Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions.

Abstract

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.