Anomalous diffusion and power-law relaxation of the time averaged mean squared displacement in worm-like micellar solutions

Abstract

We report the results of single tracer particle tracking by optical tweezers and video microscopy in micellar solutions. From careful analysis in terms of different stochastic models, we show that the polystyrene tracer beads of size 0.52-2.5 µm after short-time normal diffusion turn over to perform anomalous diffusion of the form r 2 (t) t α with α ≈ 0.3. This free anomalous diffusion is ergodic and consistent with a description in terms of the generalized Langevin equation with a power-law memory kernel. With optical tweezers tracking, we unveil a power-law relaxation over several decades in time to the thermal plateau value under the confinement of the harmonic tweezer potential, as predicted previously (Phys. Rev. E 85 021147 (2012)). After the subdiffusive motion in the millisecond range, the motion becomes faster and turns either back to normal Brownian diffusion or to even faster superdiffusion, depending on the size of the tracer beads.

Cytoplasmic RNA-Protein Particles Exhibit Non-Gaussian Subdiffusive Behavior

“…In particular, the subdiffusive continuous time random walk and heterogeneous diffusion models often exhibit a wide spread in the tMSD like that seen in Fig. 2, c and d (though with a ¼ 1) (47,48). We notice that there is a trend in the velocity autocorrelation function where the correlation becomes more positive for larger timescales of measurement (Fig.…”

“…The typical feature observed is a plateau in the MSD, as has been previously shown for proteins and chromosome loci in the E. coli cytoplasm (41,50) and the fractional Brownian motion model (51). For the fractional Brownian motion the approach to the plateau in the MSD can be significantly delayed relative to the standard Brownian motion due to the slower dynamics (48,51), while a subdiffusive continuous time random walk would exhibit a second, shallower slope on the tMSD (47,51). We do not see the plateau signature in the MSD for the timescales and cellular regions analyzed in this study ( Fig.…”

Nonergodicity, fluctuations, and criticality in heterogeneous diffusion processes

“…Brownian motion is ergodic and for sufficiently long measurement times T the equality x 2 (∆) = δ 2 (∆) holds [49,50]. Anomalous diffusion (2) described by FBM or fractional Langevin equation motion is asymptotically ergodic [32,51] but may feature transiently non-ergodic behavior [23,52] in confinement as well as transient aging [53], the explicit dependence on the time span elapsing between initial preparation of the system and start of the recording of the position, x(t).…”

Fluctuation analysis of time-averaged mean-square displacement for the Langevin equation with time-dependent and fluctuating diffusivity

“…represents the ensemble average, and α > 0 is the exponent which characterizes the diffusion behavior (α < 1, α = 1, and α > 1 correspond to the subdiffusion, normal diffusion, and superdiffusion, respectively). The anomalous behavior is observed in various systems ranging from a charge carrier transport in amorphous material [1], light diffusion [2], polymeric materials [3], to biological transports [4][5][6][7][8][9], The diffusion behavior will depend on the time scale, and thus the exponent α may take several different values depending on ∆. For example, in entangled polymers, the EAMSD of a segment exhibits four different regions which reflect the crossovers between different characteristic relaxation time scales [3].…”

“…Such an intrinsic randomness of the TAMSDs will be related to large fluctuations of the TAMSDs. (The large fluctuations are actually observed in single-particle-tracking experiments in living cells [5][6][7][8][9].) Thus it is important to calculate the statistical quantities such as the average and standard deviation of the TAMSD.…”