Quantum efficiency independence of the time integrated
emission from a fluorescent molecule
T. Hirschfeld
The sensitivity of chemical or biological analyses using fluorescent tagged reagents is limited by concentration quenching of the fluorescence at high tag concentrations and by photochemical bleaching if high illumination intensities are used. This paper shows by theoretical analysis and experimental verification that
concentration quenching lengthens bleaching lifetimes, and the integrated fluorescent emission obtained
on complete bleaching is invariant with fluorescent quantum efficiency, absorption cross section, and the
illumination's intensity and duration. This can be used to produce extremely sensitive fluorescent tagging
procedes. The procedure also improves photometric reproducibility, allows a fluorescent stain to act as a
probe of several properties in its microenvironment, and allows sample background differentiation even
when the free stain background is more fluorescent than the bound one.
Introduction
A number of very sensitive analytical procedures
in chemistry and biology use reagents tagged with fluorescent dye molecules and detect and trace these by
various microscopic or microphotometric procedures.1
While these tests have been able to detect only a few
thousand molecules of tagged reagent, requirements
exist for far higher sensitivities, down to the single
molecule level. As this lies clearly beyond current
procedures, a study of the factors establishing current
limits was undertaken.
Sensitivity Limiting Considerations in Fluorescent
Tagged Reagents
In order to increase the fluorescent signal from a
tagged reagent, attempts have been made to increase
the number of dye molecules bound to the macromolecular reagent. For steric, reaction rate, and noninterference reasons, it is necessary to assemble this
population of fluorescent molecules in a very small
tagging
space. Under these conditions, increases in the
2
level soon produce concentration quenching, reducing
first the quantum efficiency and then the total emission. 3
This can be seen in Fig. 1, which shows the quantum
efficiency and fluorescence level obtained from a tagged
The author is with Block Engineering, Inc., Cambridge, Massachusetts 02139.
Received 29 April 1976.
reagent as the number of dye molecules it contains increases. Here the fluorescent dye is fluoresceine isothiocyanate, and the reagent is y-globulin bound with
glutaraldehyde to a polyethyleneimine oligomer MW
- 20000 side chain used as a binding backbone to which
variable numbers of dye molecules are attached.4 5 The
drop in quantum efficiency is abrupt, and the maximum
emission intensity, equivalent to that of only two free
fluoresceine molecules, is reached when about 32 are
actually used.
Other attempts to increase sensitivity have used extremely bright illumination sources to increase fluorescence intensities. This, however, led to rapid photochemical destruction or bleaching of the fluorescent
molecules. 6 This is hardly surprising for such chemically reactive, highly colored compounds immersed in
a highly complex chemical environment and exposed
to very high uv light intensities. To measure this
bleaching quantitatively, a flash photometer was built
employing a fluorescence microphotometer on whose
stage an argon laser was focused after passing a fast
mechanical shutter. The fluorescence was collected by
a microscope objective, passed through appropriate
glass filters, and collected in a photomultiplier connected through a fast amplifier to an oscilloscope synchronized to the shutter. Figure 2 shows the fluorescence decay by bleaching under continuous illumination
1200 poof a 100-ppm fluoresceine solution in 5% MW
2
lyethyleneimine. The 1.24 X 104 W/cm of 4880 A
employed were enough to produce exponential
bleaching with a lie time (corrected for instrument
response) of only 3.0 msec.
A theoretical analysis of the kinetics of this process
was then undertaken, leading to a new and interesting
result.
December 1976 / Vol. 15, No. 12 / APPLIED OPTICS
3135
a fraction of all molecules is excited at any given time,
giving
dg(t)
(4)
= [TL)/(rE)1kRg(t)dt.
Here we can use instead of the reaction rate kR of the
excited molecule its reciprocal, the mean photodecomposition lifetime of the excited molecule R. Integration of Eq. (4) then gives
2. 0
(5)
g(t) = exp(-t/rB),
1.0
where TB, the bleaching lifetime of the average molecule,
is given by
(6)
TB = (TETR)/(TL),
0
25
s0
NUBE OF
75
100
LUO.ESCEINC
MOLECULES
PER EAGEIJT
Fig. 1. Quantum efficiency and effective number of dye molecules
in antibody labeled with fluoresceine loaded polyethyleneimine.
