Riemannian geometry for efficient analysis of protein dynamics data

Area of Science:

• Computational biology
• Biophysics
• Data science

Background:

• Protein dynamics data often exhibit nonlinear geometry within low-energy conformational subspaces.
• Existing data analysis tools may not adequately capture this complex, nonlinear structure.
• Modeling protein conformational landscapes requires robust geometric frameworks.

Purpose of the Study:

• To develop computationally feasible methods for analyzing protein dynamics using Riemannian geometry.
• To construct a smooth Riemannian structure directly from protein energy landscapes.
• To validate the utility of this Riemannian approach for protein data analysis tasks.

Main Methods:

• Developed a local approximation technique for efficient geodesic computation on Riemannian manifolds.
• Constructed a smooth manifold and Riemannian structure based on protein energy landscapes.
• Applied the Riemannian geometry framework to analyze protein dynamics datasets.

Main Results:

• Geodesics approximated molecular dynamics trajectories for proteins with ordered, medium-sized deformations.
• The Riemannian approach yielded physically realistic summary statistics.
• Accurately retrieved underlying data dimensions for large deformations rapidly on a laptop.

Conclusions:

• Riemannian geometry offers a powerful, computationally feasible framework for modeling protein dynamics.
• This approach effectively captures nonlinearities in protein conformational energy landscapes.
• The developed methods are practical for analyzing complex protein motion and deformations.