Serguei Krouglov

Nonlinear Optical Properties of Type I Collagen Fibers Studied by Polarization Dependent Second Harmonic Generation Microscopy

Collagen (type I) fibers are readily visualized with second harmonic generation (SHG) microscopy though the molecular origin of the signal has not yet been elucidated. In this study, the molecular origin of SHG from type I collagen is investigated using the time-dependent coupled perturbed Hartree-Fock calculations of the hyperpolarizibilities of glycine, proline, and hydroxyproline. Two effective nonlinear dipoles are found to orient in-the-plane of the amino acids, with one of the dipoles aligning close to the pitch orientation in the triple-helix, which provides the dominant contribution to the SHG polarization properties. The calculated hyperpolarizability tensor element ratios for the collagen triple-helix models: [(Gly3)n]3, [(Gly-Pro2)n]3, and [(Gly-Pro-Hyp)n]3, are used to predict the second-order nonlinear susceptibility ratios, χ(zzz)(2)/χ(iiz)(2) and χ(zii)(2)/χ(iiz)(2) of collagen fibers. From SHG microscopy polarization in, polarization out (PIPO) measurements of type I collagen in human lung tissue, a theoretical method is used to extract the triple-helix orientation angle with respect to the collagen fiber. The study shows the dominant role of amino acid orientation in the triple-helix for determining the polarization properties of SHG and provides a method for determining the triple-helix orientation angle in the collagen fibers.

Hierarchical Model of Fibrillar Collagen Organization for Interpreting the Second-Order Susceptibility Tensors in Biological Tissue

The second-order nonlinear polarization properties of fibrillar collagen in various rat tissues (vertebrae, tibia, tail tendon, dermis, and cornea) are investigated with polarization-dependent second-harmonic generation (P-SHG) microscopy. Three parameters are extracted: the second-order susceptibility ratio, R = [Formula: see text] ; a measure of the fibril distribution asymmetry, |A|; and the weighted-average fibril orientation, . A hierarchical organizational model of fibrillar collagen is developed to interpret the second-harmonic generation polarization properties. Highlights of the model include: collagen type (e.g., type-I, type-II), fibril internal structure (e.g., straight, constant-tilt), and fibril architecture (e.g., parallel fibers, intertwined, lamellae). Quantifiable differences in internal structure and architecture of the fibrils are observed. Occurrence histograms of R and |A| distinguished parallel from nonparallel fibril distributions. Parallel distributions possessed low parameter values and variability, whereas nonparallel distributions displayed an increase in values and variability. From the P-SHG parameters of vertebrae tissue, a three-dimensional reconstruction of lamellae of intervertebral disk is presented.

Three‐dimensional visualization of the first hyperpolarizability tensor

With polarization dependent second harmonic generation (SHG) microscopy becoming a more popular method for investigating the structure of biological materials, there is a need to develop tools with which to understand and interpret the observed SHG properties. Quantum mechanical calculations of the hyperpolarizability tensor have become a popular method for understanding the SHG properties of biomolecules. Visualization of the full hyperpolarizability tensor, termed the unit sphere representation, has been developed to provide insight and intuition on the relationship between SHG properties and molecules. A single vector representation is also presented, which approximates the SHG properties of molecules for certain cases, where the anisotropy is negligible.

Double Stokes Mueller polarimetry of second-harmonic generation in ordered molecular structures

Second-harmonic generation (SHG) is highly sensitive to the structure of ordered aggregates, and therefore, the polarization measurement of SHG can help to elucidate the organization of molecules in crystalline structures. The double Stokes Mueller formalism is developed for the SHG polarimetry and convenient expressions are derived for the double Mueller matrix in terms of the nonlinear susceptibilities. The polarization analysis is presented for cylindrically symmetric structures, providing the method to calculate the characteristic susceptibility component ratios and orientations of molecules in the ordered aggregates. This information, for example, can be used to investigate collagen or myosin structure in biological tissues.

Characterization of collagen in non-small cell lung carcinoma with second harmonic polarization microscopy

Polarization second harmonic microscopy was used for collagen imaging in human non-small cell lung carcinoma and normal lung tissues ex vivo and revealed significant differences in the nonlinear susceptibility component ratio, demonstrating potential use in cancer diagnosis.

Molecular Organization of Crystalline β‑Carotene in Carrots Determined with Polarization-Dependent Second and Third Harmonic Generation Microscopy

Polarization-in, polarization-out (PIPO) second harmonic generation (SHG) and third harmonic generation (THG) microscopy was used to study the crystalline organization of β-carotene molecules within individual aggregates contained in the chromoplasts of orange carrots in vivo. Multimodal PIPO SHG and PIPO THG studies of the aggregates revealed one dominant SHG and THG dipole signifying that β-carotene molecules are oriented along a single axis. Three-dimensional visualization of the orientation of β-carotene molecules with respect to the aggregate axis was also performed with both microscopy modalities and revealed organization of the aggregates as ribbon-like structures consisting of twists and folds. Therefore, PIPO SHG and PIPO THG microscopy provides information on the crystalline organization and the orientation of ordered biological structures in vivo where multimodal polarization dependent SHG and THG investigations are particularly advantageous as both noncentrosymmetric and centrosymmetric crystalline organizations can be probed.

Second harmonic generation double stokes Mueller polarimetric microscopy of myofilaments

The experimental implementation of double Stokes Mueller polarimetric microscopy is presented. This technique enables a model-independent and complete polarimetric characterization of second harmonic generating samples using 36 Stokes parameter measurements at different combinations of incoming and outgoing polarizations. The degree of second harmonic polarization and the molecular nonlinear susceptibility ratio are extracted for individual focal volumes of a fruit fly larva wall muscle.

Nonlinear Stokes Mueller Polarimetry

The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional

Second Harmonic Generation Mediated by Aligned Water in Starch Granules.

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Three-photon Stokes-Mueller polarimetry

Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.