How proteins can shape and sense membranes--a closer look at hybrid models
Freie Universität Berlin, Institute of Mathematics (Pi Building)
Biomembranes are complex fluids consisting of different lipids and membrane proteins that exhibit solid-like behaviour, such as bending rigidity or stretching elasticity, and a fundamental problem of contemporary cell biology is to understand how the membrane shape is affected and regulated by its proteins. Two relatively well-studied examples of how proteins can shape and sense membranes are the process of clathrin-mediated endocytosis  and mechanosensitive channel gating in bacteria . Roughly speaking, the remodelling is a consequence of the interplay between the elastic membrane and concerted actions of not too many, but highly specialized membrane proteins that can both sense and create membrane curvature. One of the difficulties in getting precise microscopic insight of the mechanisms involved via computer simulations lies in the vastly different length and time scales involved that make fully atomistic simulations intractible, but also exclude pure continuum modelling as the proteins often occur in low copy numbers. A central theme of the workshop will therefore be the coupling between different physical models, specifically, continuum models for the lipid bilayer with discrete (deterministic or stochastic) particle models representing the proteins as membrane inclusions or perturbations. A side theme will be the analysis of current simulation techniques for biomembranes with membrane proteins.
In hybrid models of membrane proteins, the energetic cost of a membrane deformation is described by an elastic surface energy (such as the widely accepted Canham-Helfrich energy), with the protein being considered as a rigid inclusion that can generate membrane curvature due to the shape of the hydrophobic domain and the hydrophobic mismatch between protein and bilayer; in this picture, neighbouring membrane proteins can induce overlapping surface deformations which gives rise to long-range interactions between the proteins as has been confirmed by DPD simulations using coarse-grained models of lipids and proteins . Even though the literature of hybrid models for membranes with point-like inclusions is rather rich, an open question until now is how continuum and particle models can be coupled in a consistent way. Heuristics range from coupling via boundary conditions , contact angles  or extra bilinear terms in the energy functional . Often there is no clear disctinction between model-related coupling parameters and numerical parameters, in that genuinely numerical (e.g. regularization or grid) parameters are limited by physical or biological considerations . What may appear as an advantange of the model is in fact highly unpleasant as it implies that the models depend on possibly unphysical regularization parameters; cf.~the discussion in Refs. [8,9]. Furthermore, inconsistencies arise when these parameters are sent to zero and the particles shrink to points, which assumes that one can ascribe point values to functions with square integrable second derivatives , i.e. functions minimizing the Helfrich energy. It is so far an open question whether some of the problems descriptions that are circulating in the literature, e.g. about the ultraviolet divergence in the Fourier spectrum of a fluctuating membrane , are purely mathematical problems or whether they involve genuine physical effects.
Carsten Hartmann ( Brandenburgische Technische Universität Cottbus-Senftenberg ) - Organiser
Ralf Kornhuber ( Freie Universität Berlin ) - Organiser
Frank Noe ( Free University of Berlin ) - Organiser
Thomas Weikl ( Max Planck Institute of Colloids and Interfaces ) - Organiser