Polarization-Sensitive Two-Photon Microscopy for a Label-Free Amyloid Structural Characterization

Summary

This paper describes how polarization-sensitive two-photon microscopy could be applied to characterize the local organization within label-free amyloid superstructures-spherulites. It also describes how to prepare and measure the sample, assemble the required setup, and analyze the data to obtain information about the local organization of amyloid fibrils.

Abstract

Compared to its one-photon counterpart, two-photon excitation is beneficial for bioimaging experiments because of its lower phototoxicity, deeper tissue penetration, efficient operation in densely packed systems, and reduced angular photoselection of fluorophores. Thus, the introduction of polarization analysis in two-photon fluorescence microscopy (2PFM) provides a more precise determination of molecular organization in a sample compared to standard imaging methods based on linear optical processes. In this work, we focus on polarization-sensitive 2PFM (ps-2PFM) and its application in the determination of molecular ordering within complex bio-structures-amyloid spherulites. Neurodegenerative diseases such as Alzheimer's or Parkinson's are often diagnosed through the detection of amyloids-protein aggregates formed due to an impaired protein misfolding process. Exploring their structure leads to a better understanding of their creation pathway and consequently, to developing more sensitive diagnostic methods. This paper presents the ps-2PFM adapted for the determination of local fibril ordering inside the bovine insulin spherulites and spherical amyloidogenic protein aggregates. Moreover, we prove that the proposed technique can resolve the three-dimensional organization of fibrils inside the spherulite.

Introduction

Over the past decades, although there has been significant development of numerous fluorescence microscopy techniques for bioimaging of proteins and their aggregates¹, only a few have been used to resolve their local ordering within the sample^2,3. Fluorescence lifetime imaging microscopy⁴ was used to study the intrinsic structural heterogeneity of amyloid superstructures-spherulites. Moreover, quantitative determination of the local ordering inside complex and densely-packed biostructures such as spherulites could be resolved using polarization-sensitive methods³. However, standard fluorescence techniques with superficial tissue penetration are limited since using UV-VIS wavelengths to excite fluorophores in vivo leads to high tissue light scattering⁵. In addition, such imaging often requires designing and binding specific fluorescent probes to a targeted biomolecule, thereby increasing the cost and amount of work needed to perform imaging.

Recently, to address these issues, our team has adapted polarization-sensitive two-photon excited fluorescence microscopy (ps-2PFM) for label-free imaging of biological structures^6,7. Ps-2PFM allows for the measurement of the dependence of two-photon fluorescence intensity on the direction of linear polarization of the excitation beam and analysis of the polarization of the emitted fluorescence⁸. The implementation of this technique requires supplementation of the standard multi-photon microscope setup excitation path (Figure 1) with a half-wave plate to control the light polarization plane. Then, polar graphs, depicting the dependence of two-photon excited fluorescence intensity on the polarization of the excitation laser beam, are created from signals collected by two avalanche photodiodes, thus collecting the two, mutually perpendicular components of fluorescence polarization.

The last step is the data analysis process, taking into account the impact of the optical elements, such as dichroic mirrors or a high numerical aperture objective, on polarization. Because of the nature of the two-photon process, this method provides both reduced angular photo-selection and enhanced axial resolution, as two-photon excitation of fluorophores outside the focal plane is probabilistically limited. It was also proven that similar methods could be successfully implemented for in vivo imaging of near-infrared probes (NIR) for deep-tissue imaging⁹. Ps-2PFM has been previously applied to image fluorophores in cell membranes¹⁰ and DNA^11,12, as well as non-standard fluorescent markers of biological systems, such as gold nanoparticles¹³. However, in all these examples, the information about the organization of biomolecules was obtained indirectly and required a predefined mutual orientation between a fluorophore and a biomolecule.

In one of our recent papers, we have shown that ps-2PFM could be successfully applied for determining the local polarization of the autofluorescence of amyloid superstructures and fluorescence from Thioflavin T, an amyloid-specific dye, bound to amyloid fibrils in spherulites⁶. Furthermore, in another one, we have proven that ps-2PFM could be utilized to detect amyloid fibril orientation inside amyloid spherulites in a sub-micron size regime, which was confirmed by correlating it with transmission electron microscopy (TEM) imaging⁷. The achievement of this outcome was possible thanks to i) intrinsic autofluorescence of spherulites-amyloids, when excited with either one or two photons, exhibit intrinsic autofluorescence with emission maxima located in a range from 450 to 500 nm and two-photon absorption cross sections comparable with standard fluorescent dyes¹⁴, ii) mathematical models introduced previously to describe how ps-2PEF of dyes labeling biological membranes and DNA structures could be applied to fluorescence exhibited by spherulites and dyes bound to them^8,11,15. Thus, before proceeding with the analysis, we highly recommend looking through the required theory described in both, the main text and supporting information of our first paper concerning this topic⁶. Here, we present the protocol for how to apply the ps-2PFM technique for a label-free amyloid structural characterization of bovine insulin spherulites.

