Topological Methods for Exploring Low-density States in Folding Pathways

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. We applied Mapper to simulation data from large-scale distributed computing to provide structural evidence on multiple intermediate states of the unfolding and refolding of an RNA hairpin with a GCAA tetraloop. This project contains Mapper, the RNA conformations (in contact map format), and instructions to reproduce results from this paper.<b> Motivation: </b> 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. <b> More about Mapper and the computational approach </b> 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 uninteresting structures.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. <br/><br/>This project includes the following software/data packages: <br/> <ul> <li> <a href="https://simtk.org/frs?group_id=362#pack_586">Bio-Mapper tools </a> : BIO_Mapper matlab tools for analyzing RNA hairpin folding pathways </li> <li> <a href="https://simtk.org/frs?group_id=362#pack_590">Reproduce RNA-Mapper paper </a> : This package can be used to reproduce the results of the following article,Topological Methods for Exploring Low-density States in Biomolecular Folding Pathways. Yuan Yao, Jian Sun, Xuhui Huang, Gregory Bowman, Gurjeet Singh, Michael Lesnick, Vijay Pande, Leonidas Guibas and Gunnar Carlsson. J. Chem. Phys. 130, 144115 (2009) This program is running in MATLAB 7.4 (R2007a) or above, and has following two additional requirements: 1) Matlab toolbox MatlabBGL (free): http://www.mathworks.com/matlabcentral/fileexchange/10922 2) Graphviz (free): http://www.graphviz.org/ </li> </ul>

本文提出一种基于拓扑数据分析工具Mapper的计算方法，旨在探讨生物分子折叠途径中相对稀疏的过渡或中间状态。我们应用Mapper对大规模分布式计算模拟数据进行处理，以提供具有GCAA四链环的RNA发夹结构展开和折叠的多个中间状态的构象证据。本项目包含Mapper工具、RNA构象（以接触图格式）以及复现本文结果的指令。<b>动机：</b>对瞬时中间或过渡状态的表征对于描述生物分子折叠途径至关重要，然而在实验和计算机模拟中均较为困难。此类瞬时状态在模拟样本中通常人口数量稀少。即使是如RNA发夹这样的简单系统，近期也出现了关于多个中间状态存在的激烈争论。<b>关于Mapper和计算方法：</b>该方法受数学中经典莫尔斯理论的启发，通过某些函数水平集表征高维形状的拓扑结构。在本文中，我们利用条件密度滤波器，使我们能够聚焦于途径上的结构，随后对其水平集进行聚类分析，有助于将人口数量稀少的中间结构从人口数量多的无趣结构中分离出来。该方法在处理分布的高度异质性、捕捉多个途径中的结构特征以及相对于非线性降维或几何嵌入方法对距离度量的敏感性较低方面表现有效。本文所述的方法论允许进行各种实现或扩展，以融入更多信息并适应不同环境，从而为探索复杂生物分子折叠系统中低密度中间状态提供了一种系统的工具。<br/><br>本项目包括以下软件/数据包：<br/> <ul> <li> <a href="https://simtk.org/frs?group_id=362#pack_586">Bio-Mapper工具</a>：用于分析RNA发夹折叠途径的BIO_Mapper Matlab工具</li> <li> <a href="https://simtk.org/frs?group_id=362#pack_590">复现RNA-Mapper论文</a>：本软件包可用于复现以下文章的结果：《探索生物分子折叠途径中低密度状态拓扑方法》。作者：Yuan Yao, Jian Sun, Xuhui Huang, Gregory Bowman, Gurjeet Singh, Michael Lesnick, Vijay Pande, Leonidas Guibas 和 Gunnar Carlsson。发表于《化学物理学报》130卷，144115号（2009年）。该程序在MATLAB 7.4（R2007a）或更高版本上运行，并有以下两个附加要求：1) Matlab工具箱MatlabBGL（免费）：http://www.mathworks.com/matlabcentral/fileexchange/10922 2) Graphviz（免费）：http://www.graphviz.org/ </li> </ul>