Excitation Spectra and Brightness Optimization of Two-Photon
Jo ¨rg Mu ¨tze,†‡Vijay Iyer,†John J. Macklin,†Jennifer Colonell,†Bill Karsh,†Zden? ek Petra ´? sek,‡Petra Schwille,‡
Loren L. Looger,†Luke D. Lavis,†and Timothy D. Harris†*
†Janelia Farm Research Campus, Howard Hughes Medical Institute, Ashburn, Virginia; and‡Biophysics, BIOTEC, Technische Universita ¨t
Dresden, Tatzberg, Dresden, Germany
(the detected fluorescence rate per molecule). We report two-photon molecular brightness spectra for a diverse set of organic
and genetically encoded probes with an automated spectroscopic system based on fluorescence correlation spectroscopy. The
two-photon action cross section can be extracted from molecular brightness measurements at low excitation intensities, while
peak molecular brightness (the maximum molecular brightness with increasing excitation intensity) is measured at higher inten-
sities at which probe photophysical effects become significant. The spectral shape of these two parameters was similar across
all dye families tested. Peak molecular brightness spectra, which can be obtained rapidly and with reduced experimental
complexity, can thus serve as a first-order approximation to cross-section spectra in determining optimal wavelengths for
two-photon excitation, while providing additional information pertaining to probe photostability. The data shown should assist
in probe choice and experimental design for multiphoton microscopy studies. Further, we show that, by the addition of a passive
pulse splitter, nonlinear bleaching can be reduced—resulting in an enhancement of the fluorescence signal in fluorescence
correlation spectroscopy by a factor of two. This increase in fluorescence signal, together with the observed resemblance of
action cross section and peak brightness spectra, suggests higher-order photobleaching pathways for two-photon excitation.
Two-photon probe excitation data are commonly presented as absorption cross section or molecular brightness
Multiphoton fluorescence microscopy has had profound
implications for the investigation of complex biological
samples (1). Although higher-order processes have been
investigated, most experiments involve the simultaneous
absorption of two photons by a fluorophore. In two-photon
absorption (TPA), two photons are absorbed by the ground
tronic state. TPA is a nonlinear process, as the probability of
TPA depends on the square of the excitation light intensity.
Due to this quadratic dependence, two-photon fluorescence
excitation (TPE) microscopy provides intrinsic axial
sectioning and reduced out-of-plane photobleaching (2).
microscopy are approximately double those for one-photon
excitation, providing greater penetration depth in living
tissue. Because of these advantages, TPE has achieved
the absorption spectrum can differ considerably from the
corresponding one-photon spectrum due to different selec-
tion rules governing TPA (3). Accurate determination of
TPA cross section without using a standard is a difficult
task, requiring detailed knowledge of the excitation parame-
ters and sample concentration. Because of these experi-
mental difficulties, TPE spectra have only been reported
for a limited number of fluorophores, mostly in nonphysio-
logical solvents (4–8). Yet, reliable TPE spectra for a large
and experimental design in biological TPE imaging.
Several techniques have been developed to determine
the TPA cross section, based on either direct or indirect
nonlinear transmission through a sample, such as in the
z-scan technique (9). These methods yield the TPA cross
section directly, but are hampered by poor sensitivity, high
excitation intensities, and high dye concentrations. Indirect
techniques are based on the measurement of the two-
photon-induced fluorescence emission of the dye, corre-
sponding to the TPA cross section multiplied by the
quantum efficiency (10). Fluorescence-based techniques
are highly sensitive and can be performed in very dilute
solutions, but depend strongly on system calibration. Xu
et al. (11–13) have recorded a number of TPA spectra by
means of the emitted fluorescence, either by determining
the product of cross section and quantum efficiency (termed
‘‘action cross section’’),or by comparing the data toa known
reference (14). The latter method alleviates systematic
errors associated with the strong dependence of the absorp-
tion rate on the temporal and spatial profiles of the excita-
Following earlier work (15,16), we use peak molecular
brightness as an alternative measure to the TPA cross
section. Molecular brightness, abbreviated ε, is defined as
the number of recorded counts per unit time per molecule.
It is usually measured in kilocounts per second per molecule
(kcpsm). For TPE, plotting the molecular brightness against
Submitted April 28, 2011, and accepted for publication December 7, 2011.
Editor: David P. Millar.
? 2012 by the Biophysical Society
934Biophysical JournalVolume 102February 2012 934–944
the excitation intensity produces a squared dependence that
gradually levels off at high irradiances, reaching a peak
value (17). This maximum value, termed ‘‘peak molecular
brightness’’, εmax, has been shown to be dictated by photo-
bleaching and volume saturation effects, which appear at
high excitation intensities (18,19). Previous studies have
found εmax to be a highly repeatable value that can be
used to benchmark a dye in a specific environment, as
well as the detection efficiency of the acquisition setup
(16). Furthermore, peak molecular brightness measurements
can be used to optimize the choice of excitation wavelength
for biological applications (20).
