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Topic Introduction
Multiphoton Excitation of Fluorescent Probes Chris Xu and Warren R. Zipfel
This introduction reviews the multiphoton excitation cross sections of extrinsic and intrinsic fluorophores, genetically engineered probes, and nanoparticles. We will review the known two-photon excitation cross sections of biological indicators and will discuss several related issues such as how to theoretically estimate and experimentally gauge the two-photon cross section of an indicator. We provide practical guides for experimentally estimating the excitation cross section.
INTRODUCTION
The fluorescence excitation or action cross section is a basic parameter in fluorescence imaging. The action cross section is a combined measure of how strongly a molecule absorbs at a particular excitation wavelength and of how efficiently the fluorophore converts the absorbed light into emitted fluorescence (i.e., the quantum yield). For conventional one-photon imaging, the onephoton absorption cross sections are well documented for a wide range of molecules, as are fluorescence quantum yields. However, significantly less is known about two-photon cross sections of biologically useful fluorophores. Furthermore, it is often difficult to predict multiphoton excitation spectra, especially two-photon spectra, from the one-photon data because of differences in the selection rules and the effects of vibronic coupling. Before the 1990s, two-photon excitation cross-sectional measurements were almost always performed at 694 nm (ruby laser) and 1064 nm (Nd:glass laser) on laser dyes (Smith 1986). Less effort was devoted to accurate quantitative studies of common fluorophores widely used in multiphoton microscopy. In addition, substantial disagreement (sometimes more than one order of magnitude) between published values of two-photon cross sections often exists. The lack of knowledge about two-photon excitation cross sections and spectra for common fluorophores used in biological studies has been a significant obstacle in the use of two-photon laser scanning microscopy. The emergence of the mode-locked solid-state femtosecond lasers, most commonly the Ti:sapphire lasers (Spence et al. 1991; Curley et al. 1992), have greatly facilitated the measurement of a multiphoton excitation cross section. When compared with earlier ultrafast lasers (e.g., ultrafast dye lasers), the Ti:sapphire lasers are highly robust and are widely tunable, making femtosecond pulses from 690 to 1050 nm easily accessible. A large number of fluorescent indicators, intrinsic fluorescent molecules, genetically engineered probes, and some nanoparticles (e.g., quantum dots [QDs]) have since been measured. New measurement techniques have also been developed to further improve the absolute accuracy. This review on multiphoton excitation cross sections is motivated by the application of multiphoton microscopy as a powerful tool for three-dimensionally resolved fluorescence imaging of biological samples (Denk et al. 1990; Xu et al. 1996a,b; So et al. 2000; Masters 2003; Zipfel et al. 2003a,b; Masters
Adapted from Imaging: A Laboratory Manual (ed. Yuste). CSHL Press, Cold Spring Harbor, NY, USA, 2011. © 2015 Cold Spring Harbor Laboratory Press Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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Multiphoton Excitation of Fluorescent Probes
and So 2004; Helmchen and Denk 2005). We will review the known two-photon excitation (2PE) cross sections of biological indicators and will discuss several related issues such as how to experimentally gauge the two-photon cross section of an indicator. An effort is made to compare crosssectional values obtained from various research groups in the last 10 years or so. Although we will concentrate on 2PE, three-photon excitation will also be discussed briefly. The remainder of this introduction is divided into three sections. First, we provide simple estimates of multiphoton excitations of dyes and QDs from theory. Second is the methods section, which includes practical guides for experimentally estimating the excitation cross section. The third section is a compilation of twophoton excitation cross sections of extrinsic and intrinsic fluorophores, genetically engineered probes, and nanoparticles. ESTIMATION OF MULTIPHOTON EXCITATION CROSS SECTIONS
The essence of the theory of multiphoton processes can be represented in perturbation theory. Details of the rigorous derivation can be found elsewhere (Faisal 1987). Here, for the purpose of order of magnitude estimation, a greatly simplified approach is used to describe the multiphoton excitation processes, and only the lowest-order dipole transition will be considered. The single intermediate state approximation (Birge 1983) can be used to give an order of magnitude estimation. The two-photon absorption cross section (σ2) can be obtained as s2 = sij sif tj ,
(1)
where σij and σif represent the one-photon absorption cross sections from the initial state (i) to the intermediate state (j) and from the intermediate state (j) to the final state ( f ), respectively, and tj is the intermediate state lifetime. tj can be estimated from the uncertainty principle; that is, tj must be short enough to avoid violating energy conservation. Thus, tj ≈ 1/Dv = 1/|vij − v|,
(2)
where ωij and ω are the transition frequency and the incident photon frequency, respectively. For an electronic transition (ωij) in the visible frequency range and assuming that the intermediate state and the final state are close in energy, then tj ≈ 10−15–10−16 sec. The one-photon absorption cross section of a fluorescent molecule is typically σ1 ≈ 10−16–10−17 cm2. Hence, the estimated two-photon absorption cross sections should be 10−49 cm4 sec/photon (Eq. 1), or 10 Göppert-Mayer (GM; 1 GM = 10−50 cm4 sec/photon). This description and estimation of multiphoton excitation for dye molecules needs to be modified in the case of nanocrystals, such as QDs (Efros and Efros 1982; Alivisatos 1996). A strong quantum confinement occurs when the size of the dot is much smaller than the exciton Bohr radius of the bulk material (i.e., the average physical separation between the electron and the hole in a bulk material). Although such an electron–hole pair (called an exciton) is analogous to a hydrogen atom, it should be emphasized that the charge carriers in a QD are bound by the confining potential of the boundary rather than by the Coulomb potential as in the bulk material (Wise 2000). A zeroth-order model for the description of a QD is a single particle confined in an infinite potential well. A desirable effect of the reduced dimension in a QD is the concentration of the density of state into discrete bands. Because light always interacts with one electron–hole pair regardless of the size of the material, the total or integrated absorption does not change. Thus, the concentration of the density of states significantly increases absorption at certain photon energies, at the expense of reduced absorption at other energies. A rough order of magnitude estimation of the absorption enhancement can be obtained by examining the density of states in a QD. There are 104 atoms in a QD of 5-nm radius, resulting in a total integrated number of states of 104. Assuming all these available states are concentrated in a few discrete bands, a QD will have a peak absorption strength of 104 of that of a single atom. Using the Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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estimation obtained above for a dye molecule, the two-photon absorption cross section of a QD will be 105 GM.
