PULS Group, Institut für Theoretische Physik and Cluster of Excellence, Engineering of Advanced Materials, Friedrich Alexander Universität Erlangen-Nürnberg, Erlangen, Germany; Institut Ruđer Bošković, Zagreb, Croatia.
PULS Group, Institut für Theoretische Physik and Cluster of Excellence, Engineering of Advanced Materials, Friedrich Alexander Universität Erlangen-Nürnberg, Erlangen, Germany.
Biophys J. 2019 Jan 22;116(2):283-295. doi: 10.1016/j.bpj.2018.12.003. Epub 2018 Dec 8.
The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes locally pinned by proteins is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, to the extracellular matrix, and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript, we consider a single protein (elastic spring of a finite rest length) pinning a membrane modeled in the Monge gauge. First, we determine the Green's function for the system and complement this approach by the calculation of the mode-coupling coefficients for the plane wave expansion and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behavior characterized by the correlation length. Interestingly, the latter displays a nonmonotonic behavior as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that even in the absence of the membrane deformation, the pinnings will be subject to an attractive force because of changes in membrane fluctuations.
自由膜的热涨落与力学响应之间的关系已经在理论和实验上得到了深入的研究。然而，理解蛋白质局部固定的膜的这种关系更具挑战性。由于膜与细胞细胞骨架、细胞外基质和其他内部结构的耦合对于许多细胞过程的调节至关重要，因此理解固定的作用非常重要。在本文中，我们考虑了一个单一的蛋白质（有限静止长度的弹性弹簧）固定在蒙日规范下的膜上。首先，我们确定了系统的格林函数，并通过平面波展开和正交波动模式的模式耦合系数的计算来补充这种方法，从而为固定膜的数值和分析研究构建了一套工具。此外，我们还研究了自由膜和固定膜以及膜形状的静态相关性，结果表明这三者是相互依存的，并且具有相同的长程行为，其特征是相关长度。有趣的是，后者作为膜张力的函数表现出非单调行为。重要的是，利用这些关系可以实验确定固定的弹性参数。最后但同样重要的是，我们计算了两个固定点之间的相互作用势能，并表明即使没有膜变形，由于膜涨落的变化，固定点也会受到吸引力。
