Transition path time distribution and the transition path free energy barrier

Area of Science:

• Biophysics
• Chemical Physics

Background:

• Experimental measurements of protein transition path time distributions present theoretical challenges.
• Discrepancies exist between experimental data fits and theoretical activation energies.
• Determining transition path time distributions without the Smoluchowski limit is an open theoretical question.

Purpose of the Study:

• To derive an exact expression for transition path time distribution valid for arbitrary memory friction.
• To address the discrepancy between experimental and theoretical barrier heights in protein dynamics.
• To introduce and analyze the concept of transition path barrier height.

Main Methods:

• Utilizing the normal mode transformation, fundamental to Kramers' rate theory.
• Deriving an exact expression for transition path time distribution applicable to systems with memory friction.
• Comparing transition path time distributions under absorbing and free boundary conditions.

Main Results:

• An exact expression for transition path time distribution is derived, applicable beyond the Smoluchowski limit.
• The study highlights the impact of boundary conditions (absorbing vs. free) on transition times and barrier height calculations.
• A theoretical framework is established showing transition path barrier height is consistently smaller than activation energy.

Conclusions:

• The derived exact expression resolves theoretical challenges in protein transition path time analysis.
• Understanding boundary condition effects is crucial for accurate interpretation of experimental protein dynamics data.
• The concept of transition path barrier height provides a more accurate metric for characterizing transition dynamics than activation energy alone.