Cancellation between auto- and mutual correlation contributions of protein/water dynamics in terahertz time-domain spectra

Terahertz time-domain spectra (THz-TDS) were investigated using the results of molecular dynamics (MD) simulations of Staphylococcal nuclease at two hydration states in the temperature range between 100 and 300 K. The temperature dependence of THz-TDS was found to differ significantly from that of the incoherent neutron scattering spectra (INSS) calculated from the same MD simulation results. We further examined contributions of the mutual and auto-correlations of the atomic fluctuations to THz-TDS and found that the negative value of the former contribution nearly canceled out the positive value of the latter, resulting in a monotonic increase of the reduced absorption cross section. Because of this cancellation, no distinct broad peak was observed in the absorption lineshape function of THz-TDS, whereas the protein boson peak was observed in INSS. The contribution of water molecules to THz-TDS was extremely large for the hydrated protein at temperatures above 200 K, in which large-amplitude motions of water were excited. The combination of THz-TDS, INSS and MD simulations has the potential to extract function-relevant protein dynamics occurring on the picosecond to nanosecond timescale.