Photon-counting techniques such as fluorescence correla-
tion spectroscopy (FCS) are able to determine the two-
photon fluorescence emission per molecule, independent
of dye concentration. FCS analyzes the spontaneous fluores-
cence fluctuations that arise from an ensemble of identical
emitters in the focal volume of a fluorescence microscopy
setup. The second-order autocorrelation function of the
fluorescence signal reveals the underlying dynamics and
the number of dye molecules in the observation volume
(21). The molecular brightness is easily obtained by
dividing the recorded fluorescence by the number of emit-
ters. In FCS experiments, it is the critical parameter deter-
mining the signal/noise ratio (22).
We devised a fully automated spectrophotometer that
can record two-photon peak brightness excitation spectra
of fluorescent dyes over the entire wavelength range of
a commercial Ti:Sapphire laser. The apparatus is based on
an FCS setup that collects molecular brightness data of a
fluorophore at various wavelengths and excitation intensi-
ties. We systematically present peak brightness spectra for
a large set of small molecule and protein fluorophores.
We tested common organic dyes, calcium indicators, and
fluorescent proteins, all under physiologically relevant
conditions. We found that peak molecular brightness spectra
could be reliably obtained, were similar in spectral shape
with action cross-section spectra, and were less prone to
experimental/instrument error than action cross-section
measurements. They also provide information on fluoro-
phore photostability, not given by cross-section experi-
ments. Thus, the methods and datasets that we have
determined will be of great use to experimentalists attempt-
ing to optimize the choice of dye, laser, and wavelength for
Using the same apparatus, the two-photon action cross
section can be determined from the initial data points of
molecular brightness intensity curves, where the slope is
2.0 (16). FCS has the important advantages of intrinsic
determination of the sample concentration and greatly
simplified measurement apparatus. We report action cross
sections that are in good agreement with previous reports.
Comparison of the spectral shape of action cross section
and peak brightness showed a high correlation between
these parameters for all dye families tested. A practical
consequence of these observations is that peak molecular
brightness spectra can serve as a useful proxy, to first order,
for action cross-section spectra in determining optimal
wavelengths for TPE.
The observed correlation between peak molecular bright-
ness and action cross section is not expected a priori. In the
case of a quadratic dependence of the photobleaching rate
on the excitation intensity, the peak brightness spectrum is
expected to be independent of the action cross section
(16). On the contrary, we found the two measures to be qual-
itatively similar over a wide array of probes. We reason here
that this spectral correlation of εmaxwith action cross section
is based on highly nonlinear photobleaching in TPE. To test
this hypothesis, we employed a passive pulse splitter to
increase the excitation repetition rate, which has been shown
to significantly reduce photobleaching in TPE microscopy
(23). Assuming that peak molecular brightness is limited
by photobleaching that is due to higher-order photon inter-
actions (18), this device should improve the observed εmax
values. We indeed found such an increase in peak molecular
brightness up to a factor of two, supporting the hypothesis
of highly nonlinear photobleaching in TPE. In sum, peak
molecular brightness spectra provide information about
both the absorption and photostability characteristics of
probes under two-photon excitation.
MATERIALS AND METHODS
The experimental setup is shown in Fig. 1 a. To facilitate the automated and
fast acquisition of a large number of peak brightness spectra for a variety of
two-photon excited probes, we constructed an automated fluorescence
correlation spectroscopy apparatus. Briefly, the linearly polarized output
beam of a tunable, mode-locked Ti:Sa laser (Chameleon Ultra II; Coherent,
Santa Clara, CA) was first power-adjusted, then expanded 5? by two pairs
of achromatic lenses (Linos, Go ¨ttingen, Germany) to slightly overfill
the back aperture of a 60?, 1.2 NA NIR water immersion objective
(UplanSApo 60?W; Olympus, Tokyo, Japan), mounted on an inverted
microscope (IX81; Olympus).
The laser power adjustment was accomplished using a half-wave plate in
a motorized rotation stage followed by a polarizing beam splitter cube
(Thorlabs, Newton, NJ). Part of the transmitted beam was reflected onto
a photodiode detector (Thorlabs), to constantly monitor the laser power
reaching the objective. This was related to the power at the focus of the
objective by using a photodiode, calibrated before measurements for all
wavelengths with a thermopile power meter (LabMax TO; Coherent, Santa
Clara, CA), placed after the microscope objective at the location of the
sample. Laser wavelength and power were fully computer-controlled.
Samplesconsisted of a buffer solution containingthe fluorophore, separated
from the water-immersion 60? objective by a No. 1.5 coverslip.
the excitation light by a dichroic mirror (FF670-SDi01-25?36; Semrock,
Rochester, NY) and two shortpass filters (FF01-720/SP-25, FF01-750/SP-
25; Semrock). The fluorescence signal was detected by a fiber-coupled
Avalanche Photodiode (SPCM-AQRH-14-FC; PerkinElmer Optoelec-
tronics, Vaudreuil, Quebec) that yields a 200-mm aperture (AFS200/
220Y; Thorlabs). The transistor-transistor logic output of the APD was
fed to an external correlator (Flex03LQ-01; Correlator.com, Bridgewater,
NJ), which also provided the software for the autocorrelation.
