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

来自卡耐基梅隆大学的Markus Deserno得到了化学部化学理论、模型和计算方法项目（CHE）和材料研究部凝聚态物质和材料理论项目（DMR）的支持，开发了计算方法来预测脂质膜的弹性特性，并了解吸附在这些膜上的蛋白丝如何对它们施加力。这些膜是脂肪样分子、胆固醇和蛋白质的组合，是代谢中间体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通性，以执行其广泛的生物功能。潜在的力学取决于少数参数，这些参数充分表征了这种变形的能量需求以及由它们传递的力。Deserno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众所周知难以获得的物理参数。他们还开发了定量方法来研究膜连通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、模拟和连续体建模方面的经验。正在与匹兹堡的初中和高中进行的拓展项目将通过开发与实践实验密切相关的系列讲座来扩展，以发展弹性板和梁的概念。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质膜的紧急连续弹性特性，以及(2)开发描述半柔性聚合物与曲面相互作用的理论技术。在(1)中，研究涉及扩展从模拟屈曲膜中获得的信息，不仅提取弯曲模量，而且确定其熵贡献，单个小叶的关键平面的位置以及自发单层曲率的大小。这些技术应用于计算膜模型跨越广泛的分辨率，从原子到高度粗粒度。特殊的应用包括脂质双分子层，当进入凝胶相时，脂质双分子层被强烈硬化，或被微量的小肽强烈软化。Deserno和同事们还打算通过将动态补丁闭合协议扩展到基于外部约束场的平衡测量来测量高斯曲率模量，在考虑了成分-曲率耦合后，该协议可以推广到脂质混合物的非平凡情况。在(2)中，Deserno探讨了由于将一维半柔性聚合物限制在曲面上而产生的弹性力的几何性质。以具有连续旋转和平移对称性的围柱为例，采用解析和数值相结合的方法求解该围柱形状的欧拉-拉格朗日方程，并确定其相关的应力和扭矩。移动到一个受限链面，平移对称性失去了，通常是一个潜在的正交，但是新的曲率梯度提供了许多新的物理，与边界条件，曲率局部化和聚合力有关。研究了测地线和渐近曲线作为具有各向异性弹性特性的聚合物的极限情况，附加的自发曲率和扭转使长丝成为动力长丝的优秀连续体模型。这可以预测动力蛋白螺旋在膜颈周围聚合所产生的力，这一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.