Biomembranes adopt varying morphologies that are vital to cellular functions. Many studies use computational modeling to understand how various mechanochemical factors contribute to membrane shape transformations. Compared to approximation-based methods (e.g., finite element method), the class of discrete mesh models offers greater flexibility to simulate complex physics and shapes in three dimensions; its formulation produces an efficient algorithm while maintaining coordinate-free geometric descriptions. However, ambiguities in geometric definitions in the discrete context have led to a lack of consensus on which discrete mesh model is theoretically and numerically optimal; a bijective relationship between the terms contributing to both the energy and forces from the discrete and smooth geometric theories remains to be established. We address this and present an extensible framework, $\texttt{Mem3DG}$, for modeling 3D mechanochemical dynamics of membranes based on Discrete Differential Geometry (DDG) on triangulated meshes. The formalism of DDG resolves the inconsistency and provides a unifying perspective on how to relate the smooth and discrete energy and forces. To demonstrate, $\texttt{Mem3DG}$ is used to model a sequence of examples with increasing mechanochemical complexity: recovering classical shape transformations such as 1) biconcave disk, dumbbell, and unduloid and 2) spherical bud on spherical, flat-patch membrane; investigating how the coupling of membrane mechanics with protein mobility jointly affects phase and shape transformation. As high-resolution 3D imaging of membrane ultrastructure becomes more readily available, we envision Mem3DG to be applied as an end-to-end tool to simulate realistic cell geometry under user-specified mechanochemical conditions.
翻译:许多研究都使用计算模型来理解各种机械化因素如何能促进膜膜形状的变异。与近似基方法(例如,有限元素法)相比,离散网形模型类别为模拟复杂的物理学和三个维度的形状提供了更大的灵活性;它的配方产生了一种高效的算法,同时保持了无协调的几何描述。然而,离散情况下的几何定义模糊导致对哪些离散网状模型在理论上和数字上是最佳的缺乏共识;在推动离散和光滑的几何理论理论的能量和力量之间形成了一种双向关系。与近距离基基相比,我们处理并展示一个可扩展的框架,$\textt{Mem3DG},用于根据离析的对立性地球物理测量(DDG)的离散式定义进行模型,DDDG的正式模型解决了不一致之处,并且提供了一种统一的视角,用于在离散和平流和平坦的系统内部变异变形中, 将ADM3 和正态变变变的模型与我们的工具进行。