Non-Exponential Decay: Understanding the Correlation of Wavelength and Lifetime caused by Heterogeneity

Abstract

We report work that leads naturally to the missing underlying universal physical principle accounting for the strong correlation between tryptophan (Trp) decay associated (DAS) fluorescence wavelength (λmax) and lifetime (τf), in the absence of solvent relaxation. The familiar broad fluorescence spectrum of a solvent-exposed chromophore is actually an ensemble average of single molecular λmax values, fluctuating on a femtosecond time scale typically over 4000 cm−1 or 40 nm. In this dynamic picture, those conformers having shorter wavelength emission spectra, i.e., higher average energy, have an increased probability for transient fast electron transfer (ET) during large fluctuations in environment that bring a high energy, non-fluorescent charge transfer (CT) state and the fluorescing state (S1) into resonance. For Trp, the CT state lies well above the S1 state, and the wavelength is quite sensitive to local electric field. In these cases, heterogeneity and relaxation both can lead to time dependent red shifting fluorescence, making heterogeneity difficult to prove. Studies using non-natural amino acids expose the reality of heterogeneity by contrasting behavior. The fluorescence decays of 5-fluoroTrp incorporated in proteins are much more nearly monoexponential. This probe is not as easily quenched by ET as Trp because of its higher ionization potential, but it retains full wavelength sensitivity. Abbyad et al.(2007), find that time resolved fluorescence spectra of Aladan behave oppositely. When incorporated at several sites in the protein GB1, λmax shifts to shorter wavelength on the nanosecond time scale-- unequivocally revealing ground-state heterogeneity, because relaxation always requires a red shift in time; this is consistent with the observation that τf for this probe decreases with increasing solvent polarity by an internal mechanism.