Subdiffusive-Brownian crossover in membrane proteins: a generalized Langevin equation-based approach

Area of Science:

• Biophysics
• Computational Biology
• Physical Chemistry

Background:

• Protein lateral diffusion in lipid bilayers is crucial for membrane functions.
• Understanding diffusion dynamics, including ballistic, subdiffusive, and Brownian regimes, is essential.
• Existing models may not fully capture the complex, time-dependent nature of protein diffusion.

Purpose of the Study:

• To propose a generalized Langevin equation-based model for protein lateral diffusion in lipid bilayers.
• To incorporate both viscous and elastic components into the memory kernel for a comprehensive description.
• To analyze and predict different dynamical regimes and their transitions.

Main Methods:

• Utilized a generalized Langevin equation framework.
• Modeled the memory kernel using a Dirac delta function (viscous) and a three-parameter Mittag-Leffler function (elastic).
• Imposed specific parameter relationships in the Mittag-Leffler function to capture different diffusion regimes.

Main Results:

• The model successfully retrieves ballistic, subdiffusive, and Brownian diffusion regimes.
• It accurately describes the crossover dynamics between these regimes.
• The model provides insights into transition times and relaxation time spectra.

Conclusions:

• The proposed generalized Langevin equation model offers a robust framework for describing protein lateral diffusion in lipid bilayers.
• The model's ability to reproduce various dynamical regimes and transitions is validated against molecular dynamics simulations.
• This approach enhances our understanding of protein mobility within biological membranes.