Anal. Chem. 1990, 62, 1786-1791
1786
Optimization of High-Sensitivity Fluorescence Detection Richard A. Mathies* and Konan Peck Chemistry Department, University of California, Berkeley, California 94720 Lubert Stryer Department of Cell Biology, Stanford University School of Medicine, Stanford, California 94305
We present general expressions for the number of photons emitted by a fluorescent chromophore as a function of the lntenslty and the duration of llluminatlon. The aim is to flnd opthnal condltlons for detectlng fluorescent molecules in the presence of both ground-state depletkm and photodestruction. The key molecular parameters are the a k r p t l o n coefficient c, the exclted slnglet-state llfetlme T, the exclted triplet-state decay rate k, the Intersystem crossing rate k,, and the intrlnslc photodestructlon time Td. When only dngiet saturation and photochemlstry are Important, the signal-to-noise ratio depends on two fundamental variables: k, the ratio of the absorptlon rate k, to the observed fluorescence decay rate k,, and T, the ratlo of the duration of Illumination T , to the Intrinsic photodestruction tlme 7 4 . Equations are also developed for the more complicated cases when triplet formation and photochemistry are Important. This theory was tested by measuring the fluorescence from a solution of Bphycoerythrin flowed through a focused argon ion laser beam. The dependence of the fluorescence on the lncldent light intensity and the lllumlnatlon tlme agrees well wlth the theoretical predlctlon for slnglet saturation and photochemlstry. The slgnaCto-noise ratio is optknal when the llgM Intensity and the flow rate are adlusted so that both k and T are close to unHy (5 X photons cm-2 s-' and a translt time T , of 700 ps). Thls analysls shoukl be useful for optknlzlng fluorescence detectlon In DNA sequenclng, chromatography, fluorescence microscopy, and single-molecule fluorescence detection.
INTRODUCTION Fluorescence is an exquisitely sensitive detection technique. For this reason, fluorescence is widely used in immunodiagnostics, flow cytometry, optical microscopy, chromatography, electrophoresis, and DNA sequencing (1-11). Depending on the specific application, the limiting sensitivity can range from IO3 to lo7fluorophores. Hirschfeld first pointed out that these limits can be extended significantly by using fluorescence burst detection methods, which record the passage of individual molecules through a tightly focused laser beam ( l e ) ,and several practical schemes for photon burst detection have recently been developed (13, 14). For example, we used a hard-wired version of a single-molecule counter to detect the presence of phycoerythrin (PE) a t concentrations as low as M. This work stimulated a critical examination of the optimal conditions for laser-induced fluorescence, which we report here. The illumination time and the incident laser power are two critical parameters for optimizing laser-excited fluorescence. Previous treatments of photodestruction assumed that the photodestruction rate and the rate of fluorescence are linearly related to the incident light intensity (15-17). This is true
* Corresponding author.
for weak illumination conditions but not for the high light intensity conditions that occur as one strives for the ultimate in sensitivity. At high light intensities, a significant fraction of the molecules will be pumped to their excited states, causing ground-state depletion. This will alter the signal-to-background ratio in the experiment because background scattering, unlike fluorescence, does not saturate. The optical pumping should be intense, but once the transition is saturated, increasing the light intensity further will just increase the background. Also, illuminating the molecule for a longer time will generate more fluorescent photons per molecule. However, there is no benefit in looking once the molecule has been photodestroyed. This paper presents a theory for selecting the optimal illumination intensity and illumination time. These equations are tested by application to B-phycoerythrin
(B-PE). THEORY We derive here general expressions for the number of photons emitted by a chromophore that has flowed through an exciting laser beam. The aim is to determine the optimal light intensity and transit time for detecting fluorescent molecules in the presence of background scattering. Ground-state depletion and photodestruction of the chromophore are explicitly taken into account. A molecule in the So ground state is excited to the SI state by absorption of a photon (Figure 1). The rate of absorption k , is given by
where I is the incident light intensity (photons cm-2 s-l), u, is the absorption cross section (cm2/molecule), and 6 is the decadic molar absorption coefficient (cm-' M-l). S1 can return to the ground state by emitting a photon with a rate kof or nonradiatively with a rate k,. SI can also intersystem cross to the triplet with a rate constant kI. The S1 excited-state population decays with a rate k f (SI), which is the sum of the rates of these processes
kf = k",
+ k, + kI = l / ~ f
(2)
The observed fluorescence lifetime Tf is the reciprocal of kr. The triplet population decays with an overall rate constant of kT, which is the reciprocal of the observed triplet lifetime. The fluorescence quantum yield Qf is given by Consider a solution flowing with velocity v (cm/s) through an exciting laser beam (Figure 2). For simplicity, assume a uniform square beam profile of side 1 (cm). The derivation for a more realistic Gaussian profile is given in the Appendix. The transit time T~ of the chromophore through the beam is l / u . The number of photons n emitted by an intact molecule in a time interval At is
n = ko&S1)At where
(4)
isl],the proportion of time spent in the excited state,
0003-2700/90/0362-1786$02.50/0 0 1990 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 62, NO. 17, SEPTEMBER 1, 1990
nf = (kof/kd)[l - exp{-k,kdrt/(k,
+ kf + kakI/kT)lI
1787
(11)
This equation can be simplified by substituting Qf/Qd for kof/kd and 7 d for l / k d and by introducing the dimensionless variables k = k,/kf and r = Tt/Td. nf = (Qf/Qd)[l - e x p ( - k ~ / ( k ( l + k ~ / k +~ 1111 ) (12) Figure 1. Kinetic scheme showing the ground singlet state So, the first excited singlet state S,, and the triplet state T. k , is the rate of
absorption, ko, is the natural radiative rate, k , is the radiationless decay rate, k , is the intersystem crossing rate, and k , is the overall triplet decay rate. It is assumed that relaxation from the optically pumped vibronic levels to the emitting levels is very rapid compared to the pumping rate k,. Illumination Direction
z
t
t
If we ignore saturation (k
