The CSK as a dynamic network of passive (blue) and active (red) acto-myosin stress fibers. A microbead (gray) becomes a node in the network and allows to to measure the response to externally applied forces (upper right inset), or to observe spontaneous fluctuations (lower right inset). The tractions of the active fibers create a force field (black arrows) in the surrounding matrix.
When microbeads are attached to the CSK of living cells, the beads start to move spontaneously in a random fashion. The amplitude of the bead's velocity fluctuations are on a much higher level than in the case of Brownian motion, indicating that they are not driven by thermal forces, but result from ATP-powered remodelling processes of the CSK.
Some measured example trajectories of CSK-bound beads (2-5) . For comparison, case 1 demonstrates the amount of thermal and camera noise of an immobilized bead. [Data from C. Raupach].
A detailed statistical analysis of many recorded bead trajectories reveals that the diffusion process is anomaleous in several respects: As a function of lag-time, one finds at around 1 sec a transition from sub- to superdiffusive transport, accompanied by characteristic changes of the turning angle distributions. On longer time scales, the mean squared displacement grows with a fractional powerlaw exponent. The step width distributions are non-gaussian with positive kurtosis.
The measured mean squared displacement (MSD) of 3 different diffusing, CSK-bound beads (2-4). Case 1 corresponds to an immobilized bead. The turning angle distributions (TAD) indicate antipersistence for lag times smaller than 1 sec and persistent transport for longer lags. [Data from C. Raupach]
Viewed as an abstract stochastic process, the bead motion can be described as a specific kind of persistent random walk on a white noise floor. This model can reproduce all the experimental distributions and successfully predicts new relations between certain observables. However, it cannot explain the origin of the long time correlations in the bead's transport directions.
For this purpose, we also develop more concrete, biophysical models.
The bead is described as a node in a simple network of developing stress fibers that act as springs. The biophysical remodelling of the network, i.e. the temporal growth and degradation of the fibers, corresponds to a temporal change of the spring parameters, like their rest lengths and stiffness. In this way, the long time memory of the bead's transport direction can be traced back to correlations in the fiber remodelling processes.
Since the remodelling processes are regulated by a biochemical reaction network, the correlations must be ultimately explained by a theory of fluctuations in nonlinear chemical reaction systems.
First results have been published in Metzner-07, Raupach-07 and Raupach-08 (thesis).
On a more macroscopic level, the cytoskeletal network may be described by a continuum material with complex rheological properties. The motion of any point in such a "medium" can then be explained by the interplay of the time-dependent forces acting on that point and the rheological response function of the medium. Some preliminary ideas along those lines have been presented in a talk.