Probing microscopic origins of confined subdiffusion by first-passage observables

Abstract

Subdiffusive motion of tracer particles in complex crowded environments, such as biological cells, has been shown to be widespread. This deviation from Brownian motion is usually characterized by a sublinear time dependence of the mean square displacement (MSD). However, subdiffusive behavior can stem from different microscopic scenarios that cannot be identified solely by the MSD data. In this article we present a theoretical framework that permits the analytical calculation of first-passage observables (mean first-passage times, splitting probabilities, and occupation times distributions) in disordered media in any dimensions. This analysis is applied to two representative microscopic models of subdiffusion: continuous-time random walks with heavy tailed waiting times and diffusion on fractals. Our results show that first-passage observables provide tools to unambiguously discriminate between the two possible microscopic scenarios of subdiffusion. Moreover, we suggest experiments based on first-passage observables that could help in determining the origin of subdiffusion in complex media, such as living cells, and discuss the implications of anomalous transport to reaction kinetics in cells.anomalous diffusion ͉ cellular transport ͉ reaction kinetics ͉ random motion I n the past few years, subdiffusion has been observed in an increasing number of systems (1, 2), ranging from physics (3, 4) or geophysics (5) to biology (6, 7). In particular, living cells provide striking examples for systems where subdiffusion has been repeatedly observed experimentally, either in the cytoplasm (6-9), the nucleus (10, 11), or the plasmic membrane (12-14). However, the microscopic origin of subdiffusion in cells is still debated, even if believed to be caused by crowding effects in a wide sense, as indicated by in vitro experiments (15-18).The subdiffusive behavior significantly deviates from the usual Gaussian solution of the simple diffusion equation, and is usually characterized by a mean square displacement (MSD) (1) that scales as ͗⌬r 2 ͘ ϳ t ␤ with ␤ Ͻ 1. Such a scaling law can be obtained from a few models based on different underlying microscopic mechanisms. Here, we focus on two possibilities (a third classical model of subdiffusion is given by the fractional Brownian motion that concerns processes with long-range correlations): (i) The first class of models that we consider stems from continuous time random walks (CTRWs) (1, 19) and their continuous limit described by fractional diffusion equations (1, 20). The anomalous behavior in these models originates from a heavy-tailed distribution of waiting times (21): at each step the walker lands on a trap, where it can be trapped for extended periods of time. When dealing with a tracer particle, traps can be out-of-equilibrium chemical binding configurations (22, 23), and the waiting times are then the dissociation times; traps can also be realized by the free cages around the tracer in a hard sphere-like crowded environment, and the waiting times are the life times of the ...

Simulation of diffusion in a crowded environment

“…5 The dynamics in such systems is still far from being understood as the experiments indicate the diversity of dynamic behavior and even its origin are being discussed. [6][7][8][9][10][11][12][13][14] The environment in living cells is a good example of such a system. It is mostly heterogeneous, because the motion of molecules is obstructed here by different kinds of lipids and proteins.…”

“…15,16 Experimental studies concerning the motion of proteins and lipids in cells were performed using uorescence correlation spectroscopy, [17][18][19][20] pulsed eld gradient NMR 21 and single particle tracking (SPT). 6,7,[22][23][24][25][26][27] In many cases an anomalous diffusion was detected, i.e. the mean square displacement of objects hDr 2 i scaled with time t as hDr 2 i $ t a , with a < 1.…”

Close or connected: Distance and connectivity effects on transport in networks

“…The impact of connectivity on transport properties has been put forward in [8,[23][24][25], where it was found in different examples that transport towards a target node can be favored by a high connectivity of the target, and different functional forms of the dependence of the MFPT on the target connectivity were proposed. On the other hand, the dependence of the MFPT on geometric properties, such as the volume of the network and the source to target distance, has been obtained recently in [26][27][28][29], where it was shown that the starting position of the random walker plays a crucial role in the target search problem. In this context, quantifying the relative importance of distance and connectivity effects on transport properties on complex networks remains an important and widely unanswered question, which can be summarized as follows : is it faster for a random walker to find either a close, or a highly connected target?…”

Resolving a paradox of anomalous scalings in the diffusion of granular materials

“…The mean squared displacement of a tracer particle is one of the most reliable diagnostics for anomalous transport (21), though it has been argued that even more fundamental measures are required to distinguish anomalous diffusion from other physical processes (22). In the case of axial diffusion of grains in a tumbler (11), due to the opaque nature of the granular materials, measuring individual particle trajectories is a difficult task, which only recently was achieved using high-intensity synchrotron x-rays (23).…”