Biophysical Journal 102(4) 934–944
Size and form factor of the focal spot size were determined from calibra-
tion measurements with AlexaFluor 546 (diffusion coefficient DA546¼
341 mm2s?1(24), Molecular Probes, Eugene, OR) at an excitation wave-
length of 820 nm, yielding a 1/e2radial dimension of u0¼ 393 nm and
a form factor (defined as the ratio of the axial over the lateral 1/e2radius
of the focal volume) of 4.0. The form factor was fixed in all subsequent
fitting procedures to improve the robustness of the fit. Each measurement
lasted between 10 and 300 s and was stopped after a sufficient number of
photons was collected. To control for the cover-slide thickness, the correc-
tion collar was adjusted before each data run for a particular dye. The collar
setting was found to be independent of wavelength. Laser parameters and
data acquisition were coordinated with custom software written in C,
allowing the excitation wavelength and intensity to be set to a desired
step size and range. Data sets were analyzed with a custom MATLAB script
(The MathWorks, Natick, MA).
We scanned the excitation wavelength across a range of 720–1060 nm,
corresponding to the accessible range of the Chameleon laser (Coherent).
With the spectral width of the excitation pulses on the order of 10 nm,
we chose a scanning step size of 10 nm. At each wavelength, between 10
and 15 different excitation light intensities were measured to determine
the peak brightness. For measurements where action cross section was ex-
tracted, the power rangeincluded lower powers where ε(Iave) was quadratic.
The temporal pulse width of the laser pulses was measured with an optical
autocorrelator (Carpe; APE, Berlin, Germany) using an external detector
placed at the focus of the objective. The pulse width ranged from 130 fs
at 1030 nm to 220 fs at 720 nm, assuming a squared hyperbolic secant
(sech2) pulse shape (25).
For brightness measurements, it was shown previously that peak bright-
ness does not depend on temporal pulsewidth over this pulsewidth range of
the excitation source (26). To ensure a fair comparison of TPE emission
efficiencies, the same emission filter and dichroic were used for all dyes.
As a control for setup stability and repeatability, the peak brightness of
a reference dye (AlexaFluor 546; Molecular Probes) was determined before
each measurement series. Over a 12-monthperiod,thisvaluevaried <2.5%.
The data were fitted with a model for freely diffusing molecules in three
dimensions (21), without an additional term describing molecules in the
triplet state. No rise of the correlation amplitude in the ms time range, which
would indicate a population of the triplet state, could be observed (27).
two flip mirrors coupled a passive pulse splitter (described in Ji et al. (23))
into the beam path. The configuration for N ¼ 8 required four beamsplitters
and three delay lines (see Fig. S1 in the Supporting Material). Nonpolariz-
ing beamsplitters (BS1-3; Thorlabs) divided the incoming laser beam, and
a polarizing beamsplitter (Newport, Irvine, CA) together with a half-wave
plate (Thorlabs) merged all beams into one output beam. Custom-made
delay lines (DL1-3), consisting of two opposing mirrors four inches apart
in an aluminum casing, result in three additional reflections per mirror,
increasing the path length by 2.5 ns. Due to the additional optics, the splitter
caused a slightly enlarged focal volume (u0¼ 400 nm).
RESULTS AND DISCUSSION
We investigate the TPE spectral characteristics of common
organic and genetically encoded dyes by means of fluores-
cence correlation spectroscopy and peak brightness spectra.
FCS measurements report on the fluorescence signal hF(t)i,
where hi represents time-averaging, as well as the amplitude
G(0) of the autocorrelation function that results from Pois-
sonian particle occupancy fluctuations of the dye molecules
within the TPE volume (28). A typical FCS curve for one
laser wavelength l and at one laser intensity is shown in
Fig. 1 b. The number of fluorescent molecules in the excita-
tion volume corresponds to the inverse of the amplitude
of the autocorrelation function, NAC¼ 1/G(0). For TPE, in
the absence of photobleaching and ground-state depletion,
the time-averaged rate of detected fluorescence photons
can be written as (12)
Here, C is the concentration of dye, f is the collection
efficiency, and h2is the fluorescence quantum yield. The
dimensionless quantity gp ¼ gft (gp ¼ 0.664 for a
Gaussian-shaped pulse, gp¼ 0.588 for a hyperbolic-secant
P (mW )
Fluorescein in H2O, pH 11
section based on fluorescence correlation spectroscopy (FCS). PBS, polar-
izing beam splitter; PD, photodiode; SP, shortpass emission filter; APD,
avalanche photodiode. (b) Autocorrelation curve G(t) resulting from FCS
measurement. The amplitude G(0) is proportional to the inverse of the
number of molecules in the focal volume. (c) Plot of the molecular bright-
ness versus the square of the average excitation power. (Red line) Quadratic
dependence at low excitation powers (linear in the double logarithmic plot
against squared power). (d) Comparison of cross section of fluorescein
obtained by Xu and Webb (12) and Makarov et al. (14) (plotted on left
axis), and the unscaled two-photon absorption cross section for fluorescein
as determined by this work using FCS (right axis). (e) Plot of peak bright-
ness spectra (εmax, left axis) and scaled action cross section (s2h2, right
axis) for fluorescein, where the action cross section has been scaled by
1.9? from the measured (unscaled) value based on comparison to literature
values for fluorescein.
