Fast monitoring of in-vivo conformational changes in myosin using single scan polarization-SHG microscopy

: Fast imaging of molecular changes under high-resolution and label-free conditions are essential for understanding in-vivo processes, however, current techniques are not able to monitor such changes in real time. Polarization sensitive second harmonic generation (PSHG) imaging is a minimally invasive optical microscopy technique capable of quantifying molecular conformational changes occurring below the diffraction limit. Up to now, such information is generally retrieved by exciting the sample with different linear polarizations. This procedure requires the sample to remain static during measurements (from a few second to minutes), preventing the use of PSHG microscopy from studying moving samples or molecular dynamics in living organisms. Here we demonstrate an imaging method that is one order of magnitude faster than conventional PSHG. Based on circular polarization excitation and instantaneous polarimetry analysis of the second harmonic signal generated in the tissue, the method is able to instantaneously obtain molecular information within a pixel dwell time. As a consequence, a single scan is only required to retrieve all the information. This allowed us to perform PSHG imaging in moving C. elegans, monitoring myosin’s dynamics during the muscular contraction and relaxation. Since the method provides images of the molecular state, an unprecedented global understanding of the muscles dynamics is possible by correlating changes in different regions of the sample.


Introduction
Second harmonic generation (SHG) is a promising technique for totally non-invasive highresolution optical imaging [1]. This non-linear non-resonant contrast mechanism is offering intrinsic advantages over linear optical imaging, such as optical sectioning, reduced photodamage and deeper tissue penetration depth. In particular, the contrast, generated from specific SHG active molecules is endogenous and as a consequence, no additional modification of the sample is required [2]. Moreover the SHG signals are coherent with very well defined polarizations. Polarization-based SHG (PSHG) imaging takes advantage of the molecular structure [3][4][5][6][7] and the differentiated response with respect the excitation polarization to reveal geometrical details at the molecular level in a quantitative way [8]. As a consequence, PSHG microscopy is a promising tool in disease diagnosis [9]  In all the above PSHG studies, a number of 2D images for different orientation of the linear excitation polarization (typically in steps of 10° covering from 0 to 180°) are required. These images are afterward post-processed in a pixel by pixel basis to determine the SHG intensity response in terms of the input polarization. In this way it is possible to retrieve the so-called anisotropy parameter, which allows the quantification for the information related to the molecular structure generating the SHG signal, [8,16]. To do that, typical laser scanning systems require ~1 sec to record one image of 500x500 pixels. Therefore, the sample must be static during all the process (>10 s) to ensure that the PSHG signal for the same pixel in all the images is correlated to a single point in the sample. This prevents the study of moving samples, requiring anesthesia for in vivo imaging [8]. In this case, the use of resonant scanning, reaching ~30fps could be of help to speed up the recordings. However, this still needs to be combined with the acquisition of the same image with the different polarization excitations. Even in the case of fast polarization rotation, e.g., using liquid crystal modulators [17], this would result in a maximum PSHG acquisition speed to be just under half second (~0.3 s). Although this might be adequate for some applications, there are still situations were fast movement cannot be avoided. This is the case of imaging living organisms, animals and human organs or the study of muscle dynamics.
Recently, a method that uses circular polarization excitation and Stokes analysis of the polarization has been proposed [18]. Here we introduce a similar scheme based on circular polarization excitation specifically suited for fast, Single-Scan PSHG (SS-PSHG). Our analysis shows that after exciting the sample with a circular polarization, the generated SHG signal will, in general, possess an elliptical polarization. The orientation of the SHG ellipse will then give information on the main orientation of the SHG active molecular assembly (usually organized in the form of filaments), while the ellipticity will be related with the anisotropy parameter, providing the average effective orientation θ e of the nonlinear dipoles of the SHG active molecules. Therefore, by using a simple polarimetry analysis capable to monitor in real time the orientation and ellipticity of the SHG signal, we are able to monitor fast molecular conformational changes.
In this article the SS-PSHG method is demonstrated by using different static samples, obtaining results similar to those of standard PSHG. The reliability of the method for fast analysis is then applied to monitor myosin conformational changes in living C. elegans. Finally, we demonstrate the ability of the technique to correlate muscle functionality with changes at the molecular level.

