A continuous-space analytical framework for committor functions from molecular dynamics

Area of Science:

• Computational Chemistry
• Biophysics
• Statistical Mechanics

Background:

• Biomolecular processes often involve rare transitions between metastable states.
• The committor function is crucial for describing these transitions, but traditional methods like Markov State Models (MSMs) limit spatial resolution.

Purpose of the Study:

• To develop an analytical framework for computing continuous-space committor functions directly from molecular dynamics trajectories.
• To overcome the spatial resolution limitations of existing methods for analyzing complex free-energy landscapes.

Main Methods:

• Utilizing a Liouville propagator in a basis-function representation to compute committor functions.
• Constructing the Liouville propagator and committor functions directly from basis functions without solving for eigenfunctions.
• Applying the framework to a 2D model potential, alanine dipeptide, and the FIP35 WW domain.

Main Results:

• The new framework enables computation of continuous committor functions and iso-committor surfaces without discretizing configuration space.
• Results show agreement with MSM-TPT methods but offer significantly higher spatial resolution.
• Precise identification of transition states is achieved, improving the analysis of biomolecular dynamics.

Conclusions:

• The developed analytical framework provides a versatile foundation for analyzing dynamics in biomolecular systems and other complex processes.
• The method accommodates various basis representations, including machine-learning-derived collective variables.
• This approach offers a powerful tool for understanding rare events in complex systems with high fidelity.