Subdiffusive-Brownian crossover in membrane proteins: a Generalized Langevin Equation-based approach

TL;DR

This paper introduces a GLE-based model to describe membrane protein diffusion, capturing transitions from ballistic to subdiffusive to Brownian regimes, validated against molecular dynamics simulations.

Contribution

It presents a novel GLE framework with a Mittag-Leffler memory kernel to model different diffusion regimes and their crossover in membrane proteins.

Findings

The model accurately reproduces the MSD of membrane proteins.

It identifies transition times between diffusion regimes.

The approach aligns well with MD simulation data.

Abstract

In this paper, we propose a Generalized Langevin Equation (GLE)-based model to describe the lateral diffusion of a protein in a lipid bilayer. The memory kernel is represented in terms of a viscous (instantaneous) and an elastic (non instantaneous) component modeled respectively through a Dirac delta function and a three-parameter Mittag-Leffler type function. By imposing a specific relationship between the parameters of the three-parameters Mittag-Leffler function, the different dynamical regimes, namely ballistic, subdiffusive and Brownian, as well as the crossover from one regime to another, are retrieved. Within this approach, the transition time from the ballistic to the subdiffusive regime and the distribution of relaxation times underlying the transition from the subdiffusive to the Brownian regime are given. The reliability of the model is tested by comparing the Mean Squared Displacement (MSD) derived in the framework of this model and the MSD of a protein diffusing in a membrane calculated through molecular dynamics (MD) simulations.