  On the microscopic level, biological signal transmission relies on
coordinated structural changes in allosteric proteins that involve sensor and
effector modules. The timescales and microscopic details of signal transmission
in proteins are often unclear, despite a plethora of structural information on
signaling proteins. Based on linear-response theory, we develop a theoretical
framework to define frequency-dependent force and displacement transmit
functions through proteins and, more generally, viscoelastic media. Transmit
functions quantify the fraction of a local time-dependent perturbation at one
site, be it a deformation, a force, or a combination thereof, that survives at
a second site. They are defined in terms of equilibrium fluctuations from
simulations or experimental observations. We apply the framework to our
all-atom molecular dynamics simulation data of a parallel, homodimeric
coiled-coil (CC) motif that connects sensor and effector modules of a
blue-light-regulated histidine kinase from bacterial signaling systems
extensively studied in experiments. Our analysis reveals that signal
transmission through the CC is possible via shift, splay, and twist deformation
modes. Based on the results of mutation experiments, we infer that the most
relevant mode for the biological function of the histidine kinase protein is
the splay deformation.
