What is the distance from the silver surface yielding this largest increase in fluorescence intensity? In we summarized the intensity and lifetime ratios found for increasing numbers of BSA-biotin-avidin layers. On this same figure we included results from two other experiments in which we examined Cy3- and Cy5-labeled oligomers which were bound to amine-coated slides [19
] (distance near zero) and on slides coated only with a single layer of avidin [20
], which we took to be 50 Å thick. These results showed that the optimal enhancements with SIFs is obtained with distances from the metal of 50–90 Å.
Fig. 12 Fluorescence enhancements of Cy3- and Cy5-labeled oligomers for various distances from the silver surface. Also shown are the enhancements found on amine-coated slides which were treated with 3-aminopropyltriethoxysilane (APS)  and slides with a single (more ...)
The effects of metallic particles on fluorophores can be understood at a fundamental level using theoretical models which describes the photophysical interactions [4
]. However, these models are complex and not immediately useful for designing systems for metal-enhanced fluorescence. Hence we analyzed our data (–) in terms of a phenomenological model which accounts for the expected interactions. These interactions are an increase in the nonradiative decay rate (knr
) by a factor Nnr
, which is thought to occur at short fluorophore-metal distances, an increase in the rate of radiative decay (Γ
) by a factor Nr
, and an increase in the rate of excitation by a factor Nex
. In the absence of metal the quantum yield (Q
) and lifetime (τ
) of the fluorophore are given by
is the radiative decay rate and knr
is the non-radiative decay rate, both in the absence of metal.
Now assume that the fluorophore is in interactive proximity with the metal surface at a distance d which alters the spectral parameters. The rate of quenching, emission, and excitation are increased by factors which depend on distance
, and de
are the characteristic distances over which these effects decrease 1/e
Using these expressions the quantum yield, lifetime, and total intensity (Im) at a distance d are given by
are the measured intensities in the presence and absence of metal, respectively. In Eqs. (10)
we did not explicitly include the distance d
which is understood to be contained within the N factors.
We used this model to compare with our measured intensities and lifetimes of DNA(Cy3)-biotin and DNA(Cy5)-biotin at various distances from the SIFs. The six parameter values in Eqs. (7)
were recovered by least-squares analysis to obtain a reasonable fit to the data ( and ). We were able to obtain good fit to our data with reasonable parameter values (). We recognize that these values may not be optimal, but a good fit seemed to be unique for this range of parameter values. These calculations reveal () that the quenching is very strong at short distances but decays by 1/e
for each 8.5 Å. In contrast, excitation is increased by a factor from 22 to 94 and occurs over longer distances of 25–42 Å. Importantly, the radiative rate is increased by a larger factor and this increase continues to over 120 Å. Taken together these parameters explain the largest intensity increase between 50 and 100 Å and the large decrease in lifetime observed at short distances ( and ). This is a fortunate result since one can readily obtain such distances with one or two layers of adsorbed proteins.
Comparison of the measured lifetimes and intensities of DNA (Cy3)-biotin with values calculated using the parameter values in .
Comparison of the measured lifetime and intensities of DNA (Cy5)-biotin with values calculated using the parameter values in .
Phenomenological constants describing the intensities of Cy3 and Cy5 with SIFs
It is informative to examine the distance-dependent values of the enhancement factor (N(d)) for the nr, r, or ex effects. The normalized distance-dependent factors are plotted in for DNA(Cy3)-biotin. This figure shows that the quenching interaction occurs mostly below 20 Å, enhanced excitation occurs below 40 Å, and increases in the radiative rate occur to a distance over 100 Å.
Distance-dependent values of the enhancement factor for quenching (Nnr), the radiative rate (Nr), and excitation (Nex) for DNA(Cy3)-biotin.
In summary, these results suggest that metal-enhanced fluorescence can be conveniently applied to DNA analysis whenever increased signals yield improved measurements.