Nonequilibrium Mechanics and Dynamics of Motor-Activated Gels

The mechanics of cells is strongly affected by molecular motors that generate forces in the cellular cytoskeleton. We develop a model for cytoskeletal networks driven out of equilibrium by molecular motors exerting transient contractile stresses. Using this model we show how motor activity can dramatically increase the network’s bulk elastic moduli. We also show how motor binding kinetics naturally leads to enhanced low-frequency stress fluctuations that result in nonequilibrium diffusive motion within an elastic network, as seen in recent in vitro and in vivo experiments.

Figure 1

(a) Schematic diagram of contractile motor activity in a network. A myosin minifilament (blue) slides two network filaments (red) past each other, generating an equal and opposite pair of forces (green arrows). (b) Plot of the predicted relative stiffening of a semiflexible network as a function of (normalized) motor-induced tension. The inset shows the nonlinear force-extension relation of a single semiflexible filament [3, 4, 17].

Figure 2

The displacement power spectral density (PSD) in an active gel. Here, frequency is measured in terms of $\Omega =\omega \Gamma /B$. The thermal PSD (dashed line) shows a plateau at low frequencies. Thus, the active component of the PSD dominates at low frequencies, while the thermal PSD is expected to dominate at high frequencies. (Inset) Schematic of the time-dependent force due to molecular motor activity.

Figure 3

(a) Graphs of the spatial dependence of the longitudinal parts of the parallel ($\parallel$) and perpendicular ($\perp$) response functions [Eqs. (2, 3)]. The effect of compression of the network on the response functions can be reduced to a universal form when plotted against the dimensionless quantity $r\sqrt{\Omega }=r\sqrt{\omega \Gamma /B}$, demonstrating the diffusive nature of the propagation of the network density mode. (b) The effect of network compression can be isolated in experimental data by examining the difference in the parallel and perpendicular response functions given in Eq. (4). Here we plot the predicted form of the real (Re) and imaginary (Im) parts of that difference vs the dimensionless variable $r\sqrt{\Omega }$.

Figure 4

(a) The displacement vector field of an incompressible network shown in a plane passing through the two force centers for a contractile motor acting at the origin. The forces are applied symmetrically at points ($\pm 3/4$, 0) and are each directed towards the origin. (b) The network displacement field for the compression mode shown in the limit of low frequency or weak hydrodynamic coupling ($\Gamma \to 0$). Again, the forces are applied symmetrically at points ($\pm 3/4$, 0) and are each directed towards the origin. The resulting displacement field induces network density variations in the material.