Protocol

1. Preparing the microscope slides with fully-grown spherulites

NOTE: See the Table of Materials for details about all materials, reagents, and equipment used in this protocol. All solutions were prepared with deionized water (18.2 MΩ·cm at 25 °C) obtained from the water purification system.

1. Incubate the amyloid spherulites based on the protocol described by Krebs et al¹⁶. with some modifications, as described below.
   1. Weigh 10 mg of insulin powder in a 1.5 mL tube.
   2. Dissolve the powder with a 1 mL aliquot of the deionized H₂O/HCl solution (pH 1.5).
   3. Seal the sample with the tape and put it in a thermal mixer to incubate for 24 h at 70 °C (0 rpm).
      NOTE: To perform imaging of amyloids in their native (i.e., hydrated) environment and prevent sample deformation due to dehydration, it is necessary to prepare microscope slides according to the following description (scheme shown in Figure 2).
2. Wash the microscope glass slide thoroughly with water.
3. Dip the slides in methanol and leave them to dry under ambient conditions on a dust-free wipe.
4. Take a 100 µL aliquot of the spherulite solution from the tube with an automatic pipette (step 1.1.2) and add it to the well located in the central area of the microscope slide.
5. Cover the solution with a coverslip, avoiding air bubble formation.
6. Deposit mountant along the edges of the coverslip on the slide with an automatic pipette to seal the spherulites' native solution.
   NOTE: It is of great importance to deposit slide mountant on both the coverslip as well as slide surfaces. Do this under the fuming hood because of the toxicity of the volatile solvent (xylene). See the inset in Figure 2.
7. Leave the microscope sample under ambient conditions for the mountant to harden.
   NOTE: The hardening process is temperature- and humidity-dependent but should be completed within 12 h.
8. Check if insulin spherulites were formed correctly using a polarized optical microscope (POM) with crossed polarizers. Scan through the sample looking for a characteristic pattern of bright areas, called a Maltese cross, as shown in Figure 3.
   NOTE: The amyloid spherulites can be defined as spherical superstructures characterized by a heterogeneous morphology with a core-shell structure. In detail, they are composed of an amorphous core and radially growing amyloid fibrils¹⁶. Due to the anisotropic character of spherulite structures, they can distinctively interact with polarized light (e.g., by refraction) and alter their phase, which can be easily observed under POM with crossed polarizers. This method was used to study only fully developed spherulites characterized by a model-like Maltase cross pattern. Consequently, aggregates or structurally distorted spherulites were excluded from further investigations.

2. Building and aligning the system

NOTE: A schematic representation of a polarization-sensitive two-photon microscope can be found in Figure 1.

1. Install a femtosecond laser with the output wavelength tunability in the 690-1,080 nm range, for example, operating on a mode-locked Ti: Sapphire laser with ~100 fs pulses of 80 MHz repetition rate.
2. Add a half-wave plate mounted on a rotation stage to the excitation path of the setup to control the polarization of the incident light in the XY microscope sample plane.
3. Install the dichroic mirror to cut off the excitation beam from the detecting optics.
   NOTE: The optical characteristics of a dichroic mirror should allow to reflect the excitation beam (to the specimen) in the NIR range of wavelengths and be simultaneously transparent for the wavelength range corresponding to emission from the samples.
4. Install a piezoelectric scanning stage for raster scans within the XY plane for a chosen Z.
5. Mount the high NA immersion objective, for example, an apochromatic oil immersion objective 100x/1.4 NA.
   NOTE: As the entire setup operates in an epi-fluorescence mode, the incident and emitted signals are passing by the same objective.
6. In the emission path, add a polarizing beam-splitter that splits two-photon excited emission into two orthogonally polarized components (I_X and I_Y)
7. Install two photon-counting avalanche photodiodes (APDs) in a configuration allowing them to collect light transferred and reflected using the beam-splitter, respectively (Figure 1).
8. Mount correct wavelength-dependent cut-off filters on the excitation and emission path of the system, for example, an 800 nm long-pass filter directly in the excitation optical path and a 700 short-pass filter in the emission path.
   NOTE: Analyze the emission spectra from spherulite so that any potential contribution from second harmonic generation (SHG) or laser light could be excluded using the correct emission filters. It is also worth noting that this system should also allow measurements of polarization-sensitive SHG, which could be used to resolve the ordering of biomolecules within the samples. However, the data analysis of the SHG signal differs from fluorescence, which, in more detail, was described by Aït-Belkacem et al.¹⁷.
9. Align the whole system (using the alignment mode built in many lasers) until similar signal intensities are collected using both photodiodes.
10. Check if the excitation beam focused by the high NA objective and imaged on a camera has a concentric circular shape as presented in Figure 4A.
11. Adjust the scan time and corresponding power to minimalize the damage induced by the incident laser on the sample. Exemplary point-like burning is presented in Figure 4B. Measure the nominal power using a digital handheld power meter connected to a photodiode power sensor located at the entrance to the body of the microscope.
    NOTE: Biological specimens can be easily burned due to laser illumination. In this case, the 100 -900 µW power range (at the focal point of the objective lens) was found to be an excellent trade-off between sample stability and intense emission.
12. Before the sample measurement, test the quality of alignment of optics with an isotropic reference sample (e.g., fluorescein embodied in the amorphous polymer). To perform the calibration check, follow the procedure described in section 3 using an isotropic reference instead of an amyloid sample.
    NOTE: With an assumption that the microscopy setup is ideally adjusted for the sample with isotropic properties, both 2P emission components (I_X and I_Y) detected with two APDs should be characterized by the same intensity (Figure 4C).

