= FRET donor lifetime
{c}
{title2=$\tau_D,\tau_{DA}$}
The <FRET donor lifetime> is the mean time spent in the <excited state>. For the constant-rate model of <FRET efficiency>,
$$
\tau_D=\frac1{k_D},\qquad \tau_{DA}=\frac1{k_D+k_T},\qquad E=1-\frac{\tau_{DA}}{\tau_D}.
$$
After a sufficiently brief excitation pulse, the <FRET donor>'s <fluorescence> follows <exponential decay>, $I(t)=I(0)e^{-t/\tau}$. With the illustrative values $\tau_D=4$ nanoseconds and $\tau_{DA}=2$ nanoseconds, the inferred <FRET efficiency> is $1/2$. Multiplying $I(0)$ changes brightness without changing this decay time.
The lifetime comparison requires the same nontransfer decay rates in the reference and paired samples. Changes in the <FRET donor>'s environment or a different nonradiative loss can also shorten the <FRET donor lifetime>. Heterogeneous <FRET efficiencies> or slowly varying <FRET dipole orientation factors> need an appropriate decay model; substituting any fitted average lifetime into the single-pair formula can mislead. <Quantitative time domain analysis of lifetime-based Förster resonant energy transfer measurements with fluorescent proteins: Static random isotropic fluorophore orientation distributions by Yuriy Alexandrov and others>{ref}
\Image[/fret-fluorescence-lifetime-readouts.png]
{title=<FRET sensitized emission>, optical controls and the <FRET donor lifetime>}
{description=Original schematic and synthetic curves. The spectral panel assumes equal <fluorescence> yields and collection efficiencies for the two labels; its amplitudes are illustrative, not a calibration or measured cyan/yellow spectra. The lifetime panel uses $\tau_D=4$ and $\tau_{DA}=2$ nanoseconds. Dashed optical paths require <FRET optical crosstalk> controls; they do not represent the nonradiative transfer mechanism.}
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