Fluidization and Active Thinning by Molecular Kinetics in Active Gels

We derive the constitutive equations of an active polar gel from a model for the dynamics of elastic molecules that link polar elements. Molecular binding kinetics induces the fluidization of the material, giving rise to Maxwell viscoelasticity and, provided that detailed balance is broken, to the generation of active stresses. We give explicit expressions for the transport coefficients of active gels in terms of molecular properties, including nonlinear contributions on the departure from equilibrium. In particular, when activity favors linker unbinding, we predict a decrease of viscosity with activity—active thinning—of kinetic origin, which could explain some experimental results on the cell cortex. By bridging the molecular and hydrodynamic scales, our results could help understand the interplay between molecular perturbations and the mechanics of cells and tissues.

Figure 1

Applications of our model to biological active gels. The elastic kinetic elements are depicted in green while the polar structures are shown in red. (a) Cell cortex: myosin motors are the active elastic kinetic elements within the actin network. (b) Tissues: cell-cell adhesion molecules, such as cadherins, are the elastic kinetic elements connecting cell cortices into a multicellular active polar gel. (c) Lamellipodium: cell adhesion molecules, such as integrins, are the elastic kinetic elements at the interface of the actomyosin gel layer.

Figure 2

Transport coefficients of Eqs. (5)–(6) as a function of the activity ${\mathrm{\Omega }}_0$, tuned by the ATP concentration, for ${\mathrm{\Omega }}_u=0$ and ${\mathrm{\Omega }}_q={\mathrm{\Omega }}_0$. For ${\mathrm{\Omega }}_0>0$ (see text), the viscosity $\eta =\mu {\varphi }_b/(2k_d)$ decreases with activity (active thinning) due to the reduced fraction of bound molecules ${\varphi }_b=(\alpha -{\mathrm{\Omega }}_0)/(1+\alpha -{\mathrm{\Omega }}_0)$.