Effect of cell heterogeneity on isogenic populations with the synthetic genetic toggle switch network: Bifurcation analysis of two-dimensional cell population balance models

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.