Network-level dynamics of diffusively coupled cells

TL;DR

This paper analyzes the collective behavior of diffusively coupled cells, demonstrating conditions for convergence to common or bistable states, and discusses implications for cellular decision-making robustness.

Contribution

It introduces new boundedness conditions for singularly perturbed systems and applies them to show population-level coordination and bistability in coupled cells.

Findings

Cells converge to a common equilibrium under certain conditions.

Populations of bistable cells tend to synchronize in one of two states.

Results have implications for robustness in cellular decision processes.

Abstract

We study molecular dynamics within populations of diffusively coupled cells under the assumption of fast diffusive exchange. As a technical tool, we propose conditions on boundedness and ultimate boundedness for systems with a singular perturbation, which extend the classical asymptotic stability results for singularly perturbed systems. Based on these results, we show that with common models of intracellular dynamics, the cell population is coordinated in the sense that all cells converge close to a common equilibrium point. We then study a more specific example of coupled cells which behave as bistable switches, where the intracellular dynamics are such that cells may be in one of two equilibrium points. Here, we find that the whole population is bistable in the sense that it converges to a population state where either all cells are close to the one equilibrium point, or all cells are close to the other equilibrium point. Finally, we discuss applications of these results for the robustness of cellular decision making in coupled populations.