1. Introduction

Axonemes are complex organelles, about 250 nm wide and up to several micrometers in length, made up of nine microtubule doublets plus a central pair (9+2 architecture), and involved in several important cell activities such as sperm motility or flows of mucus and cerebrospinal fluids. Defects in axoneme structure are associated with a broad range of diseases known as ciliopathies (reviewed in [1]). Thus, a non invasive technique that would allow to detect axoneme anomalies in situ would be a valuable tool for clinical investigations of ciliary diseases.

Second harmonic microscopy (SHM) provides intrinsic optical sectioning and high in-depth penetration due to the inherent localization of the nonlinear excitation at the objective focal volume, while drastically reducing out-of-focus photobleaching and phototoxicity. In addition, a variety of biological macromolecules, such as collagen or myosin, give rise to endogenous SHG signal, allowing visualization of organized biological assemblies in intact cells and tissues, in vitro or in vivo [2, 3, 4, 5, 6]. SHM has also been used to visualize polar arrays of microtubules in brain tissues, and may bring interesting insights into neurodegenerative diseases [7, 8, 9, 10].

In this paper, we have asked whether we could visualize and characterize axonemes purified from sea urchin sperm using SHM. We will show, that despite very small second harmonic (SH) signals, nonlinear optical properties of axonemes can be assessed.

2. Experimental methods

2.1. Axoneme sample preparation and Differencial Interference Contrast light Microscopy

Demembranated axonemes were purified from the sea urchin Sphaerechinus granularis according to published procedures [11]. The concentration of axonemes was chosen to avoid overlappings and aggregation. Samples were prepared by injecting 10μl of solution in a per-fusion chamber made of a slide and a coverslip separated by two strips of double-sided tape, and rinsed twice with 10μl BRB80 to keep only adsorbed axonemes. Fresh samples were immediately imaged. Video-enhanced Differencial Interference Contrast (DIC) microscopy were performed as described in [12].

2.2. SHM experimental setup

Our imaging setup was based on a modified confocal microscope composed of an Olympus IX71 inverted stand and a FluoView 300 scanning head (Olympus, Hamburg, Germany). A femtosecond Ti:Sapphire laser (Mira900-Verdi5, Coherent, Saclay, France) was coupled to the microscope and was tuned at a wavelength of 830 nm for all experiments. Linearly polarized 200-fs pulses at a repetition rate of 76 MHz were sent to a high-NA 60x water-immersion microscope objective (UplanApo/IR 60xW NA1.2, Olympus). This latter was slightly underfilled by the input laser beam to match the NA of the water-immersion condenser (IX2-TLW NA0.9, Olympus) collecting the SHG light in transmission. The average laser power in the focal plane was set to < P > = 30mW to limit photodamage (see section 3). The SH light was detected through a 2-mm thick BG39 filter (Lambda Research Optics, CA) that blocks the excitation wavelength, and a 415-nm (10-nm FWHM) bandpass filter (Edmund Optics, York, UK) by a photomultiplier tube (PMT) module with thermoelectric cooler (H7844, Hamamatsu Photonics, Massy, France). The PMT module was connected to a transimpedance amplifier (C7319, Hamamatsu) so as to match the SH signal to the full range of microscope hardware and software. The laser polarization was controlled by a zero-order half-wave plate (Edmund Optics, UK), mounted in a motorized rotation stage (PR50CC, Newport) synchronized to the image frame. The stage was inserted in the place of the fluorescent cube turret of the microscope. 512×512 SH images with zoom 10X and 12-bit intensity resolution were acquired from FluoView microscope software, then recorded as TIFF files. The pixel dwell time was ≈ 10μs.

2.3. Orientation Field-Second Harmonic Microscopy and imaging conditions

The principles of Orientation Field-Second Harmonic Microscopy (OF-SHM) were presented in [13, 14]. The main assumptions of our method are : (i) the SH intensity is interpreted from a nonlinear susceptibility tensor χ ⁽²⁾ of C_n(n ≥ 6) symmetry, with symmetry axis in the focal plane XZ at angle ϕ to X-axis ; this hypothesis is consistent with the axoneme C ₉ symmetry [15]; (ii) no polarization analysis is performed at detection ; the laser is linearly polarized at angle ψ to X-axis. Then, only the three components χ_zzz, ω_zxx and ω_xzx (Z∥ C_n≥6 symmetry axis) contribute to the intensity [16]:

with θ = ψ − ϕ the angle between laser polarization and the C _∞ symmetry axis. Only the ratios ξ = χ_zxx/χ_xzx and ρ = χ_zzz/ρ_xzx can be measured, and ϕ. An isotropic image U can be obtained by averaging intensities acquired with N polarizations nπ/N (n = 0..N − 1) when N ≥ 3. When Kleinman symmetries are further valid, ξ = 1.

