Abstract
Macromolecular complexation leading to coupling of two or more cellular membranes is a crucial step in a number of biological functions of the cell. While other mechanisms may also play a role, adhesion always involves the fluctuations of deformable membranes, the diffusion of proteins and the molecular binding and unbinding. Because these stochastic processes couple over a multitude of time and length scales, theoretical modeling of membrane adhesion has been a major challenge. Here we present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition. The latter step in the Monte Carlo approach enables us to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy, as shown by comparison to 106 times more expensive Langevin simulations. To perform this validation, the Langevin approach was augmented to simulate diffusion of proteins explicitly, together with reaction kinetics and membrane dynamics. We use the Monte Carlo scheme to gain deeper insight to the experimentally observed radial growth of micron sized adhesion domains, and connect the effective rate with which the domain is growing to the underlying microscopic events. We thus demonstrate that our technique yields detailed information about protein transport and complexation in membranes, which is a fundamental step toward understanding even more complex membrane interactions in the cellular context.
Highlights
At the origin of many biological phenomena is cell adhesion promoted by the formation of macromolecular ensembles
We solve the problem of coupling time and length scales by constructing an effective Monte Carlo simulation scheme, for which we demonstrate applicability in a very broad range of parameters
After the diffusion has been resolved, a new iteration in the time loop is started, or the simulation is terminated. Most time in this simulation scheme is consumed by fast Fourier transformations of the membrane profile and the forces, which scale like N log(N), (N is the number of considered lattice points), and not linearly like other operations
Summary
Engineering of Advanced Materials, Universität Erlangen-Nürnberg, Nägelsbachstrasse 49b, D-91052 Erlangen, Germany. We present an effective Monte Carlo scheme within which the effects of the membrane are integrated into local rates for molecular recognition The latter step in the Monte Carlo approach enables us to simulate the nucleation and growth of adhesion domains within a system of the size of a cell for tens of seconds without loss of accuracy, as shown by comparison to 106 times more expensive Langevin simulations. To perform this validation, the Langevin approach was augmented to simulate diffusion of proteins explicitly, together with reaction kinetics and membrane dynamics. We demonstrate that our technique yields detailed information about protein transport and complexation in membranes, which is a fundamental step toward understanding even more complex membrane interactions in the cellular context
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