Identification of Heterogeneous Parameters in an Intracellular Reaction Network from Population Snapshot Measurements through Sensitivity Analysis and Neural Network

Abstract

Cells in a clonal cell-population exhibit a significant degree of heterogeneity in their responses to an external stimulus. In order to model a heterogeneous intracellular process, the individual-based population model (IBPM) has been developed in the past. Specifically, the IBPM approach can represent the heterogeneous dynamics in a cell population with a system of differential equations, whose model parameters follow probability density functions (PDF) instead of being constants. Therefore, in order to accurately predict the heterogeneous cellular dynamics, it is important to infer the PDFs of the model parameters from available experimental measurements. In this study, we propose a methodology to estimate the PDFs of the model parameters from population snapshot measurements obtained from flow cytometry. First, the PDFs of the model parameters are assumed to be normal so that a finite dimensional vector will be inferred from the measurements instead of inferring PDFs. Second, the sensitivity analysis is performed to identify which PDFs of the model parameters are identifiable and should be estimated from the available measurements. Next, in order to reduce the excessive number of evaluations of the IBPM during the PDF estimation process, an NNM is developed so that the output PDFs can be computed for given parameter PDFs. Lastly, the NNM is used to estimate the PDFs of the model parameters by minimizing the difference between the measured and predicted PDFs of the output. To show the effectiveness of the proposed methodology, the PDFs of parameters of a TNFα signaling model were estimated from in silico measurements.