Kinetics of the Photochemical Bleaching Process
The total amount of fluorescence photons emitted by
a population of molecules undergoing photochemical
bleaching is
gt)dt,
SWt=nTE
(1)
°,
where n is the initial number of fluorescent molecules
present, QF their fluorescent quantum efficiency, TE the
mean interval between successive molecular excitation
events, and g(t) is the survival probability of the average
molecule as a function of time. On the reasonable assumption of a normal population distribution (TE being
much longer than the excited state lifetime TL), we can
here substitute
TE =
(hc)/IXC),
(2)
where h is Planck's constant, c the velocity of light, I
and X the illumination intensity and wavelength, and
C is the molecular absorption cross section of the fluorescent dye.
In order to evaluate g(t), a truism is useful. Since the
bleaching is photoinduced, its first step necessarily involves the excited molecule, through which the photon
energy enters the chemical system. The reactions that
it can then undergo are many fold, but nearly all of them
can be considered to fall in two categories: an unimolecular reaction of the excited molecule, or a pseudounimolecular one in which the other reactant, present
in the sample environment, is abundant enough not to
be depleted by the decomposition of a small number of
dye molecules.
Both unimolecular and pseudounimolecular reaction
kinetics are characterized by a time independent reaction rate, allowing us to write (for the excited molecule
involved)
dg*(t) = kRg*(t)dt,
APPLIED OPTICS / Vol. 15, No. 12 / December 1976
Quantum Efficiency Independence of the Integrated
Fluorescence Yield
Substitution of Eq. (5) into Eq. (1) and solving the
integral now give
S(t)
= n[(QFTB)/(rE)][l-
exp(-t/TB)I-
(7)
Here we can use the definition of fluorescence
quantum efficiency
(8)
QF = TL/TF,
where TF is the radiative lifetime of the excited state,
to circumscribe the possible reasons for QF variations.
The radiative lifetime being a function of the absorption
strength, it is invariant for any molecule unless its absorption spectrum changes. As this, to first order, is not
the case in concentration quenching, the mechanism for
QF variations must be changes in L, caused, for example, by changes in the nonradiative lifetime of the
excited state.
By substituting Eqs. (6) and (8) into Eq. (7) and going
to the limit, we can now write
S(t
'P
9
MI
-
) = n[(R)/(RF)I.
(9)
3
4
I.
1-1
2
I
11
U
0
I
1
0
(3)
where the * superscript refers to the excited molecule
involved in the reaction. If we consider the total molecular population instead, we must consider that only
3136
The exponential dependence found here agrees well
with that found in Fig. 1, and from it further deductions
can be made. In more complex environments, more
than one reaction may occur, and a summation of several exponentials may be encountered.
2
3
5s
TIME (MSEC)
Fig. 2.
100-ppm fluoresceine bleaching curve at 1.2 X 10 4 -W/cm 2
illumination.
and the known parameters of the optical system. For
the y-globulin-polyethyleneimine-fluoresceine reagent
in the last row of Table I, which contains 100 fluoresceine isothiocyanate molecules per reagent molecule,
we find TR = 35 gsec. This is in agreement with studies
of the bleaching rate of fluoresceine in use as a laser
dye.9
From this we can calculate S(t - o) = 7800 photons
per fluoresceine molecule or about 780,000 per reagent
molecule, allowing exceedingly sensitive detection of the
latter.
3
1
1)
5.0
10.0~
1 5. 0
TIME
(MSEC)
Fig. 3.
4
3330-ppm hluoresceine bleaching curve at 1.2 X 10 -W/cm
illumination.
2
This remarkable result shows the total yield of
emitted photons to be independent of the quantum
efficiency, the dye absorption cross section, and the illumination duration and intensity provided their
product is large enough!
This does not actually require an infinite time, but
only enough for substantially complete bleaching, which
can be expressed as
t >> B = (TRhc)I(IXCTFQF)-
(10)
The only intrusion of I, C, TF, and QF is through their
influence on the setting of this experimental condition.