SHG in molecules and tissues
Macromolecules, such as nucleic acids, proteins, and carbohydrates, are very large molecules commonly created by polymerization of smaller subunits. When a subunit possesses a noncentrosymmetric symmetry, the nonlinear interaction with high intense light is capable to produce SHG light. This interaction is described by a nonlinear electric dipole moment μ. The component μ ν along an axis ν of the molecule for a single subunit can then be described by: where E i is the light excitation electric field component in the ν, κ, and ζ molecule coordinate system and β νκζ is the νκζ component of the microscopic third-rank hyperpolarizability tensor β. The tensor β is therefore the ultimate responsible of the SHG scattering at the molecular level. The description of the SHG conversion is usually simplified by considering a main component β ννν in the direction of the charge transfer [19]. For example, in proteins, β ννν is associated to the peptide bound in the C-N pair, which provides the main charge-electron transfer site [20] and therefore the direction of β ννν indicates the direction of the non-linear dipole.
Once the molecular response is known, the overall SHG microscopy response within a macromolecular assembly is given by the coherent addition of β ννν , resulting in the second order susceptibility tensor χ (2) . The tensor elements χ ijk in a region with a density N of SHG scatters can be written averaging (operator ) for all the region as: where î indicates a unit vector and i,j k are indices indicating the macromolecular assembly coordinate system x, y, z. Note that the resulting average, and therefore the tensor components χ ijk , depends on the value and on the orientation distribution of β ννν [21]. Therefore, even in the case of non-null value of β ννν , the molecule and the macromolecular assembly must show structural order and non-centrosymmetric symmetry to obtain a non-null value of χ (2) . As a consequence, few tissues are capable to produce SHG signal, and are restricted to muscle (with myosin being the SHG active molecule) [6], microtubules (α-β tubulin dimer) [14], collagen (polypeptide helix) [6] in animals and starch and cellulose (amylopectin) [22] in plants. In all these samples, the SHG active macromolecular assemblies are usually described by hexagonal (C 6 ) or cylindrical (C ∞ ) symmetry, which are equivalent if Kleinman conditions are fulfilled [8]. Under these symmetry, only two tensor elements are independent, with χ xxz = χ yyz = χ zyy = χ zxx = 2 d 15 and χ zzz, = 2d 33 [23] (here, z denotes the long symmetry axis along the filament) Using azimuth φ and zenith θ angles to describe the direction ν of β ννν and assuming a constant distribution in the azimuth plane (due to the filament cylindrical symmetry), the dependence of χ ijk with φ vanishes and the ratio between the two independent tensor elements is only dependent on the β ννν distribution with respect to θ (3) Since in helical molecules the direction of β ννν follows the helical structure, the angle θ e directly provides the molecular helical pitch angle [6,16].

SHG molecule response to circular polarization excitation
Here, for simplicity, we assume that the filament is contained at the microscope sample plane. Then a lab (X, Y, Z) and a filament (x, y, z) coordinate system can be defined. In the lab system, X and Z correspond to the horizontal and vertical axis in the images, respectively, and Y is the laser beam propagation direction. In the filament system, y coincides with the lab coordinate Y, z is along the main axis of the filament, and x is contained in the sample plane. Then, the two coordinate systems are related through a rotation angle φ, which therefore determines the filament orientation in the lab coordinate system. Without loss of generality, an incident electric field with circular polarization at the sample plane (Y = 0) can be written in the filament coordinate system as: where we are assuming plane-wave approximation and that the circular polarization at the objective focus is preserved. Using a procedure similar to Ref [8]. with the nonlinear tensor with C ∞ symmetry and taking into account that the SH electric field radiated in the Y direction is proportional to the second order polarization, we obtain the SHG field as: A close look of Eq. (5) shows that the state of the SHG polarization is elliptical, with an ellipticity (d 33 /d 15 -1)/2, which includes the anisotropy parameter, and therefore is characteristic of every tissue. The long axis of the ellipse is oriented perpendicular to the filament for d 33 /d 15 < 3, and along the filament otherwise. Circular polarization is obtained for d 33 /d 15 = 3, resulting in an effective orientation θ e = 39.23°. This value coincides with the so called "magic angle" defined in Ref [24], showing maximum disorder. As a consequence no information on the filament direction can be obtained. Also note that for an anisotropy parameter d 33 /d 15 = 1 the polarization becomes linear, and perpendicular to the filament. In this model, the SHG polarization ellipse maintains the rotation direction of the circular excitation polarization for d 33 /d 15 > 1, while for d 33 /d 15 < 1 the polarization rotation direction is reversed.

