3.1.1.

Imaging

Point spread function (PSF) measurements are referred to a planachromatic Nikon 100×, 1.4 NA immersion oil objective with enhanced transmission in the infrared region. Blue fluorescent carboxylate modified microspheres 0.1 μm diameter (F-8797, Molecular Probes, OR) were used. A drop of dilute samples of bead suspensions was spread between two coverslips of nominal thickness 0.17 mm. These microspheres constitute a very good compromise toward the utilization of subresolution point scatterers and acceptable fluorescence emission. An object plane field of 18 μm×18 μm was imaged in a 512×512 frame, at a pixel dwell time of 17 μs. Axial scanning was performed and 21 optical consecutive and parallel slices have been collected at steps of 100 nm. The x–y scan step was 35 nm. The scanning head pinhole was set to open position. The 3D data sets of several specimens were analyzed. The measured full width at half maximum (FWHM) lateral and axial resolutions were 210±40 and 700±50 nm, respectively.¹⁰ In order to be sure of operating in the TPE regime the quadratic behavior of the fluorescence intensity versus excitation power was also demonstrated. Another interesting issue is given by the demonstration of the localized photobleaching as compared with the single-photon confocal case. Large fluorescent microspheres (i.e., 22 μm diameter) can be used in a three-dimensional acquisition session. Figure 3(a) shows a three-dimensional selective photobleaching in the case of one-photon confocal (left side) and two-photon (right side) imaging modes. Photobleaching has been produced performing a zoom on a 1.96 μm² squared area appreciatively in the center plane of the microsphere. Then three-dimensional imaging has been performed using confocal and TPE mode. The resulting images are intended only for qualitative comparison and the selective bleaching can be useful to have a better feeling with respect to the power commonly used. From Figure 3(a), in the case of confocal imaging it is possible to see a double-cone-like image according to imaging conditions occurring in confocal microscopy^{4 3 65 5} produced within the bead while in the TPE case the dark volume is extremely localized,^{29 33 66 67} demonstrating the main difference between these two three-dimensional imaging methods: it must be remembered that in confocal imaging, even though out of focus fluorescence is not detected, it is generated. Figure 3(b) shows a writing application of the TPE microscope. Figure 4 shows a TPE image of Saccharomices cerevisiae cells marked with DAPI. This image conjugates the autofluorescence of the sample with the DAPI–DNA fluorescence coming from the nucleus. In this figure imaging is coupled to active actions like the removal of cell layers increasing the power of the beam and residence time.

Figure 3

(a) Three-dimensional x–z projections of induced photobleaching within a large fluorescent sphere made in single-photon confocal (left) and TPE (right) mode. In confocal mode 488 nm laser beam has been used both for photobleaching and imaging keeping the pinhole at its smallest size. In TPE, 720 nm excitation wavelength has been used, at 10 mW average power. In both cases 3 μs dwell time has been used for bleaching and for imaging and a 0.5 μm axial step has been performed producing 128 optical slices. (b) Localized photobleaching used for writing in the central plane of a 22 μm sphere the characters INFM, as shown in the x–y and x–z views.

Figure 4

Three-dimensional images ( x–y central, x–z bottom, y–z lateral views) of layers of Saccharomyces cerevisiae cells obtained in TPE mode exploiting autofluorescence. Some layers of the intact sample (left) have been destroyed (right) using localized two-photon absorption.

3.1.2.

Spectroscopy

Here, the excitation volume is measured from the diffusion of yellow–green fluorescent latex microspheres of diameter 64±9 nm (Polysciences, Fluoresbrite YG, Cat. No. 17149) suspended in de-ionized and filtered (0.22 μm, Millipore filter) water. It is essential that the concentration obtained by dilution from the mother solution (corresponding to ≅400 nM), is determined by light absorption after filtering with a 0.22 μm Millipore filter. The absorbance has been measured by getting rid of the scattering contribution. All the measurements reported hereafter have been performed at room temperature. The fluorescence correlation function g_F(t)=〈δF(t)δF(0)〉/〈F(0)〉² for two photon excitation involves the numerical computation of a one-dimension integral,⁶⁸ however it can be accurately described by a simpler form of the type

Figure 5

Simulation of the autocorrelation function for two-photon excitation for a beam waist w₀=0.5 μm, λ _exc =770 nm, and diffusion coefficient D=1 μm ²/s, according to the numerical expression reported by Berland et al.; (see Ref. 68). A Gaussian error (0.3) has been added to the simulated data. The solid line represents the best fit to Eq. (1) and residues of the fit are shown in the lower panel. Inset: Best fit relaxation time obtained from the fit of the simulated autocorrelation function for two-photon excitation for different diffusion times to Eq. (1). The diffusion time is computed as τ_D=w₀ ²/(8D). The linear best fit curve corresponds to a slope=1.15±0.02.