MULTIPHOTON EXCITED FLUORESCENCE
For historical reasons, the units for two- and three-photon cross sections are a little confusing. We hope that the following discussion will provide the readers with a practical guide for using the numbers provided above. The calculation for the experimentally detected two-photon excited fluorescence (F in photon/sec) is quite simple if the sample is much thicker than the confocal length of the focused beam. Such a thick sample limit is usually valid in biological imaging with high-numerical-aperture (high-NA) lenses when the confocal lengths are typically on the order of 1 µm. Using the two-photon cross section (σ2) in units of GM, the expression for F can be obtained as F ≈ 1.28fChs2 n0
lP 2 , ft
(3)
where η is the fluorescence quantum efficiency (QE) of the dye, φ is the fluorescence collection efficiency of the measurement system, C (in μM) is the indicator concentration, λ (in μm) is the wavelength of excitation light in a vacuum, n0 is the refractive index of the sample media, P (in milliwatts) is the average incident power, f is the pulse repetition rate, and t is the excitation pulse width (full width at half-maximum). For example, if η × σ2 = 1 GM, C = 100 µM, t = 100 fsec, λ = 1 µm, n0 = 1.3, and a laser power of P = 10 mW at a repetition rate of 100 MHz, then F ≈ φ × 1.66 × 109 photon/sec. Absolute measurement of two- and three-photon cross sections requires detailed characterization of the spatial and temporal profiles of the excitation beam. Details of the measurement method can be found elsewhere (Xu and Webb 1996, 1997). An effective and simple experimental approach is to compare the generated fluorescence of the specimen with some known two- or three-photon references provided that reliable two- or three-photon standards in the wavelength range of interest exist (Kennedy and Lytle 1986; Jones and Callis 1988). (Note that there was an error in the published BisMSB cross section value by Kennedy and Lytle [1986].) We note that the collection efficiencies must be taken into account when comparing the standard with the new indicators. Thus, it is more convenient to compare the indicator with a standard of similar fluorescence emission spectra. For example, for blue-emitting indicators, Cascade Blue (fluorescence peak at 423 nm) may be used as a standard; although for orange-emitting indicators, Rhodamine B (fluorescence peak at 570 nm) is more desirable. When using such a reference method, the ratio of the experimentally measured fluorescence signals becomes (Albota et al. 1998b) kF(t)lcal fcal hcal s2cal Ccal kPcal (t)l2 ncal = , kF(t)lnew fnew hnew s2new Cnew kPnew (t)l2 nnew
(4)
where the subscripts cal and new indicate the parameters for the calibration and the new fluorophore, respectively. The two-photon excitation action cross section of a new molecular fluorophore is then related to known experimental wavelength-dependent parameters including the two-photon excitation action cross section of the calibration standard, as described by s2new (l)hnew =
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fcal hcal s2cal (l)Ccal kPcal (t)l2 kF(t)lnew ncal . fnew Cnew kPnew (t)l2 kF(t)lcal nnew
(5)
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Multiphoton Excitation of Fluorescent Probes
TABLE 1. Two-photon absorption cross section of fluorescein in water (pH = 13) Wavelength (nm)
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16 19 17 19 25 30 34 36 37 37 37 36 32 29 19 13 10 8.0
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691 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860
2PE cross section (GM) 9.0 11 14 16 23 26 23 21 18 16 17 16 13 5.3 3.2 1.0 0.23
2PE, two-photon excitation.
Table 1 lists our measured two-photon cross-sectional values for fluorescein in the wavelength range of 690–1050 nm (Xu and Webb 1996). These values can be used to calibrate the two-photon cross sections of new indicators. Although the values of the two-photon cross section appear small, one should still be aware of the possibility that fluorescence excitation can saturate. Detailed calculation of saturation can be found elsewhere (Xu and Webb 1997). As a practical guide, Rhodamine B will be used as an example. Rhodamine B has a 2PE cross section of 210 GM at 840 nm. With a mode-locked Ti:sapphire laser providing 100-fsec pulses at an 80-MHz repetition rate, the average power for the onset of saturation for Rhodamine B at 840 nm is 8 mW at the specimen assuming a diffraction-limited focus with a 1.3-NA objective lens. Criteria for other indicators and focusing NAs can be extrapolated from this number by using the scaling relationship Saturation power ≈ s2−0.5 (NA)−2 .
