Article

Saturation Dynamics Measures Absolute Cross Section and Generates Contrast within a Neuron Suraj Kumar,1 Aditya Singh,1 Vijay R. Singh,2 Jude B. George,2 and J. Balaji1,* 1

Center for Neuroscience and 2Center for Nanoscience and Engineering, Indian Institute of Science, Bangalore, Karnataka, India

ABSTRACT The intensity required to optically saturate a chromophore is a molecular property that is determined by its absorption cross section (s) and the excited state lifetime. We present an analytical description of such a system and show that fluorescence around the onset of saturation is characterized by product of absorption cross section and lifetime. Using this approach we formulate a generalized method for measuring the multiphoton cross section of fluorophores and use it to obtain the absolute three-photon cross-section spectra of tryptophan. We find that the tryptophan three-photon cross section ranges from 0.28 S.I. units (m6s2photon2) at 870 nm to 20 S.I. units at 740 nm. Further, we show that the product of molecular rate of excitation and de-excitation, denoted as b, serves as a vital contrasting agent for imaging local environment. Our contrast parameter, b, is related to fraction of the population present in the excited state and is independent of the fluorophore concentration. We show that b-imaging can be carried out in a regular two-photon microscope setup through a series of intensity scans. Using enhanced green fluorescent protein (EGFP) fluorescence from the brain slices of Thy-1 EGFP transgenic mice, we show that there is an inherent, concentration independent, variation in contrast across the soma and the dendrite.

INTRODUCTION Sensitive measurement of the absolute multiphoton absorption cross section of fluorophores is essential in multiphoton imaging (1–3), optical switching, optical limiting (4), data storage (5,6), multiphoton-initiated polymerization, lithography (7), as well as photodynamic therapy (8). Currently, several experimental techniques exist for measuring twophoton absorption cross sections. These are based either on directly measuring the transmission (9,10) or measuring the induced fluorescence (11–13). The transmission-based techniques provide the absolute n-photon absorption cross section whereas the fluorescence-based techniques estimate the action cross section of the fluorophore that is being studied. Owing to the low probable nature of the multiphoton absorption processes, the absolute measurements using the transmission-based techniques require higher intensities for the n-photon excitation cross section. The conventional methods such as the z-scan, intensity scan, etc., can be quite challenging to adapt for in-tissue measurements. Although methods such as far-field z-scan avoid this problem, they still need to measure transmission that could be significantly challenging particularly with scattering tissues.

Submitted March 17, 2016, and accepted for publication June 23, 2016. *Correspondence: [email protected] Editor: Valentin Nagerl http://dx.doi.org/10.1016/j.bpj.2016.06.044 Ó 2016 Biophysical Society.

1328 Biophysical Journal 111, 1328–1336, September 20, 2016

The nonlinear cross section of fluorescent proteins is shown to be a very sensitive reporter of local environment (14). However, the use of cross section as a contrast agent is limited by existing methods of measuring the cross section. Particularly, transmission-based cross-section estimates are not suited for these measurements as they would not be able to provide the three-dimensional resolution. In addition, the transmission-based techniques require higher concentration of the reporter molecules that in itself can produce artifacts in the form of self-aggregation, dimerization, and other intermolecular interactions. The higher fluorophore concentration could also influence the physiological cell behavior and prove highly cytotoxic (15). Further, given that these are composite systems with a variety of absorbing molecules, it would be hard to isolate the absorption purely from the molecule of interest. Use of higher laser intensities can further lead to local increase in temperatures causing both cell and tissue damage apart from fluorophore photobleaching (16). These reaction byproducts lead to concomitant change in the spectroscopic properties of the fluorophore reporters leading to systematic inaccuracies and bias in the measurement results. Because of the above reasons, interrogating the spatially resolved absolute n-photon absorption cross section in situ would be prohibitively difficult to accomplish with transmission-based methods. It would be hard to make these

