Populations of heterogeneous cells play an important role in many biological
systems. In this paper we consider systems where each cell can be modelled by
an ordinary differential equation. To account for heterogeneity, parameter
values are different among individual cells, subject to a distribution function
which is part of the model specification.
Experimental data for heterogeneous cell populations can be obtained from
flow cytometric fluorescence microscopy. We present a heuristic approach to use
such data for estimation of the parameter distribution in the population. The
approach is based on generating simulation data for samples in parameter space.
By convex optimisation, a suitable probability density function for these
samples is computed.
To evaluate the proposed approach, we consider artificial data from a simple
model of the tumor necrosis factor (TNF) signalling pathway. Its main
characteristic is a bimodality in the TNF response: a certain percentage of
cells undergoes apoptosis upon stimulation, while the remaining part stays
alive. We show how our modelling approach allows to identify the reasons that
underly the differential response.Comment: 14 pages, 5 figure