Huang H W
Biophys J. 1986 Dec;50(6):1061-70. doi: 10.1016/S0006-3495(86)83550-0.
The deformation free energy of a lipid bilayer is presented based on the principle of a continuum theory. For small deformations, the free energy consists of a layer-compression term, a splay-distortion term, and a surface-tension term, equivalent to the elastic free energy of a two-layer smectic liquid crystal with surface tension. Minimization of the free energy leads to a differential equation that, with boundary conditions, determines the elastic deformation of a bilayer membrane. When a dimeric gramicidin channel is formed in a membrane of thickness greater than the length of the channel, the membrane deformation reduces the stability of the channel. Previously this effect was studied by comparing the variation of channel lifetime with the surface tension of bilayers (Elliott, J. R., D. Needham, J. P. Dilger, and D. A. Hayden, 1983, Biochim. Biophys. Acta, 735:95-103). The tension was assumed to pull a dimer for a distance z before the channel loses ion conductivity. To account for the data, z was found to be 18 A. With the deformation free energy, the data can be accounted for with z less than or approximately to 1 A, which is consistent with the breaking of hydrogen bonds in a dimer dissociation. Increasing the strength of lipid-protein interactions is not the only consequence of the complete free energy compared with the previous discussions. It also changes the shape of membrane deformation around an embedded channel from convex to concave, and increases the range of deformation from less than 10 A to greater than 20 A. Clearly these will be important factors in the general considerations of lipid-protein interactions and membrane-mediated interactions between proteins. In addition, thermal fluctuations of a membrane are calculated; in particular, we calculate the relations between the intrinsic thickness and the experimentally measured values. The experimental parameters of monoolein-squalene membranes are used for quantitative analyses.
基于连续介质理论原理给出了脂质双层的变形自由能。对于小变形,自由能由层压缩项、展曲畸变项和表面张力项组成,这与具有表面张力的双层近晶液晶的弹性自由能相当。自由能的最小化导致一个微分方程,结合边界条件可确定双层膜的弹性变形。当在厚度大于通道长度的膜中形成二聚体短杆菌肽通道时,膜变形会降低通道的稳定性。此前通过比较通道寿命随双层膜表面张力的变化对这种效应进行了研究(Elliott, J. R., D. Needham, J. P. Dilger, and D. A. Hayden, 1983, Biochim. Biophys. Acta, 735:95 - 103)。假设张力在通道失去离子传导性之前将二聚体拉动距离z。为了解释这些数据,发现z为18埃。利用变形自由能,当z小于或约为1埃时即可解释这些数据,这与二聚体解离过程中氢键的断裂是一致的。与之前的讨论相比,完整自由能的计算结果表明,增加脂质 - 蛋白质相互作用强度并非唯一结果。它还会将嵌入通道周围膜变形的形状从凸形变为凹形,并将变形范围从小于10埃增加到大于20埃。显然,这些将是脂质 - 蛋白质相互作用以及蛋白质之间膜介导相互作用的一般考虑中的重要因素。此外,还计算了膜的热涨落;特别是,我们计算了固有厚度与实验测量值之间的关系。单油精 - 角鲨烯膜的实验参数用于定量分析。