Multiphoton Absorption Cross-Section Measurement by Fluorescence

measurements ex vivo since cells and tissues will not be tolerant to the use of higher laser intensities required for n-photon cross-section measurements. To overcome these shortcomings and to combine the prime advantage of the sensitivity of the fluorescence-based techniques and the absolute values for the cross section reported by the transmission techniques, we have developed a generalized technique that exploits the fluorescence around the optical saturation. Because the fluorescence at and around optical saturation is dependent on the cross section, we obtain an analytical description of the phenomena of optical saturation in terms of measured fluorescence and incident intensity of excitation light. Considering a three-state model of ground state, excited state, and a state where the molecules undergo photobleaching, we show that 1) there exists a quasi–steady state and 2) measuring the fluorescence at this steady state as a function of incident light intensity determines the molecular absorption cross section. Because the above formulation makes use of the intensity dependence of fluorescence as the system approaches optical saturation, the description ensures the cross section is measured in an absolute manner independent of the fluorescence quantum yield and the collection efficiency. Our method enables measurement of the absolute multiphoton absorption cross section in a spatially resolved manner with a regular two-photon microscope without a need for additional instrumentation. Furthermore, in our description the collected fluorescence is integrated over the entire excitation volume, thereby eliminating the need for incorporating a pinhole to reject the out-of-focus fluorescence. Being a generalized method, the derived analytical description of fluorescence signal is applicable to any n-photon absorption cross-section measurement for n R 1. We propose a new, to our knowledge, contrast parameter b ðh1=stgÞ that depends on the molecular absorption cross section (s), lifetime of the fluorophore excited state (t), and the photon conversion factor (g). b, so defined, emerges as a natural parameter for describing optical saturation (see Theory: Absolute n-photon absorption cross-section measurement; Eq. 7). Since the optical saturation very strongly depends on the nature of both the excited state and the ground state, we find it to be a sensitive reporter of local environment. b is independent of the fluorophore concentration and is a rather sensitive reporter of local environment. We used this contrast parameter (b) to measure spatially resolved absorption cross section across the neurons spanning the soma, dendrite, and the spines. Another implication of our result is that optical saturation can be used for multiphoton absorption cross-section measurement both in vivo and in vitro. With a constant requirement for pushing the boundaries on achieving and synthesizing highly efficient multiphoton excitable fluorophores, various researchers continue to devise novel fluorophore reporter molecules (17). Obtaining the absorption cross section for such fluorophores to be used in multiphoton microscopy becomes

important. Our method yields these measurements conveniently using existing microscope setups. In the context of deep tissue imaging, the fundamental imaging depth is further enhanced by use of three-photon microscopy using much longer wavelengths thereby expanding the need for measuring the higher-order absorption cross section. Our method can easily help estimate the three-photon absorption cross section of the fluorophores in situ. To the best of our knowledge, there is no other method that can yield absolute cross sections in situ.

MATERIALS AND METHODS The chemicals used in the experiment, L-tryptophan, fluorescein, Rhodamine B, and methanol were all obtained from Sigma-Aldrich and used as received. All aqueous solutions were constituted using deionized water. The brain slices for in situ imaging were obtained from Thy1-EGFP transgenic mice (Jackson Laboratory, Stock Number 011070). Forty micron slices were obtained using Leica Cryostat. The brains were extracted after transcardial perfusion and dehydrating the brains in sucrose solution as described previously (18). The procedures were in accordance with the Institute Animal Ethics Committee approved protocol. Optical imaging and spectroscopy were performed on a custom-built two-photon setup based on a Zeiss upright microscope (Axio Observer) equipped with a 40 water immersion objective (NA 1.0, WD 2.5 mm). A femtosecond Ti:Sapphire laser (Newport, Tsunami) was used for the two-photon excitation whose intensity was modulated using a half-wave plate (Thorlabs, AHWP05M) and a polarizer (Thorlabs, GL10-B). A galvanometric scanning X-Y mirror pair (Thorlabs, GVSM002) was used to scan the laser beam across the sample plane. The emitted fluorescence was collected using the same objective in epifluorescence mode and imaged onto a photomultiplier tube (Hamamatsu, H7422-40), driven by a power supply unit with temperature control (C8137-02), as a nondescanned detector. Epifluorescence signal was separated from excitation light using a dichroic mirror (Semrock, FF705-Di01) and emission filters (Semrock FF01-510/42 for fluorescein and EGFP, Semrock FF01-607/70 for Rhodamine B and Thorlabs FGB39 for tryptophan). Where necessary, aqueous solution of copper sulfate was used to reject infrared radiation. The photomultiplier tube photocurrent was amplified using a low noise current preamplifier (Stanford Research Systems, SR570) before digitizing the signal using a data acquisition board (National Instruments, PCI-6110). The digitized signal is saved on the computer for further analysis using Matlab (The MathWorks, Natick, MA), Origin, and ImageJ. Scanimage 3.8 was used to interface for instrument control and generation of galvanometer scan command signals. Acquisition of images is accomplished with a custom Matlab routine to interface the z-drive of the microscope.

