Modeling and Predicting Second-Harmonic Generation from Protein Molecular Structure

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Modeling and Predicting Second-Harmonic Generation from Protein Molecular Structure

Bahar Asadipour, Emmanuel Beaurepaire, Xingjian Zhang, Anatole Chessel, Pierre Mahou, Willy Supatto, Marie-Claire Schanne-Klein, and Chiara Stringari

Phys. Rev. X 14, 011038 – Published 6 March 2024

Abstract

Polarization resolved second-harmonic generation (pSHG) microscopy is increasingly used for mapping organized arrays of noncentrosymmetric proteins such as collagen, myosin, and tubulin, and holds potential for probing their molecular structure and supramolecular organization in intact tissues. However, the contrast mechanism of pSHG is complex and the development of applications in the life sciences is hampered by the lack of models accurately relating the observed pSHG signals to the underlying molecular and macromolecular organization. In this work, we establish a general multiscale numerical framework relating the micrometer-scale SHG measurements to the atomic-scale and molecular structure of the proteins under study and their supramolecular arrangement. We first develop a new method to automatically analyze pSHG signals independently of the protein type and fiber orientation. We then characterize experimentally pSHG signals in live zebrafish larvae and show that they can be used to distinguish collagen, myosin, and tubulin structures in intact tissues. We then introduce a numerical model that considers the peptide bond (PB) as the elementary SHG source in proteins and takes into account the three-dimensional (3D) distribution of PBs to predict the second-order hyperpolarizability tensor $β$ of proteins, as well as the SHG efficiency and pSHG response of an arbitrary macromolecular assembly. We show that this model accurately reproduces pSHG measurements obtained from collagen, myosin, microtubule, and actin structures, revealing the precise dependence of SHG signals on the 3D distribution of PBs within protein assemblies. We then use our model to analyze pSHG from a 3D distribution of microtubule assemblies as a function of out-of-plane angles, angular disorder, and polarity. Finally, we demonstrate that our model predicts SHG from different molecular conformations of tubulin that are highly relevant from a biomedical point of view as associated with microtubules (de)polymerization. By bridging scales from the molecular bonds to the optical wavelength, our model provides an accurate interpretation of SHG signals in terms of protein structure and supramolecular organization.

Received 2 November 2022
Revised 29 September 2023
Accepted 22 December 2023

DOI:https://doi.org/10.1103/PhysRevX.14.011038

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Nonlinear optics

Fish Proteins

Multiscale modeling Optical microscopy Optical second-harmonic generation

Physics of Living SystemsAtomic, Molecular & Optical

Authors & Affiliations

Bahar Asadipour , Emmanuel Beaurepaire , Xingjian Zhang , Anatole Chessel , Pierre Mahou , Willy Supatto , Marie-Claire Schanne-Klein , and Chiara Stringari ^*

Laboratory for Optics and Biosciences (LOB), École Polytechnique, CNRS, Inserm, Institut Polytechnique de Paris, 91128 Palaiseau, France

^*chiara.stringari@polytechnique.edu

Popular Summary

In mammalian biological tissues, the proper arrangement of three key proteins—collagen, myosin, and microtubules—plays a key role in the function of tissues, while their disorganization can lead to biological dysfunctions and pathologies. Probing and measuring the structure and the organization of these proteins is therefore scientifically, and even medically, crucial. To that end, we establish a novel experimental and theoretical framework by refining an optical microscopy technique and developing a model that links the microscopy readout with the protein molecular structure and macromolecular arrangement.

Specifically, we focus on second-harmonic generation microscopy, a technique that provides high-contrast imagery by illuminating a noncentrosymmetric structure with laser light and detecting the frequency-doubled photons radiated in response. We demonstrate how the dependence of this process with respect to the polarization of the excitation beam is sensitive to the molecular structure of the protein, and therefore to the protein type, conformation, and organization of protein assemblies. This allows us to spatially discriminate, with micrometer resolution, different protein types and map their organization in a biological sample such as a zebrafish embryo. We also establish a model relating the second-harmonic generation to the molecular structure of these proteins, which enables the quantitative interpretation of the microscopy images and the prediction of the optical response from an arbitrary protein arrangement.

Our proof-of-principle study demonstrates the promise of this model for understanding and predicting the optical response from protein molecular structures. We hope that further development of the framework will turn it into a practical method for probing the ultrastructure and rearrangement of proteins in situ in the context of physiopathological processes.

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Vol. 14, Iss. 1 — January - March 2024

