Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions

Jaeoh Shin,Andrey G Cherstvy,Ralf Metzler

doi:10.1088/1367-2630/17/11/113028

Abstract

We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction ϕ of the crowders and the crowder–crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational—but not rotational—diffusivity of the particles D is a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law with the area fraction ϕ occupied by the crowders and the critical value Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.

Highlights

Over the recent years, deviations from the standard Brownian diffusion law [1] have been observed in a broad range of systems [2, 3, 4, 5, 6, 7, 8]
Depending on the physics of the system under consideration, various theoretical models are used to describe these deviations [2, 3, 4, 5, 6, 7, 8]. Such anomalous diffusion is typically characterised by the power-law growth of the mean squared displacement (MSD) of particles with time r2(t) ≃ Kβtβ
At intermediate time scales of ∆ ∼ 0.1 . . . 10 we observe a non-monotonic behaviour of the time averaged MSD that we ascribe to the events of the first collision of a given crowder molecule with another crowder

Summary

Introduction

Deviations from the standard Brownian diffusion law [1] have been observed in a broad range of systems [2, 3, 4, 5, 6, 7, 8]. Despite the progress of analytical theories of crowded solutions some important diffusive characteristics can only be studied quantitatively by computer simulations This is true for crowders of the non-trivial of the Mercedes-Benz star like particles considered in the current paper (Fig. 1). Our main target is to gain insight into the physical behaviour of non-spherical crowders relevant for the situation in vitro where soft non-spherical and often non-inert crowders such as globular PEG and branched dextran polymers are routinely used to mimic the effects of MMC in living cells Another important experimental example is the diffusivity of anisotropic lysozyme-like proteins studied by Brownian Dynamics simulations in crowded media [62].

Simulation model and observables

Results

Discussion and conclusions