Reconstruction of Protein Structures from Single-Molecule Time Series

TL;DR

This paper introduces STAR, a novel method combining Takens' Theorem with machine learning and thermodynamics to reconstruct detailed protein structures from low-dimensional single-molecule time series data, achieving high accuracy.

Contribution

The work develops a new theoretical and computational framework for reconstructing atomistic protein structures from experimental time series data, bridging a key gap in single-molecule analysis.

Findings

Reconstructed molecular configurations with <0.2 nm RMSD accuracy.

Validated approach on molecular dynamics simulations of polymers and proteins.

Established theoretical foundations for experimental data application.

Abstract

Single-molecule experimental techniques track the real-time dynamics of molecules by recording a small number of experimental observables. Following these observables provides a coarse-grained, low-dimensional representation of the conformational dynamics but does not furnish an atomistic representation of the instantaneous molecular structure. Takens' Delay Embedding Theorem asserts that, under quite general conditions, these low-dimensional time series can contain sufficient information to reconstruct the full molecular configuration of the system up to an a priori unknown transformation. By combining Takens' Theorem with tools from statistical thermodynamics, manifold learning, artificial neural networks, and rigid graph theory, we establish an approach Single-molecule TAkens Reconstruction (STAR) to learn this transformation and reconstruct molecular configurations from time series in experimentally-measurable observables such as intramolecular distances accessible to single molecule F\"orster resonance energy transfer. We demonstrate the approach in applications to molecular dynamics simulations of a C24H50 polymer chain and the artificial mini-protein Chignolin. The trained models reconstruct molecular configurations from synthetic time series data in the head-to-tail molecular distances with atomistic root mean squared deviation accuracies better than 0.2 nm. This work demonstrates that it is possible to accurately reconstruct protein structures from time series in experimentally-measurable observables and establishes the theoretical and algorithmic foundations to do so in applications to real experimental data.