Stochastic Modelling of Gene Regulatory Mechanisms in PTEN Dynamics: Does Space Matter?

Abstract

Stochastic simulation has proven to be an invaluable tool for modelling biological processes involving small numbers of molecules, such as proteins and messenger RNA (mRNA). One aspect of sub-cellular dynamics that is often overlooked in stochastic models is the effect of spatial constraints on the behaviour of a cell; cellular processes depend not only on the number of molecules present, but also on their distribution, how they move within the cell and how they interact with each other. This type of modelling is particularly relevant in crowded media such as the cytoplasm, which is filled with organelles and other molecules. For these reasons, we hypothesise that spatially-resolved models of cells will prove to be more effective at simulating the behaviour of individual cells than spatially-averaged ones. To test this hypothesis, we studied the regulation of the mRNA of the tumour suppressor gene, PTEN, by a group of small RNAs called microRNAs. We created spatially-resolved models of the system using Smoldyn, a discrete-time, continuous-space, agent-based spatial stochastic simulation tool, and compared the results with those obtained using the spatially-averaged stochastic simulation algorithm (SSA). We measured the average time for an mRNA to be degraded or repressed by a threshold number of microRNA, and investigated the change in this mean time with the inclusion of cytoplasmic obstructions, non-uniform distributions of molecules, and competition for binding by competing endogenous RNAs (ceRNAs). Preliminary results demonstrate a considerable impact of spatial modelling on observed cellular response times, as we see a dramatic increase (>100-fold) in the time taken for microRNAs to locate mRNA binding sites in the spatially-resolved model.