ATP Level and Phosphorylation Free Energy Regulate Trigger-Wave Speed and Critical Nucleus Size in Cellular Biochemical Systems

TL;DR

This study develops a thermodynamically consistent reaction-diffusion model to analyze how ATP levels and phosphorylation energy influence trigger-wave speed, direction, and critical size in cellular biochemical systems, linking metabolism to wave dynamics.

Contribution

It introduces a novel framework connecting energetic driving with trigger-wave behavior, revealing how ATP and phosphorylation free energy regulate wave propagation and critical nucleus size.

Findings

ATP and phosphorylation energy modulate wave speed and direction.

Energetic state influences the critical excitation radius.

The framework links cellular metabolism to spatial wave dynamics.

Abstract

Trigger waves are self-regenerating propagating fronts that emerge from the coupling of nonlinear reaction kinetics and diffusion. In cells, trigger waves coordinate large-scale processes such as mitotic entry and stress responses. Although the roles of circuit topology and feedback architecture in generating bistability are well established, how nonequilibrium energetic driving shapes wave propagation is less well understood. Here, we employ a thermodynamically consistent reaction--diffusion framework to investigate trigger-wave dynamics in ATP-dependent phosphorylation--dephosphorylation systems. We first recapitulate general expressions for trigger-wave speed in the bistable regime and analyze curvature-induced corrections that determine the minimum critical nucleus required for sustained propagation in higher dimensions. We then apply this framework to two representative systems, treating ATP concentration and the nonequilibrium parameter $\gamma = [ATP]/(K_{\mathrm{eq}}[ADP][P_i])$ as independent control variables to examine how energetic driving regulates wave propagation. Our results show that ATP and $\gamma$ not only modulate wave speed, but can also reverse the direction of propagation and reshape the parameter regime supporting trigger waves. The critical excitation radius also depends on both ATP concentration and phosphorylation free energy. These findings identify the intracellular energetic state as a regulator of trigger-wave behavior, linking metabolic conditions to the spatial dynamics of wave propagation. More broadly, this framework connects classical reaction--diffusion theory with ATP-driven biochemical regulation and provides a general perspective on related energy-dependent cellular decision-making processes.