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1 2023

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Subdiffusive Behavior in Crowded Environments: Impact of Obstacle Mobility and Spatial Restrictions

Polanowski Piotr, Sikorski Andrzej

Computational Methods in Science and Technology

2023

Vol. 29, No. 1-4

27--35

Biological systems are generally dense reaction-diffusion systems. Therefore, determining the mechanism of motion in such systems is of crucial importance in understanding their dynamics. Subdiffusive behavior is very common in biological systems but its origin usually does not have a clear explanation. One attempt to explain this behavior is the presence of randomly placed stationary obstacles in a medium filled with molecules of a certain medium. With an appropriate concentration of obstacles, the molecules of the medium cease to perform classic Brownian motions and motion becomes subdiffusive. This mechanism seems to be well documented in both simulations and experiments. The question arises whether a similar effect can be obtained in systems where obstacles are not stationary, but their mobility is drastically reduced comparing to medium molecules, or the reduction in mobility is combined with a limitation in movement (the movement of obstacles resembles, for example, the Orestein-Ulhenbeck movement). Is it possible to observe subdiffusion behavior in such a situation? We try to answer this question on the basis of Monte Carlo simulations based on the Dynamic Lattice Liquid (DLL) model. Based on the concept of cooperative movements, this model has a unique feature that allows one to take into account the correlation of movements between the elements that make up the examined system, which is important in the case of high densities due to the strict correlation of movements between the moving elements. The tests concern systems where obstacles were single beads whose mobility was changed with additional restrictions imposed on the displacement. It was shown that no entrapment of medium molecules was observed and a slight deviation from normal diffusion was also shown.