(a) Setup to record molecular brightness and action cross
Biophysical Journal 102(4) 934–944
936Mu ¨tze et al.
square pulse (12)) corresponds to the temporal coherence of
the excitation pulse temporal intensity profile g ¼ hI0(t)i2/
hI0(t)i2. The value f is the pulse repetition rate of the laser
and t the temporal pulse width (full width at half-
maximum). The peak intensity I0is related to the time-aver-
aged intensity hI0(t)i ¼ Iave(defined as the average power
divided by focused beam area) by I0¼ aIave/ft, where a ¼
0.88 for a sech2pulse shape and a ¼ 0.94 for a Gaussian
pulse shape. Two photons are needed per excitation event,
represented by the factor 1/2. The emission rate for a two-
photon process is proportional to the TPA cross-section s2
and the square of the incident intensity I0at the center of
Following Xu and Webb (12), the spatiotemporal distri-
bution of the excitation intensity in the sample volume is
described by Ið~ r;tÞ ¼ Sð~ rÞI0ðtÞ, where Sð~ rÞ is a dimension-
less spatial profile representing the point spread function
(PSF) and I0(t) is the temporal distribution at the geometric
focal point. The spatial distribution is expressed in Eq. 1 by
the product gVAC. The value g, termed ‘‘volume contrast’’,
relates the number of molecules NAC, and therefore the
volume as determined from the amplitude of the FCS
autocorrelation curve to the number of molecules in the
the number of detected photons per unit time per molecule,
ε ¼ hFðtÞi=NAC. Given that NAC¼ CVAC, the molecular
brightness is found to be
VdVS2ð~ rÞ and g ¼ VPSF/VAC¼ NPSF/NAC(19).
The molecular brightness of a fluorophore is defined as
A typical intensity curve for one laser wavelength is shown
in Fig. 1 c. At low excitation intensities, the molecular
brightness increases quadratically with the excitation inten-
sity because g is constant for a given PSF (e.g., g ¼ 0.35 for
a three-dimensional Gaussian excitation volume PSF and
g ¼ 0.1875 for a Gaussian-Lorentzian PSF (29)). In this
intensity regime, the action cross-section s2h2 can be
readily extracted from the initial values in the ε(I2ave) plot
(Fig. 1 d).
At higher intensities, where ε is no longer quadratic in
Iave,g is also no longer constant, but rather is shown to
decrease due to photobleaching (18), as well as increase
due to focal volume saturation (i.e., the probability of per-
pulse excitation at the focal volume center approaches unity
(16,30)). Experimentally, the combination of these effects is
that with increasing excitation intensity, the molecular
brightness reaches a peak value before decreasing again
(Fig. 1 c). As we will discuss in subsequent sections, peak
molecular brightness spectra yield information about the
excitation wavelength-dependent performance of a dye,
similar to that of action cross-section spectra. Thus, two
separate parameters—peak molecular brightness and action
cross section—can be extracted from the FCS molecular
brightness curves, as shown for fluorescein in Fig. 1 e.
Peak brightness spectra
Figs. 2–4 show experimentally measured two-photon peak
brightness spectra collected for a diverse range of probes,
including AlexaFluor (Fig. 2), classic rhodamines (Fig. 3),
and organic and genetically encoded calcium indicators
(Fig. 4). All dyes tested obey the square-law dependence
of TPE fluorescence at low excitation intensities. Each of
the dyes could be excited by TPE, although some not at
all wavelengths. For cases where the peak brightness could
not be reached or emission was below detection threshold,
no data points are shown. This was usually observed at
wavelengths >1000 nm due to insufficient laser power or
absorption cross section of the dye.
AlexaFluor dyes are commonly used in fluorescence
microscopy as marker and calibration molecules due to their
excellent brightness, solubility, and photostability. These
dyes in PBS. Data (every 10 nm, line added to connect data points) repre-
sent peak molecular brightness.
Two-photon fluorescence excitation spectra of AlexaFluor
Biophysical Journal 102(4) 934–944
dyes are sulfonated derivatives of a wide range of dye
families, including coumarin, pyrene, rhodamine, or cya-
nine dyes (31). Fig. 2 summarizes peak brightness spectra
of the AlexaFluor dyes. AlexaFluor 546, a rhodamine
derivative, is by far the brightest dye tested, with a peak
brightness of 58 kcpsm when excited at 820 nm in
water. Measurements in phosphate-buffered saline (PBS)
(Fig. 2) or 3-(n-morpholino)propanesulfonic acid (MOPS)
(data not shown) buffer yielded slightly lower values
(~51 kcpsm), presumably due to minor fluorescence
quenching effects of the buffer.
Rhodamines, isologues of fluorescein, feature low pH
sensitivity, high extinction coefficients and quantum yields,
as well as excellent photostability. Two-photon peak bright-
ness spectra of rhodamine 101 (Rh101), 110 (Rh110), 575
(Rh575), sulforhodamine 101 (SRh101), tetramethylrhod-
and Q-rhodamine (RhQ) are shown in Fig. 3. All seven
dyes exhibit peak brightness values significantly higher
than fluorescein (Fig. 1 e), with excitation maxima ranging
from 800 (Rh110) to 900 nm (SRh101).