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Images

Figure 1
Polarization resolved SHG (pSHG) measurements on different fibrillar structures in a live zebrafish larva at 5 days post fertilization (dpf). (a) pSHG microscopy setup. A rotating half-wave plate (HWP) is installed before the objective and is used to control the direction of the incident linear polarization in the $y z$ imaging plane of the laboratory system. (b) Scheme of a zebrafish larva at 5 dpf. Collagen and myosin signals are observed in the pectoral fins (i) and in the trunks (ii), while tubulin signals are observed in the brain and spinal cord (iii). (c) pSHG images recorded at polarization angles $φ = 0 °$ , 40°, and 90° as indicated by the arrows. pSHG raw data are displayed in Movies M1–M4 in Supplemental Material [47]. (d) Dependence of the SHG intensity in a region of interest as a function of the incident polarization angle $φ - φ_{0}$ , where $φ_{0}$ is the angle of the protein fiber axis. Curves are obtained by the least square fitting of Eq. (a21) (see Table 4). (e) Maps of the relative angle of the maximum (highest minimum) SHG intensity with respect to the fiber axis for one-peaked (two-peaked) pSHG profiles extracted automatically with the structure-tensor analysis and FFT-based analysis (Appendix pp1-s2). (f) Maps of the anisotropy factor $γ$ for the three proteins calculated with the FFT-based analysis (Appendix pp1-s2) taking in account the relative angle of the maximum (highest minimum) SHG intensity. pSHG distinguishes myosin and collagen within the same image based on the anisotropy factor. 3D stack of the SHG intensity, relative angle, and anisotropy factor of the region containing both collagen and myosin are displayed in Movies M12–M14, respectively [47]. (g),(h) Pixel distribution of the total SHG intensity normalized by the square of the incident power (g) and anisotropy factor, calculated with the FFT-based analysis (h) in the three proteins of the zebrafish embryo. (i) Theoretical standard deviation $σ_{γ}$ of the anisotropy factor $γ$ as a function of the number of photons for the three types of structures: collagen (blue, $γ = 1.5$ ), myosin (red, $γ = 0.5$ ), and microtubules (green, $γ = 2.5$ ).
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Figure 2
Modeling pSHG from protein peptide bonds distribution. (a) Peptide bond (C—N) $π$ orbitals represented by their two resonance forms with a preferred hyperpolarizability axis along $z^{'}$ . (b) Multiscale distribution of peptide bonds between amino acids (AA) at the atomic scale (Å), molecular scale in helix (nm) and protein (10 nm), and at the optical scale in protein assemblies ( $μ m$ ). The $z^{'} (n)$ axis along the peptide bond $n$ between the AA ( $n$ ) and the AA ( $n + 1$ ) is defined in the $x y z$ laboratory system by the angle $θ_{z z^{'} (i)}$ . The protein axis $z_{p}$ is aligned along the $z$ laboratory axis. (c) Three-dimensional reconstruction of the peptide bonds distribution of proteins from their molecular structure extracted from PDB files: collagen triple helix [56], myosin tail [57], reconstructed microtubule in GTP-tubulin state [58], and actin filament [59]. Nitrogen atoms are represented by black dots, while carbon atoms are represented by colored dots and the PBs by colored lines. 3D reconstructions are displayed in Movies M7–M11 [47]. All the proteins are lying in the imaging plane $y z$ and their axis $z_{p}$ is aligned with the laboratory $z$ axis. (d) Distribution of $θ_{z z^{'}}$ angles between the peptide bond axis $z^{'}$ and the laboratory $z$ axis. (e) Simulated SHG intensity per number of peptide bonds as a function of the polarization incident angle $φ$ .
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Figure 3
Modeling pSHG from the peptide bond distribution is consistent with experimental observations. (a) Simulated SHG intensity per number of peptide bonds as a function of the polarization incident angle $φ$ in collagen (blue squares), myosin tail (red circles), microtubule (green triangles), and actin (magenta triangles) filaments. (b) Modeled average SHG intensity per peptide bond averaged over all the incident polarization angles $φ$ . (c) Comparison between the experimental SHG intensities normalized by the square of the incident power and the modeled SHG intensity per PB ( $I_{PB}$ ). (d) Modeled effective protein hyperpolarizability per PB ( $β_{PB}^{eff}$ ). (e) Average and standard deviation of the $θ_{z z^{'}}$ PB polar angle distribution. (f),(g) Effective protein hyperpolarizability per PB as a function of the average (f) and standard deviation of the $θ_{z z^{'}}$ PB polar angle distribution (g). (h) Modeled anisotropy factor $γ$ . (i) Comparison between the experimental anisotropy factor and the modeled anisotropy factor $γ$ . (j) Deviation from cylindrical symmetry (DCS).
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Figure 4
Modeling pSHG intensity in a 3D macromolecular distribution of microtubules (a) schematic a microtubule tilted out of the $y z$ imaging plane by an angle $α$ . (b) Schematic of a microtubule distribution with angular spread $δ$ . (c) Distribution of microtubules with the same polarity and with opposite polarity. (d)–(h) Calculated SHG intensity per peptide bond as a function of the polarization incident angle $φ$ for different out-of-plane angles $α$ (d), different values of the microtubules angular spread $δ$ (f), and percentage of microtubules with the same polarity (h). (e)–(i) Calculations of SHG intensity per PB $I_{PB}$ , anisotropy factor $γ$ (red circles), the ratio (black squares) of the hyperpolarizability tensor components $β_{z z z}$ and $β_{z x x}$ and deviation from cylindrical symmetry as a function of the microtubules out-of-plane angle $α$ (e), angular spread $δ$ (g), and polarity (i).
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Figure 5
Modeling pSHG from different microtubule molecular conformations. (a) Microtubule and tubulin dimer in GDP-bound conformation (gray) that is highly unstable and stabilized by taxol drug (cyan). High resolution structures are extracted from Ref. [58]. Tubulin dimer molecular structure is represented with ccp4 molecular graphics. (b) Distribution of $θ_{z z^{'}}$ angles between the peptide bond axis $z^{'}$ and the laboratory $z$ axis in GDP-tubulin (gray) and taxol-bound tubulin (cyan) microtubule conformation. (c) Simulated SHG intensity per number of peptide bond as a function of the polarization incident angle $φ$ in GDP-tubulin (black) and taxol-bound tubulin (cyan) microtubule conformations. (d),(e) Modeled average SHG intensity per peptide bond averaged over all the incident polarization angles $φ$ (d) and anisotropy factor $γ$ (e) in GTP-tubulin (green), GDP-tubulin (gray), and taxol-bound tubulin (cyan) microtubule conformations.
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