Analytical description of saturation dynamics To obtain the absolute n-photon absorption cross section, we derived an analytical expression for the fluorescence saturation by solving the kinetic rate equations. The schematic in Fig. 1 depicts the photophysical processes underlying our theoretical model. The population kinetics for the energy state occupancy depicted in the above scheme can be represented by the following coupled equations:

nt ¼ n þ n g þ nb ;

(1)

dn ¼ k1 ng  k1 n  kb n  k1 n ; dt

(2)

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n*

Solving the above equations using the Laplace transform method and rearranging the terms, we obtain the following:

kb k1=σI

N  ðsÞ ¼

nb

k1=σnIn

  k 1 nt 1 1  ; ag sa sg

(4)

where s is the Laplace parameter, N represents the population in the Laplace space, and a and g are the positive and the negative roots, respectively, and are given by the following:



  a

k-1

g

k ¼

 ffi þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi k 2  4k1 kb  ; 2

and k ¼ 2k1 þ kf þ kb :

ng

Finally, using the inverse Laplace transform to obtain the following expression for the excited state population as a function of time:

FIGURE 1 The kinetic model underlying the photophysical process. Upon photon absorption, the fluorophore transitions from the ground state (ng) to an excited state (n*) are shown. The solid up arrow depicts this absorption transition. Whereas most molecules relax to the ground state via fluorescence (wavy down arrow), some are lost to photobleaching (nb). The dash-downward arrow depicts stimulated emission. To see this figure in color, go online.

dnb ¼ k b n ; dt

(3)

where nt is the total number of fluorophore molecules, ng is the number of molecules in ground state, n* the number of molecules in the excited state, and nb the number of molecules lost to photobleaching. The rate constants for excitation, fluorescence decay, and photo-damage are respectively denoted by k1, k–1, and kb.

n ðtÞ ¼

k 1 nt ðeat  egt Þ: a g

(5)

Fig. 2 shows the time evolution of the fraction of molecules in the excited state as modeled by the Eq. 5. Under a steady-state illumination, there is a clear time period (shaded region in Fig. 2 a) wherein the number of molecules in the excited state reaches a quasi–steady state without much of a decline due to photobleaching. The experimentally ideal timescales for these simulation parameters are where the decline due to photobleaching is minimal. In other words, for t [ 1=k1 ; 1=kf ; and t  1=kb , that is, the time window between the fluorophore excitation and onset of photobleaching, the fluorescence is in a quasi–steady state. Experimentally during imaging this timescale is reflected in the pixel residence time (typically few microseconds). The quasi–steady state per se is reached long after the excitation but long before the manifestation of bleaching-induced loss in local fluorophore concentration (this is of the order of few 10 s of microseconds). We arrive at this estimate by assuming a femtoliter probe volume FIGURE 2 Temporal profile of fractional excitation as modeled by the photophysical process depicted in the Fig. 1. (a) The solid line depicts the fractional population in the excited state, which saturates within few femtoseconds under the typical values assumed for the rate constants: k1 ¼ 1015 s1, k–1 ¼ 109 s1, kb ¼ 103 s1. The timescale is shown linear until the break, following which it is depicted in logarithmic scale to help capture the entire timescale of the photophysical processes. The shaded region depicts the timescale as very large compared with the absorption kinetics and very small compared with the photobleaching kinetics. (b) The excited state population at quasi– steady state and its dependence on the excitation intensity is shown as a solid line. The solid line depicts the fraction of excited state population as a function of intensity in units of parameter b as shown in Eq. 6. (c) Saturation dynamics of one photon excitation and estimation of fluorophore lifetime are shown. The plot shows the fluorescence emitted by fluorescein (100 nm, in PB, pH 7.2) when excited using a 470 nm laser measured as a function of power. The fit shown in the solid red line was obtained using Eq. 7, and the fit parameter b is used to estimate fluorescein lifetime (4.3 ns). To see this figure in color, go online.

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Multiphoton Absorption Cross-Section Measurement by Fluorescence (size of a typical PSF) and bleaching efficiency of ~0.001. In this time window the Eq. 5 describing the excited state population simplifies to the following:

n ðtÞ ¼





nt  : kf þ kb k

(6)

