Quasi-two-dimensional diffusion of interacting protein monomers and dimers: A MPC simulation study

Understanding lateral diffusion of proteins along a membrane is of importance in biological soft matter science. An example in case is postsynaptic neuronal signal transduction where specific proteins diffuse alongside a postsynaptic membrane, triggering a cascade of biochemical processes. There are challenging questions to answer such as how the collective and self-diffusion of the proteins are affected by their direct and hydrodynamic interactions for larger areal protein concentrations. Using the multi-particle collision dynamics (MPC) simulation methods [1], we explore protein diffusion under quasi-two-dimensional (Q2D) confinement, for two different model systems of proteins. In the first system, the proteins are modeled as Brownian spheres interacting, respectively, by a hard-sphere potential serving as a reference potential, and by a soft potential with competing short-range attractive and long-range repulsive parts. For a minimalistic description of proteins diffusing along a cytosol-membrane interface, the Brownian spheres are confined to lateral motion in a planar monolayer embedded in an unbound three-dimensional Newtonian fluid. The time scales in the dynamic simulations extend from very short times where inertial effects are resolved, up to long times where the solvent-mediated hydrodynamic interactions between the proteins are fully developed and non-retarded [2]. By computing velocity autocorrelation functions, mean-square displacements and Fourier-space current auto-correlation functions, we quantify how concentration-induced correlations affect, e.g., the anomalous enhancement of large-scale collective diffusion under Q2D confinement [3], and the development of inter-protein hydrodynamic interactions by multiple scattering of sound and by vorticity diffusion [2]. The second model system relates to the diffusion of a human dumbbell-shaped M2 muscarinic acetylcholine receptor protein where the upper segment is embedded in the neuronal cell membrane, and the lower one in the cytosol. The protein is simply modelled by a two-beads dimer with the upper bead immersed in a high-viscosity fluid sheet (fluid A) mimicking the membrane, and the lower one in a lower-viscosity fluid B mimicking the intra- and also extracellular environment. We use a recently developed MPC scheme for generating a fluid sheet A inside another fluid B [4]. Using this mesoscale method, diffusion can be probed over time spans not accessible in atomistic MD simulations of proteins. We study the mean squared displacement and velocity autocorrelation function of the individual bead centres and the hydrodynamic centre of mobility of the dumbbell, in dependence of the viscosity ratio sheet thickness and interfacial bead distances