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: <math> J = \int f_{\rm D}(\lambda) \, \epsilon_{\rm A}(\lambda) \, \lambda^4 \, d\lambda </math>
Misurando l'efficienza della FRET, dunque, l'operatore è in grado di ricavare la distanza donatore-accettore.
<!--The FRET efficiency <math>E</math>, which is defined as
: <math> E = 1 - {\tau'_{\rm D}}/{\tau_{\rm D}} \!</math>
where <math>\tau'_{\rm D}</math> and <math>\tau_{\rm D}</math> are the donor fluorescence lifetimes in the presence and absence of an acceptor, respectively, or as
: <math> E = 1 - {F'_{\rm D}}/{F_{\rm D}} \!</math>
where <math>F'_{\rm D}</math> and <math>F_{\rm D}</math> are the donor fluorescence intensities with and without an acceptor, respectively. <math>E</math> depends on the donor-to-acceptor separation distance <math>r</math> with an inverse 6th order law due to the dipole-dipole coupling mechanism:
: <math>E=\frac{1}{(1+(r/R_0)^6)}\!</math>
with <math>R_0</math> being the Förster distance of this pair of donor and acceptor at which the FRET efficiency is 50%.
The Förster distance depends on the overlap [[integral]] of the donor emission spectrum with the acceptor absorption spectrum and their mutual molecular orientation as expressed by the following equation:
: <math> {R_0}^6 = 8.8 \times 10^{23} \; \kappa^2 \, n^{-4} \, Q_0 \, J </math>
where <math>\kappa^2</math> is the dipole orientation factor, <math>n</math> is the [[refractive index]] of the medium, <math>Q_0</math> is the [[fluorescence quantum yield]] of the donor in the absence of the acceptor, and <math>J</math> is the spectral overlap integral calculated as
: <math> J = \int f_{\rm D}(\lambda) \, \epsilon_{\rm A}(\lambda) \, \lambda^4 \, d\lambda </math>
where <math>f_{\rm D}</math> is the normalized donor emission spectrum, and <math>\epsilon_{\rm A}</math> is the acceptor [[extinction coefficient]].
''κ''<sup>2</sup> =2/3 is often assumed. This value is obtained when both dyes are freely rotating and can be considered to be isotropically oriented. If either dye is fixed or not free to rotate, then ''κ''<sup>2</sup> =2/3 will not be a valid assumption. In most cases, however, even modest reorientation of the dyes results in enough orientational averaging that ''κ''<sup>2</sup> = 2/3 does not result in a large error in the estimated energy transfer distance due to the sixth power dependence on ''κ''<sup>2</sup>. Even when ''κ''<sup>2</sup> is quite different from 2/3 the error can be associated with a shift in R<sub>0</sub> and thus determinations of changes in relative distance for a particular system are still valid. Fluorescent proteins do not reorient on a timescale that is faster than their fluorescence lifetime. In this case 0 ≤ ''κ''<sup>2</sup> ≤ 4.-->
==Applicazioni di base==
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