Polarimetry analysis
The characterization of the exact polarization state would require the use of a detection system based on Stokes parameters [18]. In our case however, we are only interested in retrieving the value of the anisotropy parameter and the filament orientation, i.e., the ellipse orientation, with respect the lab coordinate-system (retrieving the field rotation direction is not necessary). The simpler way to characterize the ellipse and to retrieve this information is to use an analyzer at three different orientations. The intensity measured after an analyzer oriented an angle α with respect the lab Z axis can be obtained from (5) as: For convenience, we choose α = 0°, 45° and 90° and substitute in (6) and the anisotropy parameter as 2  2  2  2  33  0º  90º  2  2  2  2  15  90º  0º   cos  sin  1 2 , cos sin where the negative and positive signs are used for tissues with d 33 /d 15 <1 (muscle) and d 33 /d 15 > 1 (collagen, microtubules and starch), respectively. Note that the use of analytical expressions makes possible the instantaneous display of these parameters while performing imaging.

The microscope setup
The experimental setup for single-scan PSHG (Fig. 1) is based on an inverted microscope (TE2000-U, Nikon, Japan). The beam immediately after the laser (MIRA 900f, Coherent, France, pulse duration 160fs, repetition rate 76MHz, at a central wavelength of 854nm), is passing through a neutral density wheel to control its power. Then is guided to the galvanometric mirrors (Cambridge Technology, UK) based scanning system and after a pair of relay lenses based telescope is reaching the short pass dichroic beamsplitter (FF720-SDi01, Semrock, USA). Inside the telescope we placed a linear polarizer (ThorLabs, LPNIR050, USA) in order to reduce any ellipticity or depolarization introduced by the setup. Then a zero order quarter-wave retardation plate (QWPO-850-10-4, CVI Melles Griot, USA) is following to create circular polarization before the objective (60x numerical aperture, (NA) = 1.4, Plan Apo-Achromat, Nikon, Japan). The ellipticity before the objective was measured ~4% and after the objective ~6%. The averaged power was ~25mW at the sample plane. The SHG signal is collected with a 1.4NA (Nikon, Japan) condenser while the laser is blocked with a short-pass optical glass filter (BG39, Schott, Germany). The SHG signal is guided to a specially designed mount to fit the microscope's position of the DIC optics. This mount contains a 50:50 non-polarizing beam-splitter cube (10BC17MB.1, Newport, USA), a polarizing beam-splitter cube (10FC16PB.3, Newport, USA), a linear polarizer (10LP-Vis-B, Newport, USA) at 45°, 3 bi-alkali photomultiplier tubes (PMT) (H9305-03, Hamamatsu, Japan) and 3 10 nm FWHM band-pass filters centered at 427 nm (FF01-427/10-25, Semrock, USA) exactly in front of the PMTs. The non-polarizing beam-splitter divides the beam into 2 beams. The first beam crosses the polarizer at 45° and the bandpass filter before reaching PMT 1. Consequently, only SHG photons polarized at 45° are reaching PMT 1. The second beam passes through the polarizing beam-splitter cube, resulting in a reflected SHG beam with horizontal polarization (at 0°), reaching PMT 2, and a transmitted vertical polarization (at 90°), reaching PMT 3. The 3 images (from the 3 PMTs) are formed using an interface program (lab-VIEW, National Instruments Corporation), which controls the raster scanning of the galvanometric mirrors and the data acquisition (DAQ) electronics (National Instruments, rack-mount, BNC 2090, and a National Instruments, DAQ board, PC-LPM-16, USA). In the lab-VIEW interface we have also implemented Eq. (3), (7) and (8), showing in this way the 3 SHG images and 3 images showing the angle φ, anisotropy parameter (d 33 /d 15 ) and molecular angle θ e, , along with their image histograms. We note that the formation of all those images is instantaneous thanks to the use of analytical equations, which do not introduce any extra delay in the image displaying. The pixel dwell time of our system was set to 6 μs. Thus, the frame acquisition time ranged from ~60 ms to 1sec for a 125x125 and 500x500 pixels images, respectively. In order to have good contrasted images we have set 1% of the PMT recorded voltage equal to 0V. For the calibration of the gain of the 3 PMTs we have used hydrated wheat starch granules (S5127, unmodified, Sigma-Aldrich, USA). Starch possesses radial geometry of the SHG molecules, consequently when excited with circular polarization, the resulting SHG elliptical polarization has a uniform distribution of orientations, and therefore the signal reaching the 3 PMT should be identical. Since in practice starch granules are not perfectly radial, we compensate by using several starch granules in the image. Thus, the calibration method consists of imaging many starch granules and adjusting the gain of the 3 PMTs so that they all record the same mean SHG intensity. Typical values for the applied voltage was: PMT 1 = 903 V, PMT 2 = 894 V and PMT 3 = 1005 V. In addition, we removed the SS-PSHG mount and we placed a SHG bandpass filter (FF01-427/10-25, Semrock, USA) and a polarizer (10LP-Vis-B, Newport, USA) in front of the PMTs. We then imaged hydrated starch granules and we rotated the polarizer/analyzer in steps of 5°. We measured approximately the same mean SHG intensity for all the positions of the analyzer ( ± 7%), verifying the calibration method and initial hypothesis.