3. Measurement of the bovine insulin spherulites

NOTE: To perform all the described ps-2PF measurements, hand-written software was used, which controls the positions of the piezoelectric stage and half-waveplate and collects the signal from both photodiodes, allowing for plotting of the XY scans (raster scans) from selected areas on microscope slides as well as polar graphs from specific sample coordinates. Additional notes have also been added to the protocol, which will allow users to perform the measurement without it, since both the piezo-stage and rotation stage used to rotate the half-wave plate could be controlled using their own controllers or corresponding software. Still, it is strongly recommended to write an algorithm combining the rotation angle of a half-wave plate with 2PEF intensity collected with both photodiodes since this correlation (polar graphs) is crucial for proper data analysis resulting in structural information.

1. Mount the specimen with the spherulites on the piezoelectric stage (immobilize the glass slide with tape). Be sure to mount it in a way where a thin glass side (coverslip) is facing the objective as high numerical objectives are characterized by relatively short working distances.
   NOTE: As oil immersion is used, a small drop of mineral oil should be applied to the objective before specimen mounting and focusing.
2. By changing XY and Z positions using microscope knobs, focus the objective on one of the spherulites found in the solution, but be aware that because spherulite diameters are typically in the range of tens of µm, focus within the central area of the entire structure. Look for black and white haloes around the specific spherulite as signs of under- and upper-focus, respectively. Adjust the "Z" axis to be between these extremes.
   NOTE: It is important to find an isolated sample without structural defects. Extremely small spherulites may drift off due to the material stress introduced by the objective while the biggest structures are probably aggregated or highly distorted.
3. Center the spherulite in the field of view of the observed microscopic plane and determine the size of XY scan by looking at how many piezostage steps in X and Y directions (displayed on the piezostage controller or in its software) are needed to cover the area of the whole structure.
   NOTE: It is recommended to set the system in such a way that the beginning of the XY scan is located near one of the corners of the spherulite and coincides with the zero position of the stage (X and Y = 0)
4. Adjust the following scanning parameters:
   1. Adjust the polarization of the excitation beam, and rotate the half-wave plate to obtain the polarization corresponding to the "X" and "Y" axes of the microscope sample plane.
      NOTE: This can be done by measuring the polar graphs of isotropic fluorescent medium such as fluorescein. For such materials, maximum fluorescence intensity is parallel to the excitation beam polarization; thus, rotating the half-wave plate adjusts the polarization with X and Y axis on the observation plane, also denoted as X and Y axis on polar graphs as in Figure 4C. Full polar graphs could be measured by collecting the measured 2PEF intensity on both photodiodes for 180° rotation of half-wave plate (360° rotation of excitation light polarization) and correlating the intensity with the excitation light polarization angle. It could be done manually, by measuring the emission intensity for every half-wave plate angle separately and then assembling it into a polar graph in data analysis software or automatically, using dedicated or self-written software.
   2. Adjust the piezostage parameters: scanning speed, step, and range to cover the area of the whole spherulite.
      NOTE: The scanning range must be higher than the spherulite diameter to fully frame the entire superstructure within the raster scan. Low scanning speed and step allow users to obtain high-quality images; however, this may result in sample burning. Therefore, a trade-off dependent on the spherulite size is necessary. These parameters cannot be universally applied. Exemplary parameters used in Figure 5A: scanning range 45 x 45 µm, scanning step 1 µm, and scanning speed 2 µm/s.
5. Open the shutter, turn on the photodiodes, and collect and 2P emission components for every single step of the selected scanning area-for the excitation beam polarized correspondingly to the X and then, the Y axes. Exemplary two-photon excited autofluorescence (2PAF) raster scans of insulin spherulites are presented in Figure 5A.
   NOTE: Measuring raster scans requires correlating piezo stage coordinates with and collected emission components, which could be done manually, by measuring the intensity in every single point of the selected area and then assembling it into a 2D matrix, or automatically, via self-written software. Raster scans can be presented as a summation of and emission components' intensity or distinctively for a specific emission component. As they are highly structure-dependent, structural distortions within spherulites are easily visible. However, due to the movement of the microscope stage, some samples may drift off from the field of view. Therefore, images need to be screened for artifacts. It is necessary to check the position of the spherulite before and after the scan.
6. To perform full polarization analysis from the specific spot on the sample, turn off the excitation beam.
7. Subsequently, pick specific coordinates of piezostage corresponding to the chosen location on the spherulite where the information about the orientation of molecules is required with the sub-µm resolution.
8. Adjust the piezoelectric stage to center the field of view at indicated (X, Y).
9. Turn on the excitation beam and perform full (360°) polarization analysis of and emission by turning on the rotation of the half-wave plate (180° rotation). Present 2PF Ix and Iy components in the form of a polar graph (as shown in Figure 5B).
   ​NOTE: This step can be repeated in different locations in the sample to collect a sufficient amount of data.

