Free-energy calculation methods for collective phenomena in membranes

Collective phenomena in membranes are those which involve the co-operative reorganization of many molecules. Examples of these are membrane fusion, pore formation, bending, adhesion or fission. The time and length scales, on which these processes occur, pose a challenge for atomistic simulations. Therefore, in order to solve the length scale problem it is popular to introduce a coarse-grained representation. To facilitate sampling of the relevant states additional computational techniques, which encourage the system to explore the free-energy landscape far from equilibrium and visit transition states, are needed. These computational techniques provide insights about the free-energy changes involved in collective transformations of membranes, yielding information about the rate limiting states, the transformation mechanism and the influence of architectural, compositional and interaction parameters. A common approach is to identify an order parameter (or reaction coordinate), which characterizes the pathway of membrane reorganization. However, no general strategy exists to define such an order parameter that can properly describe cooperative reorganizations in membranes. Recently developed methods can overcome this problem of the order-parameter choice and allow us to study collective phenomena in membranes. We will discuss such methods as thermodynamic integration, umbrella sampling, and the string method and results provided by their applications to particle-based simulations, particularly focusing on membrane fusion and pore formation. (topical review)