Rheology of two-dimensional F-actin networks associated with a lipid interface

We report on the surface rheology of cross-linked F-actin networks associated with a lipid monolayer at the air-water interface of a Langmuir monolayer. The rheological measurements are made using a Couette cell. These data demonstrate that the network has a finite elastic modulus that grows as a function of the cross-linking concentration. We also note that under steady-state flow the system behaves as a power-law fluid in which the effective viscosity decreases with imposed shear.

Figure 1

(Color online) A schematic diagram of the Couette trough used in the experiments. The F-actin and lipid monolayer completely fills the surface between the inner and outer Teflon cylinders. The outer cylinder is rotated at constant angular velocity and angular displacement of the inner cylinder is monitored via the magnet rigidly coupled to torsion wire.

Figure 2

Typical data set: The F-actin network has a cross linker density of $R=0.005$. At $t=0$ the outer cylinder reaches a fixed angular velocity of 0.4 rad/sec (which corresponds to a shear rate of $1.3{\text{s}}^{-1}$). The measured torque rapidly reaches a plateau and returns to zero when the outer cylinder is stopped (see Fig. 3). Inset shows a closeup of the initial rise.

Figure 3

(Color online) The torque vs time for the cessation of flow for the F-actin network with a cross linker density of $R=0.005$. The outer cylinder was rotated with a fixed angular velocity of 0.4 rad/sec (shear rate 1.3), and stopped at $t=0\text{s}$. The solid line is a fit to a double exponential decay as discussed in the text. Inset: Semilog plot of the same data showing just the early time behavior and the dominant relaxation time. The solid red line is a fit to the data with time constant 1.9 s.

Figure 4

(Color online) Torque and surface viscosity measurements on an un-cross-linked F-actin network ($R=0$, black squares) and a F-actin network with $R=0.04$ cross linker density (red circles) at standard concentration associated with the lipid monolayer. (a) Torque vs rotation rate of the outer cylinder showing a power-law dependence expected for a fluid in which the viscosity decays as a power of shear rate [see Eq. (11)]. The lines are the best fits to the data. (b) The surface viscosity of the composite monolayer extracted from the data in (a) [see Eqs. (12, 13)]. The lines are the best fit to the data.

Figure 5

(Color online) The elastic modulus as extracted from the data shown in Fig. 2 vs cross-linker density as measured by $R$.

Figure 6

(Color online) The elastic modulus vs rotation rate of the outer cylinder for a range of cross-linker concentrations. The linear dependence (best fit line in red) demonstrates a power-law dependence of the elastic modulus on rotation rate with an exponent of $-0.4$.

Figure 7

The dependence of the best fit value of $n-1$ for the dependence of the viscosity on rate of strain as a function of ratio of cross linker to G-actin concentration.