(6)
Besides 2PE, another way to image living cells is three-photon excitation (Wokosin et al. 1995; Xu et al. 1996b). Three-photon excited fluorescence provides the unique opportunity to excite intrinsic chromophores (such as amino acids, proteins, and neurotransmitters) using relatively benign excitation wavelengths accessible with commercially available near-IR lasers (Maiti et al. 1997). The combination of two- and three-photon excited fluorescence microscopy extends the useful range of nonlinear laser microscopy. TWO-PHOTON CROSS-SECTIONAL DATA
In this section, we summarize measurements of a variety of dyes, intrinsic molecules, fluorescent proteins, and QDs. The first part of this section will compare the published cross sections and/or the two-photon excitation spectra after 1996. We collected the literature by doing forward citation searches of the papers that we published in cross-sectional measurements. Thus, the literature covered in this section may not include all relevant work. Xanthene dyes (i.e., Rhodamine B, Rhodamine 6G, and fluorescein) are inexpensive, are widely available, and have good photostability and reasonably low toxicity. These dyes are natural candidates for use as calibration standards. The fact that the most reported cross sections are that of xanthene Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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dyes ensures careful examinations by many independent research groups and further enhances the confidence of using them as standards. In addition to our own measurements (Xu and Webb 1996; Albota et al. 1998b), these dyes have also been measured using both fluorescence and nonlinear transmission methods. Kaatz and Shelton measured the two-photon cross section of Rhodamine B, Rhodamine 6G, and fluorescein at 1064 nm by calibrating two-photon fluorescence to hyper-Rayleigh scattering (Kaatz and Shelton 1999). The results for Rhodamine B are in reasonable agreement with previous data, taking into account various factors such as wavelength difference. Measurements of fluorescein cross sections were repeated by Song et al. (1999). The measured value at 800 nm is 1.5 times of what we reported in 1996. A two-photon cross section of Rhodamine 6G has been measured by three other groups at 800 nm, using 2PE fluorescence calibrated against a luminance meter (Kapoor et al. 2003) and using nonlinear transmission methods (Sengupta et al. 2000; Tian and Warren 2002). Although the 2PE method obtained results nearly identical to what we published in 1998, values obtained using the nonlinear transmission methods are consistently lower by about a factor of 2. This discrepancy between the fluorescence method and the nonlinear transmission methods has been discussed in the past (Oulianov et al. 2001). By comparing the excited-state methods (i.e., fluorescence and transient spectroscopy following two-photon excitation) and nonlinear transmission methods, it is found that, although the values obtained by these two excited-state methods are comparable and agree with values obtained by the fluorescence method in the past, they differ considerably from the value obtained using the nonlinear transmission method. The intrinsic fluorescent molecule, flavin mononucleotide (FMN), has also been measured by Blab et al. (2001). The reported value and the spectral shape of FMN are very close to what we reported in 1996. The investigators also reported two-photon action cross sections of fluorescent proteins, including a value of 41 GM for enhanced green fluorescent protein (eGFP). We have measured eGFP using the fluorescence technique and have estimated an action cross-sectional value of 100 GM at 960 nm (Xu and Webb 1997). An alternative measurement, using an FCS method that essentially measures fluorescence per single molecule, gave a two-photon absorption cross section of eGFP at 180 GM (Schwille et al. 1999), which agreed very well with our measurement assuming a QE of 0.6 for eGFP (Patterson et al. 1997). Two-photon absorption of eGFP has also been measured using a combination of a nonlinear transmission method and an absorption saturation. However, the reported value is 600,000 GM at 800 nm (Kirkpatrick et al. 2001). Not only is this value four orders of magnitude larger than the values obtained by the fluorescence method, it is also two orders of magnitude larger than any reported two-photon absorption cross section. We are currently not certain about the origin of this large discrepancy. The importance of fluorescent proteins cannot be overstated. The discovery of green fluorescent protein in the early 1960s catalyzed a new era in biology by enabling investigators to apply molecular cloning methods to fuse a fluorophore moiety to a wide variety of protein and enzyme targets that could be monitored in vivo. There are now multiple mutated forms of the original jellyfish protein with improved functionality available, as well as many new fluorescent proteins from other organisms, such as coral (Tsien 2005; Zacharias and Tsien 2006). Thus, for experiments involving intact tissue or live animals in which multiphoton microscopy has real advantages, measurements of the cross sections of the available fluorescent protein are important. Below we provide a compilation of the majority of the two-photon action cross sections (twophoton absorption cross sections for fluorescein and Rhodamine B) that we have measured over the past decade. The data are presented in four figures starting with a set of conventional dyes and calcium ion indicators (Figs. 1 and 2), action cross sections of 10 commonly used fluorescent proteins (Fig. 3) (for a detailed review of fluorescent proteins, please see Shaner et al. 2005), QDs (Fig. 3D), and, finally, action cross sections of several intrinsic biological molecules found in cells or in the extracellular matrix (Fig. 4). About 70% of the data has been previously presented (Xu and Webb 1996, 1997; Xu et al. 1996a,b; Larson et al. 2003; Zipfel et al. 2003a,b), with the exception of the Alexa dyes (Fig. 1C,E) and several of the fluorescent proteins. The measured cross sections for QDs are ensemble-averaged values, given the uncertainties caused by blinking and/or nonradiant dark fractions (Yao et al. 2005). 254
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FIGURE 1. Two-photon action cross sections of conventional fluorophores used in multiphoton microscopy. (A) Fluorescein (water, pH 11) and Rhodamine B (methanol). (Numbers for fluorescein and Rhodamine B are absorption cross sections calibrated assuming that the one- and two-photon QEs are the same.) (B) Cascade Blue (water) and coumarin 307 (methanol). (C ) DAPI (4′ ,6-diamino-2-phenylindole; measured in water without DNA, values shown are multiplied by 20 to reflect the known QE enhancement from binding), Alexa 350 hydrazide (water), and pyrene (methanol). (D) DiI C-18 (methanol), Lucifer yellow (water), and BODIPY (water); note the logarithmic y-axis for C and D. (E) Alexa 488, 568, and 594 hydrazide (water). Units are GM; 1 GM = 10−50 cm4 sec/photon.
