  We derive the stochastic equations of motion for a tracer that is tightly
attached to a semiflexible polymer and confined or agitated by an externally
controlled potential. The generalised Langevin equation, the power spectrum,
and the mean-square displacement for the tracer dynamics are explicitly
constructed from the microscopic equations of motion for a weakly bending
wormlike chain by a systematic coarse-graining procedure. Our accurate
analytical expressions should provide a convenient starting point for further
theoretical developments and for the analysis of various single-molecule
experiments and of protein shape fluctuations.
