有向图上模型蛋白质的随机动力学
Stochastic dynamics of model proteins on a directed graph
摘要：
描述了一种用于重建简单多肽链的能量景观的方法。我们表明，我们可以通过一个合适的有向图构建一个等价的表示的能量景观。它的拓扑和动力学特征示出产生一个有效的估计与折叠和平衡过程的时间尺度。这一结论是通过比较恒温下的分子动力学模拟与图上由温度依赖的马尔可夫过程定义的动力学得出的。图表示的主要优点是，它的动态可以通过将节点收集到“集线器”中来自然地重新规范化，同时重新定义它们的连接性。我们表明，拓扑和动力学性质的重整化过程中保留。此外，我们得到明确的迹象表明，杂聚物表现出共同的拓扑性质，在差异与均聚物，其独特的图形结构源于其空间均匀性。为了在杂聚物中获得“快折叠”和“慢折叠”之间的明确区别，必须查看有向图的动力学特征。我们发现，快速文件夹达到其原生配置所需的平均时间比其平衡时间小两个数量级，而对于坏文件夹，这些时间尺度是可比的。因此，我们可以得出结论，本文所述的策略也可以成功地应用到更现实的模型，通过研究他们的重整化动力学的有向图，而不是进行冗长的分子动力学模拟。
英文摘要：
A method for reconstructing the energy landscape of simple polypeptidic chains is described. We show that we can construct an equivalent representation of the energy landscape by a suitable directed graph. Its topological and dynamical features are shown to yield an effective estimate of the time scales associated with the folding and with the equilibration processes. This conclusion is drawn by comparing molecular dynamics simulations at constant temperature with the dynamics on the graph, defined by a temperature dependent Markov process. The main advantage of the graph representation is that its dynamics can be naturally renormalized by collecting nodes into "hubs", while redefining their connectivity. We show that both topological and dynamical properties are preserved by the renormalization procedure. Moreover, we obtain clear indications that the heteropolymers exhibit common topological properties, at variance with the homopolymer, whose peculiar graph structure stems from its spatial homogeneity. In order to obtain a clear distinction between a "fast folder" and a "slow folder" in the heteropolymers one has to look at kinetic features of the directed graph. We find that the average time needed to the fast folder for reaching its native configuration is two orders of magnitude smaller than its equilibration time, while for the bad folder these time scales are comparable. Accordingly, we can conclude that the strategy described in this paper can be successfully applied also to more realistic models, by studying their renormalized dynamics on the directed graph, rather than performing lengthy molecular dynamics simulations.
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