Of course, the absorption cross section (which is in any
case fairly constant for a given molecule and illumination wavelength) is important through its connection
with TF.
But, provided enough exposure for complete
bleaching is used, the integrated signal obtained is totally independent of the fluorescent quantum efficiency.
To put this in a different form, when concentration
quenching or microenvironmental effects reduce QF,
bleaching lifetimes increase in the precise inverse proportion, and the integral signal remains constant.
Applications of the Technique to Tagged Reagents
Illumination to complete bleaching, and integration
of the resulting signal, have a large number of applications. The most obvious one arises from the situation
described here, when it is used in combination with reagents tagged with a polymeric binding backbone containing a large number of attached dye molecules to
increase sensitivity. By insuring a linear increase of the
signal with the number of dye molecules used, regardless
of concentration quenching, the sensitivity of the procedure can be raised to extremely high levels.
Another procedure would be to use a much larger
binding site attached to the reagent, such as a plastic
sphere.' 0 This sphere could be made large enough to
allow the use of large numbers of dye molecules while
maintaining an intermolecular separation of at least 60
A, which precludes concentration quenching. This,
however, makes the spherical tag very large and in fact
much larger than the reagent. This then becomes unable to multiply bind to a single site or to react at all
with a partially obstructed one because of simple steric
hindrance. Reaction rates would also be drastically
slowed, both due to the lower diffusivity of the larger
Table I.
Experimental Verification of QF Independent
Flu orimetry
Experimental Test of the Signal's Independence from
the Fluorescent Quantum Efficiency
Neglecting various constants, verification of the above
is equivalent to proving the constancy of the QFTB
product as QF changes for a given type of fluorescent
molecule and a given illumination intensity.
Qualitatively, this can be observed in Fig. 3, which
shows the bleaching curve of a 3330-ppm fluorescein
solution taken under the same conditions as Fig. 2.
Here we can see the longer bleaching lifetimes associated with the lowered quantum efficiency produced by
concentration quenching at this higher concentration.
Quantitatively, Table I shows the quantum efficiency
and bleaching lifetime (corrected for instrumental response and diffusion effects) of three different fluorescent tagged reagents containing similar fluorescent
groupings. It can be seen that even drastic changes in
QF produce changes in QFTB that stay within the 10%
uncertainty in the results.
The results can be interpreted quantitatively using
7 8
the known values of C, QF, and TL for free fluoresceine
Sample
Group I
(Fluoresceine in 5%
polyethylenimine)
Concentration:
100
333
1000
3330
ppm
ppm
ppm
ppm
Group II
(Fluoresceine isothiocyanate
bound to polyethyleneimine)
Dye molecules per backbone:
80
100
Group III
(Group II compounds bound
to glutaraldehyde and then
to y-globulin)
Dye molecules per backbone:
80
100
Quan- Bleaching
turn
effi- lifetime
(TB)
ciency
(QF) % msec
QF X
TB
3.0
2.9
3.9
10.1
281
249
253
305
1.79
1.32
81.1
117.4
145
155
2.03
1.21
49.5
88.9
101
108
93.7
86.0
64.9
30.2
December 1976 / Vol. 15, No. 12 / APPLIED OPTICS
3137
particle and because its ability to react on collision
would be dependent on increasingly stringent orientation requirements. Last, but not least, in order to leave
both the selectivity and the affinity of the reagent unperturbed, the large tag would have to match the nonreactive region of the reagent macromolecule.
This match must apply both to the collective chemical properties of the entire sphere and to the point by
point behavior of its entire surface. This reduces to the
contradictory requirement of simultaneously matching
two functions and their integrals over different ranges.
The extent of the resulting unavoidable mismatch grows
very rapidly with the tag size.
Another virtue of this procedure is that the signal
obtained is independent of source or illumination time
fluctuations, materially increasing the photometric
accuracy. Photometric accuracy is also aided by the
very large number of dye molecules attached to each
reagent molecule, which drastically reduces the statistical fluctuations in tagging levels. This in turn allows
a much more accurate measurement of the number of
reagent molecules present.