As an example of the analysis of the FCS measurements, we show results taken at various the excitation powers in the range 1.3<P<7 mW (at the entrance of the objective). The best fit parameters, g_F(0) and τ are reported in the upper panel of Figure 6. The behavior of g_F(0) in Figure 6 is due to the increasing effect of the uncorrelated background b_g with decreasing powers and can be accounted for by the relation¹⁶ g_F(0)=(κ/V _EXC 〈C〉)(〈F〉−b_g)²/〈F〉², where the dependence on the power P is in the total fluorescence rate 〈F〉 which scales as P², and in the background b_g, which scales as P. The average fluorescence rate 〈F〉 is a measured quantity and the background level is fit to a trend of the type, b_g=b_g0+βP. The best-fit curve is shown in the upper panel of Figure 6 and corresponds to g₀=0.29±0.008, b_g0=135±10, and β≅0.1 Hz/mW. The measured relaxation time does not vary appreciably and is constant τ=3.1±0.3 ms. From this value we can give a first estimate of the laser beam waist w₀ by exploiting the relation τ=αw₀ ²/(8D) with α≅1.15. The diffusion coefficient of the microspheres D=7.45 μm ²/s is computed according to their nominal radius R=32 nm, at T=25 °C and by employing this value we find V _EXC =πw₀ ⁴/λ=0.11±0.04 fL. On the other hand, from the g₀=0.29±0.008 value and 〈C〉≅4 nM we can compute V _EXC =κ/(g₀〈C〉)=0.11±0.005 fL, in very good agreement with the estimate obtained from the relaxation time.

Figure 6

(Lower panel) Fluorescence rate vs the excitation power at the entrance of the microscope. The solid line is a square law fit: B+A(power)^ν. The background is B=100±40 Hz and the exponent is ν=2.06±0.07. (Upper panel): Best fit parameters of the correlation functions according to Eq. (6). The solid squares (left axis) indicate the g_F(0) and the open circles (right axis) the relaxation times, τ. The solid line is the best fit of the g_F(0) to the function g_F(0)=g₀(〈F〉b_g)²/〈F〉², where 〈F〉 is the average fluorescence rate and b_g is the background rate which is assumed to depend linearly on the excitation power: b_g=b_g0+βP. The best fit values are g₀=0.29±0.008, b_g=135±10 Hz, and β=0.1. The dashed line indicates the average value of the relaxation time 〈τ〉=3.1 ms.

A further important test of the two-photon setup for spectroscopy applications is the study of the dependence of the excitation volume on the beam diameter at the entrance pupil of the objective. We give an example of such an analysis in Figure 7, where a power law fit to the data is reported as a solid line on the data of the excitation volumes obtained with the analysis reported in the previous section at various values of the beam expansion. We can write⁵⁷ the relation between V _EXC and the beam expansion N as V _EXC =πλ³(0.61/nN)⁴((f/Ф₀)²+N²)². If the ratio f/Ф₀≫N _max =3, the previous equation becomes

Figure 7

Measurements of the excitation volume vs the beam expansion as measured from the analysis of the autocorrelation functions and the photon counting histograms. The solid line is a power law fit. The best fit exponent is −3.9±0.3 (see also the text).

How robust are these methods for the determination of the excitation volume? Undesired aggregation can affect both methods since we are basically counting the number of independent fluorescence entities. Even after extensive filtering of the samples one finds a small fraction of aggregates, which however could be easily picked out of the averages. This is shown for example in Figure 8, where we plot the PCH computed on a single 1.6 s trace in which one observes a huge fluorescence peak (see inset) and from which a double peaked histogram is computed (see filled squares in Figure 8). In the same plot, for comparison, we report the PCH computed on a second 1.6 s trace where no huge peaks are detected and the histograms are of the same type as those analyzed in the previous paragraphs. The anomalous behavior shown in Figure 8 is very likely due to the passage of aggregates through the excitation volume. Such events, however, are very rare indicating that the number of aggregates is rather low and the measurements affected by aggregates can be singled out by looking at the average rate of each measurement.

