Active gels as a description of the actin-myosin cytoskeleton

Abstract

This short review presents a qualitative introduction to the hydrodynamic theory of active polar gels and its applications to the mechanics of the cytoskeleton. Active polar gels are viscoelastic materials formed by polar filaments maintained in a nonequilibrium state by constant consumption of energy. In the cytoskeleton of eukaryotic cells, actin filaments are treadmilling and form a viscoelastic gel interacting with myosin molecular motors driven by the hydrolysis of adenosine triphosphate; one can thus consider the actomyosin cytoskeleton as an active polar gel. The hydrodynamic description is generic as it only relies on symmetry arguments. We first use the hydrodynamic approach to discuss the spontaneous generation of flow in an active polar film. Then we give two examples of applications to lamellipodium motility and to instabilities of cortical actin.

Figure 1. Sketch of a thin active gel film with different boundary conditions on the solid and free surfaces.

Figure 2. Sketch of a lamellipodium advancing on a solid substrate.

The lamellipodium is advancing to the left at a velocity U. It is connected to the cell body on the right. The thickness h increases with x and is roughly constant in the central part of the lamellipodium.

Figure 3. Calculated velocity, force, and height profiles of a thin active gel layer corresponding to a lamellipodium which is moving on a substrate in the negative

-direction with velocityu=10 μm∕min. The position x is measured along the horizontal axis and given in micrometers. The flow velocity v of the gel layer relative to the substrate is given in micrometers per minute, and the gel thickness h is given in micrometers. The integrated stress across the active gel layer F is given in units of 0.5 nN∕μm. The parameter values are ζΔμ/4η=−0.21/min, ξ/4η=1/(36 μm), and u=10 μm∕min. Furthermore, we use ξ=3⋅10¹⁰ Pa s∕m and $k_p{\rho }_{\mathrm{wa}}^0=9\mu \mathrm{m}∕\min$.