Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways

Abstract

In the intracellular environment, signaling takes place in a nonideal environment that is spatially heterogeneous and that is noisy, with the noise arising from the low copy numbers of the signaling molecules involved. In this paper, we model intracellular signaling pathways as stochastic reaction-diffusion processes and adapt techniques commonly used by physicists to solve for the spatiotemporal evolution of the signaling pathways. We then apply it to study two problems of relevance to the modeling of intracellular signaling pathways. First, we show that, in the limit of small protein diffusion which is typically the case for proteins in the cytosol crowded by other macromolecules, the extent of diffusion control, in the transient regime, on reactions is greater than previous predictions. Second, we show that the presence of scaffold proteins can modify the phosphorylation activity of a mitogen-activated protein kinase cascade, and explain how this activity is modulated by the scaffold protein concentration.

Models at the single cell level

“…However, it is often not necessary, or is indeed counter-productive, to model individual molecules of every species, especially ones that are available in large concentrations, or variables such as the cell membrane shape or cytoskeletal motion. Accordingly, there are hybrid methods being created for stochastic spatial simulations, wherein the discrete reaction dynamics of some molecular components is simulated stochastically and is coupled to continuous fields of others that vary according to partial differential equations [113, 114]. …”

Can Complex Cellular Processes Be Governed by Simple Linear Rules?

“…It is daunting to know why such simplicity could hold in a heterogeneous environment where diffusion processes and molecular crowding are expected to make the response highly complex and nonlinear. 69,70 One of the reasons could be that deterministic approaches are possible for representing ensemble of cells, such as cell-culture, which show collective averaging behavior. 16,[31][32][33] This, however, is in contrast to single-cell behavior where stochastic molecular phenotypes are often observed.…”

Three-dimensional Monte Carlo simulations of intracellular diffusion and reaction of signaling proteins

“…Among the relevant theoretical studies, we may mention the use of the reaction-diffusion equation in order to analyze the probability of reaction of emitted proteins 9 and twodimensional ͑2D͒ Monte Carlo ͑MC͒ simulations of some of the problems relevant to the intracellular signaling. 10 In both these works, the cell structure is not described explicitly. The most natural way to simulate protein diffusion inside the cell with compartments is to employ the lattice MC technique.…”