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The dynamics of gene regulatory networks are often modeled with theassumption of cellular homogeneity. However, this assumption contradicts theplethora of experimental results in a variety of systems, which designates thatcell populations are heterogeneous systems in the sense that properties such assize, shape, and DNA/RNA content are unevenly distributed amongst theirindividuals. In order to address the implications of heterogeneity, we utilizethe so-called cell population balance (CPB) models. Here, we solve numericallymultivariable CPB models to study the effect of heterogeneity on populationscarrying the toggle switch network, which features nonlinear behavior at thesingle-cell level. In order to answer whether this nonlinear behavior isinherited to the heterogeneous population level, we perform bifurcationanalysis on the steady-state solutions of the CPB model. We show thatbistability is present at the population level with the pertinent bistabilityregion shrinking when the impact of heterogeneity is enhanced.

Effect of cell heterogeneity on isogenic populations with the synthetic  genetic toggle switch network: bifurcation analysis of two-dimensional Cell  Population Balance Models