4. Determination of local fibril ordering inside the bovine insulin spherulites

NOTE: All numerical calculations connected to the data analysis were done using the Python programming language and based on the functions available in libraries NumPy and SciPy. Plotting the data requires the Matplotlib library. All calculations are based on formulas presented in supporting information in one of the papers by Obstarczyk et al.⁶.

1. Simulating the intensity of two-photon fluorescence excited for the specified distribution of molecules with a selected direction of the incident light polarization (denoted by α)
   NOTE: The presented formulas are based on the assumption of parallel absorption and emission dipole moments of a fluorophore. For a discussion of other cases (e.g., different directions of the absorption and emission dipole moments, energy transfer between the fluorophores), see the paper by Le Floc'h et al⁸.
   1. Find the parameters accounting for the variation of the electric field by polarization mixing and depolarization effects caused by the dichroic mirror mounted in a setup:
      1. γ represents the amplitude factor between the reflectivity of and polarized light from a dichroic mirror.
      2. δ represents the phase shift (ellipticity) between and polarized light.
         NOTE: Correctly defining these two parameters is crucial for successful structural characterization because of their strong influence on the shape of measured polar graphs^11,18. In the case of the presented system, both parameters were determined during ellipsometry measurements of a dichroic mirror applied in a system.
   2. Calculate the incident electric field vectors propagating in the X and Y axesof every angle measured during the ps-TPFM measurement using equations (1-5).
      (1)
      (2)
      (3)
      (4)
      (5)
      NOTE If the intensity is measured over the whole 360° with step 1°, calculate electric field vectors for all 360°. All angles should be in radians. ρ parameter is connected to optical frequency ω of the simulated electric field (ρ=ω·t) and used integrated from 0 to 2π during the calculations of the incident electric field vectors propagating in X and Y axis for every angle α measured during the ps-TPFM measurement.
   3. Define the functions for transition dipole moments in directions of three axes of a cartesian system according to equations (6-8):
      (6)
      (7)
      (8)
      NOTE: φ is the orientation angle of the amyloid fibril long axis in the XY sample frame. θ and ϕ angles are the polar and azimuthal angles used to define the transition dipole moment orientation of a fluorophore. 
   4. Use the functions defined in step 4.1.3. to define functions for J_x (Φ,θ,ϕ) and J_Y (Φ,θ,ϕ), which account for the contribution of tight light focusing with high numerical aperture objective to the fluorescence polarization detection in X and Y direction using equations (9, 10). 
      (9)
      (10)
      NOTE: K₁, K₂, K₃ factors are related to the microscope objective used during the ps-TPFM measurement. In these experiments, an apochromatic oil immersion objective 100x/1.4 NA was used and K₁, K₂, K₃ factors were 2.945, 0.069, and 1.016, respectively.
   5. Define a function for f(Ω), which is a molecular angular distribution, depending on the half aperture of a fluorophore cone Ψ, with a variable thickness ΔΨ; use equation (11). The graphical representation of all three angles concerning amyloid fibril is presented in Figure 6.
        (11)
      NOTE: Be careful while writing the exponent-the power of 2 works on the function argument, not the whole function!
   6. Define all f_WWIJKL factors as shown in equations (12-21).
      (12)
      (13)
      (14)
      (15)
      (16)
      (17)
      (18)
      (19)
      (20)
      (21)
   7. Calculate two-photon excited fluorescence intensities and for every measured angle (similarly as in point 4.1.2) using equations (22, 23).
      = (22)
      = (23)
   8. Check if the simulation is working correctly using the following variable values (placed in the legend to Figure 7) and compare the obtained results with Figure 7A-C.
      NOTE: All degrees should be written in radians.
2. Fit the simulated intensities into the intensity of two-photon-excited autofluorescence of bovine insulin spherulites collected during ps-2PFM measurements.
   NOTE: Resolving the spherulite structure based on ps-2PFM measurements requires using the equations written in the protocol to simulate the theoretical intensity of two-photon excited fluorescence and fitting all the parameters connected to the ordering of molecular fluorophore. It requires multiple iterations over the various values of Φ, an angle describing the rotation of the fibril in the XY microscope sample, and ΔΨ, aberrations of the conical distribution of the emission dipole Ψ due to the molecular rotations in filaments for fixed Ψ until reaching the highest possible R² coefficient between normalized two-photon excited fluorescence signal intensity collected during measurement and normalized intensities simulated according to step 4.1 of the protocol.
   1. Determine the Ψ half-angle.
      NOTE: For bovine insulin spherulites, it should be equal to Ψ = 29°⁶.
   2. Fitting workflow:
      1. Choose the value of Φ from 0° to 180° (in Figure 8A and 8B Φ = 16° and 127°, respectively).
      2. Choose the value of ΔΨ from 0° to 90° (in Figure 8A,B, ΔΨ = 24° and 1°, respectively).
      3. Calculate (equation 22) and (equation 23) for the whole measured range of θ angles using the chosen values of Φ and ΔΨ.
      4. Compare the intensities calculated during simulations (both normalized to the maximum value of
      5. Calculate ) with normalized intensities of
      6. Calculate and (both normalized to the maximum value of ) measured during ps-2PFM measurement.
         NOTE: In the presented experiments, Pearson product-moment correlation coefficients were calculated using the “corrcoef” function from the NumPy Python library.
   3. In the end, choose the values of Φ and ΔΨ leading to the highest correlation coefficients and convergence between the simulated intensities and measured signal similar to what is shown in Figure 8.

