Solute–solvent interactions and dynamics are simulated with a fully molecular hybrid method consisting of a semiempirical quantum mechanical method with singly excited configurations for the solute and classical molecular dynamics (MD) for the solvent (H2O). The interactions are purely electrostatic, with the solute being polarizable and sharing its charge information with the MD at 5 fs intervals. The solvent charges are fixed and the results are not sensitive to the point charges used. For the solute, the results depend on the dipole moment much more than on the point charge magnitudes leading to a given dipole. This method is applied to the spectral shifts, dynamics, linewidths, and free energies of indole and 3-methylindole (3MI) in water at 300 K, including the effect of geometry changes and clarifications concerning vertical vs 0–0 transition predictions. Large fluorescence Stokes shifts are predicted, in fair agreement with observed values. The 1La excited state dipole is calculated to be about 12 D after solvent relaxation following excitation. This increase of about 5 D above that calculated in vacuum is caused by the solvent reaction field, and approximately doubles the calculated shift compared to that using the vacuum dipoles. There does not seem to be a need to invoke a solute–solvent excited state charge transfer complex (exciplex) to account for the large shifts. About 50% of the Stokes shift occurs in ∼15 fs with a Gaussian response function, and the remainder is approximately an exponential with τ=400 fs. The fast component is created by small rotational deviations in the trajectories of a few nearby waters. The change in free energy of solvation upon excitation is found to be half the sum of the absorption and fluorescence shifts.
We report quantum mechanical-molecular mechanical (QM-MM) predictions of fluorescence quantum yields for 20 tryptophans in 17 proteins, whose yields span the range from 0.01 to 0.3, using ab initio computed coupling matrix elements for photoinduced electron transfer from the 1La excited indole ring to a local backbone amide. The average coupling elements span the range 140-1000 cm-1, depending on tryptophan rotamer conformation. The matrix elements were from the singles configuration interaction matrix, and were largely insensitive to which of the three basis sets was used. Large fluctuations were seen on the time scale of tens of femtoseconds, caused primarily by side chain and backbone torsional variations for 150 ps of dynamics at 300 K. The largest coupling occurs for the chi1 = -60 degrees rotamer and is purely through-bond. There is no apparent correlation between the coupling magnitude and quantum yield, which is still dominated by energy gap and reorganization energy. The source of error bars for predicted quenching rates using the weak coupling golden rule may be due to inaccurate averaged Franck-Condon weighted densities because of inadequate simulation times and parameters and/or to failure of the weak coupled golden rule used in these predictions because of the broad distribution of Landau-Zener probabilities arising from the large variable coupling.
Tryptophan (Trp) fluorescence is potentially a powerful probe for studying the conformational ensembles of proteins in solution, as it is highly sensitive to the local electrostatic environment of the indole side chain. However, interpretation of the wavelength-dependent complex fluorescence decays of proteins has been stymied by controversy about two plausible origins of the typical multiple fluorescence lifetimes: multiple ground-state populations or excited-state relaxation. The latter naturally predicts the commonly observed wavelength-lifetime correlation between decay components, which associates short lifetimes with blue-shifted emission spectra and long lifetimes with red-shifted spectra. Here we show how multiple conformational populations also lead to the same strong wavelength-lifetime correlation in cyclic hexapeptides containing a single Trp residue. Fluorescence quenching in these peptides is due to electron transfer. Quantum mechanics-molecular mechanics simulations with 150-ps trajectories were used to calculate fluorescence wavelengths and lifetimes for the six canonical rotamers of seven hexapeptides in aqueous solution at room temperature. The simulations capture most of the unexpected diversity of the fluorescence properties of the seven peptides and reveal that rotamers having blue-shifted emission spectra, i.e., higher average energy, have an increased probability for quenching, i.e., shorter average lifetime, during large fluctuations in environment that bring the nonfluorescent charge transfer state and the fluorescing state into resonance. This general mechanism should also be operative in proteins that exhibit multiexponential fluorescence decays, where myriad other sources of conformational heterogeneity besides rotamers are possible.
Hybrid quantum mechanical/molecular mechanics (QM-MM) calculations [Callis and Liu, J. Phys. Chem. B 2004, 108, 4248-4259] make a strong case that the large variation in tryptophan (Trp) fluorescence yields in proteins is explained by ring-to-backbone amide electron transfer, as predicted decades ago. Quenching occurs in systems when the charge transfer (CT) state is brought below the fluorescing state ( 1 L a ) as a result of strong local electric fields. To further test this hypothesis, we have measured the fluorescence quantum yield in solvents of different polarity for the following systems: N-acetyl-L-tryptophanamide (NATA), an analogue for Trp in a protein; N-acetyl-L-tryptophan ethyl ester (NATE), wherein the Trp amide is replaced by an ester group, lowering the CT state energy; and 3-methylindole (3MI), a control wherein this quenching mechanism cannot take place. Experimental yields in water are 0.31, 0.13, and 0.057 for 3MI, NATA, and NATE, respectively, whereas, in the nonpolar aprotic solvent dioxane, all three have quantum yields near 0.35, indicating the absence of electron transfer. In alkyl alcohols the quantum yield for NATA and NATE is between that found for water and that found for dioxane, and it is surprisingly independent of chain length (varying from methanol to decanol), revealing that microscopic H-bonding, and not the bulk dielectric constant, dictates the electron transfer rate. QM-MM calculations indicate that, when averaged over the six rotamers, the greatly increased quenching found in water relative to dioxane can be attributed mainly to the larger fluctuations of the energy gap in water. These experiments and calculations are in complete accord with quenching by a solvent stabilized charge transfer from ring to amide state in proteins.
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