Gmachowski Lech
Warsaw University of Technology, Institute of Chemistry, 09-400 Płock, Poland.
Math Biosci. 2014 Aug;254:1-5. doi: 10.1016/j.mbs.2014.05.002. Epub 2014 Jun 5.
An equation of motion, derived from the fractal analysis of the Brownian particle trajectory, makes it possible to calculate the time dependence of the mean square displacement for early times, before the Einstein formula becomes valid. The diffusion coefficient increases with the distance travelled which can be restricted by the geometrical conditions. The corresponding diffusion coefficient cannot increase further to achieve a value characteristic for unrestricted environment. Explicit formula is derived for confined diffusivity related to the unrestricted one as dependent on the maximum particle mean square displacement possible normalized by the square of its mean free path. The model describes the lipid and protein diffusion in tubular membranes with different radii, originally fitted by the modified Saffman-Delbrück equation, and the lateral mobility of synthetic model peptides for which the diffusion coefficient is inversely proportional to the radius of the diffusing object and to the thickness of the membrane.
从布朗粒子轨迹的分形分析得出的运动方程，使得在爱因斯坦公式生效之前的早期，能够计算均方位移的时间依赖性。扩散系数随行进距离增加，而这可能受到几何条件的限制。相应的扩散系数不能进一步增加以达到无限制环境的特征值。推导出了一个明确的公式，用于描述受限扩散率与无限制扩散率的关系，该关系取决于最大粒子均方位移，该均方位移通过其平均自由程的平方进行归一化。该模型描述了不同半径管状膜中的脂质和蛋白质扩散，最初由修正的萨夫曼 - 德尔布吕克方程拟合，以及合成模型肽的横向迁移率，其扩散系数与扩散物体的半径和膜的厚度成反比。
