Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
Department of Chemistry, Princeton University, Princeton, NJ, 08540, USA.
Nat Commun. 2023 Mar 8;14(1):1280. doi: 10.1038/s41467-023-36705-8.
Living things benefit from exquisite molecular sensitivity in many of their key processes, including DNA replication, transcription and translation, chemical sensing, and morphogenesis. At thermodynamic equilibrium, the basic biophysical mechanism for sensitivity is cooperative binding, for which it can be shown that the Hill coefficient, a sensitivity measure, cannot exceed the number of binding sites. Generalizing this fact, we find that for any kinetic scheme, at or away from thermodynamic equilibrium, a very simple structural quantity, the size of the support of a perturbation, always limits the effective Hill coefficient. We show how this bound sheds light on and unifies diverse sensitivity mechanisms, including kinetic proofreading and a nonequilibrium Monod-Wyman-Changeux (MWC) model proposed for the E. coli flagellar motor switch, representing in each case a simple, precise bridge between experimental observations and the models we write down. In pursuit of mechanisms that saturate the support bound, we find a nonequilibrium binding mechanism, nested hysteresis, with sensitivity exponential in the number of binding sites, with implications for our understanding of models of gene regulation and the function of biomolecular condensates.
生物在其许多关键过程中都受益于精致的分子敏感性，包括 DNA 复制、转录和翻译、化学感应和形态发生。在热力学平衡时，敏感性的基本生物物理机制是协同结合，对于这种结合，可以证明敏感性度量的 Hill 系数不能超过结合位点的数量。推广这一事实，我们发现对于任何动力学方案，无论是在热力学平衡时还是偏离热力学平衡时，一个非常简单的结构数量，即扰动支撑的大小，总是限制有效 Hill 系数。我们展示了这个界限如何阐明和统一了各种敏感性机制，包括动力学校对和为大肠杆菌鞭毛马达开关提出的非平衡 Monod-Wyman-Changeux (MWC) 模型，在每种情况下，它都在实验观察和我们所写的模型之间建立了一种简单而精确的桥梁。在寻求饱和支撑界限的机制时，我们发现了一种非平衡结合机制，嵌套滞后，其敏感性与结合位点的数量呈指数关系，这对我们理解基因调控模型和生物分子凝聚物的功能具有重要意义。