Variations in the solvent, which tend to strongly affect QF, do not affect QF independent fluorimetry,
unless the change is such as to affect the chemical processes of photobleaching. Neither do variations in
concentration quenching between different reagent
molecules, induced by the statistical fluctuations in the
spatial distribution of the tagging molecules over the
binding backbone.
Finally, partial bleaching, a photometric perturbation
that classical photometry avoids by limiting the illumination intensity and thus the signal, is irrelevant in
QF independent fluorimetry.
QF independent fluorimetry can be implemented in
practice by visual observation or photoelectric integration of the fluorescence produced by a light pulse of
the appropriate energy. In a flow photometric system, 1 a powerful focused laser illuminator can be
combined with a appropriately slow flow speed and
photodetector response to give the proper exposure.
Independent Fluorimetry as a Molecular Probe
The various sample parameters that influence the
emitted signal can be probed 12 by measuring S(t >> TB)
and either TB or
OF
[dSlt)]
QF
(1
L dt Jt-0
TE
Given the invariance of TF, S(t >> TB) measurements
will define nTR and where n is known from the chemistry or by separate measurements, the variation of TR
can be studied. The value of TR reflects the very short
range microenvironment of a fluorescent molecule. It
is essentially influenced only by those other molecules
that are bound to or can actually contact the fluorescent
one. Thus the slightly different chemical species in
Table I, containing the same fluorescent molecule, show
a variation in QFTB that reflects this type of TR
change.
If a fluorescent tagged reagent has a structure such
3138
APPLIED OPTICS / Vol. 15, No. 12 / December 1976
that only the reagent or backbone macromolecules and
the solvent can come into the immediate environment
of the fluorescing molecule, TR will be constant as well,
and n can be determined by photometry. Knowledge
of the reagent tagging level then allows measurement
of the number of reagent molecules present.
The fluorescent quantum efficiency can also act as
a microenvironmental probe, but one of substantially
longer range. Under favorable circumstances, QF can
be strongly affected at ranges as large as 60 A. For this
we calculate
1
[dS(t)/dt]t-o
TF QF
(12)
TB
S(t
>> TB)
TE TR(
where either of the left-hand terms are experimental.
By using the known TF and TE values, the ratio QF/TR
can be calculated and used directly as a probe. Alternatively, a shielded tagged reagent as described above,
whose TR does not change on binding, can be used, and
QF changes can be measured by themselves.
Other Applications of OF Independent Fluorimetry
Much analytical fluorimetric work is done by using
fluorescent dyes as specific chemical reagents by
themselves.' 3 Aside from their necessary chemical
properties, these dyes have been required in the past to
have both a high QF and a long bleaching lifetime.
Both these restrictions can now be significantly relaxed.
Current practice calls for avoiding perceptible bleaching
levels during a photometric observation. Going to QF
independent fluorimetry can relax QF and TB requirements by almost 2 orders of magnitude. This new degree of freedom can be traded for a considerable increase
in the range of usable reagents, allowing a wider choice
of chemical characteristics. Obviously, one can elect
to achieve increased sensitivity from existing reagents
instead.
Fluorescence spectrometry enjoys an inherent SNR
advantage over absorption spectrometry, in that it
works against the background of the 0% signal line
rather than the 100% one. In a shot noise limited
spectral region, such as the UV-VIS one, this is a large
advantage. The applicability of fluorescence, however,
is limited, since strong fluorescence is much less universal than absorption. QF independent fluorimetry
allows using very low QF values and weakens this limitation.
