Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

Here, we present an augmented form of two-dimensional correlation spectroscopy, that integrates in a single format data from spectroscopic and multiple non-spectroscopic sources for analysis. The integration is affected by augmenting every spectrum in a hyperspectral data set with relevant non-spectroscopic data to permit two-dimensional correlation analysis(2D-COS) of the ensemble of augmented spectra. A k-means clustering is then applied to the results of the perturbation domain decomposition to determine which Raman peaks cluster with any of the non-spectroscopic data. We introduce and explain the method with the aid of synthetic spectra and synthetic non-spectroscopic data. We then demonstrate this approach with data using Raman spectra from human embryonic stem cell aggregates undergoing directed differentiation toward pancreatic endocrine cells and parallel bioassays of hormone mRNA expression and C-peptide levels in spent medium. These pancreatic endocrine cells generally contain insulin or glucagon. Insulin has disulfide bonds that produce Raman scattering near 513 cm-1, but no tryptophan. For insulin-positive cells, we found that the application of multisource correlation analysis revealed a high correlation between insulin mRNA and Raman scattering in the disulfide region. In contrast, glucagon has no disulfide bonds but does contain tryptophan. For glucagon-positive cells, we also observed a high correlation between glucagon mRNA and tryptophan Raman scattering (∼757 cm-1). We conclude with a discussion of methods to enhance spectral resolution and its effects on the performance of multisource correlation analysis.

Many interesting solid-state targets for biological research do not form crystalline structures; these materials include intrinsically disordered proteins, plant biopolymer composites, cell-wall polysaccharides, and soil organic matter. The absence of aligned repeating structural elements and atomic-level rigidity presents hurdles to achieving structural elucidation and obtaining functional insights. We describe strategies for adapting several solid-state NMR methods to determine the molecular structures and compositions of these amorphous biosolids. The main spectroscopic problems in studying amorphous structures by NMR are over/under-sampling of the spin signals and spectral complexity. These problems arise in part because amorphous biosolids typically contain a mix of rigid and mobile domains, making it difficult to select a single experiment or set of acquisition conditions that fairly represents all nuclear spins in a carbon-based organic sample. These issues can be addressed by running hybrid experiments, such as using direct excitation alongside cross polarization-based methods, to develop a more holistic picture of the macromolecular system. In situations of spectral crowding or overlap, the structural elucidation strategy can be further assisted by coupling 13C spins to nuclei such as 15N, filtering out portions of the spectrum, highlighting individual moieties of interest, and adding a second or third spectral dimension to an NMR experiment in order to spread out the resonances and link them pairwise through space or through bonds. We discuss practical aspects and illustrations from the recent literature for 1D experiments that use cross or direct polarization and both homo- and heteronuclear 2D and 3D solid-state NMR experiments.

We present single- and multiple-quantum correlation J-spectroscopy detected in zero (<1μG) magnetic field using a 87Rb vapor-cell magnetometer. At zero field the spectrum of ethanol appears as a mixture of 13C isotopomers, and correlation spectroscopy is useful in separating the two composite spectra. We also identify and observe the zero-field equivalent of a double-quantum transition in 13C2-acetic acid, and show that such transitions are of use in spectral assignment. Two-dimensional spectroscopy further improves the high resolution attained in zero-field NMR since selection rules on the coherence-transfer pathways allow for the separation of otherwise overlapping resonances into distinct cross-peaks.

A two-dimensional pulse sequence is introduced for correlating nuclear magnetic resonance anisotropic chemical shifts to a relaxation time (e.g., T1) in solids under static conditions. The sequence begins with a preparatory stage for measuring relaxation times, and is followed by a multiple pulse sequence for homonuclear dipolar decoupling. Data analysis involves the use of Fourier transform, followed by a one-dimensional inverse Laplace transform for each frequency index. Experimental results acquired on solid samples demonstrate the general approach, and additional variations involving heteronuclear decoupling and magic angle spinning are discussed.

Neutron scattering applications often require discriminating the elastic contribution from the inelastic contribution. For this purpose, correlation spectroscopy offers an effective tool with both pulsed and continuous neutron sources as well as several advantages: the analysis of the neutron velocity distribution can be carried out with a duty factor of 50%, independently on the resolution value; the best statistical accuracy for spectra where the elastic part encompasses most of the integrated intensity is provided. Depending on the statistical chopper position, correlation analysis can be used for both incoming and outgoing neutron velocity determination. Moreover, the correlation technique is very profitable for investigating weak signals in the presence of high background, which is often the case for small samples. To provide instrument flexibility and versatility, an innovative approach comprising tuning resolution by variable Resolution-Elastic Neutron Scattering (RENS) is proposed, offering further benefits by enabling systematic trading of intensity for resolution and vice versa. This study puts into evidence the advantages offered by the use of statistical chopper and of correlation technique for RENS in choosing the best compromise between resolution and beam intensity.