The advantages of TPE microscopy are especially prom-
inent in deep, highly scattering tissues and it has therefore
become a widely used method in neuroscience to image
inside the living brain (32). Its applications range from
studies on imaging synaptic function in brain slices and
live animals to the study of neuronal plasticity (33,34).
Neural activity is accompanied by calcium (Ca2þ) transients
that can be visualized by chemically engineered fluorescent
organic (for review, see Paredes et al. (35)) or genetically
encoded (for review, see Mank and Griesbeck (36)) Ca2þ
indicators. These reporter molecules change their emission
properties when bound to Ca2þ, allowing real-time visuali-
zation of the activity of individual neurons by noninvasive
imaging techniques. Peak brightness spectra of a number
of organic and genetically encoded calcium indicators (satu-
rated in 39 mM free Ca2þMOPS) are depicted in Fig. 4.
Spectra included the green fluorescent protein-based Ca2þ
probes GCaMP2 (37) and GCaMP3 (38). As previously
observed (38), GCaMP3 is roughly twofold brighter than
its predecessor GCaMP2, but still twofold dimmer than
enhanced green fluorescent protein. The peak brightness
FIGURE 3Peak molecular brightness spectra of rhodamine dyes in PBS.
organic Ca2þindicators in 39 mM free Ca2þcalibration buffer (30 mM
MOPS, 100 mM KCl, 10 mM CaEGTA, pH 7.2). Peak molecular brightness
spectra of OGB-1 and OGB-5N were also determined at 0 mM Ca2þ
(30 mM MOPS, 100 mM KCl, 10 mM EGTA; OGB-1 APO, OGB-5N
Peak molecular brightness spectra of genetically encoded and
Biophysical Journal 102(4) 934–944
938 Mu ¨tze et al.
spectrum of GCaMP3 exhibits a slight red shift compared to
that of GCaMP2. The absorption maximum for GCaMP3 is
~950 nm, whereas GCaMP2 is centered at ~940 nm, consis-
tent with one-photon results (38).
Depleting the MOPS buffer solution of Ca2þresulted in
a strongly reduced number of molecules in the bright state
and overall reduced fluorescence signal, yet peak brightness
values of the individual molecules in the bright state
remained largely unchanged (as shown for OGB-1 and
OGB-5N in Fig. 4). This suggests that the change in fluores-
cence emission upon Ca2þbinding is an on-off mechanism
at the single-molecule level for these specific synthetic
Action cross-section spectra
Equation 2 implies that the two-photon action cross section
(s2h2) of a fluorophore can be readily extracted from molec-
ular brightness data, as all the other parameters are constant
in the limit of low excitation powers (i.e., where the depen-
dence of ε(Iave) is quadratic). To obtain (s2h2) spectra for
a variety of dyes, we collected ε(Iave) curves including
additional points at low power levels, selecting points at
each wavelength showing quadratic dependence. It is
assumed that the g-parameter is known and constant (i.e.,
the measurement is taken in a low-power regime where
ε is proportional to I2
ave, free of photobleaching or saturation
effects (19)). The peak molecular brightness values εmax
were determined from measurements at higher power in
the same data set. The simultaneously measured εmaxand
(s2h2) spectra are shown in Fig. 5.
For the action cross-section extraction, Iavewas deter-
mined from the applied average power Pave, following the
relation Iave¼Pave/A, where A is the beam area in the focal
plane. The area was computed via the relation A ¼ pu2
where u0is the 1/e2radius of a Gaussian profile extracted
from the measured FCS diffusion time tD. For the volume
contrast parameter, we employ the value g ¼ 0.26, which
has been numerically computed for a diffraction-limited
PSF (29), to most accurately capture the axial intensity
distribution. In contrast to classic cross-section measure-
ments, the concentration was not separately measured, but
determined from the FCS data set. Information regarding
the action cross-section extraction is provided in the Sup-
Representative data for the well-known dye fluorescein
are shown in Fig. 1 d. To compare our results to prior
work, we convert the action cross-section s2to an absolute
cross section using the cited quantum efficiency h2¼ 0.9,
which is based on the assumption that h1¼ h2(12). The re-
sulting cross-section spectral shape closely follows that of
Xu and Webb (12) and Makarov et al. (14). The secondary
peak at 920 nm is lower than reported by Xu and Webb
but matches the more recent work by Makarov and co-
The absolute cross-section data in Fig. 1 d show values
approximately twofold smaller (s2¼ 20.2 GM at 780 nm)
across the spectrum compared to these prior reports
(12,14). In contrast to these other works, we have employed
a high-NA focusing system, because FCS measurements
require small focal volumes and offer a saturation intensity
for a wider spectral range (12,20). The use of high-NA
geometry creates greater uncertainty for the cross-section
value, owing to heightened optical aberrations that may
affect the true values of the focal spot area A and the
g-parameter. Because of the good agreement in spectral
shape with prior work (Fig. 1 d), our data appear accurate
to within a global scaling factor of 1.9 (20.2 vs. 38.0 GM at
780 nm). Therefore, the action cross-section data are
(H O, pH7)
(H O, pH11)
