Gmachowski Lech
Institute of Chemistry, Faculty of Civil Engineering, Mechanics and Petrochemistry, Warsaw University of Technology, 17 Łukasiewicza St., 09-400, Płock, Poland.
Eur Biophys J. 2018 Apr;47(3):309-316. doi: 10.1007/s00249-017-1264-0. Epub 2017 Nov 2.
Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.
利用分子行走的分形描述，分析了分子在含有小隔室（直径0.23μm）和大隔室（直径0.75μm）的生物膜中的横向运动。由于弹道运动的贡献，均方位移的早期时间依赖性偏离线性。在小隔室中，行走的分子没有足够的时间或空间来建立渐近关系，从实验记录推导的扩散系数低于无限制测量时的扩散系数。该模型使得从关于受限和无限制扩散系数的数据中推导分子步长参数，即步长和时间成为可能。利用亚扩散输运的实验结果也能做到这一点。从正常扩散到反常扩散的转变不会影响分子步长参数。高时间分辨率记录的分子轨迹的实验文献数据似乎证实了二油酰磷脂酰乙醇胺（DOPE）在布朗扩散和反常扩散下平均自由程长度的模拟值。尽管步长和时间给出了合适的扩散系数值，但作为它们商计算的DOPE速度比热速度低几个数量级。这被解释为分子间相互作用的结果，不同膜中其他分子的横向扩散证实了这一点。然后利用分子步长参数分析小隔室中多次访问的问题。扩散指数的模拟导致进入大隔室时平滑过渡到正常扩散，如实验中所观察到的。
