By using environmental perturbations, it is possible to collect time-series of phenotypic data resulting in a smooth objective function leading to a good estimate of the parameters used to generate the simulated phenotypes.