1

Fig. 2 b depicts the n*(t) under this approximation as a function of excitation intensity (Eq. 6) for typical values of the rate constants (k1 ~1015, kf ~109, and kb ~103). For a n-photon absorption process, Eq. 6 can be rewritten as follows in terms of the nth-power of the photon flux density:

n ðtÞ ¼

2I n

aI n ; þ bn

(7)

where bn ¼ ð1=sn t l gÞ; tl ð¼ 1= ðkf þ kb ÞÞ is the fluorescence lifetime, g is the photon conversion factor (g ¼ 2 for a two-photon process), and k1 ¼ sn I n =g. In arriving at Eq. 7 we used the intensity of the laser (I) expressed in Watts, this is constant in time for a CW laser. However, when studying multiphoton excitation, pulsed lasers are used. In such cases, we need to replace the pulsed intensity with equivalent CW intensity (13). We note that, this would be valid under the conditions where the lifetime of the fluorophore is larger than the pulse width and shorter than the interpulse separation. These assumptions are generally true as the nominal lifetimes of the fluorophore are in the range of few nanoseconds whereas the pulses can be ~100 fs to few ps and the interpulse separation is >12 ns for laser with repetition rates up to 80 MHz. Measuring the fluorescence as a function of excitation intensity close to the fluorophores optical saturation and fitting it to Eq. 7 would allow us to estimate bn from which we can estimate the absolute cross section knowing the lifetime. Further, we hypothesize that bn by itself can be a very useful imaging contrast parameter in reporting the changes in fluorophore local environment. We comment further on the b-imaging later in the article. To establish the feasibility of using optical saturation to estimate the lifetime or cross section through simple intensity scans, we performed the onephoton excitation of fluorescein dissolved in phosphate buffer (pH 7.2) and excited with a 470 nm single longitudinal mode continuous-wave laser. Fig. 2 c shows the fluorescence intensity as function of the incident laser power (open circles) and the fit (solid line) to Eq. 7. To obtain the lifetime, we rewrite Eq. 7 in terms of the measured experimental parameter of laser power (P) in the following:

n ðtÞ ¼

aP aP ¼ ; 2P þ bAε=hr 2P þ P0

where, b ¼ 1/stg as previously defined, A is the area of the focused laser spot on the sample, ε ¼ hc/l is the photon energy, and hr is laser intensity coupling efficiency. The second term in the denominator of the above expression (P0) is obtained as the fitting parameter and is used to deduce the lifetime using the following relation:

t ¼

A ε : sP0 hr

Using the spectrophotometrically determined values of cross section (s ¼ 1.15*1016cm2), we estimated the fluorescein lifetime to be 4.3 ns. This is in very good agreement with the lifetime data published by other research groups (19). For this experiment we have used a typical one-photon excitation detection scheme to monitor the fluorescence through a pinhole. This also indicates that the saturation dynamics can be used for estimating the lifetimes given the one photon cross section is known or measured.

Estimating the change in probe volume around optical saturation The advantage of two-photon excitation process is its inherent confocality offered through localized excitation. Conventional detection geometry of multiphoton microscope utilizes this property to detect the fluorescence immediately after the objective lens without the use of pin hole. However, as we approach optical saturation, the observation volume increases and to account for these changes we integrate over the observation volume after estimating the probability of excitation (Eq. 8). We note that, although one can use the pinhole after descanning the beam, such an approach would compromise the advantage of nondescanned detection. Hence, we obtain an analytical description of these changes as described below. The number of fluorescence photons emitted, F can be estimated in the following by integrating the fractional excited state population (Eq. 7) over the excitation volume:

Emitted Fluorescence Photons ðFÞ Z2p f

ZþN d4

0

ZN dz

N

; aI n ðr; zÞ rdr 2I ðr; zÞ þ bn

(8)

n

0

where the Gaussian intensity profile of the beam of radius wz propagating along the z axis is expressed as the following:

Iðr; zÞ ¼ I0 ðzÞe

2r 2= 2 uz ðzÞ ;

(9)

For the particular case of two-photon excitation (n ¼ 2), Eq. 8 simplifies to the following:

ZþN f

dz N

ha i

u2z ðzÞ ln 2I02 ðzÞb1 2 þ1 : 8

(10)

Equation 10 can be analytically integrated by recognizing that 2 2I02 ðzÞb1 2 ¼ s2 t L I0 ðzÞ: In other words, the first term in the parenthesis of the natural log term is but the product of the fluorescence lifetime and rate of excitation. Essentially, it is indicative of the fraction of excited state population. For the purpose of integration, we Taylor-expand the second term in the integrand and retain only the first two terms. Therefore, for 0 < s2 t L I02 ðzÞ < 1; and under the assumption of a Gaussian beam of radius u0 at z ¼ 0 and characterized by a radius u2z ðzÞ ¼ u20 ½1 þ ðl z=p u20 Þ2 , the number of emitted fluorescence photons then becomes the following:

F f

! 2 2 a I0;0 3 I0;0 Vp 1  : 4 b2 8 b2

(11)

Equation 11 can be used to estimate b through measuring the fluorescence (F) as a function of excitation intensity (I0,0) and fitting the data to the following parametric equation:

F ¼ Pð1Þ þ Pð2Þ  X  ½1  Pð3Þ  X;

(12)

where parameters P(1) and P(3) (¼ 3/8b) are the baseline from the uncorrelated background fluorescence and inverse of the contrast parameter (b), respectively. Parameter P(2) (¼ 2/3*aVp) is composed of product of P(3) and number of fluorophore molecules in the excitation volume (Vp). All three parameters are optimized independent of each other. It is imperative to know the beam parameters for estimating the intensity of the excitation

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Kumar et al. beam. We use the PSF of the microscope estimated through the use of 200 nm fluorescent microspheres.