correlated. Action cross section (red circles, line connects data points)
and peak brightness (blue boxes) spectra of fluorescein, BODIPY 492/
515, BODIPY-TR, rhodamine 110, 5C-TMR, Sulforhodamine 101,
AlexaFluor 430, and Resorufin, as determined by FCS. Measurements
were performed in 39 mM Ca2þMOPS, pH 7.2, buffer, except for fluores-
cein and BODIPY 492/515, which were measured in H2O at pH 11.0
and pH 7.0, respectively. Action cross-section values were normalized
to the peak of fluorescein from Makarov et al. (14). The Pearson correla-
tion coefficient r, and the associated p-test value, are given for each curve
Two-photon action cross section and peak brightness are
Biophysical Journal 102(4) 934–944
presented in Fig. 1 e and in Fig. 5 as scaled by this factor of
In addition to fluorescein as a reference dye, we focused
our action cross-section measurements on common two-
photon probes with unknown spectra in physiological
buffers. Fig. 5 shows two-photon action cross-section
spectra for several dyes from different dye families. Among
them are fluorescein and the rhodamines: rhodamine 110,
5C-TMR, and sulforhodamine 101. The boron-dipyrrome-
thene (BODIPY) dyes BODIPY 492/515 and BODIPY-TR
dyes are bright, environmentally insensitive dyes. Alexa-
Fluor 430 is a sulfonated aminocoumarin, whereas resorufin
belongs to the phenoxazine dye family. For BODIPY 492/
515 in water solution, the shape, peak location (920 nm),
and relative magnitude at the peak (s2h2¼ 14.4 GM) ob-
tained using the FCS technique in this work agrees quite
well with Xu and Webb (12) (s2h2¼ 17 GM at 920 nm
peak). This provides further confidence in the accuracy of
the relative magnitudes and shapes of the action cross-
section spectra obtained in this work.
A resemblance between the spectral shape of s2h2and
εmax is observed for all tested dyes—the maxima and
minima seen in each type of spectrum are apparent in the
other (Fig. 5). This similarity was quantified by a Pearson
correlation coefficient over the entire wavelength range
indicating significant correlation (p < 0.001 for six dyes,
p < 0.01 for resorufin) for each of the dyes except
substitute for cross-section measurements in determining
the optimal excitation wavelength(s) of a dye. Experimen-
tally, peak brightness is obtained faster and more easily
than cross section. The resemblance between s2h2 and
εmaxspectra is not obvious from first principles: action cross
section is determined at low powers, whereas peak bright-
ness requires high excitation powers leading to photobleach-
ing of the dye. In the following discussion, we will argue
that the spectral similarity of peak brightness and action
cross section most likely arises from the presence of highly
nonlinear (>quadratic) photobleaching in the probes we
tested. From Eq. 2, it follows that the molecular brightness
increases quadratically with the excitation intensity Iaveand
depends on the action cross section and volume contrast g.
This form is also valid in the case of saturation and/or
spatially variable concentration due to photobleaching,
only g has to be modified/redefined such that it covers the
appropriate geometrical changes (18). Here we will first
discuss the effects of saturation and photobleaching on
peak molecular brightness individually and subsequently
the combination of both.
In the case of focal volume saturation only, as the excita-
tion intensity is increased, the number of absorption events
per molecule per pulse approaches unity. We define the
mean number of absorption events per laser pulse at the
focal volume center as
With Eqs. 2 and 3, the molecular brightness is then
Further, we define Isatso that Isat¼ Iavewhen m(I2ave) ¼ 1.
Isatcorresponds to the intensity at which one absorption
event occurs per pulse. With Eq. 3, we get
The mean number of absorption events per pulse m(I2ave), as
defined by Eq. 3, can increase indefinitely with increasing
Iave. In reality, though, more than one absorption event per
pulse cannot be exceeded. Limiting the maximum number
of excitation events per pulse to 1 and modeling a Poisson
process, the actual number of absorption events can then
be expressed as (16)
where the exponential term is the Poissonian probability of
no absorption event taking place. The value of msat(I2ave)
defined by Eq. 6 asymptotically approaches unity with
increasing intensity. When Iave approaches and exceeds
Isat, a breakdown of the quadratic dependence of the fluores-
cence in intensity results. The degree of saturation is deter-
mined by the excitation profile: molecules in the center of
the volume are saturated first (19). As a result, the effective
size and shape of the observation volume are altered,
changing the volume contrast. The observation volume
increases dramatically, forming a flatter, top-hat shape
spatial profile (19). The volume contrast gsat,maxasymptoti-
cally approaches a constant value that depends on the func-
tional form of Sð~ rÞ. As a result, the peak brightness
spectrum, in the case of saturation only, becomes a flat,
wavelength-independent spectrum of constant value:
¼ 1 ? e?mðI2
aveÞ¼ 1 ? e?I2
εsat;max ¼ h2ffgsat;max:
Here it is assumed that h2 is wavelength-independent
(Kasha-Vavilov rule (39)).