In the case ξ = 1, we showed that combining only 4 images acquired at laser polarizations nπ/4 allows the determination of the unknowns U, ϕ and ρ [13, 14].However, if ξ is unknown, all the parameters can be determined from at least 6 images acquired at polarizations nπ/6 using a nonlinear least-square fit of pixel intensities with Eq. 1. Image analysis was performed with homemade routines written in Matlab (the Math Works, Natick, MA).

3. Results and discussion

Typical DIC and SHM images with the same field of view are presented in Figs. 1(a) and (b) respectively. The axonemes are well resolved, and most of them are straight. Note that, in contrast to DIC, the SHM is background free and that the axoneme profile can be resolved.

Figure 1(c) displays a zoom of a vertical axoneme, with transverse intensity profiles.

The two-photon Point Spread Function (PSF ²) of the microscope is well represented by a gaussian ~ exp[-(r/w_xy)²] where w_xy is the radius at 1/e maximum intensity [4]. As shown in Fig. 1(c), axoneme profiles are well fitted by gaussians ~ exp[-(r/w)²], with w ≈ 0.21μm. Assuming that the profile can be approximated by the convolution of the PSF ² with the axoneme cylindrical profile of radius R, we obtained $w\approx \sqrt{w_{\mathrm{xy}}^2+\alpha R^2}$ with a α ≈ 1. When NA > 0.7, w_xy = 0.23λ/(NA ^0.91), and we obtained for our experimental set-up w_xy ≈ 0.16 − 0.19μm (NA ~ 1.2-1 when the objective entrance pupil is respectively overfilled or slightly underfilled). The diameter of the axonemes was measured by electron microscopy as R = 0.125μm. Thus for NA ~ 1.2 − 1, w ≈ 0.2 − 0.22 μm. These values are consistent with our experimental results.

Moreover, the detection of the SHG signal from the axonemes pushed our confocal based SHG microscope to its limits, indicating that the SHG signal emitted by the axonemes is very small. The number n of photoelectrons delivered by the PMT photocathode can be roughly estimated from the hypothesis that the signal S = gn, with g a gain. n obeys Poisson statistics (therefore, the mean < n > and the variance var(n) are equal). Under this hypothesis, the variance var(S) is a linear function of the mean < S > (with slope g = ∂var(S) / ∂< S >).

 

Fig. 1. (color online) :(a) DIC images of axonemes; (b) Isotropic SHG images of axonemes ( both images 23.5 × 23.5 μm²); (c) SHG: 2.4 × 5.5μm² zoom on a vertical axoneme . Right: two examples of horizontal profiles. Bottom : mean profile integrated along all the axoneme. Continuous lines represent the best gaussian fits of the data.

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As shown in Fig. 2(a), var(S) is indeed a linear function of < S > , in agreement with a Poisson photoelectron statistics. The mean number of photoelectrons < n > per pixel was deduced from the relationship < n > ≈ < S >²/Var(S), which histogram is presented in Fig. 2(b). It demonstrates that an average of about 1 photoelectron per 10μs pixel dwell time is detected at 415nm for an average laser excitation intensity < I > ~ 300mW/μm ² at 830nm (< I > =< P > /S with S = 7π w_xy ²). Despite such a very small signal, we will show that the optical nonlinear properties of axonemes can be addressed. During scanning, the SHG intensity delivered by the axonemes was found to decrease (Fig. 2(c)), as a result of photodamage. The evolution of the mean SHG intensity as a function of the number of scans t is presented in Fig. 2(d). The decrease is strongly nonlinear, and the data are well fitted by the logistic function [17] f(n,k,t _1/2) = 1/[1 + exp(k(t − t _1/2))], where k ≈ 0.65 determines the curvature of the curve and t _1/2 ≈ 8 is the scan number at which the intensity is halved.

 

Fig. 2. (color online) : (a) Linear relationship between SHG signal mean and variance ; (b) Histogram of the mean number of photoelectrons < n > per pixel. (c) Axoneme photodamage induced by repetitive laser scanning (23.5×23.5 μm²). The number represents the image scan number. (d) Axoneme mean SHG intensity as a function of scan number. The continuous line represent the best fit with a logistic function.

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This photodamage process limits the number of images that can be acquired, thus the number of polarizations that can be addressed. Then, if a decrease of ~10–20% of the intensity is accepted, a maximum of 6 polarizations (6 scans) can be used to keep a detection level around one photoelectron per image pixel. This justifies the use of OF-SHM that requires only 4 images to reconstruct orientation fields and estimate ρ when ξ = 1, or 6 images to further estimate ξ.