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FIGURE 2. Two-photon action cross sections of calcium indicating dyes. (A) Indo-1 (±Ca in water) and Fura-2 (±Ca in water). Error bars on Fura-2 represent the standard error of the mean of three independent measurements of the action cross-sectional spectra. (B) Calcium bound forms of Fluo-3, Calcium Crimson, Calcium Orange, and Calcium Green1N. Units are GM; 1 GM = 10−50 cm4 sec/photon. Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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FIGURE 3. Two-photon action cross-sectional spectra of fluorescent proteins and QDs. (A) Three variants of green fluorescent protein: eGFP, monomeric enhanced green fluorescent protein (meGFP), and wild-type green fluorescent protein (wtGFP). Error bars for meGFP represent the standard error of the mean for two independent measurements. Concentrations for wtGFP and eGFP were based on measurements of protein concentration; meGFP concentration was measured by fluorescence correlation spectroscopy (FCS) using G(0) of the autocorrelation and a focal volume calibration based on a known concentration of Rhodamine Green. (B) Three blue and cyan fluorescent proteins (CFPs): Sapphire, CFP, and a monomeric form of the cerulean protein. Error bars for CFP and mCerulean represent the standard error of the mean for two independent measurements. Concentrations of CFP and mCerulean were measured by FCS; Sapphire concentration was based on measurement of protein concentration. (C) Four yellow and red fluorescent proteins: monomeric Citrine (mCIT), yellow fluorescent protein (YFP), monomeric Venus, and dsRed. Error bars for mCIT, YFP, and mVenus represent the standard error of the mean for two independent measurements. Concentrations of mCIT, YFP, and mVenus were measured by FCS; dsRed concentration was based on measurement of protein concentration. (D) Two-photon action cross sections of water soluble, high quantum yield (>90%) batch of 535-nm emitting cadmium selenide QDs. The dotted line is the single-photon absorption line shape plotted at double the wavelength for comparison. Error bars represent the standard error of the mean from two independent cross-sectional determinations from the same batch of QDs. The concentration of nanoparticles was determined using FCS. Units are GM; 1 GM = 10−50 cm4 sec/photon.
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FIGURE 4. Two-photon action cross sections for five intrinsic biological compounds. (A) Nicotinamide adenine dinucleotide plus hydrogen (NADH) at pH 7.0 in free and enzyme-bound form. Protein–NADH complexes were prepared by adding excess purified enzyme to free NADH. Measurements of both enzymes free of NADH showed no two-photon generated fluorescence in the 450- to 530-nm range using excitation in the wavelength range shown. Error bars on free NADH represent the standard deviation from four independent measurements. MDH, malate dehydrogenase. AD or ADH, alcohol dehydrogenase. (B) Four intrinsic fluorophores commonly found in cells and tissues measured in phosphate-buffered saline solution (pH 7.0) in free form. As with bound and free NADH, the brightness (QY) of these compounds can vary greatly depending on the environment and the binding. Note: The y-axis is logarithmically scaled; units are GM; 1 GM = 10−50 cm4 sec/photon.
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FIGURE 5. Two-photon action cross sections of eight commercial dyes for long-wavelength multiphoton microscopy. Solid lines are guides for the eye.
Recently, the advantages of longer wavelength multiphoton imaging for deep tissue penetration have been shown. When compared with imaging at the 800-nm region, multiphoton microscopy at 1300 nm can penetrate twice as deep in both ex vivo and in vivo brain tissues (Kobat et al. 2009). In addition, an increased ability to image through blood vessels and a greater ability to suppress endogenous fluorescence background with the 1300-nm excitation are also observed. Combined with the earlier observations that longer excitation wavelengths also reduce tissue photodamage (Chen et al. 2002), multiphoton microscopy at the 1300-nm spectral window is highly promising for in vivo deep tissue imaging. Figure 5 shows the measured two-photon action cross sections of several commercially available fluorophores from 1220 to 1320 nm (Kobat et al. 2009) following the methodology described in Xu and Webb (1996). Two of these fluorophores (Alexa680 and Cy5.5) have two-photon excitation peaks within the measured wavelength range, and their two-photon action cross sections (50–75-GM range) are comparable with those of widely used shorter wavelength excitable dyes such as Rhodamine B and fluorescein (Xu and Webb 1996). We have not included measurements of some of the synthesized large cross-sectional molecules (e.g., Albota et al. 1998a) because these dyes have not yet found many actual uses in biological imaging because of their highly lipophilic nature and toxicity. These compounds, however, have cross sections an order of magnitude higher than the conventional dyes and indicators in use today and suggest that two-photon imaging could be further improved by the rational design of fluorophores specifically for nonlinear excitation. In addition, there are currently only a handful of fluorescent indicators for multiphoton microscopy at the longer-wavelength window of 1300 nm. Significant future effort is required for developing longer-wavelength dyes and fluorescent proteins. REFERENCES Albota M, Beljonne D, Bredas JL, Ehrlich JE, Fu JY, Heikal AA, Hess SE, Kogej T, Levin MD, Marder SR, et al. 1998a. Design of organic molecules with large two-photon absorption cross sections. Science 281: 1653–1656. Albota MA, Xu C, Webb WW. 1998b. Two-photon excitation cross sections of biomolecular probes from 690 to 980 nm. Appl Opt 37: 7352–7356. Alivisatos 1996. Semiconductor clusters, nanocrystals, and quantum dots. Science 271: 933–937.
