Transition path time distributions

Area of Science:

• Biophysics
• Chemical Physics
• Statistical Mechanics

Background:

• Biomolecular folding is often modeled as a two-state transition on a free energy landscape.
• Transition paths are critical segments of molecular dynamics trajectories crossing energy barriers.
• Experimental measurements of transition path times and their distributions are increasingly available for biomolecules.

Purpose of the Study:

• To calculate the full transition path time distribution for a single stochastic particle crossing a parabolic barrier.
• To incorporate inertial terms, often neglected, into the analysis of transition path dynamics.
• To compare results with the high friction limit and assess the influence of inertia.

Main Methods:

• Derivation of the full transition path time distribution for a stochastic particle.
• Inclusion of inertial terms in the stochastic dynamics model.
• Analytical calculation of average transition path times.

Main Results:

• The full transition path time distribution was derived, accounting for inertial effects.
• Average transition path times were calculated.
• Similarities and differences between the inertial and high friction limits were identified.

Conclusions:

• Inertial terms significantly influence short-time dynamics relevant to transition paths.
• The derived distribution provides a more complete model for understanding biomolecular transition dynamics.
• This work bridges theoretical calculations with experimental observations in biomolecular folding.