Biopolymers Display Multiexponential or Heterogeneous Decays

In diis expressitm the Oi values are called the preexponen-tial factors. A flumophore usually displays the same radiative decay rate in different environm ts. Thus, for the same flucnroiirfitMre in different environments, the wilues of 

CU represent the fractional amount of flucvoi tm in eadi enndronmrat. Hence, for the protein shown in Hguie 4.4, one expects tti ttz a 0.5. The presoice of twodecay times results in curvature In the plot of log /(r) versus time, represented by the dashed line in the upp plot. The g l of the intensity decay measurements is to recover the decay times (Xi) and amj itudes (ad from the /(r) measuremrats. 

The presence of two decay times can also be delected using the FD method. In this case one examines the frequency response of the sample, which consists of a plot of phase and modulation on the log frequency axis (Figiure 4.4, bottom). The longer-lifelime tryptophan (T = 5 ns solid curve) and the shorter-lifetime tryptophan (T2 1 ns dotted curve) each display the curves characteristic of a single decay time. In the presence of both decay times (Tj =5 ns and X2 = 1 ns dashed curve), the frequency response displays a mc e complex shape which is charac lsdc of the heterogeneous or multiexponentlaJ intensity decay. As for the TD measurements, the FD data are used to recover the individual decay times (Xf) and amplitudes (a associated with each decay time, typically using the procedure of nonlinear least squares. 

In this ex vession nj is the anisotrc y at f = 0, which is characteristic of the fluorophore. The rotational correlation 

Anisotropy decays can be more complex than those rqsresented by Eqs. [4.9] and [4.10] and are typically presented as a sum of exponentials 

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