C. elegans Samples
The strain N2 [wild type] was cultured and grown in large quantities using methods reported by S. Brenner [25]. A number of healthy adult hermaphrodites were mounted on a 2% agar pad with 0,8μl of 15mM sodium azide (NaN 3 ) between two Thickness#0 cover slides. We used anesthesia such that the worms were starting moving ~30min after their complete immobilization. First movements were slow and we were able to have the worms in our field of view. SS-PSHG imaging was lasting approximately 20min, comprising the worm somnolence period between the first movements and the instant where the anesthesia effect has completely vanished. After this point the worm's movements were too fast to maintain it in the field of view. The mounts were sealed with melted paraffin for stabilization. Laboratory temperature was 21°C.

Results
In order to retrieve the SHG polarization orientation and ellipticity, the SHG signal is simultaneously analyzed at three different polarization orientations at 0°, 45° and 90° (see the set up in Fig. 1) for every pixel in the image. Once the intensities for each polarization in each pixel are obtained, their value is introduced inside the analytical derivation described above to retrieve the anisotropy parameters (or θ e ). This process is reproduced for every pixel in the whole image and only one single scan is necessary to obtain all the required information. As result, the imaging speed is reduced almost one order of magnitude when compared to typical PSHG. Furthermore, the parameter retrieval is based on an analytical method and the molecular information in each pixel can therefore be retrieved in real time, i.e., simultaneously to the scanning. This opens up the way to practical in-vivo and clinical applications of PSHG imaging.

Validation of the technique with static samples
To validate our SS-PSHG method, we first conducted experiments with different static and standard specimens (starch, collagen, myosin and microtubules), comparing the results with that obtained with standard PSHG technique based on the rotation of the excitation linear polarization [3, 6-8, 11, 15, 17].
Starch granules have a radial organization of SHG-active molecules, and therefore provide the ideal test bench to show the capability of the method to retrieve the molecular orientation and the anisotropy parameter. The images for hydrated starch granules are shown in Fig. 2(a). As can be seen, the typical radial organization is retrieved and the anisotropy parameter, and thus the nonlinear dipole effective orientation θ e , coincides with previous works [22]. We then proceed to use our technique to retrieve the same parameters for tendon collagen type I (Fig. 2(b)), myosin from the body wall muscles of a C. elegans nematode (Fig. 2(c)) and microtubules corresponding to the mitotic spindles imaged from an embryo division inside the worm (Fig. 2(d)). As for starch, in all the cases, the retrieved parameters show a nice agreement with previous results obtained with standard PSHG [3,8,16].
The SS-PSHG imaging performed in the mitotic spindles (in which the SHG source is the microtubule) was performed in an anesthetized worm and deserves special attention. This is a typical case where the measurement is not possible with standard PSHG, due to the rapid mitosis of the embryo. Nevertheless, even with the weak and noisy generated signal, we were able to image a few frames with SS-PSHG. In this case, we obtained a low signal to noise ratio image and no efficient background subtraction could be performed. In this case, noise resulted in a similar voltage in the three PMTs and the model interpreted the situation as a microtubule orientation near 135°. This might be the reason of the secondary peak shown in Fig. 2(d), which is probably an artifact. However, even under this challenging situation, the method was able to retrieve the molecular information, whose results were similar to those obtained in previous works for axon microtubules [14].

