The Two-State Model of Relaxation

According to the two-state model, the spectrum of the relaxed state has a mean frequency vR and is shifted relative to the spectrum of the initial state, which has a mean frequency vF. If relaxation does not occur during the process of emission (xR xF), the mean frequency of the fluorescence 

This model permits xR to be determined using information on the fluorescence decay in a very simple way. If unrelaxed fluorophores are excited, the decay is exponential beyond the relaxation range and, in this range, consists of two components t, and r2. These components will be simple functions of xR and t . If we assume that emission on the short-wavelength side occurs only from the unrelaxed state and that the simultaneous loss of emitting quanta occurs due to relaxation, then the longer component, t, equals xF, and the shorter one, t2, equals 1(1/t + jxF). Unfortunately, this approach is difficult to apply when the decay is nonexponential, which is almost always the case with proteins (see Section 2.3.1.). 

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Figure 2.5. Energy level diagram (top) and spectra (bottom) illustrating the two-state model of relaxation. The energy of the absorbed quantum is Av , and the energies of the emitted quanta are hvfl (unrelaxed) and hvF (relaxed). The fluorescence spectrum of the unrelaxed state (solid curve) is shifted relative to the absorption spectrum (dotted curve) due to the Stokes shift. The emission intensity from the unrelaxed state decreases and that from the relaxed state (dashed curve) increases as a result of relaxation.

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