Analysis of heterogeneous cell populations: A density-based modeling and identification framework

Abstract

Abstract In many biological processes heterogeneity within clonal cell populations is an important issue. One of the most striking examples is a population of cancer cells in which after a common, identical death signal some cells die whereas others survive. The reason for this heterogeneity is intrinsic and extrinsic noise. In this paper we present a mechanistic multi-scale modeling framework for cell populations, in which the dynamics of every individual cell is captured by a parameter dependent stochastic differential equation (SDE). Heterogeneity among individual cells is accounted for by differences in parameter values, modeling extrinsic influences. Based on the statistical properties of the extrinsic noise and the SDE model for the individual cell, a partial differential equation (PDE) model is derived. This PDE describes the evolution of the population density. To determine the statistics of the extrinsic noise from experimental population data, a density-based statistical data model of the noise-corrupted data is derived. Employing this data model we show that the statistics of the extrinsic can be computed using a convex optimization. This efficient way of assessing the parameters allows for a so far infeasible uncertainty analysis via bootstrapping. 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 densities in this model are well estimated by the proposed method.