  We adapt Fluorescence Correlation spectroscopy (FCS) formalism to the studies
of the dynamics of semi-flexible polymers and derive expressions relating FCS
correlation function to the longitudinal and transverse mean square
displacements of polymer segments. We use the derived expressions to measure
the dynamics of actin filaments in two experimental situations: filaments
labeled at distinct positions and homogeneously labeled filaments. Both
approaches give consistent results and allow to measure the temporal dependence
of the segmental mean-square displacement (MSD) over almost five decades in
time, from ~0.04ms to 2s. These noninvasive measurements allow for a detailed
quantitative comparison of the experimental data to the current theories of
semi-flexible polymer dynamics. Good quantitative agreement is found between
the experimental results and theories explicitly accounting for the
hydrodynamic interactions between polymer segments.
