Cell population balance and hybrid modeling of population dynamics for a single gene with feedback

Latest research on biological systems is steadily shifting from isolated single cells to entire cell populations. The latter are inherently heterogeneous, and their modeling requires approaches that explicitly account for this property. A comprehensive such approach is the cell population balance (CPB), which, however, is computationally expensive and becomes intractable for multi-variable models.In this work, we demonstrate the use of model-reduction to efficiently simulate cell population heterogeneity in a genetic network of a single gene with feedback. Starting from a 4-species model, we use singular perturbation analysis to derive a single equation for the intracellular protein concentration. We subsequently incorporate this equation to a hybrid model consisting of a CPB for the cell volume, and a continuum equation for the protein concentration. We finally compare the results obtained with the hybrid model with those of the full CPB, demonstrating the accuracy and computational efficiency of the hybrid methodology.

► Models for a single gene with feedback are reduced using singular perturbation. ► The reduced models are used in cell population balance and hybrid frameworks. ► Error analysis demonstrates the high accuracy of the hybrid framework. ► CPU time comparisons show the computational savings of the hybrid framework.