Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran.
J Theor Biol. 2018 Oct 7;454:330-344. doi: 10.1016/j.jtbi.2018.06.021. Epub 2018 Jun 28.
Shape transformations in biological membranes are crucial in a variety of cellular processes such as transport in the Golgi apparatus and endoplasmic reticulum, shaping the cell organelles and signaling in neuronal synapses. Dynamic analysis of lipid bilayer membranes is popular among researchers as valuable information about cell functions can be retrieved. There are several limitations in experimental tests and simulations such as computational and implementation cost while in theoretical studies, different phenomena can be modeled and the effect of each parameter can be investigated. In this paper, a continuum model including elastic energies and dissipation functions is utilized with energy approach to obtain the governing equations of an enclosed lipid bilayer membrane. The governing equations are solved numerically for vesicles initially disturbed and the relaxation dynamics is studied. The stationary shape of the vesicles for different values of reduced volume and reduced area difference is obtained to explore the phase diagram and verify the governing equations. Then, the density asymmetry in bilayers caused by the change in the density or the equilibrium density of the outer monolayer is studied. This leads to the formation of buds, tubules, and pearls. This can be observed in the recruitment of proteins to the outer monolayer or pH gradients of the environment of a vesicle. The effect of density difference and curvature on creation and growth of tubules are investigated. An interesting metastable state in the adsorption of the final bud due to the increase in the density of the outer monolayer is observed in which the shape of the vesicle is almost unchanged. A prolate vesicle relaxes toward an oblate or a stomatocyte vesicle when the equilibrium density of the outer monolayer increases.
生物膜的形状变化在各种细胞过程中至关重要，例如高尔基体和内质网中的运输、细胞细胞器的形成以及神经元突触中的信号传递。脂质双层膜的动态分析在研究人员中很受欢迎，因为可以从中获取有关细胞功能的有价值信息。在实验测试和模拟中存在一些限制，例如计算和实施成本，而在理论研究中，可以对不同的现象进行建模并研究每个参数的影响。在本文中，利用包含弹性能量和耗散函数的连续体模型以及能量方法来获得封闭脂质双层膜的控制方程。对初始受扰的囊泡进行数值求解，并研究其弛豫动力学。得到了不同的折合体积和折合面积差下囊泡的稳定形状，以探索相图并验证控制方程。然后，研究了由于外单层密度或平衡密度的变化引起的双层中的密度不对称性。这导致了芽、小管和珍珠的形成。这可以在蛋白质向单层募集或囊泡环境的 pH 梯度中观察到。研究了密度差和曲率对小管形成和生长的影响。观察到由于外单层密度增加导致最终芽的吸附处于有趣的亚稳状态，其中囊泡的形状几乎不变。当外单层的平衡密度增加时，长形囊泡会向扁形或口形囊泡松弛。