Application of the technique to moving C. Elegans
We now focus on the capability of SS-PSHG to monitor muscle dynamics. In muscle structures, the SHG active molecule is myosin, which possesses a helicoidal geometry with a helical pitch angle measured using X-ray diffraction of 68.6° [26]. This protein is composed of two parts, the light meromyosin, corresponding to the static part that lies on the myosin filament, and the heavy meromyosin, which is a dynamic part that extends from the myosin filament to attach to the actin molecule producing contraction [27]. The nonlinear dipole response in peptides is usually associated to the C-N bond pair [20], and therefore, the orientation of this bond along the myosin chain (reproducing the molecular helical geometry) determines the molecular nonlinear dipole effective orientation θ e with respect to the molecular (helix) axis. As a consequence, the value of θ e retrieved with the PSHG analysis in a relaxed muscle, where the heavy and light meromyosin are aligned along the thick filament axis, directly provides the helical pitch angle [6]. However, dynamic changes of the heavy meromyosin under contraction can modify the distribution of the nonlinear dipole orientation, θ e . As a consequence, the value of the retrieved anisotropy parameter is altered. This effect was demonstrated by standard PSHG measurements in semi-static conditions in demembranated rabbit and frog muscle fibers [27]. In such case, contraction was slowly produced, and to gain in recording speed a single line scanning methodology was employed. In what follows we will show how our technique can be used in moving living specimens, such as the C. elegans nematode, to produce fast 2D images for analyzing muscle dynamics and to obtain both the orientation of the thick filaments and the anisotropy parameter in vivo. Figure 3 shows the results for a SS-PSHG analysis performed in an area of the worm comprising body-walls and the most posterior lobe (or terminal bulb) of the pharynx. We used an imaging speed of 1 frame per second to obtain eight consecutive 500x500 pixels images. Figure 3(b) shows the orientation retrieved at every pixel for the myosin thickfilaments. A uniform orientation of the striated muscles along the body wall can be observed. This is in contrast with the more complex organization in the pharynx, which in the terminal bulb includes cells from three different muscle groups with filaments showing a radial distribution. The sequence of the images is able to describe, at every pixel, the orientation change of the thick filament during the worm movement. The SS-PSHG image for the retrieved anisotropy parameter is shown in Fig. 3(c), showing a uniform distribution all along the field of view. The average value in the anisotropy parameter was 0.29 ± 0.11, which results in an average value of θ e ≈69°, in accordance with that obtained for relaxed muscle. Notice, however, that the last image in Fig. 3(c) shows a change of color (greener) in the top part of the left-hand body-wall (red square in the figure). This corresponds to a higher value of the anisotropy parameter around 0.52 ± 0.13 (lower values of θ e ≈63°). Interestingly, this increase in the value of the anisotropy parameter coincides with an area where there is a clear contraction of the body-wall muscle (maximum curvature of the worm). This result is in agreement with the measurements performed in demembranated muscle fibers [27]. The relation between contraction (relaxation) and increase (decrease) of the anisotropy parameter (angle θ e ) is illustrated in detail in the next subsection.

