Protein lateral movement in lipid bilayers. Monte Carlo simulation studies of its dependence upon attractive protein-protein interactions

Abstract

We have studied the random movement of hexagons on a triangular lattice where the only mechanisms hindering diffusion are (i) the hard-core repulsion between hexagons which block pathways and (ii) attractive interactions between pairs of hexagons which can give rise to hexagon aggregation. This is an extension of earlier work (Pink, D.A. (1985) Biochim. Biophys. Acta 818, 200–204) which studied how diffusion of hexagons on a lattice was affected only by (i). This system is a simple model of the movement of integral proteins, in the plane of a lipid bilayer, under the influence of random forces. In contrast to the case where (ii) was absent, we find that there are two kinds of behaviour determined by a critical attractive interaction energy, K v ∗(c) less than 0 which depends upon the hexagon concentration, c, (i.e. upon lipid:protein ratio). For attractive interaction energies, K v, lying between 0 and K v ∗(c) , the diffusion coefficient D is essentially constant, whereas if K v is less than K v ∗(c) then D decreases by orders of magnitude as K v decreases. In the region where D changes rapidly with K v, long-lived dynamical clusters, which is the form that the aggregation takes, appear. We conclude that, in contrast to hard-core repulsions between hexagons which can decrease D by up to about one order of magnitude depending upon the hexagon concentration, the attractive, cluster-inducing, interaction can decrease D by many orders of magnitude. We have related our results to measurements of the lateral diffusion of bacteriorhodopsin in DMPC bilayers at 30°C and predict that dynamical protein clusters or aggregates with lifetimes ranging from 1 to 10 ms should become apparent when the lipid:protein ratio falls below 100. As the ratio becomes smaller, the lifetimes of the clusters should increase.