Rheology of Active Filament Solutions

We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.

Figure 1

(a) The steady-state shear viscosity on both sides of the IN transition for passive and active nematics. (b) The “motility” parameter $\chi$ [see Eq. (17)] relating the magnitude of the active component of shear stress to the “activity” $\mu$ ($\sim \mathrm{ATP}$ consumption). Inset: Phase diagram showing the IN transition.