Department of Mechanical and Aerospace Engineering, University of California San Diego, La Jolla CA, USA.
J R Soc Interface. 2019 Sep 27;16(158):20190354. doi: 10.1098/rsif.2019.0354. Epub 2019 Sep 4.
Cellular membranes display an incredibly diverse range of shapes, both in the plasma membrane and at membrane bound organelles. These morphologies are intricately related to cellular functions, enabling and regulating fundamental membrane processes. However, the biophysical mechanisms at the origin of these complex geometries are not fully understood from the standpoint of membrane-protein coupling. In this study, we focused on a minimal model of helicoidal ramps representative of specialized endoplasmic reticulum compartments. Given a helicoidal membrane geometry, we asked what is the distribution of spontaneous curvature required to maintain this shape at mechanical equilibrium? Based on the Helfrich energy of elastic membranes with spontaneous curvature, we derived the shape equation for minimal surfaces, and applied it to helicoids. We showed the existence of switches in the sign of the spontaneous curvature associated with geometric variations of the membrane structures. Furthermore, for a prescribed gradient of spontaneous curvature along the exterior boundaries, we identified configurations of the helicoidal ramps that are confined between two infinitely large energy barriers. Overall our results suggest possible mechanisms for geometric control of helicoidal ramps in membrane organelles based on curvature-inducing proteins.
细胞膜显示出令人难以置信的多样化形状，无论是在质膜上还是在膜结合细胞器上。这些形态与细胞功能密切相关，使基本的膜过程得以实现和调节。然而，从膜蛋白耦联的角度来看，这些复杂几何形状的起源的生物物理机制还没有被完全理解。在这项研究中，我们专注于代表专门内质网隔室的螺旋形斜坡的最小模型。对于螺旋形的膜几何形状，我们要问的是，需要什么样的自发曲率分布来使其在力学平衡中保持这种形状？基于具有自发曲率的弹性膜的 Helfrich 能量，我们推导出了最小曲面的形状方程，并将其应用于螺旋形。我们表明，与膜结构的几何变化相关的自发曲率的符号存在着转变。此外，对于沿外部边界的预定的自发曲率梯度，我们确定了螺旋形斜坡的配置，这些配置被限制在两个无限大的能量势垒之间。总的来说，我们的结果表明，基于曲率诱导蛋白，膜细胞器中螺旋形斜坡的几何控制可能存在一些机制。
