Effective Riemannian Diffusion Model for Conformational Dynamics of Biomolecular Systems

Area of Science:

• Computational chemistry
• Biophysics
• Theoretical physics

Background:

• Biomolecular simulations often use collective variables to study conformational changes.
• Standard methods can be sensitive to coordinate choices, complicating free energy calculations.
• Understanding the intrinsic geometry of these spaces is crucial for accurate dynamics.

Purpose of the Study:

• To develop a Riemannian formalism for biomolecule diffusion in collective variable spaces.
• To provide a robust framework for conformational free energy calculations.
• To incorporate the intrinsic geometry of collective variables into enhanced sampling techniques.

Main Methods:

• Formulation of Riemannian diffusion in collective variable spaces.
• Mathematical equivalence to Euclidean diffusion with a position-dependent diffusion tensor.
• Application to enhanced sampling techniques like umbrella sampling (US).

Main Results:

• The Riemannian potential of mean force (PMF) and minimum free energy path (MFEP) are invariant under coordinate transformations.
• The formalism provides a more convenient framework for free energy calculations and path-finding algorithms.
• Demonstrated on a 3D toy model and met-enkephalin in explicit solvent.

Conclusions:

• The Riemannian approach offers a geometrically sound and robust method for analyzing biomolecular conformational dynamics.
• This formalism enhances the accuracy and reliability of free energy calculations and path identification.
• It provides a powerful tool for understanding the effective conformational dynamics of biomolecules.