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.

The selective values of alleles in a molecular network model are context dependent.

Classical quantitative genetics has applied linear modeling to the problem of mapping genotypic to phenotypic variation. Much of this theory was developed prior to the availability of molecular biology. The current understanding of the mechanisms of gene expression indicates the importance of nonlinear effects resulting from gene interactions. We provide a bridge between genetics and gene network theories by relating key concepts from quantitative genetics to the parameters, variables, and performance functions of genetic networks. We illustrate this methodology by simulating the genetic switch controlling galactose metabolism in yeast and its response to selection for a population of individuals. Results indicate that genes have heterogeneous contributions to phenotypes and that additive and nonadditive effects are context dependent. Early cycles of selection suggest strong additive effects attributed to some genes. Later cycles suggest the presence of strong context-dependent nonadditive effects that are conditional on the outcomes of earlier selection cycles. A single favorable allele cannot be consistently identified for most loci. These results highlight the complications that can arise with the presence of nonlinear effects associated with genes acting in networks when selection is conducted on a population of individuals segregating for the genes contributing to the network.