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Topic Introduction
Multiphoton Excitation of Fluorescent Probes Chris Xu and Warren R. Zipfel
This introduction reviews the multiphoton excitation cross sections of extrinsic and intrinsic fluorophores, genetically engineered probes, and nanoparticles. We will review the known two-photon excitation cross sections of biological indicators and will discuss several related issues such as how to theoretically estimate and experimentally gauge the two-photon cross section of an indicator. We provide practical guides for experimentally estimating the excitation cross section.
INTRODUCTION
The fluorescence excitation or action cross section is a basic parameter in fluorescence imaging. The action cross section is a combined measure of how strongly a molecule absorbs at a particular excitation wavelength and of how efficiently the fluorophore converts the absorbed light into emitted fluorescence (i.e., the quantum yield). For conventional one-photon imaging, the onephoton absorption cross sections are well documented for a wide range of molecules, as are fluorescence quantum yields. However, significantly less is known about two-photon cross sections of biologically useful fluorophores. Furthermore, it is often difficult to predict multiphoton excitation spectra, especially two-photon spectra, from the one-photon data because of differences in the selection rules and the effects of vibronic coupling. Before the 1990s, two-photon excitation cross-sectional measurements were almost always performed at 694 nm (ruby laser) and 1064 nm (Nd:glass laser) on laser dyes (Smith 1986). Less effort was devoted to accurate quantitative studies of common fluorophores widely used in multiphoton microscopy. In addition, substantial disagreement (sometimes more than one order of magnitude) between published values of two-photon cross sections often exists. The lack of knowledge about two-photon excitation cross sections and spectra for common fluorophores used in biological studies has been a significant obstacle in the use of two-photon laser scanning microscopy. The emergence of the mode-locked solid-state femtosecond lasers, most commonly the Ti:sapphire lasers (Spence et al. 1991; Curley et al. 1992), have greatly facilitated the measurement of a multiphoton excitation cross section. When compared with earlier ultrafast lasers (e.g., ultrafast dye lasers), the Ti:sapphire lasers are highly robust and are widely tunable, making femtosecond pulses from 690 to 1050 nm easily accessible. A large number of fluorescent indicators, intrinsic fluorescent molecules, genetically engineered probes, and some nanoparticles (e.g., quantum dots [QDs]) have since been measured. New measurement techniques have also been developed to further improve the absolute accuracy. This review on multiphoton excitation cross sections is motivated by the application of multiphoton microscopy as a powerful tool for three-dimensionally resolved fluorescence imaging of biological samples (Denk et al. 1990; Xu et al. 1996a,b; So et al. 2000; Masters 2003; Zipfel et al. 2003a,b; Masters
Adapted from Imaging: A Laboratory Manual (ed. Yuste). CSHL Press, Cold Spring Harbor, NY, USA, 2011. © 2015 Cold Spring Harbor Laboratory Press Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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and So 2004; Helmchen and Denk 2005). We will review the known two-photon excitation (2PE) cross sections of biological indicators and will discuss several related issues such as how to experimentally gauge the two-photon cross section of an indicator. An effort is made to compare crosssectional values obtained from various research groups in the last 10 years or so. Although we will concentrate on 2PE, three-photon excitation will also be discussed briefly. The remainder of this introduction is divided into three sections. First, we provide simple estimates of multiphoton excitations of dyes and QDs from theory. Second is the methods section, which includes practical guides for experimentally estimating the excitation cross section. The third section is a compilation of twophoton excitation cross sections of extrinsic and intrinsic fluorophores, genetically engineered probes, and nanoparticles. ESTIMATION OF MULTIPHOTON EXCITATION CROSS SECTIONS
The essence of the theory of multiphoton processes can be represented in perturbation theory. Details of the rigorous derivation can be found elsewhere (Faisal 1987). Here, for the purpose of order of magnitude estimation, a greatly simplified approach is used to describe the multiphoton excitation processes, and only the lowest-order dipole transition will be considered. The single intermediate state approximation (Birge 1983) can be used to give an order of magnitude estimation. The two-photon absorption cross section (σ2) can be obtained as s2 = sij sif tj ,
(1)
where σij and σif represent the one-photon absorption cross sections from the initial state (i) to the intermediate state (j) and from the intermediate state (j) to the final state ( f ), respectively, and tj is the intermediate state lifetime. tj can be estimated from the uncertainty principle; that is, tj must be short enough to avoid violating energy conservation. Thus, tj ≈ 1/Dv = 1/|vij − v|,
(2)
where ωij and ω are the transition frequency and the incident photon frequency, respectively. For an electronic transition (ωij) in the visible frequency range and assuming that the intermediate state and the final state are close in energy, then tj ≈ 10−15–10−16 sec. The one-photon absorption cross section of a fluorescent molecule is typically σ1 ≈ 10−16–10−17 cm2. Hence, the estimated two-photon absorption cross sections should be 10−49 cm4 sec/photon (Eq. 1), or 10 Göppert-Mayer (GM; 1 GM = 10−50 cm4 sec/photon). This description and estimation of multiphoton excitation for dye molecules needs to be modified in the case of nanocrystals, such as QDs (Efros and Efros 1982; Alivisatos 1996). A strong quantum confinement occurs when the size of the dot is much smaller than the exciton Bohr radius of the bulk material (i.e., the average physical separation between the electron and the hole in a bulk material). Although such an electron–hole pair (called an exciton) is analogous to a hydrogen atom, it should be emphasized that the charge carriers in a QD are bound by the confining potential of the boundary rather than by the Coulomb potential as in the bulk material (Wise 2000). A zeroth-order model for the description of a QD is a single particle confined in an infinite potential well. A desirable effect of the reduced dimension in a QD is the concentration of the density of state into discrete bands. Because light always interacts with one electron–hole pair regardless of the size of the material, the total or integrated absorption does not change. Thus, the concentration of the density of states significantly increases absorption at certain photon energies, at the expense of reduced absorption at other energies. A rough order of magnitude estimation of the absorption enhancement can be obtained by examining the density of states in a QD. There are 104 atoms in a QD of 5-nm radius, resulting in a total integrated number of states of 104. Assuming all these available states are concentrated in a few discrete bands, a QD will have a peak absorption strength of 104 of that of a single atom. Using the Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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estimation obtained above for a dye molecule, the two-photon absorption cross section of a QD will be 105 GM.