Representative Results

The presented protocol provides step-by-step guidance through the preparation of amyloid superstructures for testing with ps-2PFM, construction of the microscopic system, and measurements of the proper sample. However, before the final set of measurements, it is vital to properly align the APDs with an isotropic reference, which should result in collecting a symmetrical signal of similar shape and intensity on both detectors (Figure 4C). Even minimal differences between the intensities measured on the detectors in X and Y axes should be taken into account in further measurements and especially, during the analysis as an appropriate correction factor. After mounting, the sample containing single spherulites, giving a characteristic Maltese cross on the POM as in Figure 2B, and after performing a 2PFM raster scan, the image should look similar to what is shown in Figure 5A, which is consistent with reported 2PFM raster scans of spherulites^6,7 and different organized biomolecules^11,12. One may observe some changes in the location of the axis with the highest brightness, which is related to the fact that fluorescence signal intensity strongly depends on the polarization of the excitation beam. Therefore, it is necessary to verify which position of the half-waveplate corresponds to the excitation of the sample along the X (Figure 5A, top) and Y (Figure 5A, bottom) axes. It is also worth noting how polar graphs change while performing a full polarization analysis from different selected spots. Outside the spherulite, the polar graph looks like a collection of artifacts and random signal noise spikes (Figure 5B, I). Such a graph may also indicate the drift of the spherulite between measurements and require finding new coordinates of the entire structure by another 2PF raster scan. Properly measured polar graphs from highly ordered locations of insulin spherulite along the X and Y axes are shown in Figure 5B II and III, respectively. They can have different shapes and geometries, depending on the local orientation and organization of fluorophores measured from the selected spot⁷.

The last step of the protocol is focused on the analysis of the obtained data using an algorithm based on a mathematical model combining the orientation of amyloid fibers in the XY plane Φ, the associated fluorophore transient dipole moments Ψ, and their aberrations ΔΨ (Figure 6) with intensity and of two-photon induced fluorescence. Correctly implemented functions presented in the protocol should, after entering the appropriate input data (protocol step 4.9), produce identical polar graphs as those presented in Figure 7. Any deviations-different data orientation, intensities, or shapes of simulated and -indicate errors in the code. If the model works, one can proceed to the last step of the protocol-fitting the simulated data to real data obtained from the ps-2PFM measurement. Chosen values of Φ and ΔΨ with the highest correlation coefficients and convergence between the simulated intensities and measured signal should lead to similar images as shown in Figure 8. There should be the best possible fit of and functions to the overall orientation and shape of and and the values of Φ and ΔΨ should correspond to the local orientation of fibrils and fluorophores in the measured spot on spherulite. Similar models and fitting methods could also be used for the determination of the local organization of other biomolecules like DNA¹¹.

