Parameter estimation for reaction rate equation constrained mixture models. 

The elucidation of sources of heterogeneity in cell populations is crucial to fully understand biological processes. A suitable method to identify causes of heterogeneity is reaction rate equation (RRE) constrained mixture modeling, which enables the analysis of subpopulation structures and dynamics. These mixture models are calibrated using single cell snapshot data to estimate model parameters which are not measured or which cannot be assessed experimentally. In this manuscript, we evaluate different optimization methods for estimating the parameters of RRE constrained mixture models under the normal distribution assumption. We compare gradient-based optimization using sensitivity analysis with two other optimization methods – gradient-based optimization with finite differences and a stochastic optimization method – for simulation examples with artificial data. Furthermore, we compare different numerical schemes for the evaluation of the log-likelihood function. We found that gradient-based optimization using sensitivity analysis outperforms the other optimization methods in terms of convergence and computation time.