RESULTS AND DISCUSSION Absolute absorption cross-section measurement in vitro Fig. 3 shows the spectral dependence of the measured absolute two-photon absorption cross section for Rhodamine B in methanol. To obtain the cross-section values, the collected fluorescence with varying intensity at a given wavelength is fit to Eq. 12 and value of the cross section estimated, with previous knowledge of the fluorophore lifetime (t ¼ 4 ns). Within the wavelength window of our experimental results, we see very good agreement with action cross-section results reported by Xu et al. (11) for Rhodamine B, suggesting that our method is sensitive enough to measure the absolute absorption cross section. Absolute three-photon cross section of L-tryptophan Tryptophan is one of the naturally occurring amino acids and has a native fluorescence in the near UV range. Since its absorption spectra peaks at ~280 nm, the two-photon excitation can be performed in the visible range of the electromagnetic spectrum and the three-photon excitation with the infrared. The three-photon excitation of tryptophan is well within the available wavelength tuning window of our Ti:Sapphire laser. Although the two-photon absolute cross section of tryptophan has been earlier reported (20), in this article we use three-photon excitation to study tryptophan. At the time of writing this article, we are not aware

Brain slices of Thy-1 GFP transgenic mice with enhanced green fluorescent protein (EGFP) were prepared as mentioned earlier. Fig. 5 a shows a high-resolution image of brain slice obtained by two-photon excitation at 890 nm. The same field of view was imaged at varying incident laser light intensities. Using a specific region of interest, the integrated pixel intensity was plotted against the incident power. Such a plot is shown in Fig. 5 b. The data is then fitted to Eq. 11 to estimate the two-photon absorption cross section. To obtain the spectral two-photon excitation profile of EGFP in slice, two-photon images are first captured as a function of wavelength and the process repeated. The two-photon absorption cross section obtained using our technique is in good agreement with that reported (~113 GM) by Heikal et al. (22), where they measured the two-photon excitation of EGFP as a function of the in vitro buffer solution pH. We note that our estimate of EGFP cross section in the fixed brain slice is closer to cross sections reported in Heikal et al. than that is estimated for eGFP in solution (pH 7.4). Given that our estimate is from fixed brain slices whereas the previously reported values were in free solutions, we do expect disparities owing to the difference in local environments. Furthermore, we report b

4

Fluorecsence(A.U)

Absolute absorption cross-section measurement of GFP in brain slice

1.05x10

3

7.00x10

3

3.50x10

0.00

0.0

-4

4.0x10

-4

8.0x10

-3

1.2x10

Power2

Absolute Cross section(GM)

a

of any previous studies reporting the detailed absolute threephoton absorption spectra of tryptophan (20,21). Fig. 4 b shows the three-photon spectral excitation profile for 20 mM tryptophan in phosphate buffer (pH 7). Although we report the results from studies in vitro, our method is easily adapted for in vivo measurements as well.

600 500 400 300 200 100 0 720

750

780

810

840

870

900

Wavelength (nm)

FIGURE 3 The intensity scan of the two photon excitation of Rhodamine B in methanol at 740 nm. (a) The intensity scans were carried out for power 0–37 mw (as measured at the sample plane), and the plot depicts the fluorescence measured (open circles) as a function of power-squared. The solid line shows the fit to Eq. 11, and the dash dot line represents the initial slope to show the deviation from the linearity due to saturation. The fit parameter, b2, was obtained for six different wavelengths, and the absolute cross section was estimated to be 141 (740 nm), 169 (770 nm), 336 (800 nm), 292 (840 nm), 135 (870 nm), and 66 (895 nm) GM. (b) The absolute cross sections were obtained for the entire spectrum (730 to 910 nm) by normalizing the fluorescence values with the absolute cross sections obtained using intensity scan as shown in Fig. 3 a. To see this figure in color, go online.

