变构的机制：对比诱导适应和人口转移情景
Mechanics of allostery: contrasting the induced fit and population shift scenarios
摘要：
在变构蛋白中，结合配体可以影响远端位置的功能，例如通过改变活性位点处底物的结合亲和力。诱导适合和人口迁移模型，不同的假设数量的稳定配置，从热力学的角度解释这种合作结合。然而，理解什么机械原理约束这些模型仍然是一个挑战。在这里，我们提供了一个实证研究34蛋白质支持的想法，变构构象变化通常发生沿软弹性模式呈现扩展区域的高剪切。我们认为，基于一个详细的分析，如何沿这样的模式的能量分布依赖于绑定，在诱导适合的情况下，有一个最佳的刚度$k_a^*\sim 1/N$合作绑定，其中$N$是参与变构反应的残基的数量。我们发现，人口转移的情况下是更强大的突变影响刚度，作为绑定变得越来越多的合作与刚度相同的特征值$k_a^*$，超过该合作饱和，而不是衰减。我们在数值上证实了这些发现在一个非线性力学模型。动力学的考虑表明，$k_a^*$级的刚度在这种情况下也是有利的，支持了蛋白质为了实现适当的功能，必须进化出一种功能弹性模式，这种模式随着它们的尺寸增加而变得更软。与此观点相一致，我们发现在我们的数据集中，变构反应的刚度和蛋白质大小之间存在显著的正相关。
英文摘要：
In allosteric proteins, binding a ligand can affect function at a distant location, for example by changing the binding affinity of a substrate at the active site. The induced fit and population shift models, which differ by the assumed number of stable configurations, explain such cooperative binding from a thermodynamic viewpoint. Yet, understanding what mechanical principles constrain these models remains a challenge. Here we provide an empirical study on 34 proteins supporting the idea that allosteric conformational change generally occurs along a soft elastic mode presenting extended regions of high shear. We argue, based on a detailed analysis of how the energy profile along such a mode depends on binding, that in the induced fit scenario there is an optimal stiffness $k_a^*\sim 1/N$ for cooperative binding, where $N$ is the number of residues involved in the allosteric response. We find that the population shift scenario is more robust to mutation affecting stiffness, as binding becomes more and more cooperative with stiffness up to the same characteristic value $k_a^*$, beyond which cooperativity saturates instead of decaying. We confirm numerically these findings in a non-linear mechanical model. Dynamical considerations suggest that a stiffness of order $k_a^*$ is favorable in that scenario as well, supporting that for proper function proteins must evolve a functional elastic mode that is softer as their size increases. In consistency with this view, we find a significant anticorrelation between the stiffness of the allosteric response and protein size in our data set.
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