Distribution Analysis with Frequency-Domain Data

Distance Distribution Analysis with Frequency-Domain Data 

We now consider how the time-resolv data for dansyl-melittin were analyzed to recover die distance distribution. While the description is for the FD data, the same steps are taken for analysis of the TD data. The first stq in any distance distribution analysis is determination of the inten sity decay of the donor alone, followed by use of tiiis decay law in die P r) analysis. For any form of die decay law, die phase ( ) and modulation (hicm) at a given frequency can be calculated (c) from 

tjm depends on distance r, as can be seen from Eq. [144]. The value of xiu cooesponds to the lifr4ime of the donor for a particular distance r. As was described rimve, these specific molecules cannot be observed. Only the entire population can be measured, hence the integrals over r in [14.9] and [14.10]. Analytical expressions for 

Nm and Z) are not available, so these values are calculated numerically. Tite parameta Values desoibing die distance distribution are recovered from nonlinear least squares analysis minimizatitm of 3,  

Tlie values and Sm are the expoimental uncertainties in phase and moduladon, respectively. 

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B. Distance Distribution Analysis with Frequency-Domain Data... 

Frequency-domain measurements of fluorescence energy transfer are used to determine the end-to-end distance distribution of donor-acceptor D-A) pairs linked by flexible alkyl chains. The length of the linker is varied from 11 to 2B atoms, and two different D-A pairs are used. In each case the D-A distributions are recovered from global analysis of measurements with different values for the FSrster distance, which are obtained by collislonal quenching of the donors. In all cases essentially the same distance distribution Is recovered from the frequency-domain data for each value of tha Ffirster distance. The experimentally recovered distance distributions are compared with those calculated from the RIS model. The experimentally recovered distance distributions for the largest chain molecules are In agreement with the predictions of the RIS model. However, the experimental and RIS distributions are distinct for the shorter D-A pairs. 

In spite of its prevalence in the fluorescence decay literature, we were not universally successful with this fitting method. Most reports of hi- or multiexponential decay analysis that use a time-domain technique (as opposed to a frequency-domain technique) use time-correlated photon counting, not the impulse-response method described in Section 2.1. In time-correlated photon-counting, noise in the data is assumed to have a normal distribution. Noise in data collected with our instrument is probably dominated by the pulse-to-pulse variation of the laser used for excitation this variation can be as large as 10-20%. Perhaps the distribution or the level of noise or the combination of the two accounts for our inconsistent results with Marquardt fitting. 

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