Bistability versus Bimodal Distributions in Gene Regulatory Processes from Population Balance

Abstract

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the “off” state, and the other at the high end representing the “on” state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the “off” state and the other in the “on” state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.

Mathematical Modeling of Microbial Community Dynamics: A Methodological Review

“…In advanced simulations, stochastic events such as gene regulatory processes were incorporated into PBMs. For example, Shu et al [120] applied the PBM framework to investigate the effect of bistability of cells (represented as two distinct levels of PrG protein concentration) on biomodal distributions of the population. Spatial heterogeneity can also be accounted for through coupling PBMs with a reactive-transport model, e.g., using computational fluid dynamics (CFD) [121].…”

Cell mass and cell cycle dynamics of an asynchronous budding yeast population: Experimental observations, flow cytometry data analysis, and multi‐scale modeling

“…The proposed model can be regarded as a tool for investigating these dynamics under different scenarios, for example, pulse experiments, and comparing the different assumptions against the experimental observations. It was concluded that, although it is often believed that the occurrence of bimodal distributions results from a bistability of the gene regulatory network (e.g., Hasty et al, 2002;Thattai and van Oudenaarden, 2001), this bimodality may arise even if the stochastic bistability does not occur (Shu et al, 2011). Recently, the occurrence of distribution of protein levels (concentrations) for a cell population was studied in silico using a PBM that incorporated a stochastic description for gene expression (Shu et al, 2011(Shu et al, , 2012.…”

“…In the case of continuous or fed-batch fermentations where the glucose concentration in the feed is high, the integration of the proposed model and a computational fluid dynamics (CFD) model describing the distribution of substrate within the reactor provides a valuable tool to study in silico the effect of non-ideal mixing, and resulting substrate gradients, on the development of heterogeneous cell populations. Recently, the occurrence of distribution of protein levels (concentrations) for a cell population was studied in silico using a PBM that incorporated a stochastic description for gene expression (Shu et al, 2011(Shu et al, , 2012. It was concluded that, although it is often believed that the occurrence of bimodal distributions results from a bistability of the gene regulatory network (e.g., Hasty et al, 2002;Thattai and van Oudenaarden, 2001), this bimodality may arise even if the stochastic bistability does not occur (Shu et al, 2011).…”

Revitalizing Personalized Medicine: Respecting Biomolecular Complexities Beyond Gene Expression

“…43 Robust computational approaches are available to incorporate these multiple sources of stochasticity and heterogeneity, which enable prediction of population behavior. 28,44 The relationship between cellular heterogeneity and unpredictable clinical response is less obvious but extremely critical. For example, in cancer cells, protein expression outliers allow some cells to fall outside the drug's range of efficacy, enabling those cells to survive ongoing treatments.…”