A maximum likelihood estimator for parameter distributions in heterogeneous cell populations

In many biologically relevant situations, cells of a clonal population show a heterogeneous response upon a common stimulus. The computational analysis of such situations requires the study of cell-cell variability and modeling of heterogeneous cell populations. 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 modeled via differences in parameter values and initial conditions. Both are subject to a distribution function which is part of the cell population model. We present a novel approach to estimate the distribution of parameters and initial conditions from single cell measurements, e.g. flow cytometry and cytometric fluorescence microscopy. Therefore, a maximum likelihood estimator for the distribution is derived. The resulting optimization problem is reformulated via a parameterization of the distribution of parameters and initial conditions to allow the use of convex optimization techniques. To evaluate the proposed method, artificial data from a model of TNF signal transduction are considered. It is shown that the proposed method yields a good estimate of the parameter distributions in case of a limited amount of noise corrupted data.