Figure 8

Distribution of photon counts for a C=1.2 nM solutions of microspheres collected for 20 kHz of sampling frequency corresponding to 50 μs of sampling time. Open circles refers to the histogram computed on a trace where no evidence of aggregates is found (lower line of the inset) and filled squares refer to the histogram of a trace where large ones are find (higher line of the inset).

A second and more critical experimental issue that can be attacked by looking at the fluorescence fluctuations, is whether the laser beam at the object plane is well shaped, i.e., it follows a Gaussian–Lorentzian shape. We have to this purpose performed a series of measurements versus the sample concentration in a case when approximately half of the laser beam cross section (which was expanded three times) was blocked at the entrance of the microscope by a misplaced diaphragm. The analysis of the auto correlation functions (ACFs) gives reasonable results although the residuals always indicate the presence of a second fast component that was more evident at higher sample concentrations (data not shown). If we force fit the ACFs to Eq. (1), the dependence of the g_F(0) and the relaxation time τ upon the concentration is in reasonable agreement with the expected laws, i.e., g_F(0) decreases with the concentration and τ is approximately constant (data not shown). However the estimate of the excitation volume from these two data sets disagree significantly, since V _EXC =0.5±0.05 fL, from the g_F(0) analysis, and V _EXC =0.26±0.05 fL from the relaxation time. These values are sensibly larger than the result found when no perturbation of the laser cross section was present, V _EXC ≅0.1 fL. It must be noted that beside the larger value of the excitation volume, the expectations of the theoretical trends of the best fit parameters are not fulfilled when the beam cross section is perturbed.

3.1.3.

Two-Photon Lifetime Decays

A single component model can satisfactorily analyze the lifetime decays for the Rhodamine 6G (Fluka Chemika, Cat. No. 83698) solutions to give a lifetime τ_F=3.95±0.2 ns. The two quantities measured are the phase shifts and the demodulation ratios at the harmonics of the laser repetition frequency ≅80 MHz. These data were fit versus the frequency by a two-exponential decay scheme using the GLOBALS UNLIMITED software,⁶⁹ in order to obtain the fluorescence lifetimes of the fluorophore. We can also show as an example of protein studies, the fluorescence decay of the Alexa dye (succymidil-esther derivative by Molecular Probes) bound to the Beta-lactoglobulin B (Sigma Chemical Co., Cat. no. L-8005, Lot. No. 13H7150) where a double exponential decay is found. The main decay component corresponds to a lifetime τ_F=3.4±0.4 ns, and there is a tiny amount (<1) of a faster decay (≅0.4 ns).

3.1.4.

Microscope Polarization Response and Fluorescence Polarization Anisotropy

Two anisotropy components are often needed to satisfactorily interpret the differential phase shifts and polarized demodulation ratios. We ascribe these decays to the same fluorophore according to the time domain form:

In order to measure the fluorescence polarization anisotropy (FPA) it is essential to correctly measure the components of the fluorescence intensity with polarization directions parallel I_∥ and perpendicular I_⊥ to the direction of the polarization of the excitation light. Therefore the microscope transmission function for the light with different polarizations must be measured.

In the FPA experiments the exciting light coming from the laser is polarized in the plane determined by the direction of the light entering the microscope from the epifluorescence port and the vertical direction. The reflections on the microscope optical components (dichroic beam splitters, mirrors) and the polarization of the excitation light are always in this plane. The fluorescence light from the sample, instead, is partially depolarized and the polarization direction of the fluorescence collected by the photomutiplier can be selected by a Glan–Thompson polarizer. We indicate by two subscripts the polarization of the excited light and the position of the emission polarizer, respectively, measured by the detector. For example, I _VH corresponds to vertical polarized excitation light and horizontal position of the emission polarizer. We disregard for the moment the finite size of the excitation volume in which we assume that the polarization of the light is homogenous. For vertically polarized excitation light the observed fluorescence intensities are

As an example on our setup, the measurements on Rhodamine 6G solutions in 60 Glycerol/water give in the range 80–800 MHz a nearly constant value, G=0.864±0.003 and this has been used to correct all the anisotropy measurements reported here.

We have tested the characterization of the response of the microscope to the light polarization by measuring the FPA decay on protein (Beta-lactoglobulin B) solutions at high dilution corresponding to the limit of ≅1 molecule per excitation volume or less.