MULTIPHOTON EXCITED FLUORESCENCE
For historical reasons, the units for two- and three-photon cross sections are a little confusing. We hope that the following discussion will provide the readers with a practical guide for using the numbers provided above. The calculation for the experimentally detected two-photon excited fluorescence (F in photon/sec) is quite simple if the sample is much thicker than the confocal length of the focused beam. Such a thick sample limit is usually valid in biological imaging with high-numerical-aperture (high-NA) lenses when the confocal lengths are typically on the order of 1 µm. Using the two-photon cross section (σ2) in units of GM, the expression for F can be obtained as F ≈ 1.28fChs2 n0
lP 2 , ft
(3)
where η is the fluorescence quantum efficiency (QE) of the dye, φ is the fluorescence collection efficiency of the measurement system, C (in μM) is the indicator concentration, λ (in μm) is the wavelength of excitation light in a vacuum, n0 is the refractive index of the sample media, P (in milliwatts) is the average incident power, f is the pulse repetition rate, and t is the excitation pulse width (full width at half-maximum). For example, if η × σ2 = 1 GM, C = 100 µM, t = 100 fsec, λ = 1 µm, n0 = 1.3, and a laser power of P = 10 mW at a repetition rate of 100 MHz, then F ≈ φ × 1.66 × 109 photon/sec. Absolute measurement of two- and three-photon cross sections requires detailed characterization of the spatial and temporal profiles of the excitation beam. Details of the measurement method can be found elsewhere (Xu and Webb 1996, 1997). An effective and simple experimental approach is to compare the generated fluorescence of the specimen with some known two- or three-photon references provided that reliable two- or three-photon standards in the wavelength range of interest exist (Kennedy and Lytle 1986; Jones and Callis 1988). (Note that there was an error in the published BisMSB cross section value by Kennedy and Lytle [1986].) We note that the collection efficiencies must be taken into account when comparing the standard with the new indicators. Thus, it is more convenient to compare the indicator with a standard of similar fluorescence emission spectra. For example, for blue-emitting indicators, Cascade Blue (fluorescence peak at 423 nm) may be used as a standard; although for orange-emitting indicators, Rhodamine B (fluorescence peak at 570 nm) is more desirable. When using such a reference method, the ratio of the experimentally measured fluorescence signals becomes (Albota et al. 1998b) kF(t)lcal fcal hcal s2cal Ccal kPcal (t)l2 ncal = , kF(t)lnew fnew hnew s2new Cnew kPnew (t)l2 nnew
(4)
where the subscripts cal and new indicate the parameters for the calibration and the new fluorophore, respectively. The two-photon excitation action cross section of a new molecular fluorophore is then related to known experimental wavelength-dependent parameters including the two-photon excitation action cross section of the calibration standard, as described by s2new (l)hnew =
252
fcal hcal s2cal (l)Ccal kPcal (t)l2 kF(t)lnew ncal . fnew Cnew kPnew (t)l2 kF(t)lcal nnew
(5)
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Multiphoton Excitation of Fluorescent Probes
TABLE 1. Two-photon absorption cross section of fluorescein in water (pH = 13) Wavelength (nm)
2PE cross section (GM)
Wavelength (nm)
16 19 17 19 25 30 34 36 37 37 37 36 32 29 19 13 10 8.0
870 880 890 900 910 920 930 940 950 960 970 980 992 1008 1020 1034 1049
691 700 710 720 730 740 750 760 770 780 790 800 810 820 830 840 850 860
2PE cross section (GM) 9.0 11 14 16 23 26 23 21 18 16 17 16 13 5.3 3.2 1.0 0.23
2PE, two-photon excitation.
Table 1 lists our measured two-photon cross-sectional values for fluorescein in the wavelength range of 690–1050 nm (Xu and Webb 1996). These values can be used to calibrate the two-photon cross sections of new indicators. Although the values of the two-photon cross section appear small, one should still be aware of the possibility that fluorescence excitation can saturate. Detailed calculation of saturation can be found elsewhere (Xu and Webb 1997). As a practical guide, Rhodamine B will be used as an example. Rhodamine B has a 2PE cross section of 210 GM at 840 nm. With a mode-locked Ti:sapphire laser providing 100-fsec pulses at an 80-MHz repetition rate, the average power for the onset of saturation for Rhodamine B at 840 nm is 8 mW at the specimen assuming a diffraction-limited focus with a 1.3-NA objective lens. Criteria for other indicators and focusing NAs can be extrapolated from this number by using the scaling relationship Saturation power ≈ s2−0.5 (NA)−2 .
