Biological membranes constitute boundaries of cells and cell organelles. These membranes are soft fluid interfaces whose thermodynamic states are dictated by bending moduli, induced curvature fields, and thermal fluctuations. Recently, there has been a flood of experimental evidence highlighting active roles for these structures in many cellular processes ranging from trafficking of cargo to cell motility. It is believed that the local membrane curvature, which is continuously altered due to its interactions with myriad proteins and other macromolecules attached to its surface, holds the key to the emergent functionality in these cellular processes. Mechanisms at the atomic scale are dictated by protein-lipid interaction strength, lipid composition, lipid distribution in the vicinity of the protein, shape and amino acid composition of the protein, and its amino acid contents. The specificity of molecular interactions together with the cooperativity of multiple proteins induce and stabilize complex membrane shapes at the mesoscale. These shapes span a wide spectrum ranging from the spherical plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the relation between the protein-induced deformations at the molecular scale and the resulting mesoscale morphologies is key to bridging cellular experiments across the various length scales. In this review, we focus on the theoretical and computational methods used to understand the phenomenology underlying protein-driven membrane remodeling. Interactions at the molecular scale can be computationally probed by all atom and coarse grained molecular dynamics (MD, CGMD), as well as dissipative particle dynamics (DPD) simulations, which we only describe in passing. We choose to focus on several continuum approaches extending the Canham - Helfrich elastic energy model for membranes to include the effect of curvature-inducing proteins and explore the conformational phase space of such systems. In this description, the protein is expressed in the form of a spontaneous curvature field. The approaches include field theoretical methods limited to the small deformation regime, triangulated surfaces and particle-based computational models to investigate the large-deformation regimes observed in the natural state of many biological membranes. Applications of these methods to understand the properties of biological membranes in homogeneous and inhomogeneous environments of proteins, whose underlying curvature fields are either isotropic or anisotropic, are discussed. The diversity in the curvature fields elicits a rich variety of morphological states, including tubes, discs, branched tubes, and caveola. Mapping the thermodynamic stability of these states as a function of tuning parameters such as concentration and strength of curvature induction of the proteins is discussed. The relative stabilities of these self-organized shapes are examined through free-energy calculations. The suite of methods discussed here can be tailored to applications in specific cellular settings such as endocytosis during cargo trafficking and tubulation of filopodial structures in migrating cells, which makes these methods a powerful complement to experimental studies.

中文翻译：

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曲率诱导蛋白对膜双层重塑的中尺度计算研究


生物膜构成细胞和细胞器的边界。这些膜是软流体界面，其热力学状态由弯曲模量、诱导曲率场和热波动决定。最近，大量的实验证据强调了这些结构在许多细胞过程中的积极作用，从货物运输到细胞运动。据信，局部膜曲率由于其与附着在其表面的无数蛋白质和其他大分子的相互作用而不断改变，是这些细胞过程中出现功能的关键。原子尺度的机制由蛋白质-脂质相互作用强度、脂质组成、蛋白质附近的脂质分布、蛋白质的形状和氨基酸组成及其氨基酸含量决定。分子相互作用的特异性以及多种蛋白质的协同作用在介观尺度上诱导并稳定了复杂的膜形状。这些形状涵盖了从球形质膜到复杂的高尔基体池的广泛范围。绘制分子尺度上蛋白质诱导的变形与由此产生的介观形态之间的关系是跨不同长度尺度的细胞实验的关键。在这篇综述中，我们重点关注用于理解蛋白质驱动的膜重塑现象学的理论和计算方法。分子尺度的相互作用可以通过所有原子和粗粒度分子动力学（MD、CGMD）以及耗散粒子动力学（DPD）模拟来计算探测，我们只是顺便描述一下。 我们选择关注几种连续方法，扩展膜的 Canham-Helfrich 弹性能模型，以包含曲率诱导蛋白的影响，并探索此类系统的构象相空间。在本说明书中，蛋白质以自发曲率场的形式表达。这些方法包括仅限于小变形范围的场理论方法、三角表面和基于粒子的计算模型，以研究在许多生物膜的自然状态下观察到的大变形范围。讨论了应用这些方法来了解蛋白质均匀和非均匀环境中生物膜的特性，其基本曲率场是各向同性或各向异性的。曲率场的多样性引发了丰富多样的形态状态，包括管、盘、分支管和凹穴。讨论了将这些状态的热力学稳定性映射为调整参数（例如蛋白质的浓度和曲率感应强度）的函数。通过自由能计算检查这些自组织形状的相对稳定性。这里讨论的这套方法可以针对特定细胞环境中的应用进行定制，例如货物运输过程中的内吞作用和迁移细胞中丝状结构的管状作用，这使得这些方法成为实验研究的有力补充。