Figure 1: Two-photon polarization-sensitive microscopy setup. Scheme showing the two-photon microscope setup used for the polarization-sensitive two-photon excited fluorescence measurements of bovine insulin spherulites. Two-photon excited emission horizontally and vertically polarized (to microscope sample plane) components are depicted with I_X, and I_Y, respectively. Abbreviations: SP = sample plane; O = objective; DM = dichroic mirror; λ/2 = half-wave plate; LPF = long-pass filter; BE = beam expander; P = Glan polarizer; Ti: Sa = Titan: sapphire laser light source; M = Mirror; SPF = short pass filter; PBS = polarization beam splitter; L = optical lens; APD = avalanche photodiode. Please click here to view a larger version of this figure.

Figure 2: Scheme showing the slide preparation/photo. (A) Scheme showing the sealed sample preparation; (B) photographs of the subsequent steps for the sample sealing. I: a 100 µL aliquot of the spherulite solution on the microscopy slide with a well, II: coverslip dropped on top of the solution; III: tight seal formed from deposited polymer (mountant). Please click here to view a larger version of this figure.

Figure 3: Quality control of the insulin spherulites under a polarized-light microscope. (A1,B1) Brightfield mode as well as under (A2,B2) crossed polarizers. Characteristic Maltese cross pattern can be observed on the corresponding images taken with crossed polarizers. (A) Spherulites aggregates with structural distortions, (B) high-quality isolated spherulite. Scale bars = 5 µm. Please click here to view a larger version of this figure.

Figure 4: Testing the alignment of the ps-2PFM system. (A) Concentric defocused image of the fluorescein fluorescence as seen without (A1) and with (A2) dichroic mirror, (B) photodamaged spherulite with burned holes arising due to the elongated polarization analysis in selected points along x and y directions, (C) two-photon excited emission components in dependence on incident light polarization angle as registered for an isotropic sample (fluorescein solution). and denote emission components measured by avalanche photodiodes measuring the X and Y emission polarization axis, respectively. Scale bars = 5 µm (A1,A2), 10 µm (B). Please click here to view a larger version of this figure.

Figure 5: Exemplary 2PFM raster scans and polar graphs from label-free insulin spherulite. (A) 2PF intensity raster scans of label-free insulin spherulites: polarization of excitation light: (A1) horizontal polarization, (A2) vertical polarization, and emission are denoted with white arrows, and the inset shows the same spherulite imaged under a standard polarized light microscope with crossed polarizers. (B) Polar graphs derived from three spots denoted on the A1 scan (B1, I; B2, II; B3, III). I_x and I_y denote emission components measured by avalanche photodiodes measuring the X and Y emission polarization axis, respectively. Abbreviation: 2PF = two-photon fluorescence. Please click here to view a larger version of this figure.

Figure 6: Conical distribution of the emission dipole of the dye (half angle, Ψ) with respect to the long fibril axis. The dashed line shows the long fibril axis. The rotation of the fibril in the XY microscope sample plane is described by the angle. Aberrations of Ψ due to the molecular rotations in filaments are described by ΔΨ. This figure is from Obstarczyk et al⁶. Please click here to view a larger version of this figure.

Figure 7: Simulated intensity of polarized two-photon excited fluorescence. Fluorescence calculated for (A) Φ = 1°, Ψ = 1°, ΔΨ = 1°; (B) Φ = 1°, Ψ = 30°, ΔΨ = 1°; (C) Φ = 1°, Ψ = 30°, ΔΨ = 60°. Red, blue, and yellow lines correspond to , , and + , respectively. Φ angle describes the rotation of the fibril in the XY microscope sample plane, Ψ - conical distribution of the emission dipole, and ΔΨ- aberrations of Ψ due to the molecular rotations in filaments. All other parameters were identical in all cases: K1 = 2.945, K2 = 0.069, K3 = 1.016, γ = 0.01, and δ = 0.98845. Please click here to view a larger version of this figure.

Figure 8: Polar graphs of experimental datasets. (A,B) Exemplary polar graphs after fitting two experimental datasets collected during ps-TPFM measurements of bovine insulin spherulites. Measured and two-photon excited emission components for X and Y emission polarization axis are presented with red and blue dots, respectively; meanwhile, solid lines present the corresponding simulated two-photon excited fluorescence emission components for X and Y emission polarization axis and . Please click here to view a larger version of this figure.

Discussion

Polarization-sensitive two-photon microscopy is a valuable tool for studying the local ordering of fibrils inside the amyloid superstructures, requiring only small modifications of the standard multiphoton setup. Since it operates on nonlinear optical phenomena, reduced angular photo-selection and enhanced axial resolution can be achieved compared to one-photon excited fluorescence microscopy methods. In addition, it leads to lower light scattering, lower phototoxicity, and deeper sample penetration when compared to the one-photon excitation fluorescence microscopy techniques^19,20. As we already proved, it is well-suited for measurements of densely-packed aggregates of proteins such as spherulites, which can be performed in a label-free manner²¹.

