Compliance of actin filament networks measured by particle-tracking microrheology and diffusing wave spectroscopy

We monitor the time-dependent shear compliance of a solution of semi-flexible polymers, using diffusing wave spectroscopy (DWS) and video-enhanced single-particle-tracking (SPT) microrheology. These two techniques use the small thermally excited motion of probing microspheres to interrogate the local properties of polymer solutions. The solutions consist of networks of actin filaments which are long semi-flexible polymers. We establish a relationship between the mean square displacement (MSD) of microspheres imbedded in the solution and the time-dependent creep compliance of the solution, (Δr²(t)>=(k_BT/πa)J(t). Here, J(t) is the creep compliance, (Δr²(t)> is the mean-square displacement, and a is the radius of the microsphere chosen to be larger than the mesh size of the polymer network. DWS allows us to measure mean square displacements with microsecond temporal resolution and Angstrom spatial resolution. At short times, the mean square displacement of a 0.96 μm diameter sphere in a concentrated actin solution displays sub-diffusion. (Δr²(t)>*t^α, with a characteristic exponent α=0.78±0.05, which reflects the finite rigidity of actin. At long times, the MSD reaches a plateau, with a magnitude that decreases with concentration. The creep compliance is shown to be a weak function of polymer concentration and scales as J_p*c^-1.2±0.3. This exponent is correctly described by a recent model describing the viscoelasticity of semi-flexible polymer solutions. The DWS and video-enhanced SPT measurements of the compliance plateau agree quantitatively with compliance measured independently using classical mechanical rheometry for a viscous oil and for a solution of flexible polymers. This paper extends the use of DWS and single-particle-tracking to probe the local mechanical properties of polymer networks, shows for the first time the proportionality between mean square displacement and local creep compliance, and therefore presents a new, direct way to extract the visco-elastic properties of polymer systems and complex fluids.