2021 Annual Meeting
(118h) Data-Driven Reconstruction of Molecular Folding Trajectories from Single-Molecule Experimental Measurements
Single molecule fluorescence resonance energy transfer (smFRET) measures intramolecular distances in real time, allowing for experimental tracking of dynamics of molecules. These distances serve as low-dimensional observables of the molecular trajectory but do not directly furnish the high-dimensional atomistic trajectory. Takensâ Delay Embedding Theorem asserts that under sufficiently long and frequent sampling a time series of generic scalar observables contain the same dynamical systems information as the all-atom trajectory up to symmetries in the observable. By combining Takensâ Theorem with manifold learning, deep learning, and molecular simulations we present an approach termed Single-molecule TAkens Reconstruction (STAR) to reconstruct atomistic trajectories from experimentally measurable observables. We demonstrate the approach in applications to long all-atom simulations the proteins Chignolin, BBL, Villin and NTL9. In addition, we investigate the role noise, data and time resolution to show that the robust denoising and filtering properties of the manifold learning techniques enable molecular trajectories can be reconstructed to within 0.2 nm accuracy in the mean atomic positions under realistic conditions of experimental smFRET data collection. This synthesis of dynamical systems theory, data-driven learning, and statistical thermodynamics establishes STAR as a useful new tool to analyze and process single molecule measurements allowing for robust extraction of atomistic molecular trajectories.