Assuming only photobleaching effects, the volume
contrast decreases with Iavedue to the depletion of fluoro-
phores. The rate of photobleaching is most pronounced in
the center of the volume, where the excitation intensity is
highest, reducing the fluorescence emission from the central
region of the volume. If the bleaching rate depends on the
second power of the excitation intensity Iave(that is, kb¼
ave, where the bleaching quantum efficiency is hb),
Biophysical Journal 102(4) 934–944
940Mu ¨tze et al.
then the volume contrast can also be expressed with respect
to the bleaching rate kb, becoming a function of hbs2I2
ing on Iave, the molecular brightness is expressed as
Thus, in the case of bleaching only, the peak molecular
brightness depends on the cross-section s2and excitation
intensity Iaveonly via the product s2I2
of s2changes with wavelength, the same peak molecular
brightness is reached but at a shifted reference threshold
value of Iave. The molecular brightness initially increases
with Iave; for higher excitation intensities, the quadratic
dependence is lost, reaching a peak value εmaxdetermined
by the bleaching quantum efficiency hb. Here, hbis assumed
to be independent of excitation wavelength or to exhibit
spectral dependence of a form independent of s2.
When both saturation and bleaching depend on s2and Iave
only via the product s2I2
independent of s2. It follows directly from this that when
combining both effects εmaxis also independent of cross
section. Experimentally, however, a significant resemblance
between εmaxand action cross-section spectra is observed
(Fig. 5). In case of a quadratic dependence of photobleach-
ing on Iave, this correlation is only possible if hbwere itself
to show spectral variation anticorrelated with s2. As soon as
photobleaching becomes other than quadratic in Iave, hb
becomes effectively a function of Iaveand the dependence
of εblon s2and Iaveis not simply via the product s2I2
Then hbbecomes effectively spectrally anticorrelated with
s2, i.e., bleaching becomes effectively stronger where the
cross section is decreased because bleaching increases
more rapidly with intensity than absorption. A global
maximum will exist for a particular pair of s2and I2
and a notable correlation between εmaxand s2h2spectra
emerges. Previous studies have reported highly nonlinear
photobleaching, with dependencies on the order of 2.5
(40), 3.0 (41,42), or up to 4.0 (43). We therefore conclude
highly nonlinear photobleaching to be the dominant mecha-
nism underlying the observed similarity in shape of the εmax
and action cross-section spectra at the wavelengths and
intensities used for the dyes in Fig. 5, and aim to demon-
strate this experimentally using a passive pulse splitter in
the next section.
Peak brightness values and spectra are thus integrative
measurements, incorporating a dye’s absorption cross
section as well as providing additional information about
its photostability. In general, large brightness values result
from a combination of a large TPE action cross section
and low photobleaching. A large TPE action cross section
alone does not automatically imply a high brightness value.
Table S1 in the Supporting Material summarizes the
maximal peak brightness and action cross section obtained
from each spectrum. For this comparison, the peak bright-
ave) (18). For this quadratic dependence of bleach-
εbl ¼ gbl
ave. When the value
ave, both represent functional forms
ness values were normalized by their emission-spectra over-
lap with the detection spectrum, relative to fluorescein. It
can be seen, for instance, that BODIPY 492/515 has the
highest peak molecular brightness, greater than SRh101,
even though its action cross section is an order-of-
magnitude lower. The peak brightness metric thus reveals
that BODIPY 492/515 may be an attractive candidate for
two-photon probe development for applications where pho-
tostability is paramount. In addition to these rank-order
differences in magnitude, a trend for the ratio of εmax/s2h2
to be relatively higher at longer wavelengths is observed
(see Fig. S2), suggesting that the deteriorating effects of
photobleaching may be less pronounced at longer wave-
lengths. Peak molecular brightness spectra can therefore
complement action cross-section spectra to provide a fuller
picture of a probe’s performance.
Improvement of brightness by means of a passive
To validate the presence of higher-order photobleaching and
to test strategies that improve peak brightness, we imple-
mented a recently developed passive pulse splitter that
increases the repetition rate of the excitation pulses (23).