(6)
Besides 2PE, another way to image living cells is three-photon excitation (Wokosin et al. 1995; Xu et al. 1996b). Three-photon excited fluorescence provides the unique opportunity to excite intrinsic chromophores (such as amino acids, proteins, and neurotransmitters) using relatively benign excitation wavelengths accessible with commercially available near-IR lasers (Maiti et al. 1997). The combination of two- and three-photon excited fluorescence microscopy extends the useful range of nonlinear laser microscopy. TWO-PHOTON CROSS-SECTIONAL DATA
In this section, we summarize measurements of a variety of dyes, intrinsic molecules, fluorescent proteins, and QDs. The first part of this section will compare the published cross sections and/or the two-photon excitation spectra after 1996. We collected the literature by doing forward citation searches of the papers that we published in cross-sectional measurements. Thus, the literature covered in this section may not include all relevant work. Xanthene dyes (i.e., Rhodamine B, Rhodamine 6G, and fluorescein) are inexpensive, are widely available, and have good photostability and reasonably low toxicity. These dyes are natural candidates for use as calibration standards. The fact that the most reported cross sections are that of xanthene Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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dyes ensures careful examinations by many independent research groups and further enhances the confidence of using them as standards. In addition to our own measurements (Xu and Webb 1996; Albota et al. 1998b), these dyes have also been measured using both fluorescence and nonlinear transmission methods. Kaatz and Shelton measured the two-photon cross section of Rhodamine B, Rhodamine 6G, and fluorescein at 1064 nm by calibrating two-photon fluorescence to hyper-Rayleigh scattering (Kaatz and Shelton 1999). The results for Rhodamine B are in reasonable agreement with previous data, taking into account various factors such as wavelength difference. Measurements of fluorescein cross sections were repeated by Song et al. (1999). The measured value at 800 nm is 1.5 times of what we reported in 1996. A two-photon cross section of Rhodamine 6G has been measured by three other groups at 800 nm, using 2PE fluorescence calibrated against a luminance meter (Kapoor et al. 2003) and using nonlinear transmission methods (Sengupta et al. 2000; Tian and Warren 2002). Although the 2PE method obtained results nearly identical to what we published in 1998, values obtained using the nonlinear transmission methods are consistently lower by about a factor of 2. This discrepancy between the fluorescence method and the nonlinear transmission methods has been discussed in the past (Oulianov et al. 2001). By comparing the excited-state methods (i.e., fluorescence and transient spectroscopy following two-photon excitation) and nonlinear transmission methods, it is found that, although the values obtained by these two excited-state methods are comparable and agree with values obtained by the fluorescence method in the past, they differ considerably from the value obtained using the nonlinear transmission method. The intrinsic fluorescent molecule, flavin mononucleotide (FMN), has also been measured by Blab et al. (2001). The reported value and the spectral shape of FMN are very close to what we reported in 1996. The investigators also reported two-photon action cross sections of fluorescent proteins, including a value of 41 GM for enhanced green fluorescent protein (eGFP). We have measured eGFP using the fluorescence technique and have estimated an action cross-sectional value of 100 GM at 960 nm (Xu and Webb 1997). An alternative measurement, using an FCS method that essentially measures fluorescence per single molecule, gave a two-photon absorption cross section of eGFP at 180 GM (Schwille et al. 1999), which agreed very well with our measurement assuming a QE of 0.6 for eGFP (Patterson et al. 1997). Two-photon absorption of eGFP has also been measured using a combination of a nonlinear transmission method and an absorption saturation. However, the reported value is 600,000 GM at 800 nm (Kirkpatrick et al. 2001). Not only is this value four orders of magnitude larger than the values obtained by the fluorescence method, it is also two orders of magnitude larger than any reported two-photon absorption cross section. We are currently not certain about the origin of this large discrepancy. The importance of fluorescent proteins cannot be overstated. The discovery of green fluorescent protein in the early 1960s catalyzed a new era in biology by enabling investigators to apply molecular cloning methods to fuse a fluorophore moiety to a wide variety of protein and enzyme targets that could be monitored in vivo. There are now multiple mutated forms of the original jellyfish protein with improved functionality available, as well as many new fluorescent proteins from other organisms, such as coral (Tsien 2005; Zacharias and Tsien 2006). Thus, for experiments involving intact tissue or live animals in which multiphoton microscopy has real advantages, measurements of the cross sections of the available fluorescent protein are important. Below we provide a compilation of the majority of the two-photon action cross sections (twophoton absorption cross sections for fluorescein and Rhodamine B) that we have measured over the past decade. The data are presented in four figures starting with a set of conventional dyes and calcium ion indicators (Figs. 1 and 2), action cross sections of 10 commonly used fluorescent proteins (Fig. 3) (for a detailed review of fluorescent proteins, please see Shaner et al. 2005), QDs (Fig. 3D), and, finally, action cross sections of several intrinsic biological molecules found in cells or in the extracellular matrix (Fig. 4). About 70% of the data has been previously presented (Xu and Webb 1996, 1997; Xu et al. 1996a,b; Larson et al. 2003; Zipfel et al. 2003a,b), with the exception of the Alexa dyes (Fig. 1C,E) and several of the fluorescent proteins. The measured cross sections for QDs are ensemble-averaged values, given the uncertainties caused by blinking and/or nonradiant dark fractions (Yao et al. 2005). 254
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B
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FIGURE 1. Two-photon action cross sections of conventional fluorophores used in multiphoton microscopy. (A) Fluorescein (water, pH 11) and Rhodamine B (methanol). (Numbers for fluorescein and Rhodamine B are absorption cross sections calibrated assuming that the one- and two-photon QEs are the same.) (B) Cascade Blue (water) and coumarin 307 (methanol). (C ) DAPI (4′ ,6-diamino-2-phenylindole; measured in water without DNA, values shown are multiplied by 20 to reflect the known QE enhancement from binding), Alexa 350 hydrazide (water), and pyrene (methanol). (D) DiI C-18 (methanol), Lucifer yellow (water), and BODIPY (water); note the logarithmic y-axis for C and D. (E) Alexa 488, 568, and 594 hydrazide (water). Units are GM; 1 GM = 10−50 cm4 sec/photon.