In many applications of fluorescent staining to biology, stained samples can be observed against the free
dye background because the dye used sharply increases
its QF on binding.14 In practice, dyes without this enhancement, and even more those that show a QF loss on
binding,' 5 have had relatively little application. In QF
independent fluorimetry, a bright background having
high QF can be discriminated against while a low QF
sample is not affected at all. This is done by delaying
the time gating of the electronics or of an observation
shutter so that they open after the start of the illumination or, for a moving sample, by illuminating a sample
region larger than the observed one. The the high QF
background will have been almost completely bleached
before the low QF sample is seriously attenuated. It can
be shown' 6 that if a signal loss SL can be tolerated in the
sample, a gating delay
td =
B
(13)
lnSL
is necessary, where TB refers to the background
bleaching lifetime. The ratio of the signal's to the
background's effective fluorescence intensities per unit
molecule will then be
RF = [(QS)/(QB)SL(1 QBIQS),
(14)
where QB and Qs are the background and sample fluorescent efficiencies. Clearly large RF values can be
achieved at modest SL values.
Conclusions
QF independent fluorimetry maximizes the signal
obtained from a given fluorescent reagent and allows
this to increase linearly with the number of fluorescent
tags attached to it, allowing extreme analytical sensithis techtivity. A further paper describes how to use
nique to detect single reagent molecules,17 an ultimate
level of sensitivity.
By eliminating the effects of fluorescent quantum
efficiency changes, many kinds of solvent effects, concentration quenching, statistical tagging level variations,
changes in illumination time or intensity, and partial
bleaching, the photometric accuracy is improved.
When the amount of fluorescent dye is known, QF
independent fluorimetry acts as a short range microenvironmental probe for bleaching reactivity. With
specially designed reagents, it allows separate measurement of the number of dye molecules present and
their fluorescent quantum efficiency as a longer range
microenvironmental probe.
By relaxing the quantum efficiency and photochemical stability demands on fluorometric reagents
and samples for spectrofluorimetry, QF independent
Season's (qreainys
W
V
veilleurs Vxux,
HFelices Fiesras
C HO5bIM
OAOM
<Frohe 'Resua e
fluorimetry increases the flexibility and widens the
scope of these procedures.
Delayed time gating observations partway through
the bleaching process allows sample/background differentiation in those biological fluorescent staining
procedures where the dye's quantum efficiency declines
on binding.
The chemical procedure for synthesizing the reagents
here described was developed jointly with D. Eaton of
G. D. Searle & Co. Inc, High Wycombe, Buckinghamshire, England, who also did the actual synthesis. This
work shall be reported on elsewhere in detail.
References
1. M. Goldman, FluorescentAntibody Methods (Academic, New
York, 1968).
2. I. Vierosanu, J. Chim Phys. 71, 61 (1974).
3. S. Shu, J. Deng, S. Vetter, and W. H. Bentner, Ann. N.Y. Acad.
Sci. 180, 550 (1974).
4. T. Hirschfeld, "Staining Antibodies," Application for Letters
Patent (1973).
5. T. Hirschfeld and D. Eaton, "Antigen Detecting Reagents,"
Applications for Letters Patent (1974).
6. G. I. Kaufman, J. F. Nester, and D. E. Wasserman, J. Histochem
Cytochem. 19, 469 (1971).
7. G. G. Guilbault, PracticalFluorescence (Marcel Dekker, New
York, 1973).
8. R. F. Chen, G. V. Vurek, and N. Alexander, Science 156, 949
(1967).
9. A. D. Britt and W. B. Moriz, IEEE J. Quantum Electron. QE-8,
913 (1972).
10. W. J. Dreyer, U.S. Patent 3,853,987 (10 December 1974).
11. W. A. Bonner, H. R. Hulett, R. G. Sweet, and L. A. Herzenberg,
Rev. Sci. Instrum. 43, 404 (1972).
12. L. Stryer, Science 162, 526 (1968).
13. S. Udenfriend, Fluorescence Assay in Biology and Medicine
14.
15.
16.
17.
(Academic, New York, 1969), Vol. 2.
J. B. Le Pecq and C. Paoletti, J. Mol. Biol. 27, 87 (1967).
V. W. Burns, Biophys. J. 14, 189 (1974).
T. Hirschfeld and W. Mueller, Histochem. J., to be published.
T. Hirschfeld, Appl. Opt. 15, 2965 (1976).
Yeace on Tahr)
?aixsurl&gerrC
?az en e Hwrr
Ha3av4y.
peup
W
IF
December 1976 / Vol. 15, No. 12 / APPLIED OPTICS
3139