Measurements and characterization of the dynamics of tracer particles in an actin network

Abstract

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models

“…In recent years, certain combinations of models were proposed, including switching-diffusivity 11,13,[70][71][72][73][74][75][76][77] and annealed-transienttime models (ATTM), 78 BM with fluctuating or diffusing diffusivity (DD), 70,[79][80][81][82][83][84][85] BM-and anomalous-diffusion-models with ''superstatistically'' distributed model parameters, [86][87][88][89] compound diffusion processes of SBM-DD, 84 SBM-HDPs, 90,91 FBM-DD, 92 FBM-HDPs, 19,93 SBM with exponentially and logarithmically varying D(t), 94 CTRWs with random walks on fractal (RWFs), 95 CTRW-FBM, 16,[96][97][98] as well as several other models, 74,[99][100][101][102][103][104][105][106][107][108][109]…”

Non-ergodicity of a globular protein extending beyond its functional timescale

“…Observational non-ergodicity has been documented on the time window of 0.01 ~ 100 seconds in various biological phenomena, including the transport of protein molecules or nanoparticles through complex macroscopic biological systems, such as cell membranes, living cells, and actin filaments. [38][39][40][41][42][43] These systems are large enough (> 1 μm) and have structures that are complex and heterogeneous enough to produce complex, non-ergodic dynamics. Single-molecule force-clamp spectroscopy has demonstrated non-ergodicity to occur when unfolding a protein molecule at the time window of 0.01 ~ 10 s. 18,59 However, unfolding or folding corresponds to a dramatic perturbation of the biomolecule, far away from its folded globular functional state.…”

“…Indeed, the internal dynamics of SHP2 ages with the observation time. This aging behavior is often interpreted by the framework of continuos-time random walk (CTRW), [38][39][40][41][42][43] and thus why we derive the waiting time distribution in Fig. S7.…”

“…Hence, again, the inter-domain motion of the protein is non-ergodic and heterogeneous over the 1 ps $ 100 ns time window probed by MD. Non-ergodic phenomena have been reported in various complex biological systems, such as the diffusion of a nanoparticle in an actin lament network, 38,39 the lateral movement of protein molecules in the cell membrane, 40,41 and the transportation of protein granules in the cytoplasm of living cells. 42,43 Accompanying the non-ergodicity, these systems oen show striking aging phenomena in which the effective mobility of the studied particle is reduced upon increasing the observation time, 36,37 as manifested as a decay of the TEA-MSD over t at a given D. Non-ergodicity is related to the aging properties of the processes involved, that is, the dependence of physical observables on the time span between the initialization of the system and the start of the measurement.…”

Anomalous statistics of laser-cooled atoms in dissipative optical lattices

“…The ability to precisely tune the control parameters, and hence the ensuing anomaly, is a unique advantage of atomic systems. It is not common that a basic theory such as that of Sisyphus cooling can lead to a detailed theoretical understanding of the origins of anomalous diffusion, usually found in truly complex settings such as biological systems (Barkai et al, 2012;Levin et al, 2021;Lo et al, 2002), economics (Plerou et al, 2000) or turbulent flows (Richardson, 1926). Furthermore, these atomic systems enable both one-shot ensemble averaging of millions of particles, single-particle tracking (Bouton et al, 2020;Katori et al, 1997;Kindermann et al, 2016) and the application of advanced spectral analysis tools.…”