Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning
Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning
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通过延迟嵌入和流形学习从单分子时间序列恢复蛋白质折叠漏斗
DOI：
10.1021/acs.jpcb.8b08800
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
Ferguson, Andrew L.
中科院分区：
文献类型：
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作者：
Wang, Jiang;Ferguson, Andrew L.
蛋白质的稳定性和折叠是由基本的单分子自由能表面(SmFES)控制的，该表面映射了分子的自由能作为构型状态的函数。确定sMFES对于理解和工程蛋白质的结构和功能具有重要价值。通过集成动力系统理论和非线性流形学习的工具，我们描述了一种从单个可实验测量的可观测的时间序列中重建蛋白质的多维SMFE的方法。我们利用Takens的延迟嵌入将时间序列投影到高维空间中，在高维空间中投影的动力学与真实的系统动力学等价，并使用扩散映射来恢复与真实的smFES等价的sMFES的低维重构直到光滑且可逆的变换。我们在Trp-Cage、Villin和BBA的分子动力学模拟中验证了该方法，以证明从头尾距离的单变量时间序列恢复的景观在拓扑上是相同的--它们精确地保持了亚稳态和折叠路径--并且在拓扑上近似--自由能垒的高度和深度被近似地保持--与由所有原子坐标的完全知识确定的真实景观相同。我们继续证明，重建的景观可靠地预测了温度变性，并识别了点突变和对折叠至关重要的突变组。这些结果表明，蛋白质折叠漏斗可以从实验上可测量的时间序列中重建出来，并用于理解和设计折叠。
The stability and folding of proteins is governed by the underlying single-molecule free energy surface (smFES) mapping the free energy of the molecule as a function of configurational state. Ascertaining the smFES is of great value in understanding and engineering protein structure and function. By integrating tools from dynamical systems theory and nonlinear manifold learning, we describe an approach to reconstruct the multidimensional smFES for a protein from a time series in a single experimentally measurable observable. We employ Takens’ delay embeddings to project the time series into a high-dimensional space in which the projected dynamics areC1-equivalent to the true system dynamics and employ diffusion maps to recover a low-dimensional reconstruction of the smFES that is equivalent to the true smFES up to a smooth and invertible transformation. We validate the approach in molecular dynamics simulations of Trp-cage, Villin, and BBA to demonstrate that landscapes recovered from univariate time series in the head-to-tail distance are topologically identical—they precisely preserve the metastable states and folding pathways—and topographically approximate—the free energy barrier heights and well depths are approximately preserved—to the true landscapes determined from complete knowledge of all atomic coordinates. We go on to show that the reconstructed landscapes reliably predict temperature denaturation and identify point mutations and groups of mutations critical to folding. These results demonstrate that protein folding funnels can be reconstructed from experimentally measurable time series and used to understand and engineer folding.