Semi-flexible Network Dynamics - A View From Inside

The thermally driven dynamics of a polymer network are studied by direct view observation of the motion of a single point within a single polymer. Taking advantage of rather rigid biological microtubules as a case study, we expand the space and time scales of the system to those accessible by optical microscopy and standard video tools. Tracking is achieved by chemically attaching an optically resolved micro-sphere to a single point on the filament. We measure a sequence of instantaneous positions, from which we compute the mean squared displacement vs time. Typical behavior in a network shows two distinct regimes. At short times, we observe anomalous diffusion with power law 3/4. At long times (seconds) the undulation amplitude saturates as a consequence of the finite length of the polymer. In the network, entanglements effectively divide the filament into segments shorter than the physical length. In a pre-stressed network we find a short time sub-diffusive regime with power law 0.4-0.5, interpreted as a signature of tension along the individual filament.