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

In this work, we propose a generalized Langevin equation-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 (noninstantaneous) component modeled through a Dirac d function and a three-parameter Mittag-Leffler type function, respectively. By imposing a specific relationship between the parameters of the three-parameter 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 spectrum 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-square displacement derived in the framework of this model and the mean-square displacement of a protein diffusing in a membrane calculated through molecular dynamics simulations.

Automated summary

In this work, a generalized Langevin equation-based model is proposed to describe the lateral diffusion of a protein in a lipid bilayer. By imposing a specific relationship between the parameters, different dynamical regimes and the transition between them are identified, with the transition time and spectrum of relaxation times given. The model's reliability is tested by comparing its results with molecular dynamics simulations.