However, to effectively use the method described here, attention should be paid to several key issues. Starting with sample preparation and its quality, namely, incubation, always ensure that amyloid superstructures have grown correctly. In the case of spherulites, we used a polarized optical microscope with crossed polarizers to localize mature spherulites, which give a characteristic Maltese cross pattern, and have a radius of ~5 µm¹⁶. However, spherulites are heterogeneous, and distinctive structures can be observed within the sample. Therefore, it is crucial to pick separated and non-distorted species. As for the measurement system itself, it is crucial to control the polarization of incident light so that the polarization of the beam at the entrance to the microscope body should be precisely determined and the depolarization introduced by the optical elements used should be minimized²². To assure the best performance, we recommend using high-quality silver mirrors and optical filters matched to the excitation and fluorescence emission wavelengths. Due to the key role of light polarization also in the emission path, it is essential to measure an isotropic reference sample before the actual measurement. If the excitation path and APD detectors are aligned correctly, one should see an equally intense signal on both detectors as presented in Figure 4C. Reference should generate a strong two-photon excited fluorescence at relatively low laser power to avoid photobleaching; we used fluorescein since its two-photon absorption cross-sections for different wavelengths were already reported in the literature²³.

To correctly determine the arrangement of structures inside the spherulites, a lot of attention should also be devoted to data analysis. The basic assumption of this model is the collinearity of the transition dipole moment of light absorption and emission. Under that assumption, aligning the transition dipole moment of the molecule parallel to the polarization of the incident light allows for its combination with the internal structure of the tested sample, yielding the highest emission intensity. The given model can also be used as a good approximation for small differences in the angle between the two dipole moments⁸ but requires further modifications for large deviations. Therefore, as described, some assumptions regarding the sample must be taken into consideration a priori to imaging and data analysis. In the model case on which the simulation and the equations used in this method are based, the main source of depolarization in the system is the dichroic mirror. Therefore, before proceeding with the data analysis, it is necessary to determine the parameters responsible for the depolarization introduced by the dichroic mirror due to their impact on the shape of the collected polar graphs and consequently, the correct determination of the organization of the molecules within the examined structure during fitting¹⁸. This becomes a key problem, especially in the case of measurements for several wavelengths, since the change in the ellipticity of the dichroic mirror is distinctively wavelength-dependent¹². Induction of depolarization can strongly affect the characteristics of the collected signal¹¹. Last but not least, when creating the script for data analysis, one should pay attention while introducing mathematical functions and variables presented in the last part of the protocol. To avoid errors, focus on features such as multiple function calling and global parameters, which will also significantly speed up the analysis time.

We should also mention the most common problems one may encounter when using the described method. The sample preparation time is very much dependent on the speed of mountant hardening. To speed this up, we recommend that the samples be prepared in a warm, dry place and the spherulite solution is sealed before mounting it in a microscope. Measurements performed too early may lead to unsealing of the slide and destruction of the used objective lens. In addition, despite proper sample preparation, small spherulites may float in the solution during the measurement due to the material stress introduced by the objective. To avoid this, we advise scanning isolated middle-size structures since the largest ones are commonly aggregates. It is recommended to check whether the scanned spherulite has moved after data acquisition, in comparison to the image before starting the measurement. In addition, despite the correct alignment of all optical elements and detectors used to measure the ps-2PFM, the measured intensities and of the isotropic reference may still differ slightly in intensity. In such a case, it is necessary to take this into account when analyzing the data from the sample measurements by multiplying one of the intensities by the correction factor determined during the reference measurements. Last, but not least, it is possible that during the fitting procedure, the script will not be able to find any matching values of Φ and ΔΨ. This may be due to several factors-data were collected from a disorganized spot on a sample, for example, the core of a spherulite; the studied structure was not fully formed during incubation; incorrect simulation of and ; using incorrect dichroic mirror parameters γ and δ; too large step set for Φ and ΔΨ angles between each iteration during fitting. In the case of a disorganized spot, we recommend trying to collect data from points lying closer to the perimeter of the examined structure. In the case of an incompletely formed structure, repeat the incubation or search the slide for other structures. In the case of incorrect simulations, manually check whether by changing the parameters Φ, Ψ, and ΔΨ, the simulated intensities and change and correct any errors in the code. In the case of incorrect dichroic mirror parameters, carefully check the γ and δ parameters of the dichroic mirror used during the measurements. In the case of a large step set for the angles during fitting, reduce the step between successive iterations to 2º or 1º. It should also be remembered that in the case of strong local disorganization of the structure, R² will always be lower, often in the range of 0.5–0.6. This is because the presented model describes highly ordered molecules where most of the transient dipole moments are aligned in a similar direction; hence, matching amorphous or highly disordered structures leads to lower correlation coefficients. Therefore, it is crucial to possess at least some structural information on the sample before the measurement to correctly analyze the obtained data.

