Abney J R, Scalettar B A, Owicki J C
Cell and Molecular Biology Division, Lawrence Berkeley Laboratory, California 94720.
Biophys J. 1989 May;55(5):817-33. doi: 10.1016/S0006-3495(89)82882-6.
A two-dimensional version of the generalized Smoluchowski equation is used to analyze the time (or distance) dependent self diffusion of interacting membrane proteins in concentrated membrane systems. This equation provides a well established starting point for descriptions of the diffusion of particles that interact through both direct and hydrodynamic forces; in this initial work only the effects of direct interactions are explicitly considered. Data describing diffusion in the presence of hard-core repulsions, soft repulsions, and soft repulsions with weak attractions are presented. The effect that interactions have on the self-diffusion coefficient of a real protein molecule from mouse liver gap junctions is also calculated. The results indicate that self diffusion is always inhibited by direct interactions; this observation is interpreted in terms of the caging that will exist at finite protein concentration. It is also noted that, over small distance scales, the diffusion coefficient is determined entirely by the very strong Brownian forces; therefore, as a function of displacement the self-diffusion coefficient decays (rapidly) from its value at infinite dilution to its steady-state interaction-averaged value. The steady-state self-diffusion coefficient describes motion over distance scales that range from approximately 10 nm to cellular dimensions and is the quantity measured in fluorescence recovery after photobleaching experiments. The short-ranged behavior of the diffusion coefficient is important on the interparticle-distance scale and may therefore influence the rate at which nearest-neighbor collisional processes take place. The hard-disk theoretical results presented here are in excellent agreement with lattice Monte-Carlo results obtained by other workers. The concentration dependence of experimentally measured diffusion coefficients of antibody-hapten complexes bound to the membrane surface is consistent with that predicted by the theory. The variation in experimental diffusion coefficients of integral membrane proteins is greater than that predicted by the theory, and may also reflect protein-induced perturbations in membrane viscosity.
广义斯莫卢霍夫斯基方程的二维形式被用于分析浓缩膜系统中相互作用的膜蛋白随时间（或距离）变化的自扩散。该方程为描述通过直接力和流体动力相互作用的粒子扩散提供了一个成熟的起点；在这项初步工作中，仅明确考虑了直接相互作用的影响。给出了描述在存在硬核排斥、软排斥以及具有弱吸引力的软排斥情况下扩散的数据。还计算了相互作用对来自小鼠肝脏间隙连接的真实蛋白质分子自扩散系数的影响。结果表明，自扩散总是受到直接相互作用的抑制；这一观察结果可根据有限蛋白质浓度下存在的笼效应来解释。还应指出的是，在小距离尺度上，扩散系数完全由非常强的布朗力决定；因此，作为位移的函数，自扩散系数从其在无限稀释时的值迅速衰减到其稳态相互作用平均值。稳态自扩散系数描述了从大约10纳米到细胞尺寸范围内的距离尺度上的运动，并且是在光漂白实验后的荧光恢复中测量的量。扩散系数的短程行为在粒子间距离尺度上很重要，因此可能影响最近邻碰撞过程发生的速率。这里给出的硬磁盘理论结果与其他研究人员获得的晶格蒙特卡罗结果非常吻合。与膜表面结合的抗体 - 半抗原复合物实验测量的扩散系数的浓度依赖性与理论预测一致。整合膜蛋白实验扩散系数的变化大于理论预测，这也可能反映了蛋白质引起的膜粘度扰动。
