Emma L. DeWalt

Polarization-resolved second-harmonic generation microscopy as a method to visualize protein-crystal domains

Polarization-resolved second-harmonic generation (PR-SHG) microscopy is described and applied to identify the presence of multiple crystallographic domains within protein-crystal conglomerates, which was confirmed by synchrotron X-ray diffraction. Principal component analysis (PCA) of PR-SHG images resulted in principal component 2 (PC2) images with areas of contrasting negative and positive values for conglomerated crystals and PC2 images exhibiting uniformly positive or uniformly negative values for single crystals. Qualitative assessment of PC2 images allowed the identification of domains of different internal ordering within protein-crystal samples as well as differentiation between multi-domain conglomerated crystals and single crystals. PR-SHG assessments of crystalline domains were in good agreement with spatially resolved synchrotron X-ray diffraction measurements. These results have implications for improving the productive throughput of protein structure determination through early identification of multi-domain crystals.

Polarization-modulated second harmonic generation ellipsometric microscopy at video rate.

Fast 8 MHz polarization modulation coupled with analytical modeling, fast beam-scanning, and synchronous digitization (SD) have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and polarized laser transmittance imaging with image acquisition rates up to video rate. In contrast to polarimetry, in which the polarization state of the exiting beam is recorded, NOSE enables recovery of the complex-valued Jones tensor of the sample that describes all polarization-dependent observables of the measurement. Every video-rate scan produces a set of 30 images (10 for each detector with three detectors operating in parallel), each of which corresponds to a different polarization-dependent result. Linear fitting of this image set contracts it down to a set of five parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the incident beam. These parameters can in turn be used to recover the Jones tensor elements of the sample. Following validation of the approach using z-cut quartz, NOSE microscopy was performed for microcrystals of both naproxen and glucose isomerase. When weighted by the measurement time, NOSE microscopy was found to provide a substantial (>7 decades) improvement in the signal-to-noise ratio relative to our previous measurements based on the rotation of optical elements and a 3-fold improvement relative to previous single-point NOSE approaches.

Modeling the SHG activities of diverse protein crystals

A symmetry-additive ab initio model for second-harmonic generation (SHG) activity of protein crystals was applied to assess the likely protein-crystal coverage of SHG microscopy. Calculations were performed for 250 proteins in nine point-group symmetries: a total of 2250 crystals. The model suggests that the crystal symmetry and the limit of detection of the instrument are expected to be the strongest predictors of coverage of the factors considered, which also included secondary-structural content and protein size. Much of the diversity in SHG activity is expected to arise primarily from the variability in the intrinsic protein response as well as the orientation within the crystal lattice. Two or more orders-of-magnitude variation in intensity are expected even within protein crystals of the same symmetry. SHG measurements of tetragonal lysozyme crystals confirmed detection, from which a protein coverage of ~84% was estimated based on the proportion of proteins calculated to produce SHG responses greater than that of tetragonal lysozyme. Good agreement was observed between the measured and calculated ratios of the SHG intensity from lysozyme in tetragonal and monoclinic lattices.

Rapid Discrimination of Polymorphic Crystal Forms by Nonlinear Optical Stokes Ellipsometric Microscopy

The use of nonlinear optical Stokes ellipsometric (NOSE) microscopy for rapid discrimination of two polymorphic forms of the small molecule d-mannitol is presented. Fast (8 MHz) polarization modulated beam-scanning microscopy and a recently developed iterative, nonlinear least-squares fitting algorithm were combined to allow discrimination of orthorhombic and monoclinic crystal structures of d-mannitol with data acquisition times of <7 s per field of view with a signal-to-noise ratio (SNR) of ∼300. Discrimination between polymorphic forms within the 99.99% confidence interval was achieved by standard statistical tests of the recovered probability density functions for the measured observables following two class linear discriminant analysis. These measurements target bottlenecks in small-volume, high-throughput solid form screening experiments for polymorph discovery in the development of emerging active pharmaceutical ingredients.

Unified Theory for Polarization Analysis in Second Harmonic and Sum Frequency Microscopy

A unified theoretical framework for the recovery of second-order nonlinear susceptibility tensors and sample orientations from polarization-dependent second harmonic generation and sum frequency generation microscopy was developed. Jones formalism was extended to nonlinear optics and was used to bridge the experimental observables and the local-frame tensor elements. Four commonly used experimental architectures were explicitly explored, including polarization rotation with no postsample optics, polarization-in polarization-out measurement, and polarization modulation with and without postsample optics. Polarization-dependent second harmonic generation measurement was performed on Z-cut quartz and the local-frame tensor elements were calculated. The recovered tensor elements agree with the expected values dictated by symmetry.