1332 Biophysical Journal 111, 1328–1336, September 20, 2016

Multiphoton Absorption Cross-Section Measurement by Fluorescence

b

Fluorescence(A .U )

800.0

600.0

400.0

200.0

0.0 0.0

-5

1.0x10

-5

2.0x10

-5

3.0x10

-5

4.0x10

Power3

Three-Photon Cross Section

a

25 20 15 10 5 0 720

740

760

780

800

820

840

860

880

Wavelength (nm)

FIGURE 4 The intensity scan of the three-photon excitation of L-tryptophan in phosphate buffer saline (pH ¼ 7) with excitation at 740 nm. (a) The intensity scans were carried out for power 0–37 mw as measured at the sample plane. The plot depicts the fluorescence measured as a function of power-cubed. The solid line shows the fit function, and the dash dot line represents the initial slope to show the deviation from the linearity due to saturation. The fit parameter, b3, was obtained for three different wavelengths, and the absolute three-photon cross section was estimated to be 7*1091(730 nm), 11*1091(750 nm), and 9*1091(760 nm) m6 s2 photon2. (b) The absolute cross sections were obtained for the entire spectrum (730 to 870 nm) by normalizing the fluorescence values with the absolute cross sections obtained using intensity scan as shown in Fig. 4 a. The three-photon cross section is measured in m6 s2 photon2. To see this figure in color, go online.

the absolute cross-section measurements for EGFP whereas the other results were for the action cross section. This leads to a discrepancy in the reported results by factors relating to the estimation of the fluorescence quantum yield and the fluorescence collection efficiency. Given these factors, we posit that the measurements from these two methods are within the limits of error involved in the nature of these experiments. Since we have the ability to estimate the multiphoton absorption cross section in vivo too, a natural application of this would be as imaging contrast parameter.

Whereas in fluorescence lifetime imaging microscopy (FLIM), the contrast is provided by the lifetime of the fluorophore in its microenvironment, the b-imaging would provide contrast using two parameters—the natural lifetime of the fluorophore and also its n-photon absorption cross section. A major advantage the b-imaging offers over the FLIM is that b-imaging is a steady-state measurement can be easily used in scattering samples as well as in vivo. Further, it has been shown earlier that the two-photon absorption cross section has a large dependence on the

FIGURE 5 The two-photon image stacks of whole brain obtained from Thy1-EGFP transgenic mice (which expresses EGFP sporadically across the hippocampus and cortex). (a) The pixel densities (or mean pixel density) within the ROI (red outline) were calculated for images obtained at different excitation light intensities. (b) The intensity scan is generated at wavelength 855 nm by measuring the fluorescence of the soma outlined in Fig. 5 a. The fit parameter estimated a cross section of ~240 GM. (c) The absolute cross sections were obtained for the entire spectrum (780 to 915 nm) by normalizing the fluorescence values with the absolute cross sections obtained using intensity scan at 855 nm. To see this figure in color, go online.

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local electric field of the fluorophore (14), and this will provide a huge contrast and will be a sensitive reporter of the local environment. Such changes are not necessarily captured in FLIM image. The other parameters that provide the lifetime contrast will also contribute to the b-contrast. We checked if the b-parameter was sensitive to local environment differences between neuronal structures like soma, dendrites, and spine. It showed larger values for spine and dendrites compared with that for the soma. For some regions the b-values for spines were up to 75% higher than soma. Fig. 6 shows the two-photon microscopy images of the Thy1-EGFP mice brain slice as represented by the raw fluorophore intensity (Fig. 6 a), the parameter relating to the number of fluorophore molecules in the probe volume (Fig. 6 b) and the corresponding b-parameter (Fig. 6 c). Evidently, the beta image manifests the latent contrast in the regions of soma, dendrite, and spine that remains concealed in the raw intensity image. This inherent contrast emerges from the distinctive local environment in different spatial regions of the neuron. Figs. 6, d and f, highlight a region of the dendrite enclosed in red rectangle. Whereas the raw intensity image (Fig. 6 d) shows a largely featureless and monotonous profile, the concentration related image (Fig. 6 e) displays hotspots of high-concentration fluorophores along the dendrite. These could be fluorophore aggregates causing the absorption cross section and the fluorescence lifetime to move in opposite directions thereby revealing a

smeared-out contrast in the b-image (Fig. 6 f) that lies midway between the other two images. The images were generated in Matlab using the unconstrained optimization routine (‘‘fminunc’’) for curve fitting. It was deemed necessary to use a binary mask to remove the background. The mask was generated from the highestintensity image after thresholding and applied to all the images to extract the relevant foreground without changing the pixel values. Each pixel from the images acquired as a function of intensity was read and the objective function defined by Eq. 12 minimized till convergence achieved. It typically required 38 iterations for fit convergence. CONCLUSION We have presented a generalized method that enables measuring the spectral variation of the absolute n-photon absorption cross section using fluorescence around saturation. This method allows for measurements to be done at very high sensitivity and independent of the size and shape of the excitation volume. Since the need to separate the infocus fluorescence from the out-of-focus ones is obviated, the increased sensitivity permits this technique to be easily adopted for both in vitro and in vivo measurements. Two critical concerns for performing in vivo b-imaging are the time of sample exposure and the excitation intensities implemented. If we compare our method with the other contrast enhancement techniques such as lifetime, both