Correlating muscle functionality at the molecular level in an image
An important advantage of SS-PSHG is that the frame by frame-image analysis allows for a global understanding of the muscle dynamics. To illustrate this aspect, we imaged the posterior lobe of the pharynx (Fig. 4(a)) and we monitored its evolution with time just when the worm was waking up from anesthesia. In this situation, the pharynx was showing some activity while the body wall muscles were still relaxed, avoiding the worm to escape from the field of view. Supplementary Media 1 shows the time evolution for the angular orientations for the thick filaments and the anisotropy parameter. We can observe small movements for the different muscle groups, which collaborate in producing a given task in the posterior lobe. To better analyze synergetic movement of the muscles, we analyzed and monitored the time evolution of two nearby regions of interest (ROI). Focusing on the first seconds of ROI 1 (Fig. 4(b)), at second 4, a variation on the thick filament angle is observed, which is correlated with a local decrease in the anisotropy parameter. This suggests a change from muscular relaxation to a contraction state, which produced a change in the thick filament orientation. We can therefore use the average value in a ROI to monitor the evolution during long periods for both, the thick filament orientation and anisotropy parameter. This is performed in Fig. 4(c) for the two highlighted ROI in Fig. 4(a). The results for all the monitored time show that the averaged value of the anisotropy parameter in ROI 1 is around 0.45, indicating that during all the period the muscle is mainly in a contracted state. The situation is the contrary in ROI 2, where the averaged anisotropy parameter is 0.2, indicating relaxation. Fig. 4. Monitoring of muscular contraction and relaxation with SS-PSHG. The images (500x500 pixels) of the posterior lobe of a C. elegans worm waking up after anesthesia are analyzed for 30 seconds. a) The total detected SHG signal (left), the thick filament orientation (center) and the anisotropy parameter (right) with the two region of interest (ROI) are shown (Media 1). b) Five frames for ROI 1 showing the changes on the thick filaments orientation (top) and anisotropy parameter (bottom). Note the change in color at second 4. c) Evolution of average values for the thick filaments orientation (top) and anisotropy parameter (bottom) in ROI 1 (left) and ROI 2 (right). Note that an increase on the anisotropy parameter is associated to a contraction process, while a decrease is associated to a relaxation process. Error-bars corresponds to standard deviation within the ROI.
The method can also be used to compare different ROI. For example, the two considered ROIs undergo eventual changes of state; from contraction to relaxation in ROI 1, and from relaxation to contraction in ROI 2. In all cases, these changes of state are associated to a change in the orientation of the thick filaments. In addition, this analysis allows determining if the two ROIs are cooperating. For example, we can observe that the relaxation observed in ROI 1 at 8 s and 27 s corresponds to a contraction in ROI 2, showing that both muscular groups may be cooperating in this particular case. On the contrary, this cooperation does not exist at 7 s (relaxation in ROI 1 without contraction in ROI 2) and at 18 s (contraction in ROI 2 without relaxation in ROI 1). Here, the muscle may be cooperating with other muscular groups. Similar analysis can therefore be performed in other areas of interest, being in principle possible to correlate different ROIs, establishing in this way the global molecular dynamics associated to the different muscular groups and their interconnections.

Discussion and conclusions
The results above shows that SS-PSHG has similar capabilities that standard PSHG in retrieving molecular information in static samples, such as starch, collagen, myosin and microtubules. Similarly to standard PSHG, the theoretical model does not take into account changes caused by the tissue birefringence or scattering on both, the excitation and the SHG polarization. In addition, the existence of molecules oriented off-the plane will require a more careful treatment, as it is also the case in standard PSHG [22]. Nevertheless, the analyzed samples, including the C. elegans worm are almost transparent and the thick filaments of the body walls are mainly parallel to the sample plane. In this sense, the values of the anisotropy parameter are in agreement with the one obtained with standard PSHG methods.
The main advantage of the method is its potential to globally analyze in-vivo, fast muscle dynamics at the molecular level, which is especially suited for diagnosis of muscular dysfunctions [2]. Moreover, the technique is ideal for minimally invasive in-vivo acquisition of dynamical molecular information, since only one laser scan with circular polarization is required and the information is analyzed in real-time in each pixel. Additionally, the method can be extended to other SHG active biological structures, such as the study of collagen biomechanics [28], in which motion can affect the PSHG results or in microtubules which undergo fast changes during a cell division process. Moreover, since the single scan methodology minimizes exposition to light, it opens the door to the use of exogenous SHG markers for PSHG in which absorption was present and photobleaching was a major drawback [29]. Since the speed of the technique is only limited by the scanning method, higher speeds can be obtained by decreasing the number pixels of the image, using resonant galvanometric mirrors, which would allow to reach video-rate imaging and simultaneous analysis, or by overpassing the scanning system using temporal focusing [30]. In this last case, speed would be limited only by the signal to noise ratio of the images obtained by the 2D array detector.