Oscillations, Waves, and Interactions - GWDG

DPI60plus – a future with biophysics 453
3.4 Fluid dynamics, polymer networks, colloids and model systems for cells studied
by microrheology
The machinery that drives essential functions of cells such as locomotion and division
is based on an elastic network of interconnected semiflexible protein filaments, collectively
referred to as the cytoskeleton. A major component of the cytoskeleton is the
actin cortex, a dense meshwork of cross-linked actin filaments beneath the plasma
membrane that is controlled by a host of accessory proteins. The physical construction
of the cytoskeleton with its complex hierarchy of structural length scales enables the
cell to produce large changes in physical properties by small chemical interventions,
such as length- or crosslink-control or regulated attachments to other structures in
the cell. The unique sensitivity of cytoskeletal networks stems in large part from the
semiflexible character of its constituents, i. e., the fact that their thermal persistence
length lp (17 µm for filamentous-actin (F-actin)) is orders of magnitude larger than
molecular scales (7 nm filament diameter of actin). The mechanical and dynamical
(rheological) properties of semiflexible polymers have been the focus of intense research
in recent years. Apart from their biological role, these networks have proven
to be unique polymeric materials in their own right. In contrast to flexible polymer
networks, the shear modulus of a semiflexible polymer network can be varied over
many orders of magnitude by small changes in cross-linking, and exhibits strong nonlinearities.
The dynamics of semiflexible solutions and gels have proven to be much
richer than those of flexible polymers. Even for single filaments there are multiple
distinct modes of relaxation that are qualitatively distinct from those of conventional
polymers. It has proven challenging, however, to quantitatively probe those dynamic
regimes experimentally, because of the extensive bandwidth required [11].
Microrheology based on optical traps and interferometric detection of particle motions
can meet those challenges. Having a bandwidth of 6 orders of magnitude in frequency
from 0.1 Hz to 100 kHz, however, provides other interesting options. It makes
it also possible to study general issues of fluid dynamics. A fundamental problem in
hydrodynamics is the response of a liquid to the motion of a small embedded particle.
At sufficiently long times, the well known Stokes velocity field, which decreases as 1/r
away from the particle, will describe this fluid response. For an initial disturbance
due to a local force in the liquid, however, only a small region of the liquid can be
set in motion due to the inertia of the liquid. If the liquid is incompressible, backflow
occurs that is characterized by a vortex ring surrounding the point disturbance. Since
vorticity diffuses within the (linearized) Navier-Stokes equation, propagation of shear
in the fluid drives the expansion of this vortex ring as a function of time t as √ t.
The 1/r Stokes flow is established only in the wake of this vortex. While this basic
picture has been known theoretically for simple liquids since Oseen [12], and has been
observed in simulations since the 1960’s [19], this vortex flow pattern has not been
observed directly in experiment. In a recent project we have used the correlations
in thermal fluctuations of small probe particles to resolve this vortex flow field on
the micrometer scale along with its diffusive propagation. We found good agreement
between measured flow patterns and theoretical calculations for simple viscous fluid.
Furthermore, we could demonstrate similar vortex-like flow in viscoelastic media. In
the viscoelastic case, interestingly, vorticity spreads super-diffusively.