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Macromolecular complexation leading to coupling of two or more cellularmembranes is a crucial step in a number of biological functions of the cell.While other mechanisms may also play a role, adhesion always involves thefluctuations of deformable membranes, the diffusion of proteins and themolecular binding and unbinding. Because these stochastic processes couple overa multitude of time and length scales, theoretical modeling of membraneadhesion has been a major challenge. Here we present an effective Monte Carloscheme within which the effects of the membrane are integrated into local ratesfor molecular recognition. The latter step in the Monte Carlo approach enablesus to simulate the nucleation and growth of adhesion domains within a system ofthe size of a cell for tens of seconds without loss of accuracy, as shown bycomparison to $10^6$ times more expensive Langevin simulations. To perform thisvalidation, the Langevin approach was augmented to simulate diffusion ofproteins explicitly, together with reaction kinetics and membrane dynamics. Weuse the Monte Carlo scheme to gain deeper insight to the experimentallyobserved radial growth of micron sized adhesion domains, and connect theeffective rate with which the domain is growing to the underlying microscopicevents. We thus demonstrate that our technique yields detailed informationabout protein transport and complexation in membranes, which is a fundamentalstep toward understanding even more complex membrane interactions in thecellular context.

new journal of physics

Multiscale approaches to protein-mediated interactions between membranes  - Relating microscopic and macroscopic dynamics in radially growing adhesions