  The dynamics of gene regulatory networks are often modeled with the
assumption of cellular homogeneity. However, this assumption contradicts the
plethora of experimental results in a variety of systems, which designates that
cell populations are heterogeneous systems in the sense that properties such as
size, shape, and DNA/RNA content are unevenly distributed amongst their
individuals. In order to address the implications of heterogeneity, we utilize
the so-called cell population balance (CPB) models. Here, we solve numerically
multivariable CPB models to study the effect of heterogeneity on populations
carrying the toggle switch network, which features nonlinear behavior at the
single-cell level. In order to answer whether this nonlinear behavior is
inherited to the heterogeneous population level, we perform bifurcation
analysis on the steady-state solutions of the CPB model. We show that
bistability is present at the population level with the pertinent bistability
region shrinking when the impact of heterogeneity is enhanced.
