Anomalous diffusion due to binding: a Monte Carlo study

Abstract

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

“…There is a region with a linear decreasing of log(<r 2 >/t), which corresponds to an anomalous diffusion behaviour, followed by a region with a smaller constant diffusion coefficient (D*) characteristic of normal diffusion. It should be noticed that, as it was reported in other studies 17,[36][37][38][39][40][41] , the initial region of normal diffusion (when the diffusing particles are not still affected by the crowding obstacles) is not observed in the present onlattice simulations. The plot starts at a position, D 0 '(f), lower than D 0 (f) (the initial normal diffusion coefficient given by eqn (7) not observed in the simulation), which value depends on the discretization of the lattice, the obstacle size and the excluded volume, and immediately decreases to reach the linear anomalous diffusion region.…”

“…Experimental and theoretical data 14,23,25,[27][28]31,[39][40][41] reveal that, in crowded media, there is a succession of diffusion behaviours that can be identified with the three distinct regions observed in the log(<r 2 >/t) versus log(t) plots:…”

“…These simulations, and in particular the extensive work of Saxton 14,[36][37][39][40][41]51 have shown that, in crowded media, diffusion presents two behaviours: it is anomalous (time dependent diffusion coefficient) for short times and normal (constant diffusion coefficient) for long-times.…”

“…With respect to the diffusion coefficient value, it has been shown that: it diminishes when the concentration of obstacles increases 41,51 , it is dependent on the relative mobility of tracers and obstacles [39][40][41]52 , and it also depends on the size of tracers and obstacles [36][37]50 . In addition, the results show that in a uniform distribution of the obstacles the diffusion coefficient is greater than in a random distribution 50 .…”

Spatio-temporal anomalous diffusion imaging: results in controlled phantoms and in excised human meningiomas

“…As well demonstrated by many studies based on Monte Carlo simulations of particle diffusion in 2D [22][23][24][25][26][27][28] and 3D crowded media [29], particle diffusion in media comprised of mono-sized obstacles uniformly and randomly distributed, is characterized by the following representative behaviors:…”