Modeling and Predicting Second-Harmonic Generation from Protein Molecular Structure

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.