Directional memory and caged dynamics in cytoskeletal remodelling

Abstract

We report directional memory of spontaneous nanoscale displacements of an individual bead firmly anchored to the cytoskeleton of a living cell. A novel method of analysis shows that for shorter time intervals cytoskeletal displacements are antipersistent and thus provides direct evidence in a living cell of molecular trapping and caged dynamics. At longer time intervals displacements are persistent. The transition from antipersistence to persistence is indicative of a time-scale for cage rearrangements and is found to depend upon energy release due to ATP hydrolysis and proximity to a glass transition. Anomalous diffusion is known to imply memory, but we show here that memory is attributed to direction rather than step size. As such, these data are the first to provide a molecular-scale physical picture describing the cytoskeletal remodelling process and its rate of progression.

FIG. 1

Mean square displacements, 2(Δt)>, computed from spontaneous motion of RGD-coated beads (400 to 720 beads per group). (a) <r²(Δt)> at different thermodynamic temperatures, from 12°C to 41°C. (b) <r²(Δt)> under baseline condition (23°C), and after challenge with DBcAMP (decreases cell contractility, 1 mM), jasplakinolide (stabilizes actin, 1 μM), cytochalasin-D (disrupts actin filaments, 2 μM), and after depleting ATP. ATP concentration after depletion was from 2 to 7% of that in control samples. Noise level on bead position is discussed in Bursac et al.[1] and in Online Supplement 2.

FIG. 2

Probability density functions of angles, p(Δt,θ), for baseline condition (23°C) at different time intervals Δt, (a) from 0.08 s to 6.60 s and (b) from 6.60 s to 60.25 s. p(Δt,θ) is computed from the same bead trajectories as 2(Δt)> (Fig. 1), averaging over 428 beads, yielding from 1.7×10⁶ events at Δt = 0.082 s down to 1.3×10³ events at Δt = 60.25 s. When averaging, time intervals do not overlap in order to avoid artifactual correlations between angles. Bin size is 2π/15. Solid line is uniform distribution u(θ) = 1/2π.

FIG. 3

The departure of p(Δt,θ) from a uniform distribution is quantified using the Kolmogorov-Smornov statistical test, K(Δt), (a) at different thermal temperatures, and (b) with different CSK treatments, and after ATP depletion.

FIG. 4

(a) Transition time, Δt*, from antipersistent to persistent behaviour vs. x. where x-1 is the power-law dependence of g′ upon frequency. (b) Maximum value of K(Δt), K_max, as a function of x. Color coding same as Fig. 1 and Fig. 3. K_max for ATP depletion could not be calculated, but does not fall within other values. Dotted line is a guide for the eyes.s