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.

Digital Deconvolution Filter Derived from Linear Discriminant Analysis and Application for Multiphoton Fluorescence Microscopy

A digital filter derived from linear discriminant analysis (LDA) is developed for recovering impulse responses in photon counting from a high speed photodetector (rise time of ∼1 ns) and applied to remove ringing distortions from impedance mismatch in multiphoton fluorescence microscopy. Training of the digital filter was achieved by defining temporally coincident and noncoincident transients and identifying the projection within filter-space that best separated the two classes. Once trained, data analysis by digital filtering can be performed quickly. Assessment of the reliability of the approach was performed through comparisons of simulated voltage transients, in which the ground truth results were known a priori. The LDA filter was also found to recover deconvolved impulses for single photon counting from highly distorted ringing waveforms from an impedance mismatched photomultiplier tube. The LDA filter was successful in removing these ringing distortions from two-photon excited fluorescence micrographs and through data simulations was found to extend the dynamic range of photon counting by approximately 3 orders of magnitude through minimization of detector paralysis.

Synchronous-digitization for Video Rate Polarization Modulated Beam Scanning Second Harmonic Generation Microscopy

Fast beam-scanning non-linear optical microscopy, coupled with fast (8 MHz) polarization modulation and analytical modeling have enabled simultaneous nonlinear optical Stokes ellipsometry (NOSE) and linear Stokes ellipsometry imaging at video rate (15 Hz). NOSE enables recovery of the complex-valued Jones tensor that describes the polarization-dependent observables, in contrast to polarimetry, in which the polarization stated of the exciting beam is recorded. Each data acquisition consists of 30 images (10 for each detector, with three detectors operating in parallel), each of which corresponds to polarization-dependent results. Processing of this image set by linear fitting contracts down each set of 10 images to a set of 5 parameters for each detector in second harmonic generation (SHG) and three parameters for the transmittance of the fundamental laser beam. Using these parameters, it is possible to recover the Jones tensor elements of the sample at video rate. Video rate imaging is enabled by performing synchronous digitization (SD), in which a PCIe digital oscilloscope card is synchronized to the laser (the laser is the master clock.) Fast polarization modulation was achieved by modulating an electro-optic modulator synchronously with the laser and digitizer, with a simple sine-wave at 1/10th the period of the laser, producing a repeating pattern of 10 polarization states. This approach was validated using Z-cut quartz, and NOSE microscopy was performed for micro-crystals of naproxen.

Nonlinear optical Stokes ellipsometric (NOSE) microscopy for imaging the nonlinear susceptibility tensors of collagen

Nonlinear optical Stokes ellipsometric (NOSE) microscopy was demonstrated for the analysis of collagen structure in a mouse tail section. NOSE is based on polarization-dependent second harmonic generation (SHG) imaging. The fast polarization-modulation was achieved using an electro-optic modulator (EOM), allowing for the potential of video-rate NOSE analysis. The signal to noise advantages associated with suppression of 1/f noise by rapid polarization modulation allowed reliable recovery of the local-frame tensor on a per-pixel basis. An iterative approach involving laboratory to local frame coordinate transformation was developed to recover the spatial distribution of local-frame nonlinear susceptibility tensor elements of collagen as well as the polar and azimuthal orientation angles of the collagen structure.

Second harmonic generation correlation spectroscopy for characterizing translationally diffusing protein nanocrystals

Second harmonic generation correlation spectroscopy (SHG-CS) is demonstrated as a new approach to protein nanocrystal characterization. A novel line-scanning approach was performed to enable autocorrelation analysis without sample damage from the intense incident beam. An analytical model for autocorrelation was developed, which includes a correction for the optical scattering forces arising when focusing intense, infrared beams. SHG-CS was applied to the analysis of BaTiO3 nanoparticles ranging from 200 to ∼500 nm and of photosystem I nanocrystals. A size distribution was recovered for each sample and compared with the size histogram measured by scanning electron microscopy (SEM). Good agreement was observed between the two independent measurements. The intrinsic selectivity of the second-order nonlinear optical process provides SHG-CS with the ability to distinguish well ordered nanocrystals from conglomerates and amorphous aggregates. Combining the recovered distribution of particle diameters with the histogram of measured SHG intensities provides the inherent hyperpolarizability per unit volume of the SHG-active nanoparticles. Simulations suggest that the SHG activity per unit volume is likely to exhibit relatively low sensitivity to the subtle distortions within the lattice that contribute to resolution loss in X-ray diffraction, but high sensitivity to the presence of multi-domain crystals.