arXiv:1002.4089v1 [physics.bio-ph] 22 Feb 2010 Coarse-Grained Simulations of Membranes under Tension J¨ org Neder ∗ and Peter Nielaba Department of Physics, University of Konstanz, Germany Beate West Department of Physics, University of Bielefeld, Germany Friederike Schmid Institute of Physics, University of Mainz, Germany We investigate the properties of membranes under tension by Monte-Carlo simulations of a generic coarse-grained model for lipid bilayers. We give a comprising overview of the behavior of several membrane characteristics, such as the area per lipid, the monolayer overlap, the nematic order, and pressure profiles. Both the low-temperature regime, where the membranes are in a gel L β ′ phase, and the high-temperature regime, where they are in the fluid Lα phase, are considered. In the L β ′ state, the membrane is hardly influenced by tension. In the fluid state, high tensions lead to structural changes in the membrane, which result in different compressibility regimes. The ripple state P β ′ , which is found at tension zero in the transition regime between Lα and L β ′ , disappears under tension and gives way to an interdigitated phase. We also study the membrane fluctuations in the fluid phase. In the low tension regime the data can be fitted nicely to a suitably extended elastic theory. At higher tensions the elastic fit consistently underestimates the strength of long- wavelength fluctuations. Finally, we investigate the influence of tension on the effective interaction between simple transmembrane inclusions and show that tension can be used to tune the hydrophobic mismatch interaction between membrane proteins. I. INTRODUCTION Biological membranes are made of lipid bilayers with incorporated proteins. These barriers define the inside and the outside of a cell, separate the functional com- partments in cells, and are indispensable for life [1]. The microscopic surface tension of membranes is usually small or vanishes altogether [2], but there may also be situ- ations, where membranes are under considerable stress due to osmotic pressure differences. For example, ep- ithelial cells exposed to transmembrane osmotic gradients can be expected to develop a state of tension under phys- iological conditions [3]. Similarly, osmotically induced tension may play a decisive role during conformational changes, fission or fusion of cells [4, 5]. Another situation where membranes experience stress is under the influence of ultrasonic pulses [6]. Applied perpendicular to a lipid membrane, shock pulses can promote significant struc- tural changes similar to those induced by lateral tension. The effect of such pulses on membranes is of considerable medical interest. In this context Koshiyama et al. have studied phospholipid bilayers under the action of a shock wave in atomistic molecular dynamics simulations [7]. Despite the advances in computer technology through- out the past decades, atomistic modeling of lipid bilayers on length scales of a few nanometer still requires huge computing resources or even goes beyond the current ca- pabilities of high performance architectures. This mo- tivates the use of coarse-grained models. They can give * Electronic address: joerg.neder@uni-konstanz.de fundamental insights into the physics of a certain system, and, moreover, they provide powerful tools for the inter- pretation of the behavior of complex systems, like lipid membranes [8–12]. The aim of the work presented here is to study the effect of an externally applied tension on the physical properties of a model bilayer, and on the behavior of in- corporated model proteins. We employ a generic coarse- grained model of amphiphiles developed in a top-down approach[13]. For tensionless systems this model has al- ready been used very successfully to reproduce various bilayer phases including the symmetric and asymmetric ”rippled” P β ′ states [14, 15] and to study membrane- protein interactions [16]. Recent simulations on mem- branes under mechanical stress have often dealt with the formation, structure and stability of hydrophilic pores [17–19] or with the influence of surface tension on trans- membrane channel stability and function [20, 21]. In this paper, we will primarily be concerned with the structural changes of pure membranes in response to lateral stresses, focussing on unporated systems. Since our model ex- hibits a rather realistic phase behavior of the model mem- brane at different temperatures, we can study different membrane states, i.e., the liquid, the ripple, and the gel state Our paper is organized as follows: First we describe the underlying lipid model and outline the simulation meth- ods. Then the simulation results are presented starting with a phenomenological introduction, where the effects of an external tension on the model bilayer in different phases are described. Thereafter a quantitative analysis of these bilayers is performed and the characteristics of the bilayers are examined with respect to their behavior