Reconstruction of protein structures from single-molecule time series

Area of Science:

• Computational Chemistry
• Biophysics
• Machine Learning

Background:

• Single-molecule experiments capture real-time molecular dynamics through limited observables, yielding low-dimensional data.
• These low-dimensional representations lack atomistic detail of instantaneous molecular structures.
• Takens's theorem suggests that low-dimensional time series can theoretically reconstruct full molecular configurations.

Purpose of the Study:

• To develop a method for reconstructing atomistic molecular configurations from experimentally measurable time series data.
• To combine theoretical principles with computational tools to bridge the gap between low-dimensional observables and high-dimensional molecular structures.

Main Methods:

• Integration of Takens's theorem with statistical thermodynamics, manifold learning, artificial neural networks, and rigid graph theory.
• Development of the Single-molecule TAkens Reconstruction (SMTR) algorithm to learn the transformation from observables to configurations.
• Application to molecular dynamics simulations of a polymer chain (C24H50) and the mini-protein chignolin using synthetic time series data.

Main Results:

• SMTR successfully reconstructs molecular configurations from time series of head-to-tail distances.
• Achieved atomistic root mean squared deviation accuracies better than 0.2 nm in simulations.
• Demonstrated the feasibility of accurate protein structure reconstruction from experimentally accessible observables.

Conclusions:

• It is possible to accurately reconstruct protein structures from time series of experimentally measurable observables.
• The study establishes the theoretical and algorithmic foundations for applying SMTR to real single-molecule experimental data.
• This approach offers a powerful tool for detailed molecular structure analysis in biophysical studies.