The correlation of electron counts from two detectors illuminated by a coherent electron beam is analyzed by associating the path of the electron beam through the lenses with the direct Coulomb interaction between two individual electrons. This is shown to lead to a full statistical description of the electron counts. The dominant contribution to the correlation is found to be due to the trajectory displacement caused by the repulsive Coulomb interaction between the first anode and the cathode tip, and the correlation of electron counts is found to depend on the amount of defocusing on the shift of the virtual source for two electrons within the correlation time. The Coulomb scatterings, which altered the direction of two neighbor electrons, occur during the acceleration, leading to a significant decrease in the electron density. The Coulomb potential with no screening will then cause large-angle scattering of nearest-neighbor electrons within the correlation time. These results are consistent with those obtained by a previous experiment.

Photon statistics is a powerful tool for characterizing the emission dynamics of nanoscopic systems and their photophysics. Recent advances that combine correlation spectroscopy with scanning tunneling microscopy induced luminescence (STML) have allowed the measurement of the emission dynamics from individual molecules and defects, demonstrating their nature as single-photon emitters. The application of correlation spectroscopy to the analysis of the dynamics of a well-characterized adsorbate system in an ultrahigh vacuum remained to be demonstrated. Here, we combine single-photon time correlations with STML to measure the dynamics of individual H2 molecules between a gold tip and an Au(111) surface. An adsorbed H2 molecule performs recurrent excursions below the tip apex. We use the fact that the presence of the H2 molecule in the junction modifies plasmon emission to study the adsorbate dynamics. Using the H2 molecule as a chopper for STM-induced optical emission intensity, we demonstrate bunching in the plasmonic photon train in a single measurement over 6 orders of magnitude in the time domain (from microseconds to seconds) that takes only a few seconds. Our findings illustrate the power of using photon statistics to measure the diffusion dynamics of adsorbates with STML.

OBJECTIVE: To propose and evaluate a novel multidimensional approach for imaging subvoxel tissue compartments called Diffusion-Relaxation Correlation Spectroscopic Imaging.
METHODS: Multiexponential modeling of MR diffusion or relaxation data is commonly used to infer the many different microscopic tissue compartments that contribute signal to macroscopic MR imaging voxels. However, multiexponential estimation is known to be difficult and ill-posed. Observing that this ill-posedness is theoretically reduced in higher dimensions, diffusion-relaxation correlation spectroscopic imaging uses a novel multidimensional imaging experiment that jointly encodes diffusion and relaxation information, and then uses a novel constrained reconstruction technique to generate a multidimensional diffusion-relaxation correlation spectrum for every voxel. The peaks of the multidimensional spectrum are expected to correspond to the distinct tissue microenvironments that are present within each macroscopic imaging voxel.
RESULTS: Using numerical simulations, experiment data from a custom-built phantom, and experiment data from a mouse model of traumatic spinal cord injury, diffusion-relaxation correlation spectroscopic imaging is demonstrated to provide substantially better multicompartment resolving power compared to conventional diffusion- and relaxation-based methods.
CONCLUSIONS: The diffusion-relaxation correlation spectroscopic imaging approach provides powerful new capabilities for resolving the different components of multicompartment tissue models, and can be leveraged to significantly expand the insights provided by MRI in studies of tissue microstructure. Magn Reson Med 78:2236-2249, 2017. © 2017 International Society for Magnetic Resonance in Medicine.

This article reviews the methodological aspects of detecting low-abundant J-coupled metabolites via 1D spectral editing techniques and 2D nuclear magnetic resonance (NMR) methods applied in vivo, in humans, with a focus on the brain. A brief explanation of the basics of J-evolution will be followed by an introduction to 1D spectral editing techniques (e.g., J-difference editing, multiple quantum coherence filtering) and 2D-NMR methods (e.g., correlation spectroscopy, J-resolved spectroscopy). Established and recently developed methods will be discussed and the most commonly edited J-coupled metabolites (e.g., neurotransmitters, antioxidants, onco-markers, and markers for metabolic processes) will be briefly summarized along with their most important applications in neuroscience and clinical diagnosis.