Predicting emergent continuum-elastic properties of lipid membranes from molecular-level simulations via consistent and model-free scale bridging

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Markus Deserno from Carnegie Mellon University is supported by the Chemical Theory, Models and Computational Methods Program of the Chemistry Division (CHE) and the Condensed Matter and Materials Theory Program of the Division of Materials Research (DMR) to develop computational approaches to predict the elastic properties of lipid membranes and to understand how protein filaments adsorbed onto these membranes exert forces upon them. These membranes, a combination of fat-like molecules, cholesterol and proteins, are complex entities across which metabolic intermediates enter and exit cells. Most cellular membranes require frequent changes of their shape or even connectivity in order to execute their wide spectrum of biological functions. The underlying mechanics depends on a small number of parameters, which fully characterize both the energetic requirements for such deformations as well as the forces transmitted by them. Deserno and his research group develop a set of new simulation strategies for predicting these parameters in computer simulations. The aim is to gain access to physical parameters that have been controversial or notoriously hard to obtain. They also develop quantitative approaches to investigate one of the most common processes by which membrane connectivity is changed. Graduate and undergraduate students working on these projects will gain experience in soft matter, biophysics, simulation, and continuum modeling. Ongoing outreach projects with both middle- and high schools in Pittsburgh will be extended by developing a lecture series closely tied with hands-on experimentation that develops the concept of elastic sheets and beams. This award supports theoretical and computational research and education to (1) measure emergent continuum-elastic properties of lipid membranes from molecular-level simulations via consistent and model-free scale bridging and to (2) develop theoretical techniques for describing the interaction of semi-flexible polymers with curved surfaces. In (1) the research involves expanding the information obtainable from simulating buckled membranes to extract not only the bending modulus, but identify its entropic contribution, the position of the pivotal plane of a single leaflet, and the magnitude of the spontaneous monolayer curvature. These techniques are applied to computational membrane models spanning a wide range of resolution, from atomistic to highly coarse-grained. Particular applications include lipid bilayers that are strongly stiffened when entering a gel phase, or strongly softened by trace amounts of small peptides. Deserno and coworkers also aim to measure the Gaussian curvature modulus by expanding the dynamic patch closure protocol to an equilibrium measurement based on externally confining fields, which after accounting for composition-curvature coupling can be generalized to the nontrivial case of lipid mixtures. In (2) Deserno explores the geometric nature of elastic forces that result from confining one-dimensional semi-flexible polymers to curved surfaces. Building on the case of a confining cylinder, which has both a continuous rotation and translation symmetry, the Euler-Lagrange equations for the shape are to be solved through a combination of analytical and numerical techniques, and the associated stresses and torques are identified. Moving on to a confining catenoid, translational symmetry is lost, as is generally a potential quadrature, but the new curvature gradients provide a host of new physics, linked to boundary conditions, curvature localization, and polymerization forces. Geodesics and asymptotic curves are studied as limiting cases for polymers with anisotropic elastic properties, and additional spontaneous curvature and twist render the filament an excellent continuum model for dynamin filaments. This allows the prediction of forces exerted by dynamin helices polymerizing around membrane necks, a process that is believed to underlie many cellular membrane fission events, but whose mechanistic underpinning is still not understood.