Time-resolved absorption and fluorescence spectroscopy are used to study the dynamics of protein structural changes subsequent to rapid mixing or excitation with short laser pulses. Molecular kinetic models are used to fit and interpret the measured data. We have developed a novel method for measuring the kinetics of loop formation in peptides in which one position is labeled with tryptophan and the another with cysteine or cystine. The trypophan, excited to its lowest triplet state by a 280-290 nm laser pulse, is efficiently quenched by the sulfur-containing residue upon loop formation. Our recent work has focussed on quantitatively characterizing this method so that it can be applied to studies of the dynamics of unfolded and partially-folded polypeptides. (A) We have shown that the diffusion-limited rate, which is the rate of contact formation, can be obtained from measurements of the temperature- and viscosity-dependence of the quenching rates. These experiments also provide values for the reaction-limited quenching rates, in which diffusion is much faster than the quenching process. The results show that the observed rates in water at room temperature are close to reaction-limited, and that diffusion-limited rates are only obtained when the viscosity is increased above ~ 5 cp. The reaction-limited rates provide information on the end-to-end distribution at equilibrium, which is critical for obtaining information on the chain dynamics from the diffusion-limited rates. (B) To interpret the measured quenching rates we determined the dependence of the quenching rate of the tryptophan triplet by cysteine by embedding the free amino acids in a trehalose glass at room temperature. The decay of the triplet population is extended in time and can be explained by a quenching rate which decreases exponentially with distance. The decay is steep, with the rate falling off as exp(-4r) where r is the separation in angstroms. Using this dependence, quenching when diffusion is rapid takes place within 1 A of contact. (C) We have found that both rates can be accurately calculated by treating the dynamics as diffusion on a one-dimensional potential of mean force corresponding to the end-to-end distance distribution for a worm-like chain, and the distance-dependence of the quenching rate described in (B). The apparent turnover in the reaction-limited rate at short chain lengths can be attributed to the stiffness of a chain having a persistence length of 0.8 nm. The diffusion coefficient for the chain ends required to fit the diffusion-limited rates is about 2(10-6) cm^2s-1 at a viscosity of 1 cp, approximately 8 times smaller than the value expected for free diffusion of the contacting residues. (D) We have carried out molecular dynamics simulations using a Ramachandran-like potential in which attractive van-der-waals and electrostatic interactions are not included. The results have been used to test the one-dimensional diffusion model and show that it provides a remarkably accurate description of the peptide dynamics.
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