Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells

Abstract

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our stimulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Spatiotemporal dynamics of membrane surface charge regulates cell polarity and migration

“…Previously, the spatiotemporal behavior of these networks has been modeled as an excitable network consisting of positive and delayed negative feedback loops 9,57,[66][67][68][69] . Independent studies suggest that the delayed negative feedback loop required for excitability includes the action of substrates of AKTs and possibly other refractory state molecules 57,70 . The positive feedback was implemented as a mutually inhibitory interaction between front and back states, consisting of Ras/Rap and PI(4,5)P2 or PI(3,4)P2, respectively 9,28,57 .…”

A dynamic partitioning mechanism polarizes membrane protein distribution

“…a complete excursion in the phase space, when stochastic noise can cross the threshold of the network. This, in turn, generates defined patterns in two dimensions which underlies protrusion formation 28,31,64 . To include realistic random stochastic noise, we simulated an unstructured mesh based spatiotemporal reaction diffusion system (Figure S9A) using URDME framework (see Methods for details).…”

“…The core of the excitable signal transduction network was modelled using three interacting states of the membrane: F (front), B(back), and R(refractory) 9,28,31,64 . As shown in Figure 6A, F activates R, while R inhibits F via a delayed negative feedback; F and B mutually inhibit each other, creating a autocatalytic loop effect.…”

“…We also used the same initial condition derived from a previous simulation. The detailed implementation of the reactions with respective propensity functions are discussed in supplementary method of Biswas et al 64 .…”

Balancing at the edge of excitability: Implications for cell movement

“…In the context of biochemical signaling in which states represent concentration of various species, the FHN system is not realizable, as it allows the state variables to be negative. Through a series of papers [12,24,25], we proposed a biochemically plausible model of the excitable system regulating cell motility and validated it experimentally [19]. Consider the following set of equations.…”