High suitability of tryptophan residues as a spectroscopic thermometer for local temperature in proteins under nonequilibrium conditions

Vibrational energy flow in the many degrees of freedom in proteins governs energy-barrier-crossing processes, such as conformational exchanges and thermal reactions. The intensity of anti-Stokes Raman bands arises from vibrationally excited populations and can thus function as a selective probe for the excess energy. Time-resolved observations of the anti-Stokes ultraviolet resonance Raman (UVRR) intensity of amino acid residues provide information about the flow of excess energy in proteins, with the spatial resolution of an amino acid residue. The answer to the question of whether the extent of vibrational excitation in any given vibrational modes reflects the extent of excitation in the whole molecule under nonequilibrium conditions is not straightforward. Here, we calculated the occupation probabilities of vibrational states for model compounds of amino acids under equilibrium and nonequilibrium conditions. At a given temperature, the occupation probability of the model compound of tryptophan under nonequilibrium conditions was nearly identical to that under equilibrium conditions at high temperature. Thus, the anti-Stokes band intensities of Trp residues in the nonequilibrium condition indicate the temperature of the molecules with equivalent energy in the equilibrium condition. In addition, we showed that the temperatures calculated on the basis of two UVRR bands of tryptophan in a time-resolved spectrum agreed with each other within the experimental uncertainty. The present results demonstrate that anti-Stokes UVRR bands of Trp residues serve as an excellent spectroscopic thermometer for determining the local temperature in proteins under nonequilibrium conditions.