Noise, data and time resolution limits for reconstruction of all-atom protein structures from single molecule FRET time series

Single molecule FRET (smFRET) is an experimental technique used to record protein dynamics by periodically measuring a small set of scalar observables. Takens' Theorem states that under specific conditions, time series vectors constructed from scalar observables of a dynamical system embed full dimensional system dynamics. Single molecule Takens' reconstruction (STAR) combines smFRET measurements with Takens' Theorem to reconstruct the all atom molecular trajectory through manifold learning and artificial neural networks. Applying synthetic noise characteristic of smFRET, time binned observation data, and limited learning data, we employ molecular dynamics simulations to test the experimental limits of STAR in terms of data volume, time resolution, and signal-to-noise ratio to place limits on anticipated reconstruction accuracy. Our results show that Chignolin can be reconstructed with RMSDs of 0.2 nm, Villin to within 0.4 nm, and BBL to within 0.5 nm under conditions representative of realistic smFRET experiments.