Density-based modeling and identification of biochemical networks in cell populations

In many biological processes heterogeneity within cell populations is an important issue. In this work we consider populations where the behavior of every single cell can be described by a system of ordinary differential equations. Heterogeneity among individual cells is accounted for by differences in parameter values and initial conditions. Hereby, parameter values and initial conditions are subject to a distribution function which is part of the model specification. Based on the single cell model and the considered parameter distribution, a partial differential equation model describing the distribution of cells in the state and in the output space is derived. For the estimation of the parameter distribution within the model, we consider experimental data as obtained from flow cytometric analysis. From these noise-corrupted data a density-based statistical data model is derived. Employing this model of the data the parameter distribution within the cell population is computed using convex optimization techniques. To evaluate the proposed method, a model for the caspase activation cascade is considered. It is shown that for known noise properties the unknown parameter distributions in this model are well estimated by the proposed method.