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Characterization of states, the essential components of the underlying energy landscapes, is one of the most intriguing subjects in single-molecule (SM) experiments due to the existence of noise inherent to the measurements. Here we present a method to extract the underlying state sequences from experimental SM time-series. Taking into account empirical error and the finite sampling of the time-series, the method extracts a steady-state network which provides an approximation of the underlying effective free energy landscape. The core of the method is the application of rate-distortion theory from information theory, allowing the individual data points to be assigned to multiple states simultaneously. We demonstrate the method's proficiency in its application to simulated trajectories as well as to experimental SM fluorescence resonance energy transfer (FRET) trajectories obtained from isolated agonist binding domains of the AMPA receptor, an ionotropic glutamate receptor that is prevalent in the central nervous system.

Histopathology requires the expertise of specialists to diagnose morphological features of cells and tissues. Raman imaging can provide additional biochemical information to benefit histological disease diagnosis. Using a dietary model of nonalcoholic fatty liver disease in rats, we combine Raman imaging with machine learning and information theory to evaluate cellular‐level information in liver tissue samples. After increasing signal‐to‐noise ratio in the Raman images through superpixel segmentation, we extract biochemically distinct regions within liver tissues, allowing for quantification of characteristic biochemical components such as vitamin A and lipids. Armed with microscopic information about the biochemical composition of the liver tissues, we group tissues having similar composition, providing a descriptor enabling inference of tissue states, contributing valuable information to histological inspection.

We use Raman microscopic images with high spatial and spectral resolution to investigate differences between human follicular thyroid (Nthy-ori 3-1) and follicular thyroid carcinoma (FTC-133) cells, a well-differentiated thyroid cancer. Through comparison to classification of single-cell Raman spectra, the importance of subcellular information in the Raman images is emphasized. Subcellular information is extracted through a coarse-graining of the spectra at high spatial resolution (∼1.7 μm2), producing a set of characteristic spectral groups representing locations having similar biochemical compositions. We develop a cell classifier based on the frequencies at which the characteristic spectra appear within each of the single cells. Using this classifier, we obtain a more accurate (89.8%) distinction of FTC-133 and Nthy-ori 3-1, in comparison to single-cell spectra (77.6%). We also infer which subcellular components are important to cellular distinction; we find that cancerous FTC-133 cells contain increased populations of lipid-containing components and decreased populations of cytochrome-containing components relative to Nthy-ori 3-1, and that the regions containing these contributions are largely outside the cell nuclei. In addition to increased classification accuracy, this approach provides rich subcellular information about biochemical differences and cellular locations associated with the distinction of the normal and cancerous follicular thyroid cells.

Hierarchical features of the energy landscape of the folding/unfolding behavior of adenylate kinase, including its dependence on denaturant concentration, are elucidated in terms of single-molecule fluorescence resonance energy transfer (smFRET) measurements in which the proteins are encapsulated in a lipid vesicle. The core in constructing the energy landscape from single-molecule time-series across different denaturant concentrations is the application of rate-distortion theory (RDT), which naturally considers the effects of measurement noise and sampling error, in combination with change-point detection and the quantification of the FRET efficiency-dependent photobleaching behavior. Energy landscapes are constructed as a function of observation time scale, revealing multiple partially folded conformations at small time scales that are situated in a superbasin. As the time scale increases, these denatured states merge into a single basin, demonstrating the coarse-graining of the energy landscape as observation time increases. Because the photobleaching time scale is dependent on the conformational state of the protein, possible nonequilibrium features are discussed, and a statistical test for violation of the detailed balance condition is developed based on the state sequences arising from the RDT framework.

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An essential challenge in diagnosing states of nonalcoholic fatty liver disease (NAFLD) is the early prediction of progression from nonalcoholic fatty liver (NAFL) to nonalcoholic steatohepatitis (NASH) before the disease progresses. Histological diagnoses of NAFLD rely on the appearance of anomalous tissue morphologies, and it is difficult to segment the biomolecular environment of the tissue through a conventional histopathological approach. Here, we show that hyperspectral Raman imaging provides diagnostic information on NAFLD in rats, as spectral changes among disease states can be detected before histological characteristics emerge. Our results demonstrate that Raman imaging of NAFLD can be a useful tool for histopathologists, offering biomolecular distinctions among tissue states that cannot be observed through standard histopathological means.

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