Topological methods for exploring low-density states in biomolecular folding pathways
Topological methods for exploring low-density states in biomolecular folding pathways
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DOI：
10.1063/1.3103496
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发表时间：
2009-04-14
影响因子：
4.4
通讯作者：
Carlsson, Gunnar
中科院分区：
文献类型：
--
作者：
Yao, Yuan;Sun, Jian;Carlsson, Gunnar
瞬态中间或过渡态的表征对于描述生物分子折叠途径至关重要，然而这在实验和计算机模拟中都很困难。这种瞬态在模拟样本中通常属于低群体。即使对于 RNA 发夹这样的简单系统，最近关于多个中间态是否存在的争论也越来越多。在本文中，我们基于拓扑数据分析工具 MAPPER 以及来自大规模分布式计算的模拟数据，开发了一种计算方法来探索生物分子折叠路径中相对较低的过渡态或中间态。该方法受到数学中经典莫尔斯理论的启发，该理论通过一些功能水平集来表征高维形状的拓扑。在本文中，我们利用条件密度过滤器，使我们能够专注于路径上的结构，然后对其水平集进行聚类分析，这有助于将低填充中间体与高填充折叠/展开结构分开。这种方法的成功应用是一个令人兴奋的例子，即具有 GCAA 四环的 RNA 发夹，我们能够通过计算机模拟提供多种中间状态的结构证据，并展示有关展开和重折叠途径的不同图片。该方法可以有效处理分布的高度异质性，捕获多个路径中的结构特征，并且与非线性降维或几何嵌入方法相比对距离度量不太敏感。本文描述的方法允许各种实现或扩展以纳入更多信息并适应不同的设置，从而提供了探索复杂生物分子折叠系统中的低密度中间态的系统工具。
Characterization of transient intermediate or transition states is crucial for the description of biomolecular folding pathways, which is, however, difficult in both experiments and computer simulations. Such transient states are typically of low population in simulation samples. Even for simple systems such as RNA hairpins, recently there are mounting debates over the existence of multiple intermediate states. In this paper, we develop a computational approach to explore the relatively low populated transition or intermediate states in biomolecular folding pathways, based on a topological data analysis tool, MAPPER, with simulation data from large-scale distributed computing. The method is inspired by the classical Morse theory in mathematics which characterizes the topology of high-dimensional shapes via some functional level sets. In this paper we exploit a conditional density filter which enables us to focus on the structures on pathways, followed by clustering analysis on its level sets, which helps separate low populated intermediates from high populated folded/unfolded structures. A successful application of this method is given on a motivating example, a RNA hairpin with GCAA tetraloop, where we are able to provide structural evidence from computer simulations on the multiple intermediate states and exhibit different pictures about unfolding and refolding pathways. The method is effective in dealing with high degree of heterogeneity in distribution, capturing structural features in multiple pathways, and being less sensitive to the distance metric than nonlinear dimensionality reduction or geometric embedding methods. The methodology described in this paper admits various implementations or extensions to incorporate more information and adapt to different settings, which thus provides a systematic tool to explore the low-density intermediate states in complex biomolecular folding systems.