Second harmonic generation theory for a helical macromolecule with high sensitivity to structural disorder

Double Stokes polarimetric microscopy for chiral fibrillar aggregates

Second harmonic generation (SHG) microscopy is a powerful tool for imaging collagen and other noncentrosymmetric fibrillar structures in biological tissue. Polarimetric SHG measurements provide ultrastructural information about the fibrillar organization in a focal volume (voxel). We present a reduced nonlinear polarimetry method named double Stokes polarimetry (DSP) for quick characterization of chiral C 6 symmetry fibers without data fitting that simplifies and speeds up the polarimetric analysis. The method is based on double Stokes-Mueller polarimetry and uses linear and circular incident and outgoing polarization states. The analytical expressions of DSP polarimetric parameters are defined in terms of conventional SHG Stokes vector components. A complex chiral susceptibility (CCS) model is assumed to derive expressions of ultrastructural parameters consisting of the magnitude and phase of molecular complex-valued chiral susceptibility ratio, real-valued achiral ratio, and fiber orientation in a voxel. The ultrastructural parameters are expressed in terms of directly measurable DSP polarimetric parameters. DSP is validated with rat tail tendons sectioned at different orientations. DSP can be applied to investigate the origin of chiral complex-valued susceptibility of collagen, to study modifications of collagen in cancerous tissue, and to map ultrastructural parameters of large areas for whole-slide histopathology.

Polarimetric second-harmonic generation microscopy of partially oriented fibers I: Digital modeling

Second-harmonic generation (SHG) in biological tissues originates predominantly from noncentrosymmetric fibrillar structures partially oriented within a focal volume (voxel) of a multiphoton excitation microscope. This study is aimed to elucidate fibrillar organization factors influencing SHG intensity, as well as achiral, R, and chiral, C, nonlinear susceptibility tensor component ratios. SHG response is calculated for various configurations of fibrils in a voxel using the digital nonlinear microscope. The R and C ratios are calculated using linear incident and outgoing polarization states that simulate polarization-in polarization-out polarimetric measurements. The investigation shows strong SHG intensity dependence on parallel/antiparallel fiber organization. The R and C ratios are strongly influenced by the fiber chirality, tilting of the fibers out of the image plane, and crossing of the fibers. The computational modeling provides the basis for the interpretation of polarimetric SHG microscopy images in terms of the ultrastructural organization of fibers in each voxel of the samples. The modeling results are employed in the accompanying paper to investigate the ultrastructures with parallel/antiparallel fibers and two-dimensional and tree-dimensional crossing fibers in biological and biomimetic structures.

Polarimetric second harmonic generation microscopy of partially oriented fibers II: Imaging study

Polarimetric second harmonic generation (SHG) microscopy imaging is employed to investigate the ultrastructural organization of biological and biomimetic partially oriented fibrillar structures. The linear polarization-in polarization-out SHG microscopy measurements are conducted with rat tail tendon, rabbit cornea, pig cartilage, and biomimetic meso-tetra(4-sulfonatophenyl)porphine (TPPS4) cylindrical aggregates, which represent different two- and three-dimensional (2D and 3D) configurations of C6 symmetry fibril structures in the focal volume (voxel) of the microscope. The polarization-in polarization-out imaging of rat tail tendon reveals that SHG intensity is affected by parallel/antiparallel arrangements of the fibers, and achiral (R) and chiral (C) susceptibility component ratio values change by tilting the tendon fibers out of image plane. The R ratio changes for the 2D crossing fibers observed in cornea tissue. The 3D crossing of fibers also affects R ratio in cartilage tissue. The distinctly different dependence of R on crossing and tilting of fibers is demonstrated in collagen and TPPS4 aggregates, due to the achiral molecular susceptibility ratio having values below and above 3, respectively. The polarimetric microscopy results correspond well with the analytical expressions of amplitude and R and C ratios dependence on the crossing angle of the fibers. The experimentally measured SHG intensity and R and C ratio maps are consistent with the computational modeling of various fiber configurations presented in the preceding article. The demonstrated SHG intensity and R and C ratio dependencies on fibril configurations provide the basis for interpreting polarimetric SHG microscopy images in terms of 3D ultrastructural organization of fibers in each voxel of the samples.

High numerical aperture imaging allows chirality measurement in individual collagen fibrils using polarization second harmonic generation microscopy

Second harmonic generation (SHG) microscopy is a commonly used technique to study the organization of collagen within tissues. However, individual collagen fibrils, which have diameters much smaller than the resolution of most optical systems, have not been extensively investigated. Here we probe the structure of individual collagen fibrils using polarization-resolved SHG (PSHG) microscopy and atomic force microscopy. We find that longitudinally polarized light occurring at the edge of a focal volume of a high numerical aperture microscope objective illuminated with linearly polarized light creates a measurable variation in PSHG signal along the axis orthogonal to an individual collagen fibril. By comparing numerical simulations to experimental data, we are able to estimate parameters related to the structure and chirality of the collagen fibril without tilting the sample out of the image plane, or cutting tissue at different angles, enabling chirality measurements on individual nanostructures to be performed in standard PSHG microscopes. The results presented here are expected to lead to a better understanding of PSHG results from both collagen fibrils and collagenous tissues. Further, the technique presented can be applied to other chiral nanoscale structures such as microtubules, nanowires, and nanoribbons.

Wide-field Stokes polarimetric microscopy for second harmonic generation imaging

We employ wide-field second harmonic generation (SHG) microscopy together with nonlinear Stokes polarimetry for quick ultrastructural investigation of large sample areas (700 μm × 700 μm) in thin histology sections. The Stokes vector components for SHG are obtained from the polarimetric measurements with incident and outgoing linear and circular polarization states. The Stokes components are used to construct the images of polarimetric parameters and deduce the maps of ultrastructural parameters of achiral and chiral nonlinear susceptibility tensor components ratios and cylindrical axis orientation in fibrillar materials. The large area imaging was employed for lung tumor margin investigations. The imaging shows reduced SHG intensity, increased achiral susceptibility ratio values, and preferential orientation of collagen strands along the boarder of tumor margin. The wide-field Stokes polarimetric SHG microscopy opens a possibility of quick large area imaging of ultrastructural parameters of tissue collagen, which can be used for nonlinear histopathology investigations.