Ab initio prediction of tryptophan fluorescence quenching by protein electric field enabled electron transfer

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.