Memory function for protein diffusion

Area of Science:

• Computational physics
• Biophysics
• Physical chemistry

Background:

• Standard diffusion constant calculations rely on mean-squared displacement or velocity autocorrelation functions.
• These methods do not account for the physical nature of the random forces involved.
• The force route, utilizing the Kirkwood equation, addresses this limitation for diffusive particles.

Purpose of the Study:

• To formulate and validate the force route for calculating diffusion constants in molecular dynamics (MD) simulations.
• To compare the accuracy and system-size dependence of the force route against traditional methods.
• To investigate protein diffusion using MD simulations of green fluorescent protein and plastocyanin mutants.

Main Methods:

• Molecular dynamics (MD) simulations of six charge mutants of green fluorescent protein and plastocyanin.
• Calculation of memory functions to determine memory time.
• Application of the Kirkwood equation using the force route and comparison with velocity/displacement routes.
• Analysis of system-size effects on diffusion constant calculations.

Main Results:

• The force route, using memory time, provides a more accurate calculation of the diffusion constant compared to standard methods.
• The Kirkwood equation, when applied via the force route, overestimates protein diffusion constants by approximately a factor of four.
• Diffusion constants calculated via velocity/displacement routes exhibit strong system-size dependence, with standard corrections showing significant flaws for protein diffusion.
• Diffusion constants derived from the force route demonstrate minimal system-size dependence, yielding corrected values largely independent of system size.

Conclusions:

• The force route offers a more robust and accurate method for calculating diffusion constants, particularly for proteins, by accounting for the physical nature of forces.
• Traditional methods for calculating diffusion constants and correcting for finite-size effects are inadequate for protein diffusion.
• The force route's reduced system-size dependence makes it a superior approach for accurate diffusion analysis in complex biological systems.