Goldstein B, Wiegel F W
Theoretical Division, Los Alamos National Laboratory, New Mexico 87545.
Biophys J. 1988 Feb;53(2):175-84. doi: 10.1016/S0006-3495(88)83079-0.
Bretscher (1983) has shown that on uniformly spread giant HeLa cells, the receptors for low density lipoprotein (LDL) and transferrin are concentrated toward the periphery of the cells. To explain these nonuniform distributions, he proposed that on giant HeLa cells, recycling receptors return to the cell surface at the cell's leading edge. Since the distribution of coated pits on these cells is uniform, Bretscher and Thomson (1983) proposed that there is a bulk membrane flow toward the cell centers. Here we present a mathematical model that allows us to predict the distribution of cell surface proteins on a thin circular cell, when exocytosis occurs at the cell periphery and endocytosis occurs uniformly over the cell surface. We show that on such a cell, a bulk membrane flow will be generated, whose average velocity is zero at the cell center and increases linearly with the distance from the cell center. Our model predicts that proteins that aggregate in coated pits will have concentrations that are maximal at the cell periphery. We fit our theory to the data of Bretscher and Thomson (1983) on the distribution of ferritin receptors for the following cases: the receptors move by diffusion alone; they move by bulk membrane flow alone; they move by a combination of diffusion and bulk membrane flow. From our fits we show that tau m greater than 3.5 tau p, where tau m and tau p are the lifetimes of the membrane and the ferritin receptor on the cell surface, and that tau pD less than 6.9 X 10(-7) cm2, where D is the ferritin receptor diffusion coefficient. Surprisingly, we obtain the best fits to the data when we neglect membrane flow. Our model predicts that for proteins that are excluded from coated pits, the protein concentration will be Gaussian, being maximal at the cell center and decreasing with the distance from the cell center. If on giant HeLa cells a protein with such a distribution could be found, it would strongly support Bretcher's proposal that there is an inward membrane flow.
布雷彻（1983年）已经证明，在均匀铺展的巨大海拉细胞上，低密度脂蛋白（LDL）和转铁蛋白的受体集中在细胞周边。为了解释这些非均匀分布，他提出在巨大海拉细胞上，循环受体在细胞前沿返回细胞表面。由于这些细胞上被膜小窝的分布是均匀的，布雷彻和汤姆森（1983年）提出存在朝向细胞中心的大量膜流。在此，我们提出一个数学模型，当胞吐作用发生在细胞周边且胞吞作用在细胞表面均匀发生时，该模型能让我们预测薄圆形细胞上细胞表面蛋白的分布。我们表明在这样的细胞上，会产生大量膜流，其平均速度在细胞中心为零，并随距细胞中心的距离线性增加。我们的模型预测，聚集在被膜小窝中的蛋白浓度在细胞周边最大。我们将我们的理论与布雷彻和汤姆森（1983年）关于铁蛋白受体分布的数据进行拟合，用于以下几种情况：受体仅通过扩散移动；它们仅通过大量膜流移动；它们通过扩散和大量膜流的组合移动。从我们的拟合结果可知，τm大于3.5τp，其中τm和τp分别是膜和细胞表面铁蛋白受体的寿命，并且τpD小于6.9×10⁻⁷平方厘米，其中D是铁蛋白受体扩散系数。令人惊讶的是，当我们忽略膜流时，我们得到了与数据的最佳拟合。我们的模型预测，对于被排除在被膜小窝之外的蛋白，其蛋白浓度将呈高斯分布，在细胞中心最大，并随距细胞中心的距离减小。如果在巨大海拉细胞上能找到具有这种分布的蛋白，将有力支持布雷彻关于存在向内膜流的提议。
