Topographical complexity of multidimensional energy landscapes
Topographical complexity of multidimensional energy landscapes
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DOI：
10.1073/pnas.0608517103
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发表时间：
2006-12
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通讯作者：
Gareth J Rylance;R. Johnston;Y. Matsunaga;Chun-Biu Li;A. Baba;T. Komatsuzaki
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作者：
Gareth J Rylance;R. Johnston;Y. Matsunaga;Chun-Biu Li;A. Baba;T. Komatsuzaki
提出了一种利用基于主成分的不连通性图和超级盆地相对“大小”的香农熵来可视化和量化多维能源景观和多路径复杂性的方案。基于主成分的不连通性图结合了系统驻点之间的度量关系，这使我们不仅能够捕获超级盆地的实际分配，而且能够捕获多维配置空间中每个超级盆地的大小。景观复杂性度量量化了多维能量景观的地形复杂程度，并告诉我们主路径的能量状态分支在哪个位置变得重要，使系统更有可能在动力学上陷入局部最小值。路径复杂性度量量化了系统通过所讨论的路径达到连接的局部最小值所遇到的困难，这意味着沿路径的分支点越重要，最终达到所需的局部最小值就越困难。作为一个说明性的例子，我们将此分析应用于两种小型模型蛋白质系统，它们表现出高度受挫和理想的漏斗状能量景观。
A scheme for visualizing and quantifying the complexity of multidimensional energy landscapes and multiple pathways is presented employing principal component-based disconnectivity graphs and the Shannon entropy of relative “sizes” of superbasins. The principal component-based disconnectivity graphs incorporate a metric relationship between the stationary points of the system, which enable us to capture not only the actual assignment of the superbasins but also the size of each superbasin in the multidimensional configuration space. The landscape complexity measure quantifies the degree of topographical complexity of a multidimensional energy landscape and tells us at which energy regime branching of the main path becomes significant, making the system more likely to be kinetically trapped in local minima. The path complexity measure quantifies the difficulty encountered by the system to reach a connected local minimum by the path in question, implying that the more significant the branching points along the path the more difficult it is to end up in the desired local minimum. As an illustrative example, we apply this analysis to two kinds of small model protein systems exhibiting a highly frustrated and an ideal funnel-like energy landscape.