A curved axoneme was selected to illustrate the effectiveness of OF-SHM using 4 polarizations nπ/4. The 4 images of Figs. 3(a1)–(a4) show the strong sensitivity of the SHG contrast to laser polarization. As expected, the isotropic image of Fig. 3(b) show that the SHG intensity is roughly independent of the local orientation of the axonemes, with higher intensities at axoneme crossings. The orientation field of Fig. 3(c), where each small bar represents the orientation of the χ ⁽²⁾ symmetry axis, is clearly tangent to the axoneme direction. The correlation between the axoneme direction and χ ⁽²⁾ symmetry axis is presented in Figs. 3(d),(e). The data are well aligned on the bissectrix, with correlation coefficients R = 0.998 and R = 0.999 respectively for 4 or 6 polarizations. Again, this shows that OF-SHM gives the orientation with high reliability, despite the very low SHG signal level.

 

Fig. 3. (color online) : OF-SHM studies of axonemes (512×512 images, zoom 10X, full scale 23.5μm). (a1–a4) A set of 4 SHG polarization images indicated by the double white arrows; (b) isotropic image U; (c) orientation field represented by bars directed along the symmetry axis of χ ⁽²⁾. For clarity, only a few bars are represented; (d)–(e) Correlation between the orientation ω of the axonemes, and ϕ of the principal axis of χ ⁽²⁾ for 4 (d) or 6 (e) polarizations. Lines represent the bissectrices.

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We finally address the problem of the estimation of ξ and ρ. To this end, up to 119 individual non-overlapping linear axonemes of different orientations were selected, with lengths of typically 4±1μm. The mean intensity of each axoneme for each polarization nπ/6 was calculated. To improve the reliability of the nonlinear least-square fitting procedure with Eq. 1, we used our finding that the orientation of an axoneme is parallel to its χ ⁽²⁾ symmetry axis. Angle ϕ was thus imposed in Eq. 1, lowering the number of fitting parameters to 3 (~ χ_xzx, ~ χ_zzz,~ χ_zxx) for 6 data points. Thus, the system is overdetermined.

Two methods were used. In the first one, the mean intensity of each axoneme was fitted with Eq. 1 as a function of laser polarization. Typical fits are presented in Fig. 4(a), and the histograms of the nonlinear coefficients appear in Fig. 4(b). The histograms are well fitted with gaussians, and we obtained ξ = 1.2 ± 0.1, ρ = 3.9 ± 0.4. The second method makes the assumption that the 119 selected axonemes have equivalent nonlinear optical properties, thus providing an almost homogeneous distribution of orientations. We then constructed a master curve of the intensity of each axoneme normalized to its isotropic value U as a function of 0. To avoid bias, the orientation angles were selected to obtain a uniform distribution when the bin width is 5°. The resulting curve is presented in Fig. 4(c). The intensity is clearly maximum when the laser polarization is aligned along the axoneme. The best fit with Eq. 1 leads to ξ = 1.1 ± 0.2 and ρ = 3.9 ± 0.5 (R = 0.997). Another estimation with the same set of data was obtained by averaging this master curve over intensities binned every 5° (Fig. 4(d)), gives ξ = 1.2 ± 0.2, ρ = 3.7 ± 0.4 (R = 0.93). All these methods give consistent results. To the best of our knowledge, this is the first time these quantities have been experimentally determined for axonemes.

 

Fig. 4. Determination of ξ and ρ by OF-SHM with 6 polarization nπ/6. (a) Examples of fits of the SHG polarization data derived from 3 axonemes of different orientations. (b) Histograms of the ratios χ_αβγ/X, where X = χ_zxx + χ_xzx + χ_zzz. Continuous lines represents the best fit with gaussians. (c) Master curve obtained from the intensities as a function of θ for all the axonemes. (d) Mean intensity curve obtained by binning the intensity over bins of 5° width. Continuous lines are best fits with Eq. 1.

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Interestingly, the ratio ξ = 1.1 ± 0.2 is close to unity, indicating that Kleinman symmetry is, at least, approximately verified, like for collagen and myosin. In a model of axisymmetric supramolecules built from uniaxial harmonophores with only one nonzero molecular hyper-polarizability component β_zzz, ξ = 1. Moreover, ρ = 2/tan² φ, where φ is the polar angle of the harmonophores. φ was found consistent with the helix pitch angle in collagen or myosin [18]. Here, we obtain φ = 35±2°. Although some proteins, like nexin, form helical structures in axonemes [15], further ultrastructural work will be needed to assign this angle to a given structural feature of axonemes.

In conclusion, we have characterized, for the first time to our best knowledge, the nonlinear optical properties of axonemes. This opens the possibility of SHM characterization of such supramolecular structures in vivo.