[论文解读] ATP Level and Phosphorylation Free Energy Regulate Trigger-Wave Speed and Critical Nucleus Size in Cellular Biochemical Systems

Jianwei Li, Kai Meng+2 more|arXiv (Cornell University)|Mar 11, 2026

Microtubule and mitosis dynamics被引用 0

一句话总结

本文发展了一个热力学一致的反应扩散框架，展示ATP水平与磷酸化自由能（gamma）如何调控触发波速与ATP驱动的双稳态系统的临界核大小，并对Rad53和CDK激活电路提出预测。

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 $γ= [ATP]/(K_{\mathrm{eq}}[ADP][P_i])$ as independent control variables to examine how energetic driving regulates wave propagation. Our results show that ATP and $γ$ 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.

研究动机与目标

• 说明非平衡能量驱动如何塑造细胞双稳态电路中的波传播。
• 开发一个热力学一致的反应扩散模型，将ATP和gamma作为控制参数纳入。
• 推导平面触发波速与曲率修正的解析表达式。
• 将该框架应用于Rad53激活和CDK激活，预测能量状态如何影响波传播。

提出的方法

• 将双稳态反应扩散方程与能量驱动动力学结合。
• 定义势函数F(u; theta)并将波速与DeltaF联系起来：c0 = DeltaF / ∫(du/dz)^2。
• 推导球形前沿的曲率修正，得到dR/dt = c0 - D(d-1)/R以及Rc = D(d-1)/c0。
• 引入gamma = [ATP]/(K_eq[ADP][Pi])作为非平衡驱动，显示其对双稳态与波速的影响。
• 给出在代表性电路中以ATP和gamma表示的c0的解析表达式。
• 进行一维和三维偏微分方程仿真以验证前沿速度、传播方向和曲率效应。

实验结果

研究问题

• RQ1 细胞内ATP浓度与磷酸化自由能gamma如何影响双稳态反应扩散系统中的触发波速与方向？
• RQ2 在更高维度中，ATP与gamma对临界核大小的依赖关系是什么？
• RQ3 曲率如何与代谢驱动相互作用，以在三维几何中允许或抑制触发波传播？
• RQ4 框架是否能预测能量变化下Rad53样电路和CDK样触发波的定性与定量变化？
• RQ5 哪些实验测试可以验证ATP和gamma依赖的触发波分相图？

主要发现

• 触发波速依赖热力学驱动DeltaF和代谢速率，ATP和gamma同时调控速度与传播方向。
• 在三维中，曲率通过稀释项降低前沿速度，得到球形前沿的临界核半径Rc = D(d-1)/c0。
• 一般而言，增加ATP会提高平面波速并在双稳态区降低持续传播所需的临界核大小。
• ATP–gamma相空间中的双稳态区域与波传播模式（向前、静止、向后）发生位移，存在将反向波、静止波与向前波分离开的相图。
• 对于Rad53样电路，c0在某些范围内与√[ATP]成比例关系，较高的能量驱动扩展了向前传播的区间，而较高的gamma增强了非平衡驱动。
• 对于CDK激活模型，双稳态仅在ATP–gamma的有限区域存在，且波速对总CDK复合物浓度和能量状态都敏感。