Department of Physics, University of Chicago, Chicago, Illinois 60637, United States.
Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States.
J Chem Theory Comput. 2023 Jul 25;19(14):4654-4667. doi: 10.1021/acs.jctc.2c00920. Epub 2023 Jan 26.
Single-molecule Förster resonance energy transfer (smFRET) is an experimental methodology to track the real-time dynamics of molecules using fluorescent probes to follow one or more intramolecular distances. These distances provide a low-dimensional representation of the full atomistic dynamics. Under mild technical conditions, Takens' Delay Embedding Theorem guarantees that the full three-dimensional atomistic dynamics of a system are diffeomorphic (i.e., related by a smooth and invertible transformation) to a time-delayed embedding of one or more scalar observables. Appealing to these theoretical guarantees, we employ manifold learning, artificial neural networks, and statistical mechanics to learn from molecular simulation training data the a priori unknown transformation between the atomic coordinates and delay-embedded intramolecular distances accessible to smFRET. This learned transformation may then be used to reconstruct atomistic coordinates from smFRET time series data. We term this approach Single-molecule TAkens Reconstruction (STAR). We have previously applied STAR to reconstruct molecular configurations of a CH polymer chain and the mini-protein Chignolin with accuracies better than 0.2 nm from simulated smFRET data under noise free and high time resolution conditions. In the present work, we investigate the role of signal-to-noise ratio, data volume, and time resolution in simulated smFRET data to assess the performance of STAR under conditions more representative of experimental realities. We show that STAR can reconstruct the Chignolin and Villin mini-proteins to accuracies of 0.12 and 0.42 nm, respectively, and place bounds on these conditions for accurate reconstructions. These results demonstrate that it is possible to reconstruct dynamical trajectories of protein folding from time series in noisy, time binned, experimentally measurable observables and lay the foundations for the application of STAR to real experimental data.
单分子Förster 共振能量转移（smFRET）是一种实验方法，通过荧光探针跟踪分子的实时动力学，以跟踪一个或多个分子内距离。这些距离提供了全原子动力学的低维表示。在温和的技术条件下，Takens 的延迟嵌入定理保证了系统的全三维原子动力学与一个或多个标量观测值的时间延迟嵌入是同胚的（即通过平滑和可逆变换相关）。利用这些理论保证，我们采用流形学习、人工神经网络和统计力学，从分子模拟训练数据中学习到原子坐标和 smFRET 可访问的延迟嵌入分子内距离之间的先验未知变换。然后，这个学习到的变换可以用于从 smFRET 时间序列数据中重建原子坐标。我们将这种方法称为单分子 Takens 重建（STAR）。我们之前已经应用 STAR 从无噪声和高时间分辨率条件下的模拟 smFRET 数据中重建 CH 聚合物链和 Chignolin 小型蛋白的分子构象，精度优于 0.2nm。在本工作中，我们研究了信噪比、数据量和时间分辨率在模拟 smFRET 数据中的作用，以评估 STAR 在更能代表实验现实条件下的性能。我们表明，STAR 可以分别将 Chignolin 和 Villin 小型蛋白重建到 0.12nm 和 0.42nm 的精度，并对这些条件进行了准确重建的限制。这些结果表明，从时间序列中噪声、时间分组、可测量的实验观测值中重建蛋白质折叠的动态轨迹是可能的，并为 STAR 在真实实验数据中的应用奠定了基础。
