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首页> 外文期刊>Proceedings of the National Academy of Sciences of the United States of America >Topographical complexity of multidimensional energy landscapes
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Topographical complexity of multidimensional energy landscapes

机译：多维能源景观的地形复杂性

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摘要

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.
机译：利用基于主成分的不连续性图和超级流域的相对“大小”的香农熵，提出了一种可视化和量化多维能量格局和多路径复杂性的方案。基于主成分的不连通图包含系统固定点之间的度量关系，这使我们不仅可以捕获超级盆地的实际分配，还可以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性程度，并告诉我们主路径的哪个能量状态分支变得显着，从而使系统更容易被动力学困在局部极小值中。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，这意味着沿该路径的分支点越重要，最终达到所需局部最小值的难度就越大。作为说明性示例，我们将此分析应用于表现出高度挫败和理想的漏斗状能量态势的两种小型模型蛋白质系统。

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