Nonequilibrium fluctuations of a remodeling in vitro cytoskeleton

Motor proteins actively contract the actin cytoskeleton of cells and thereby give rise to nonequilibrium fluctuations as well as changes in the architecture of the cytoskeleton. Here, we show, by video microrheology of a reconstituted cytoskeleton, that motors generate time-dependent nonequilibrium fluctuations, which evolve as the network is remodeled. At earlier times, the fluctuation spectrum is dominated by strong non-Gaussian fluctuations, which arise from large displacements. At later times, directed displacements are infrequent and finally disappear. We show that these effects are due to contractile coarsening of the network into large actin-myosin foci.

Figure 1

(a) Ensemble-averaged mean square displacements of probe particles in left: motor-driven active gels and in right: passive gels devoid of motors at different sample ages (indicated as numbers in minutes). Gray insets: example trajectories (box width 4 μm). Large inset: dark holes: homogenously distributed probe particles in an actin-myosin gel (red: actin; green: myosin). (b) Ensemble-averaged van Hove correlation functions of probe particles in large circles: active and small circles: passive gels for different sample ages $t$ at lag time τ $=$ 10 s. Solid (dashed) line: Gaussian fit to active (passive) data. Large open circles indicate displacement probabilities after removal of directed motion events from particle trajectories.

Figure 2

Quantification of active fluctuations as functions of sample age $t$ and lag time τ. (a) Ratio of widths of Gaussian fits to ensemble-averaged van Hove correlation functions of active and passive samples. Circles: Maxima at given $t$. (b) Non-Gaussian parameter of van Hove correlation functions of active samples. Brown (upper) surface: original data. Green (lower) grid: data after removal of directed motion events from particle trajectories.

Figure 3

Left: thresholding of the frame-to-frame directional change $\Delta {\Theta }_n$ to retrieve time spans of directed motion shown for a short segment of a particle trajectory in an active gel. Right: Calculation of $\Delta {\Theta }_n$ from window averaged (window 1 s) velocity components.

Figure 4

(a) Confocal fluorescence micrographs of an active actin-myosin gel, showing coarsening in three phases. The red: actin network and the green: myosin distribution are initially homogeneous ($t$ $=$ 5 min). Within 10 min, myosin filaments coalesce into foci. After 35 min, foci are surrounded by shells of condensed actin. After 75 min, actomyosin foci have coalesced into large clusters. (b) Multiple measures of nonequilibrium activity decay on a time scale of 40 min (see the Supplemental Material [23] for a sample-to-sample variability of results): from top to bottom, diffusive coefficient α, the Gaussian standard deviation ratio β, the non-Gaussian parameter ξ at lag time 10 s, and the probability for a particle to undergo directed motion $p_{\mathrm{dir}}$. The dashed line indicates the transition to steady state. Triangles show ξ after removal of directed motion events.