Paijmans Joris, Lubensky David K, Ten Wolde Pieter Rein
FOM Institute AMOLF, Amsterdam, The Netherlands.
Department of Physics, University of Michigan, Ann Arbor, Michigan, United States of America.
PLoS Comput Biol. 2017 Mar 15;13(3):e1005415. doi: 10.1371/journal.pcbi.1005415. eCollection 2017 Mar.
The principal pacemaker of the circadian clock of the cyanobacterium S. elongatus is a protein phosphorylation cycle consisting of three proteins, KaiA, KaiB and KaiC. KaiC forms a homohexamer, with each monomer consisting of two domains, CI and CII. Both domains can bind and hydrolyze ATP, but only the CII domain can be phosphorylated, at two residues, in a well-defined sequence. While this system has been studied extensively, how the clock is driven thermodynamically has remained elusive. Inspired by recent experimental observations and building on ideas from previous mathematical models, we present a new, thermodynamically consistent, statistical-mechanical model of the clock. At its heart are two main ideas: i) ATP hydrolysis in the CI domain provides the thermodynamic driving force for the clock, switching KaiC between an active conformational state in which its phosphorylation level tends to rise and an inactive one in which it tends to fall; ii) phosphorylation of the CII domain provides the timer for the hydrolysis in the CI domain. The model also naturally explains how KaiA, by acting as a nucleotide exchange factor, can stimulate phosphorylation of KaiC, and how the differential affinity of KaiA for the different KaiC phosphoforms generates the characteristic temporal order of KaiC phosphorylation. As the phosphorylation level in the CII domain rises, the release of ADP from CI slows down, making the inactive conformational state of KaiC more stable. In the inactive state, KaiC binds KaiB, which not only stabilizes this state further, but also leads to the sequestration of KaiA, and hence to KaiC dephosphorylation. Using a dedicated kinetic Monte Carlo algorithm, which makes it possible to efficiently simulate this system consisting of more than a billion reactions, we show that the model can describe a wealth of experimental data.
蓝藻细长聚球藻生物钟的主要起搏器是一个由三种蛋白质（KaiA、KaiB和KaiC）组成的蛋白质磷酸化循环。KaiC形成一个同六聚体，每个单体由两个结构域CI和CII组成。两个结构域都能结合并水解ATP，但只有CII结构域可以在两个特定残基上按照明确的序列进行磷酸化。虽然这个系统已经得到了广泛研究，但生物钟如何由热力学驱动仍然不清楚。受近期实验观察结果的启发，并基于之前数学模型的思路，我们提出了一个新的、热力学一致的生物钟统计力学模型。其核心有两个主要观点：i）CI结构域中的ATP水解为生物钟提供了热力学驱动力，使KaiC在磷酸化水平趋于上升的活性构象状态和趋于下降的非活性构象状态之间切换；ii）CII结构域的磷酸化为CI结构域的水解提供了定时器。该模型还自然地解释了KaiA如何作为核苷酸交换因子刺激KaiC的磷酸化，以及KaiA对不同KaiC磷酸化形式的差异亲和力如何产生KaiC磷酸化的特征时间顺序。随着CII结构域中磷酸化水平的上升，CI结构域中ADP的释放减慢，使KaiC的非活性构象状态更加稳定。在非活性状态下，KaiC结合KaiB，这不仅进一步稳定了这种状态，还导致KaiA被隔离，从而使KaiC去磷酸化。使用一种专门的动力学蒙特卡罗算法，使得能够有效地模拟这个由超过十亿个反应组成的系统，我们表明该模型可以描述大量的实验数据。
