On the microscopic level, biological signal transmission relies on coordinated transient structural changes in allosteric proteins that involve sensor and effector modules. The time scales 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 the 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 distant site. They are defined in terms of equilibrium fluctuations from simulations or experimental observations. We apply the framework to our all-atom molecular dynamics simulations of a bacterial histidine kinase protein extensively studied in experiments. For the isolated coiled-coil (CC) motif that connects sensor and effector modules, our analysis reveals that signal propagation through the CC is possible via shift, splay, and twist deformation modes, which is confirmed by simulations of the entire protein. Based on mutation experiments, we infer that the most relevant mode for the biological function of the histidine kinase is the splay deformation. For the β2-adrenergic receptor, a transmembrane protein involved in the G-protein signaling pathway, we compare signal transmission across its different structural domains involved in receptor activation.
