Protein drift-diffusion in membranes with non-equilibrium fluctuations arising from gradients in concentration or temperature

We investigate proteins within heterogeneous cell membranes where non-equilibrium phenomena arises from spatial variations in concentration and temperature. We develop simulation methods building on non-equilibrium statistical mechanics to obtain stochastic hybrid continuum-discrete descriptions which track individual protein dynamics, spatially varying concentration fluctuations, and thermal exchanges. We investigate biological mechanisms for protein positioning and patterning within membranes and factors in thermal gradient sensing. We also study the kinetics of Brownian motion of particles with temperature variations within energy landscapes arising from heterogeneous microstructures within membranes. The introduced approaches provide self-consistent models for studying biophysical mechanisms involving the drift-diffusion dynamics of individual proteins and energy exchanges and fluctuations between the thermal and mechanical parts of the system. The methods also can be used for studying related non-equilibrium effects in other biological systems and soft materials.Author summary: We introduce theoretical frameworks and computational simulation methods for modeling and investigating protein dynamics within heterogeneous membranes in non-equilibrium regimes. A hybrid discrete-continuum approach is developed allowing for tracking individual proteins and their coupling to spatial variations in concentration and temperature captured by continuum fluctuating fields. Investigations are performed of biological processes and related phenomena arising from fluctuations, gradients in concentration, variations in temperature, and other non-equilibrium effects.