FIGURE 6 Two-photon image of Thy-1 EGFP mice brain slice with excitation at 860 nm. (a–c) Image of Thy-1 EGFP mice brain slice as represented by (a) the raw intensity, (b) the concentration-equivalent parameter, and (c) the beta-parameter. (d–f) Zoomed-in view of a dendritic shaft (enclosed within red rectangle) of, respectively, the raw intensity image, the concentration-equivalent image, and the beta-image. These representations were obtained by fitting to Eq. 11 the pixel values from the raw intensity images acquired as a function of intensity. Whereas the raw intensity image shows no features, the concentration-equivalent image displays clustering of fluorophores in the dendritic shafts, a small portion of which is highlighted in (e). To see this figure in color, go online.

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require multiple frames to generate the required contrast. However, unlike in TCSPC or in phase modulation for lifetime measurements, the number of time points required to obtain b is much smaller. This results in relatively shorter sample exposure time. Furthermore, the intensities required for these measurements are same as the intensities used for regular imaging; this is so because of the following reasons: 1) Our model is applicable in the intensity regime where the fluorescence just starts to deviate from linearity as we model the approach to saturation rather than the fluorescence at saturation. 2) Best signal-to-noise with minimal exposure (required for any imaging, particularly so for in vivo) is achieved when there is efficient excitation of the fluorophore. To achieve this it is necessary to maximally excite the fluorophore. Our measurements make use of the laser power at which this is achieved. Furthermore, because this method measures the fluorescence as function of intensity and obtained on a quasi-asymptotic curve, there is no rigorous requirement to consider the fluorescence collection efficiency and hence the results are immune to any uncertainties associated with estimates of two- and three-photon excitation cross sections. Further, being a generalized method, we extend it easily to measure the absolute threephoton cross section of tryptophan. The b-imaging is a powerful contrast parameter for imaging with different fluorophores and can function as a sensor for the fluorophore microenvironment. It can incorporate a contrast based just only on fluorophore microenvironment independent of concentration. In our theoretical analysis we have considered the excitation through one dominant order; however, for a general case of simultaneous multiple orders of excitation, the fluorescence needs to be plotted against the incident power directly (as against the square of incident power done in the manuscript) and fit to a more general equation as we now show. To account for multiorder interactions, we reformulate k1 in Eq. 6 to incorporate the following interactions of order n and order m: k1 ¼ sn I =gn þ sm I =gm : n

m

The excited state population then becomes the following: n ðtÞ ¼

I n nt a½1 þ GI d  ; 2I n ½1 þ GI d  þ bn

where G ¼ sm gm =sn gn ; d ¼ m  n; sm and sn are the absorption cross sections of order m and n, respectively; and gm and gn are the photon-conversion factors. Even though this equation has more free parameters, this can serve as a good method in separating a mixture of fluorophores (it is highly unlikely that two fluorophores have similar emission spectrum, n- and nþ1-photon absorption spectrum).

AUTHOR CONTRIBUTIONS S.K. performed the bulk of the experiments, analyzed the data, and helped in developing the theory and discussions. A.S. helped in writing the article, estimating one photon cross section, preparing samples for two-photon cross-section measurement, and discussing and analyzing the experimental data. V.R.S. wrote the article, took part in theoretical analysis, and helped with design of the experiments and discussions. J.B.G. helped with the Matlab fitting routine for fitting the image data. B.J. designed the experiments, developed the theory, analyzed the data, lead the discussions, and wrote the article.

ACKNOWLEDGMENT The work was supported by DSTO/BCN/BJ/1102 (Ramanujan fellowship to J.B.), DBTO/BCN/BJ/0402, DSTO/BCN/BJ/1297, JTT/MUM/INST/ IIOS/201314/0033 (Tata Trust), DBT IISc-Partnership Program, CSIR09/079(2561)2012-EMR-I (CSIR Fellowship to S.K.), and CSIR-09/ 079(2590)/2012-EMR-I (CSIR Fellowship to A.S.). V.R.S. is supported by the industrial postdoctoral fellowship at the Centre for Nanoscience and Engineering, Indian Institute of Science.