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FIGURE 2. Two-photon action cross sections of calcium indicating dyes. (A) Indo-1 (±Ca in water) and Fura-2 (±Ca in water). Error bars on Fura-2 represent the standard error of the mean of three independent measurements of the action cross-sectional spectra. (B) Calcium bound forms of Fluo-3, Calcium Crimson, Calcium Orange, and Calcium Green1N. Units are GM; 1 GM = 10−50 cm4 sec/photon. Cite this introduction as Cold Spring Harb Protoc; doi:10.1101/pdb.top086116
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FIGURE 3. Two-photon action cross-sectional spectra of fluorescent proteins and QDs. (A) Three variants of green fluorescent protein: eGFP, monomeric enhanced green fluorescent protein (meGFP), and wild-type green fluorescent protein (wtGFP). Error bars for meGFP represent the standard error of the mean for two independent measurements. Concentrations for wtGFP and eGFP were based on measurements of protein concentration; meGFP concentration was measured by fluorescence correlation spectroscopy (FCS) using G(0) of the autocorrelation and a focal volume calibration based on a known concentration of Rhodamine Green. (B) Three blue and cyan fluorescent proteins (CFPs): Sapphire, CFP, and a monomeric form of the cerulean protein. Error bars for CFP and mCerulean represent the standard error of the mean for two independent measurements. Concentrations of CFP and mCerulean were measured by FCS; Sapphire concentration was based on measurement of protein concentration. (C) Four yellow and red fluorescent proteins: monomeric Citrine (mCIT), yellow fluorescent protein (YFP), monomeric Venus, and dsRed. Error bars for mCIT, YFP, and mVenus represent the standard error of the mean for two independent measurements. Concentrations of mCIT, YFP, and mVenus were measured by FCS; dsRed concentration was based on measurement of protein concentration. (D) Two-photon action cross sections of water soluble, high quantum yield (>90%) batch of 535-nm emitting cadmium selenide QDs. The dotted line is the single-photon absorption line shape plotted at double the wavelength for comparison. Error bars represent the standard error of the mean from two independent cross-sectional determinations from the same batch of QDs. The concentration of nanoparticles was determined using FCS. Units are GM; 1 GM = 10−50 cm4 sec/photon.
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FIGURE 4. Two-photon action cross sections for five intrinsic biological compounds. (A) Nicotinamide adenine dinucleotide plus hydrogen (NADH) at pH 7.0 in free and enzyme-bound form. Protein–NADH complexes were prepared by adding excess purified enzyme to free NADH. Measurements of both enzymes free of NADH showed no two-photon generated fluorescence in the 450- to 530-nm range using excitation in the wavelength range shown. Error bars on free NADH represent the standard deviation from four independent measurements. MDH, malate dehydrogenase. AD or ADH, alcohol dehydrogenase. (B) Four intrinsic fluorophores commonly found in cells and tissues measured in phosphate-buffered saline solution (pH 7.0) in free form. As with bound and free NADH, the brightness (QY) of these compounds can vary greatly depending on the environment and the binding. Note: The y-axis is logarithmically scaled; units are GM; 1 GM = 10−50 cm4 sec/photon.
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Wavelength (nm)
FIGURE 5. Two-photon action cross sections of eight commercial dyes for long-wavelength multiphoton microscopy. Solid lines are guides for the eye.
Recently, the advantages of longer wavelength multiphoton imaging for deep tissue penetration have been shown. When compared with imaging at the 800-nm region, multiphoton microscopy at 1300 nm can penetrate twice as deep in both ex vivo and in vivo brain tissues (Kobat et al. 2009). In addition, an increased ability to image through blood vessels and a greater ability to suppress endogenous fluorescence background with the 1300-nm excitation are also observed. Combined with the earlier observations that longer excitation wavelengths also reduce tissue photodamage (Chen et al. 2002), multiphoton microscopy at the 1300-nm spectral window is highly promising for in vivo deep tissue imaging. Figure 5 shows the measured two-photon action cross sections of several commercially available fluorophores from 1220 to 1320 nm (Kobat et al. 2009) following the methodology described in Xu and Webb (1996). Two of these fluorophores (Alexa680 and Cy5.5) have two-photon excitation peaks within the measured wavelength range, and their two-photon action cross sections (50–75-GM range) are comparable with those of widely used shorter wavelength excitable dyes such as Rhodamine B and fluorescein (Xu and Webb 1996). We have not included measurements of some of the synthesized large cross-sectional molecules (e.g., Albota et al. 1998a) because these dyes have not yet found many actual uses in biological imaging because of their highly lipophilic nature and toxicity. These compounds, however, have cross sections an order of magnitude higher than the conventional dyes and indicators in use today and suggest that two-photon imaging could be further improved by the rational design of fluorophores specifically for nonlinear excitation. In addition, there are currently only a handful of fluorescent indicators for multiphoton microscopy at the longer-wavelength window of 1300 nm. Significant future effort is required for developing longer-wavelength dyes and fluorescent proteins. REFERENCES Albota M, Beljonne D, Bredas JL, Ehrlich JE, Fu JY, Heikal AA, Hess SE, Kogej T, Levin MD, Marder SR, et al. 1998a. Design of organic molecules with large two-photon absorption cross sections. Science 281: 1653–1656. Albota MA, Xu C, Webb WW. 1998b. Two-photon excitation cross sections of biomolecular probes from 690 to 980 nm. Appl Opt 37: 7352–7356. Alivisatos 1996. Semiconductor clusters, nanocrystals, and quantum dots. Science 271: 933–937.
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