Recovering hidden degrees of freedom using Gaussian processes

Area of Science:

• Computational Chemistry
• Biophysics
• Machine Learning

Background:

• Molecular Dynamics (MD) simulations generate vast sequential data.
• Conventional dimensionality reduction methods often ignore the temporal nature of MD data.
• Extracting meaningful insights requires methods that respect the time-dependent structure of simulations.

Purpose of the Study:

• To develop a novel dimensionality reduction framework for MD data that explicitly accounts for temporal dependencies.
• To create a physics-informed representation learning approach that preserves the Markovian property of the reduced data.
• To enhance the analysis of complex biomolecular systems by capturing essential dynamics missed by traditional methods.

Main Methods:

• Integration of Gaussian processes with variational autoencoders for representation learning.
• Utilization of time-dependent kernel functions (e.g., Matérn kernel) to impose temporal correlation structure.
• Application to a 3D toy model and a 50 μs T4 lysozyme MD trajectory.

Main Results:

• Demonstrated successful identification and separation of dynamically distinct states in a toy model, even when geometrically similar.
• Uncovered previously unresolved conformational substates in T4 lysozyme by analyzing temporal correlations.
• Revealed functional relationships in biomolecular systems that are only apparent when time-aware dynamics are considered.

Conclusions:

• The proposed physics-informed, time-aware framework effectively captures essential dynamics in MD simulations.
• This approach offers a powerful new perspective for understanding complex biomolecular systems.
• It overcomes limitations of conventional methods by preserving temporal correlations and Markovianity in the reduced representation.