It is also worth noting that the presented method possesses several limitations. Data analysis could result in several values of Φ and ΔΨ angles with high enough correlation factors, requiring the experimenter to use their knowledge and experience to select appropriate values. In this case, the boundary conditions must be taken into account, such as that fluorophore cone half-angle Ψ must always be bigger than its aberration ΔΨ. In addition, when comparing our data with the literature, it is worth noting that some papers describe Ψ as a full-cone angle, while we operate on a half-cone angle. Another limitation is the measurement resolution, limited to a sub-micron resolution. Because of that, the photo-selectivity of the system and resulting local organization determination are based on the averaged signal from fibrils excited in the focal spot rather than single structures. Moreover, the sample itself needs to possess sufficient fluorescence quantum yield, as long exposure under fs incident laser power (necessary to acquire data for polar graphs) may be destructive and impact the results. 

Despite these difficulties, we believe that the method presented in this paper has a wide range of applications, for label-based and label-free imaging of biostructures in hydrated and complex environments. We had previously shown that local fibril ordering calculated from ps-2PEF data correlates with information derived from transmission electron microscopy⁷. Therefore, we confirmed the validity of ps-2PEF in bio-imaging and further expanded the knowledge on the structural ordering of amyloid superstructures. This method can be applied to learn about the origin of intrinsic fluorescence observed in the case of various components of biological samples, such as the autofluorescence of protein aggregates—amyloids. Given relevant data about the orientation of absorption/emission dipole moment directions with respect to the long axis of amyloid fibrils, the optical properties of the fibrils can be correlated with their structure⁶. We indicated that for structures with an already-determined Ψ angle, this technique allows the detection of distinct structural features of amyloid superstructures and polymorphs of insulin superstructures based on the level of their organization⁷. As previously noted in the protocol, the presented setup could also be applied for polarization-sensitive second harmonic generation measurements, which is also a label-free two-photon microscopy technique²⁴. This will require not only mounting different optical filters but also changing the formulas used for data analyses²⁵. Moreover, with the addition of a properly aligned quarter waveplate, it could be used to excite the sample with circularly polarized light, which might lead to the generation of chiral nonlinear optical properties of amyloids since they are chiral biopolymers with confirmed strong chiroptical properties²⁶. However, in such a case, the constantly rotating electric vector would lead to the constantly changing direction of the excited emission, making it impossible to determine any structural information using the equations presented in this manuscript. All in all, ps-2PEF is a promising tool for the determination of the organization within numerous complex bio-structures with ordered emission dipoles, such as protein aggregates, DNA, or tissues in a non-invasive way.

Materials

Name	Company	Catalog Number	Comments
Sample preparation
Coverslips, 24 x 24 mm	Chemland	04-298.202.04
DPX mountant for histology	Sigma-Aldrich	6522	Slide mountant
Eppendorf Safe-Lock tubes, 1.5 mL, polypropylene	Chemland	02-63102
Eppendorf ThermoMixer C	Eppendorf		Used for spherulite incubation
HLP 5UV Water purification system	Hydrolab		Source of dionized water used in sample preparation
Hydrochloric acid (≥37%, APHA ≤10),	Sigma-Aldrich	30721-M
Insulin powder from the bovine pancreas (≥25 units/mg (HPLC))	Sigma-Aldrich	I5500
Methanol (HPLC grade)	Sigma-Aldrich	270474
Microscope slides with a concave, 76 x 26 x 1 mm	Chemland	04-296.202.09
Olympus BX60	Olympus		Polarized Optical Microscope used in Figure 2
PTFE thread seal tape, 12 mm x 12 mm x 0.1 mm, 60 gm2	Chemland	VIT131097
Microscope ps-2PFM setup
Chameleon Ultra II	Coherent
FELH0800 - Ø25.0 mm Longpass Filter	Thorlabs
FESH0700 - Ø25.0 mm Shortpass Filter	Thorlabs
IDQ100 photon-counting avalanche photodiodes	ID Quantique
Multiphoton short-pass emission filter 720 nm	Semrock
Mounted Achromatic Half-Wave Plate, 690-1200 nm	Thorlabs
Nikon Plan Apo Oil Immersion 100x/1.4 NA	Nikon
piezo 3D stage	Piezosystem Jena
Polarizing Beamsplitter	Thorlabs
S130C - Slim Photodiode Power Sensor, Si, 400 - 1100 nm, 500 mW	Thorlabs
Software
LabView 2018	National Instruments		Version 18.0.1f2
Matplotlib library			Version 3.3.2
NumPy library			Version 1.19.2
SciPy library			Version 1.5.2
Spyder Python 3 IDE			Version 4.1.5