The correlation functions of the fluctuations of vibrational frequencies of azide ions and carbon monoxide in proteins are determined directly from stimulated photon echoes generated with femtosecond infrared pulses. The asymmetric stretching vibration of azide bound to carbonic anhydrase II exhibits a pronounced evolution of its vibrational frequency distribution on the time scale of a few picoseconds, which is attributed to modifications of the ligand structure through interactions with the nearby Thr-199. When azide is bound in hemoglobin, a more complex evolution of the protein structure is required to interchange the different ligand configurations, as evidenced by the much slower relaxation of the frequency distribution in this case. The time evolution of the distribution of frequencies of carbon monoxide bound in hemoglobin occurs on the Ϸ10-ps time scale and is very nonexponential. The correlation functions of the frequency fluctuations determine the evolution of the protein structure local to the probe and the extent to which the probe can navigate those parts of the energy landscape where the structural configurations are able to modify the local potential energy function of the probe.Chemical reactions in biology can be controlled by the fluctuations in the energies of the reactant states. When the reactions involve charge translocations, the motions of the charges in the surrounding medium cause changes in the electric fields in the neighborhood of the reacting species, which in turn cause fluctuations of the reactant energies. These fluctuations occur on the time scale of the nuclear motions of the medium. For chemical processes occurring in a protein environment, such as in enzyme catalysis, the dynamics of the protein nuclei can control the reaction. Therefore, it is very important to determine experimentally the essential properties of the fluctuations associated with various observables, such as their mean values, time-correlation functions, and structural origins.The experimental approaches to determining time-correlation functions include spectroscopic line shape measurements and time-domain responses. In the vibrational frequency regime the line-shape approach is a common one (1), although it does not always expose the underlying physical origins of the fluctuations. Time-domain techniques were also developed some time ago that enabled investigations of the various contributions to the line width such as pure dephasing and population relaxation (2). The dephasing times of vibrational transitions having static inhomogeneous distributions can be measured by means of two-pulse photon echoes (3-5). Silvestri et al. (6) have shown that for optical transitions, a photon echo with three pulses can also yield the dynamics of the inhomogeneous distribution. There were many applications of this nonlinear technique in the electronic spectroscopy of dye molecules (refs. 6-8, and see ref. 9 for a review) and of cofactors in biological systems [light-harvesting complex II (10), reaction center (11...