We have performed measurements of the fluctuation of the fluorescence, i.e., FCS, and of FPA. The analysis of the fluorescence ACFs provide us directly with the average number of molecules per excitation volume ≅κ/g_F(0) that is in the range 0.4–17 (see inset of Figure 9). The average relaxation time τ=210±20 μs corresponds to a diffusion coefficient D_T≅1.15w₀ ²/8τ=100±10 μm ²/s.

Figure 9

Result of the analysis of FCS measurements on Beta-lactoglobulin B solutions vs the protein concentration. Upper panel reports the relaxation time, τ. Lower panel shows the zero lag time ACF, g_F(0), together with a fit to Eq. (1) with B≅0. The inset in the lower panel reports the average number of molecules per excitation volume for each concentration.

The FPA measurements on the same solutions are shown in Figure 10 together with the best-fit functions according to the two-component model described by Eq. (3). The rotational time, τ _ROT =9±1.5 ns, corresponds to a rotational diffusion coefficient D _ROT =18±3 MHz. The implicit assumption that we have done on the origin of fast relaxation time τ_W is supported by its value (averaged for C>100 nM ) τ_W=400±40 ps, which could not correspond to the rotational relaxation time of the free dye. In fact, this should be ≅200 ps in water, according to its molecular weight.

Figure 10

Differential phase shifts (upper panel) and polarized modulation ratios (lower panel) spectra for solutions of Beta-lactoglobulin B at protein concentrations C=5.5 μM (circles), 275 nM (diamonds), 110 nM (down triangles), and 44 nM (up triangles). The solid lines are the best fit of the data according to a two-component model. The inset in the upper panel shows the uncertainty on the differential phase shift (filled circles) and on the polarized modulation ratios (open squares) at 320 MHz to be displayed on the same scale of the phase uncertainties, the uncertainties on the modulations have been multiplied by 100.

The check of the alignment and the polarization response characterization of the setup that we have described above is fulfilled by noticing that the value of the translational diffusion coefficient that is measured by FCS and FPA is in agreement with the size and shape of Beta lactoglubulin (BLG). The computations made by Garcia de la Torre et al.;⁷² indicate for the dimer form of BLG at T=20 °C a value D_T≅78.5 μm ²/s, that corresponds to ≅84 μm²/s at T≅22.5 °C. Our experimental estimate D_T=100±10 μm ²/s is ≅20 larger than the theoretical value and corresponds approximately to the value expected for the monomer of BLG. This discrepancy is due to the fact that most of the BLG dimers have dissociated into monomers at concentrations C<280 nM that corresponds to a mass concentration ≅0.01 g/L. In fact we expect ≅90 of BLG monomers in the solution at C=280 nM and at ionic strength =50 mM. Also our estimate of the rotational diffusion coefficient of the Beta-lactoglobulin B by FPA measurements corresponds closely to the prediction that can be done for the monomer of this protein. The theoretical predictions made by Garcia de la Torre et al.;⁷² for the average rotational diffusion coefficient of the BLG dimer reported at T≅22.5 °C gives D _ROT ≅8 MHz. We expect the rotational diffusion of the BLG monomer to be roughly double this figure, since the rotational diffusion scales approximately with the inverse of the molecular volume. The theoretical prediction of ≅16 MHz for the BLG monomer is therefore in good agreement with our experimental estimate D _ROT =18±3 MHz.

We can now compare the estimate of the excitation volumes obtained on the ports for imaging and spectroscopy of the microscope. The PSF of the imaging port corresponds to a three-dimensional Gaussian and from the values of the FWHM lateral and axial resolutions ( w_r0=210±40 nm and z₀=700±50 nm ), we can estimate the excitation volume on the imaging port as V _EXC ≅(π/4 ln(2))^1.5 w_r0 ²z₀≅0.03±0.013 fL.

For both the imaging and the spectroscopy ports the values of the excitation volumes are close to the minimum that can be reached by optical setup. The ≅3 times smaller excitation volume observed for the imaging port is therefore to be ascribed to the different optical paths. For the spectroscopy port a collimated beam fitting the entrance aperture of the objective is used, while in the imaging path a point source is conjugated on the sample plane. We suggest that the parallel use of the two paths for microspectroscopy must be made with caution since the volumes from which the fluorescence is sampled are different in the two ports.