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An interpretation of fluctuations in enzyme catalysis rate, spectral diffusion, and radiative component of lifetimes in terms of electric field fluctuations

Time-dependent fluctuations in the catalysis rate (δk(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 δω0(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 (δE(t)) as a contributor to δk(t) and relate the latter to δω0(t). The resulting relation between δk(t) and δω0(t) is a dynamic analog of the solvatochromism used in interpreting solvent effects on organic reaction rates. The effect of the postulated δE(t) on fluctuations in the radiative component (δγr−1(t)) of the fluorescence decay of chromophores in proteins also is examined, and a relation between δγr−1(t) and δω0(t) is obtained. Experimental tests will determine whether the correlation functions for δk(t), δω0(t), and δγr−1 are indeed similar for any enzyme. Measurements of dielectric dispersion, ε(ω), for the enzyme discussed elsewhere will provide further insight into the correlation function for δE(t). They also will determine whether fluctuations in the nonradiative component γnr−1 of the lifetime decay has a different origin, fluctuations in distance for example.