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

卡内基梅隆大学的Markus Deserno得到了化学系（CHE）的化学理论、模型和计算方法项目以及材料研究系（DMR）的凝聚态物质和材料理论项目的支持，开发计算方法来预测脂膜的弹性特性并了解吸附在这些膜上的蛋白质丝如何对其施加力。这些膜是脂肪样分子、胆固醇和蛋白质的组合，是代谢中间产物进出细胞的复杂实体。 大多数细胞膜需要频繁改变其形状甚至连接性，以执行其广泛的生物功能。基本的力学取决于少量的参数，这些参数充分表征了这种变形的能量要求以及由它们传递的力。 Alberno和他的研究小组开发了一套新的模拟策略，用于在计算机模拟中预测这些参数。其目的是获得有争议或难以获得的物理参数。 他们还开发了定量方法来研究膜连接性改变的最常见过程之一。 从事这些项目的研究生和本科生将获得软物质，生物物理学，模拟和连续建模方面的经验。正在进行的推广项目与初中和高中在匹兹堡将通过开发一个系列讲座密切联系在一起的动手实验，开发弹性板和梁的概念。 该奖项支持理论和计算研究和教育，以（1）通过一致和无模型的尺度桥接从分子水平模拟测量脂膜的紧急连续弹性特性，并（2）开发用于描述半柔性聚合物与曲面相互作用的理论技术。在（1）中，研究涉及扩展通过模拟屈曲膜获得的信息，不仅提取弯曲模量，还确定其熵贡献、单个瓣叶的枢轴平面位置以及自发单层曲率的大小。这些技术被应用到计算膜模型跨越了广泛的分辨率，从原子到高度粗粒度。特别的应用包括当进入凝胶相时强烈硬化或被痕量小肽强烈软化的脂质双层。 Alberno及其同事还旨在通过将动态补丁闭合协议扩展到基于外部限制场的平衡测量来测量高斯曲率模量，在考虑成分-曲率耦合之后，可以将其推广到脂质混合物的非平凡情况。在（2）中，Reyno探索了将一维半柔性聚合物限制在曲面上所产生的弹性力的几何性质。建立在一个封闭的圆柱体的情况下，它有一个连续的旋转和平移对称，欧拉-拉格朗日方程的形状是通过分析和数值技术相结合来解决，并确定相关的应力和扭矩。移动到一个封闭的悬链线，平移对称性丢失，因为通常是一个潜在的正交，但新的曲率梯度提供了一个新的物理主机，连接到边界条件，曲率局部化，和聚合力。测地线和渐近曲线的研究，作为限制情况下的聚合物具有各向异性的弹性性能，和额外的自发曲率和扭曲使长丝一个很好的连续模型dynamin长丝。这允许预测由围绕膜颈聚合的动力蛋白螺旋所施加的力，该过程被认为是许多细胞膜裂变事件的基础，但其机制基础仍然不清楚。

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.