Optimal experimental design (OED) aims to design more effective experiments and thereby save resources. Applications of OED most often design experiments for model parameter estimation, but rarely for model selection. In addition, few OED methods exist for biological systems with considerable cell-to-cell variability, where population models such as non-linear mixed effect (NLME) models can help elucidate sources of variability. Here, we address this gap with an OED method for designing dynamic inputs selecting between NLME models. Specifically, we propose a novel utility function for NLME model discrimination based on the separation of predicted population distributions. Our utility provides an interpretable output: a separability score denotes the expected number of pairwise model separations after conducting the experiment. We demonstrate our approach to optimal input design by separating candidate models for the variance components in a simple gene expression circuit. We show that with the suggested optimal design we can separate 4 out of 5 candidate models from one another. We consider this proof of principle as a first step towards designing more efficient experiments to elucidate the mechanisms of cell-to-cell variability. We envisage future extensions to larger model selection problems in systems and synthetic biology.