Quantitative Membrane Bending Energies at Extreme Curvatures from Molecular Dynamics Simulations

Abstract

At mesoscopic length scales and small curvatures, Helfrich's well established continuum model [1] provides accurate membrane bending and stretching energies. For the small nanometer scales and extreme curvatures relevant for fundamental biological processes like synaptic fusion and tubulation, however, its validity is unclear. To test whether or not the bending energy remains a harmonic function of curvature, described by a simple bending modulus, we developed and applied a new type of collective umbrella sampling molecular dynamics (MD) simulations. Most MD simulations computing bending moduli are limited to thermally accessible energies (a few kBT) and curvatures. In this limited regime, the harmonic approximation has been repeatedly confirmed. Very few simulation strategies exist to compute bending energies at higher curvatures, due to the inherent difficulty of controlling membrane structures. These simulation studies have generally verified the harmonic bending approximation but were limited by the requirements of a soft coarse grained lipid model[2], and unavoidable coupling between bending and stretching[3]. To overcome these limitations, we have developed a novel approach to control membrane curvature thereby accessing the regime of <10nm curvature radii and ∼50 kBT energies. Our preliminary results show that at high curvatures, moduli have a small positive deviation from the harmonic approximation, that would not be discernible in the flat/thermal regime. As expected, we observe that increasing temperature decreases the elastic moduli and that ethanol and cholesterol act to soften and stiffen membranes, respectively. [1] W. Helfrich, Naturforsch [C] 28, p693 (1973). [2] V.A. Harmandris and M. Deserno, JCP 125, p204905 (2006). [3] W.K. den Otter and W.J. Briels, JCP 118, p4712 (2003).