Time-dependent fluctuations in the catalysis rate (␦k(t)) observed in single-enzyme experiments were found in a particular study to have an autocorrelation function decaying on the same time scale as that of spectral diffusion ␦0(t). To interpret this similarity, the present analysis focuses on a factor in enzyme catalysis, the local electrostatic interaction energy (E) at the active site and its effect on the activation free energy barrier. We consider the slow fluctuations of the electrostatic interaction energy (␦E(t)) as a contributor to ␦k(t) and relate the latter to ␦0(t). The resulting relation between ␦k(t) and ␦0(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated ␦E(t) on fluctuations in the radiative component (␦␥ r
؊1(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between ␦␥ r ؊1 (t) and ␦0(t) is obtained. Experimental tests will determine whether the correlation functions for ␦k(t), ␦0(t), and ␦␥ r ؊1 are indeed similar for any enzyme. Measurements of dielectric dispersion, (), for the enzyme discussed elsewhere will provide further insight into the correlation function for ␦E(t). They also will determine whether fluctuations in the nonradiative component ␥ nr ؊1 of the lifetime decay has a different origin, fluctuations in distance for example.fluorescence ͉ single enzyme S ingle-molecule experiments on proteins have revealed novel phenomena, including fluctuations in the rates of enzyme catalysis (1-3), on-off blinking behavior in proteins (4-6), and oscillations under a near-denatured condition of a green fluorescent protein (7). The on-off blinking behavior of proteins and the fluctuations in the enzyme catalysis rate in the experiments were interpreted in terms of fluctuations of the protein/enzyme between various conformational substates (2, 3). The rates of enzyme-catalyzed reactions themselves occur typically on the milliseconds-to-seconds time scale, and the millisecond dynamics of enzymes are believed to contribute to the ''functional dynamics'' of the enzyme (8). Single-molecule enzyme experiments on cholesterol oxidase revealed an autocorrelation function of the rate of catalysis that decayed on a time scale about the same as that for the decay of the autocorrelation function of the spectral diffusion of a chromophore in the same enzyme in the absence of the substrate (1), thus suggesting a common origin for the two fluctuations.Significant insight into the functioning of enzymes has been achieved by using computer simulations (9-11) and empirical valence bond (9) and hybrid quantum mechanical/molecular mechanics (10) methods, among others. In these studies the catalysis is affected by several factors: electrostatic effects of the enzyme on the substrate (9) and coupling of protein fluctuations with motions of the substrate-coenzyme pair in the transition state (e.g., ref. 8). Electrostatic effects have been seen to be significant in enzymatic catalysis (9,(1...