REFERENCES 1. Denk, W., J. H. Strickler, and W. W. Webb. 1990. Two-photon laser scanning fluorescence microscopy. Science. 248:73–76. 2. Helmchen, F., and W. Denk. 2005. Deep tissue two-photon microscopy. Nat. Methods. 2:932–940. 3. Xu, C., W. Zipfel, ., W. W. Webb. 1996. Multiphoton fluorescence excitation: new spectral windows for biological nonlinear microscopy. Proc. Natl. Acad. Sci. USA. 93:10763–10768. 4. Tutt, L. W., and T. F. Boggess. 1993. A review of optical limiting mechanisms and devices using organics, fullerenes, semiconductors and other materials. Prog. Quantum Electron. 17:299–338. 5. Hunter, S., F. Kiamilev, ., P. M. Rentzepis. 1990. Potentials of twophoton based 3-D optical memories for high performance computing. Appl. Opt. 29:2058–2066. 6. Strickler, J. H., and W. W. Webb. 1991. Three-dimensional optical data storage in refractive media by two-photon point excitation. Opt. Lett. 16:1780–1782. 7. Kawata, S., H.-B. Sun, ., K. Takada. 2001. Finer features for functional microdevices. Nature. 412:697–698. 8. Ogawa, K., and Y. Kobuke. 2013. Two-photon photodynamic therapy by water-soluble self-assembled conjugated porphyrins. BioMed Res. Int. 2013:125658. 9. Ajami, A., W. Husinsky, ., N. Pucher. 2010. Two-photon absorption cross section measurements of various two-photon initiators for ultrashort laser radiation applying the Z-scan technique. J. Opt. Soc. Am. B. 27:2290. 10. Sengupta, P., J. Balaji, ., S. Maiti. 2000. Sensitive measurement of absolute two-photon absorption cross sections. J. Chem. Phys. 112:9201– 9205. 11. Albota, M. A., C. Xu, and W. W. Webb. 1998. Two-photon fluorescence excitation cross sections of biomolecular probes from 690 to 960 nm. Appl. Opt. 37:7352–7356. 12. Rumi, M., and J. W. Perry. 2010. Two-photon absorption: an overview of measurements and principles. Adv. Opt. Photonics. 2:451–518. 13. Xu, C., and W. W. Webb. 1996. Measurement of two-photon excitation cross sections of molecular fluorophores with data from 690 to 1050 nm. J. Opt. Soc. Am. B. 13:481–491. 14. Drobizhev, M., N. S. Makarov, ., A. Rebane. 2011. Two-photon absorption properties of fluorescent proteins. Nat. Methods. 8:393–399. 15. Alford, R., H. M. Simpson, ., P. L. Choyke. 2009. Toxicity of organic fluorophores used in molecular imaging: literature review. Mol. Imaging. 8:341–354.

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Kumar et al. 16. Simanovski, D., M. Sarkar, ., D. Palanker. 2005. Cellular tolerance to pulsed heating. Proc. SPIE. 5695:254–259. 17. Yan, Y. X., H. H. Fan, ., X. M. Chen. 2007. Synthesis and two-photon absorption property of new p-conjugated dendritic fluorophores containing styrylpyridyl moieties. Mater. Chem. Phys. 101:329–335. 18. Han, J.-H., S. A. Kushner, ., S. A. Josselyn. 2007. Neuronal competition and selection during memory formation. Science. 316:457–460. 19. Seybold, P. G., M. Gouterman, and J. Callis. 1969. Calorimetric, photometric and lifetime determinations of fluorescence yields of fluorescein dyes. Photochem. Photobiol. 9:229–242.

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20. Maiti, S., J. B. Shear, ., W. W. Webb. 1997. Measuring serotonin distribution in live cells with three-photon excitation. Science. 275:530–532. 21. Gryczynski, I., H. Malak, and J. R. Lakowicz. 1996. Three-photon excitation of a tryptophan derivative using a fs-Ti: sapphire laser. Biospectroscopy. 2:9–15. 22. Heikal, A. A., S. T. Hess, and W. W. Webb. 2001. Multiphoton molecular spectroscopy and excited-state dynamics of enhanced green fluorescent protein (EGFP): acid-base specificity. Chem. Phys. 274: 37–55.

Saturation Dynamics Measures Absolute Cross Section and Generates Contrast within a Neuron.

The intensity required to optically saturate a chromophore is a molecular property that is determined by its absorption cross section (σ) and the exci...
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