A cell population balance model describing positive feedback loop expression dynamics

Biological systems are inherently heterogeneous in the sense that cellular content is unevenly distributed amongst the cells of the population. In this work, we develop a cell population balance-modeling framework, which integrates biological detail at the single-cell level to accurately predict the dynamics of the distribution of cellular properties at the cell population level. The developed cell population balance model describes the dynamics of the distribution of lac operon expression levels amongst the cells of a cell population. Detailed numerical simulations elucidate the influence of key operating and molecular parameters on the phenotype of the cell population both transiently and at steady state. The system was found to exhibit bistability for a certain region of the parameter space. Moreover, due to the autocatalytic nature of the lac operon network, increase in the extracellular inducer concentration or slower growth led to higher average expression levels with a simultaneous spreading of the distribution of expression levels. Asymmetric partitioning and sharp division thresholds led to bimodal distributions both transiently and at steady state. These results are explained on the basis of the interplay between the specific genetic architecture and various division and partitioning mechanisms. Thus, the presented model offers a unique insight into systems with positive feedback features that can be utilized for rigorous strain development and control of the underlying cell population dynamics.