This device has been demonstrated to reduce photobleach-
ing while achieving the same fluorescence rate as no splitter
at all. For TPE, splitting a laser pulse train by N increases
the repetition rate f by N, while reducing the squared peak
according to Eq. 2. To restore the original emission rate,
the average power needs to be increased by
regime, the squared peak intensity I2
the case where photobleaching scales as with the power
b of intensity, and b > 2, bleaching is reduced by the factor
In our splitter setup, three beamsplitters divide the input
beam into eight beams (Fig. S1). The beams are delayed
with respect to each other and recombined into an output
beam with an 8? higher repetition rate. The resulting output
beam has an excitation frequency of 640 MHz and an inter-
pulse spacing of >1 ns. Using this assembly, we addressed
the dependence of molecular brightness on excitation inten-
sity and repetition rate. Fig. 6 a shows ε versus P2avecurves
for rhodamine 110 at excitation rates of 80 (N ¼ 1) and
640 (N ¼ 8) MHz. The squared power is normalized by
the splitting ratio N (either 1 or 8). At low irradiance, the
curves follow the squared dependence and overlap. At
high excitation powers, the 8? splitter assembly results in
an increase in peak brightness by a factor of ~2 for rhoda-
mine 110. Table S2 summarizes the effect of increasing
the repetition rate on peak brightness for the common
organic dyes TMR, AlexaFluor 546, Oregon Green, and
Photobleaching of dye molecules is a complex phe-
nomenon, because there are in general several possible
0by N2, together reducing the emission hF(t)i
; in this
0is reduced by N. In
Biophysical Journal 102(4) 934–944
mechanisms by which a fluorophore can be irreversibly pho-
tobleached. Absorption of multiple photons by excited
singlet or triplet states can yield unstable species. Because
of its long lifetime, the triplet state is considered to be an
important precursor for photobleaching pathways. No triplet
state dynamics are usually visible in two-photon FCS
experiments, possibly due to saturated transitions from the
long-lived triplet state into higher excited triplet states and
subsequent photobleaching of the molecule (44). Observa-
tions of increased fluorescence yield when reducing the
excitation repetition rate to allow transient triplet states to
relax before the next excitation cycle support this view
(45). Thus, in two-photon FCS, due to the high irradiances
involved, there seems to be no recovery from the triplet
state, whereas under single photon excitation, a fluorophore
in the triplet state is capable of relaxation to the singlet
Here, we employ a reducing agent that lowers the photo-
phore. We use ascorbic acid (AA), an antioxidant, as
a stabilizing reagent. As previously reported (27), the addi-
tion of AA (without using the splitter) results in a strongly
increased brightness (Fig. 6 a (46)). The effects of photo-
bleaching can also be inferred from the reduction in the
apparent residence time of the molecule in the focus. The
characteristic decay of the autocorrelation function is asso-
ciated with the dwell time of the molecule in the focal
volume. A molecule that undergoes photodestruction during
transitthrough the focus appears tohave a reduced residence
time tD. Fig. 6 b shows the decrease in the apparent diffu-
sion time with increasing excitation intensity. The onset of
bleaching is shifted to higher excitation intensities with
AA treatment. When applying the 8? splitter in combina-
tion with AA treatment, the positive effects roughly add,
resulting in an increase in peak brightness up to a factor
of ~4 (see Table S2) in combination with a delayed onset
of bleaching, as observed in the apparent diffusion time
(Fig. 6 b). Increase of peak brightness by means of a passive
pulse splitter and reduction of photoionized fluorophores
by an antioxidant, appear to be two largely independent
We showed that by increasing the excitation repetition
rate by means of a passive pulse splitter, the signal/noise
ratio in two-photon FCS measurements could be increased
by a factor of two. Together with the addition of ascorbic
acid, the peak molecular brightness was increased up to
a factor offour. These improvements can be vital, especially
in intracellular FCS applications, increasing the statistical
accuracy of the data or reducing the necessary measurement
times. Higher splitting ratios N are possible, at least up to
128 (23), albeit with additional complexity in the splitter
design. These may provide a further increase in the peak
brightness. We plan to explore this in future work.
The spectroscopic properties of two-photon excited probes
have been investigated by a fully automated two-photon
FCS apparatus. Two-photon excitation spectra in the form
of peak brightness spectra of 37 common, commercially
available organic dyes and Ca2þindicators have been
screened in the tuning range of a mode-locked Ti:Sapphire
laser. This comprehensivedata set can be used as a reference
in the selection of dyes and wavelengths for optimal signal/
noise ratio in two-photon imaging as well as FCS. For
example, peak brightness spectra play a crucial role in
optimizing choice of fluorophores and wavelength for
Different selection rules for one- and two-photon absorption
allow efficient excitation of spectrally separable dyes
with a single wavelength. Thus, it is possible to study the
interaction of two differently labeled molecules, eliminating
problems associated with two excitation sources, such as
poor beam overlap (20).
Molecular brightness intensity curves can also be used to
determine the two-photon action cross section of a fluoro-
phore. Our experimentally determined peak brightness
spectra resemble action cross-section spectra, corroborating
that peak brightness is a relevant means to describe the spec-
tral performance of a dye and identify optimal TPE wave-
lengths. Compared to action cross section, peak brightness
N = 1
N = 8
N = 1, AA
N = 8, AA
N = 1
N = 8
N = 1, AA
N = 8, AA
/ N (mW )
/ N (mW )
ness per molecule as a function of squared excitation intensity divided by
the splitting ratio N (N ¼ 1 or 8). (b) 8? splitting as well as ascorbic
acid reduce the effects of bleaching. Apparent residence time (normalized
to the initial values) decreases with increasing illumination intensity. Addi-
tion of ascorbic acid or the splitter increases the bleaching effect thresholds.
Effect of passive pulse splitter on Rhodamine 110. (a) Bright-
Biophysical Journal 102(4) 934–944
942Mu ¨tze et al.
values and spectra are integrative measures containing addi-
tional information pertaining to probe photostability. The
notable similarity between peak brightness and action
cross-section spectra can be theoretically explained by the
presence of higher-order photobleaching effects. This has
been experimentally confirmed with a passive pulse splitter,
increasing the peak brightness in two-photon FCS experi-
ments by up to twofold.
Two tables, two figures, and reference (47) are available at http://www.
The authors thank Na Ji for assistance with the pulse splitter.
J.M. was supported by a German Academic Exchange Service fellowship.
This research was funded by the Howard Hughes Medical Institute.
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