TABLE I.

Overview of the experimental parameters and the corresponding model parameters.

Model		Experiment
Probability distribution	↔	Random realization
Expected value	↔	Experimental observable
Probability density function	↔	Histogram
FRET-lines	↔	Distribution of FRET efficiency, fluorescence lifetime, or related quantities
Expectation value of FRET efficiency	↔	Species-averaged FRET efficiency
$E=1-\frac{\overline{{\tau }_{D\left(A\right)}}}{{\tau }_{D\left(0\right)}}$	$\stackrel{\wedge }{=}$	$E=\frac{F_{A|D}}{F_{A|D}+F_{D|D}}=1-\frac{{⟨{\tau }_{D\left(A\right)}⟩}_x}{{\tau }_{D\left(0\right)}}$
First moment of the lifetime distribution	↔	Species-averaged lifetime
$\overline{{\tau }_{D(A)}}=\underset{0}{\overset{\infty }{\int }}{\tau }_{D(A)}p\left({\tau }_{D(A)}\right)d{\tau }_{D(A)}$	$\stackrel{\wedge }{=}$	${⟨{\tau }_{D\left(A\right)}⟩}_x=\left(1-E\right){\tau }_{D\left(0\right)}$
Second moment of the lifetime distribution	↔	Species-averaged squared lifetime
$\overline{{\tau }_{D(A)}^2}=\underset{0}{\overset{\infty }{\int }}{\tau }_{D(A)}^{2}p\left({\tau }_{D(A)}\right)d{\tau }_{D(A)}$	$\stackrel{\wedge }{=}$	${⟨{\tau }_{D\left(A\right)}^2⟩}_x={⟨{\tau }_{D\left(A\right)}⟩}_F\left(1-E\right){\tau }_{D(0)}$
Ratio of the second and first moments of the	↔	Intensity-weighted average fluorescence lifetime, average delay time
lifetime distribution
$\frac{\overline{{\tau }_{D(A)}^2}}{\overline{{\tau }_{D(A)}}}$	$\stackrel{\wedge }{=}$	${⟨{\tau }_{D\left(A\right)}⟩}_F\mathrm{or}⟨t⟩$
No equivalent	↔	Intensity-weighted average FRET efficiency
$1-\frac{1}{{\tau }_{D\left(0\right)}}\frac{\overline{{\tau }_{D(A)}^2}}{\overline{{\tau }_{D(A)}}}$	$\stackrel{\wedge }{=}$	$E_{\tau }=1-\frac{{⟨{\tau }_{D\left(A\right)}⟩}_F}{{\tau }_{D(0)}}$
Variance of the lifetime distribution	↔	No equivalent
$\mathrm{Var}\left({\tau }_{D\left(A\right)}\right)=\overline{{\tau }_{D(A)}^2}-{\overline{{\tau }_{D\left(A\right)}}}^2=\mathrm{Var}\left(E\right){\tau }_{D(0)}^2$	$\stackrel{\wedge }{=}$	$\left(1-E\right)\left(E-E_{\tau }\right){\tau }_{D\left(0\right)}^2$
Difference between the normalized first and second	↔	No equivalent
moments of the lifetime distribution
$\mathrm{\Gamma }=\frac{\overline{{\tau }_{D(A)}}}{{\tau }_{D\left(0\right)}}-\frac{\overline{{\tau }_{D(A)}^2}}{{{\tau }_{D\left(0\right)}}^2}$	$\stackrel{\wedge }{=}$	(1 − E)Eτ