Multiagent Consensus Equilibrium in Molecular Structure Determination.

Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.

Spatially encoded polarization-dependent nonlinear optics.

A single fixed optic is combined with the sample translation capabilities inherent to most microscopes to achieve precise polarization-dependent second harmonic generation microscopy measurements of thin tissue sections. Although polarization measurements have enabled detailed structural analysis of collagen, challenges in integrating rotation stages or fast electro-optic/photoelastic modulation have complicated the retrofitting of existing systems for precise polarization analysis. Placing a static microretarder array in the rear conjugate plane resulted in spatially encoded polarization modulation across the field of view. A complete set of polarization rotation measurements was acquired at each pixel by sample translation, recovering local-frame tensors relating to structure within collagenous tissue.

Second Harmonic Generation of Unpolarized Light.

A Mueller tensor mathematical framework was applied for predicting and interpreting the second harmonic generation (SHG) produced with an unpolarized fundamental beam. In deep tissue imaging through SHG and multiphoton fluorescence, partial or complete depolarization of the incident light complicates polarization analysis. The proposed framework has the distinct advantage of seamlessly merging the purely polarized theory based on the Jones or Cartesian susceptibility tensors with a more general Mueller tensor framework capable of handling partial depolarized fundamental and/or SHG produced. The predictions of the model are in excellent agreement with experimental measurements of z-cut quartz and mouse tail tendon obtained with polarized and depolarized incident light. The polarization-dependent SHG produced with unpolarized fundamental allowed determination of collagen fiber orientation in agreement with orthogonal methods based on image analysis. This method has the distinct advantage of being immune to birefringence or depolarization of the fundamental beam for structural analysis of tissues.

Imaging the Nonlinear Susceptibility Tensor of Collagen by Nonlinear Optical Stokes Ellipsometry.

Nonlinear optical Stokes ellipsometric (NOSE) microscopy was demonstrated for the analysis of collagen-rich biological tissues. NOSE is based on polarization-dependent second harmonic generation imaging. NOSE was used to access the molecular-level distribution of collagen fibril orientation relative to the local fiber axis at every position within the field of view. Fibril tilt-angle distribution was investigated by combining the NOSE measurements with ab initio calculations of the predicted molecular nonlinear optical response of a single collagen triple helix. The results were compared with results obtained previously by scanning electron microscopy, nuclear magnetic resonance imaging, and electron tomography. These results were enabled by first measuring the laboratory-frame Jones nonlinear susceptibility tensor, then extending to the local-frame tensor through pixel-by-pixel corrections based on local orientation.

Supramolecular Assembly of His-Tagged Fluorescent Protein Guests within Coiled-Coil Peptide Crystal Hosts: Three-Dimensional Ordering and Protein Thermal Stability.

The use of biomaterials for the inclusion and stabilization of biopolymers is an ongoing challenge. Herein, we disclose three-dimensional (3D) coiled-coil peptide crystals with metal ions that include and overgrow His-tagged fluorescent proteins within the crystal. The protein guests are found within two symmetry-related growth sectors of the crystalline host that are associated with faces of the growing crystal that display ligands for metal ions. The fluorescent proteins are included within this "hourglass" region of the crystals at a notably high level, display order within the crystal hosts, and demonstrate sufficiently tight packing to enable energy transfer between a donor-acceptor pair. His-tagged fluorescent proteins display remarkable thermal stability to denaturation over extended periods of time (days) at high temperatures when within the crystals. Ultimately, this strategy may prove useful for the prolonged storage of thermally sensitive biopolymer guests within a 3D crystalline matrix.

Mueller Tensor Nonlinear Optical Polarization Analysis in Turbid Media.

A mathematical framework to treat partial polarization in second harmonic generation imaging of nonlinear optical susceptibility is described and applied to imaging tissue sections 5, 40, and 70 µm thick, sufficient to introduce significant depolarization of the incident field. Polarization analysis becomes complicated in turbid media, in which scattering can result in degradation of polarization purity. The simplest framework for describing the polarization of purely polarized light is the Jones framework, which has been applied to great effect in the polarization analysis of second harmonic generation. However, the Jones framework lacks the necessary generality to describe a partially polarized electric field, (i.e., ones positioned within the volume of the Poincaré sphere rather than on the surface). Recent work connecting the Jones framework to the Mueller-Stokes framework has enabled interpretation of results with the more intuitive Jones framework while maintaining generality of the Mueller-Stokes method. The magnitude and nature of linear interactions of the tissue with the incident infrared field are discussed. Despite substantial depolarization, the nonlinear optical susceptibility tensor elements of collagen was recoverable at each pixel images of thick tissue utilizing the described framework. For thick and thin tissues, values of the tensor element ratio ρ were recovered in good agreement with previous studies. Both hyperpolarizing and depolarizing effects of SHG were observed, and the mechanism of hyperpolarization was determined to rest upon the interplay of orientation and relative contribution of polarized and depolarized incident light to elicit SHG.

Theoretical Foundation for Electric-Dipole-Allowed Chiral-Specific Fluorescence Optical Rotary Dispersion (F-ORD) from Interfacial Assemblies.

Fluorescence optical rotary dispersion (F-ORD) is proposed as a novel chiral-specific and interface-specific spectroscopic method. F-ORD measurements of uniaxial assemblies are predicted to be fully electric-dipole-allowed, with corresponding increases in sensitivity to chirality relative to chiral-specific measurements in isotropic assemblies that are commonly interpreted through coupling between electric and magnetic dynamic dipoles. Observations of strong chiral sensitivity in prior single-molecule fluorescence measurements of chiral interfacial molecules are in excellent qualitative agreement with the predictions of the F-ORD mechanism and challenging to otherwise explain. F-ORD may provide methods to suppress background fluorescence in studies of biological interfaces, as the detected signal requires both polar local order and interfacial chirality. In addition, the molecular-level descriptions of the mechanisms underpinning F-ORD may also potentially apply to aid in interpreting chiral-specific Raman and surface-enhanced Raman spectroscopy measurements of uniaxially oriented assemblies, opening up opportunities for chiral-specific and interface-specific vibrational spectroscopy.