Effect of molecular organization on the image histograms of polarization SHG microscopy

Abstract

Based on its polarization dependency, second harmonic generation (PSHG) microscopy has been proven capable to structurally characterize molecular architectures in different biological samples. By exploiting this polarization dependency of the SHG signal in every pixel of the image, average quantitative structural information can be retrieved in the form of PSHG image histograms. In the present study we experimentally show how the PSHG image histograms can be affected by the organization of the SHG active molecules. Our experimental scenario grounds on two inherent properties of starch granules. Firstly, we take advantage of the radial organization of amylopectin molecules (the SHG source in starch) to attribute shifts of the image histograms to the existence of tilted off the plane molecules. Secondly, we use the property of starch to organize upon hydration to demonstrate that the degree of structural order at the molecular level affects the width of the PSHG image histograms. The shorter the width is the more organized the molecules in the sample are, resulting in a reliable method to measure order. The implication of this finding is crucial to the interpretation of PSHG images used for example in tissue diagnostics.

Keywords: (180.4315) Nonlinear microscopy; (190.2620) Harmonic generation and mixing.

Fig. 1

Coordinates system of the 3D PSHG biophysical model. (a) SHG image of starch with the lab coordinate system (blue axis) and polarization orientation for the incident electric field (red). (b) Tensor (molecule) coordinate system (green axis). In purple, radius R and pitch P, helical pitch angle θ_e and hyperpolarizability β. The dimensions of the figure are nominal and do not correspond to reality.

Fig. 2

3D-PSHG in hydrated starch (a) mean intensity of the 9 PSHG images. Scale bar corresponds to 10 μm. (b) Angle ϕ giving the orientation of the molecule in the focal plane. The radial architecture of amylopectin is shown in the evolution of the angle. (c) A = d₃₁/d₁₅ checks the validity of the model assumptions. (d) anisotropy parameter B defined by Eq. (11). (e) Pixel resolution representation of the helical pitch angle θ_e. (f) Pixel resolution representation of the tilted-off the plane angle δ.

Fig. 3

Equatorial histograms of hydrated starch. (a) A = d₃₁/d₁₅ peak at 1.01, width of 0.50. (b) B parameter, peak at 3.54, width of 1.14. (c) Helical pitch angle θ_e retrieved from B considering the 2D approach. Peak at 36.1°, width of 4.9°. (d) Tilted-off the plane angle δ, peak at 48°, mean 44,8°, width of 36 °.

Fig. 4

(a) Schematics of the measurement preformed in the starch granule, showing the two imaged planes for the B parameter at the equator and ~5µm up from this position. Comparison of the image histograms obtained from the two measurements for (b) A, (b) B, (c) θe, and (d) δ, showing the effect of the existence of a large number of molecules tilted-off the plane: The peak shifts between the two imaged planes for B, θ_e and δ, but not for A parameter.

Fig. 5

The left image shows the distribution of the anisotropy parameter B in the equator of a starch granule. The three histogram for the angle δ on the right have been obtained from the three numbered regions of interest (ROI) shown in the left image.

Fig. 6

Comparison between equatorial 2D and 3D-PSHG of the same dried and hydrated starch. The image histograms for the helical pitch are centered at θ_e(dried) = 37.5°and θ_e(hydrated) = 37.8° indicating that the helical pitch angle of amylopectin does not change under hydration. Under hydration starch is more organized and the width for the retrieved B parameter is ~33% narrower for the hydrated than the width of the less organized dried one. This is translated in a δ off-plane width ~17% narrower in hydrated starch.