The Complexity of Combinations of Qualitative Constraint Satisfaction Problems

The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathrm{CSP}(T_1)$ and $\mathrm{CSP}(T_2)$ are decidable (or polynomial-time decidable). We show that for a large class of $\omega$-categorical theories $T_1, T_2$ the Nelson-Oppen conditions are not only sufficient, but also necessary for polynomial-time tractability of $\mathrm{CSP}(T_1 \cup T_2)$ (unless P=NP).Comment: Version 2: stronger main result with better presentation of the proof; multiple improvements in other proofs; new section structure; new example

Multiplexed Surrogate Analysis of Glycotransferase Activity in Whole Biospecimens

Dysregulated glycotransferase enzymes in cancer cells produce aberrant glycanssome of which can help facilitate metastases. Within a cell, individual glycotransferases promiscuously help to construct dozens of unique glycan structures, making it difficult to comprehensively track their activity in biospecimensespecially where they are absent or inactive. Here, we describe an approach to deconstruct glycans in whole biospecimens then analytically pool together resulting monosaccharide-and-linkage-specific degradation products (“glycan nodes”) that directly represent the activities of specific glycotransferases. To implement this concept, a reproducible, relative quantitation-based glycan methylation analysis methodology was developed that simultaneously captures information from N-, O-, and lipid linked glycans and is compatible with whole biofluids and homogenized tissues; in total, over 30 different glycan nodes are detectable per gas chromatography–mass spectrometry (GC-MS) run. Numerous nonliver organ cancers are known to induce the production of abnormally glycosylated serum proteins. Thus, following analytical validation, in blood plasma, the technique was applied to a group of 59 lung cancer patient plasma samples and age/gender/smoking-status-matched non-neoplastic controls from the Lung Cancer in Central and Eastern Europe (CEE) study to gauge the clinical utility of the approach toward the detection of lung cancer. Ten smoking-independent glycan node ratios were found that detect lung cancer with individual receiver operating characteristic (ROC) c-statistics ranging from 0.76 to 0.88. Two glycan nodes provided novel evidence for altered ST6Gal-I and GnT-IV glycotransferase activities in lung cancer patients. In summary, a conceptually novel approach to the analysis of glycans in unfractionated human biospecimens has been developed that, upon clinical validation for specific applications, may provide diagnostic and/or predictive information in glycan-altering diseases

Distributions and ROC curves for the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to heavy glucose or heavy GlcNAc.

<p>Patient distributions are shown in (a-d). The Kruskal-Wallis test was performed followed by Dunn’s post hoc test. The letters at the top of the data points show statistically significant differences between the patient groups; groups with same letter do not have a significant difference. (e-h) ROC curves for the different sub-cohorts of UCC patients vs. healthy individuals. Areas under the ROC curves are provided in parenthesis next to the stated patient groups. As explained in the Discussion, despite the promising AUCs and shapes of some of these ROC curves, these data do not indicate that plasma/serum glycan nodes will potentially serve as clinically useful diagnostic markers of UCC.</p

Correlation between age and the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to heavy glucose or heavy GlcNAc.

<p>Pearson correlation was used to evaluate this correlation. The common age range between all cohorts was 45–67. “NS” next to the r-value indicates that the Pearson correlation was not statistically significant. Distribution of the healthy controls is demonstrated by red dots. Distribution of the different sub-cohorts of UCC patients is demonstrated by black triangles.</p

Conceptual overview of the glycan “node” analysis concept.

<p>The procedure consists of applying glycan methylation analysis (i.e., linkage analysis) to whole biofluids. Intact normal and abnormal glycans including O-glycans, N-glycans and glycolipids, are processed and transformed into partially methylated alditol acetates (PMAAs, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201208#pone.0201208.g001" target="_blank">Fig 1</a>), each of which corresponds to a particular monosaccharide-and-linkage-specific glycan “node” in the original polymer. As illustrated, analytically pooling together the glycan nodes from amongst all the aberrant intact glycan structures provides a more direct surrogate measurement of abnormal glycosyltransferase activity than any individual intact glycan, while simultaneously converting unique glycan features such as “core fucosylation”, “α2–6 sialylation”, “bisecting GlcNAc”, and “β1–6 branching” into single analytical signals. Actual extracted ion chromatograms from 9-μL blood plasma samples are shown. Numbers adjacent to monosaccharide residues in glycan structures indicate the position at which the higher residue is linked to the lower residue. Figure adapted with permission from Borges CR et al. Anal. Chem. 2013, 85(5):2927–2936. Copyright 2013 American Chemical Society.</p

Statistically significant differences between controls and bladder cancer patient sub-cohorts^a.

<p>Statistically significant differences between controls and bladder cancer patient sub-cohorts<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0201208#t001fn001" target="_blank">^a</a>.</p

Distributions and ROC curves for the most highly elevated glycan node markers in former & current UCC patients relative to healthy controls when data were normalized to sum of endogenous Hexoses or HexNAcs.

<p>Patient distributions are shown in (a-d). The Kruskal-Wallis test was performed followed by Dunn’s post hoc test. The letters at the top of the data points show statistically significant differences between the patient groups; groups with a common letter do not have a significant difference. (e-h) ROC curves for different groups of bladder cancer patients vs. certifiably healthy individuals. Area under the ROC curves are provided in parenthesis next to the stated patient groups. “NS” next to the area under the ROC curves shows that there is no significant difference between the two groups that are being compared. These data do not indicate that plasma/serum glycan nodes will potentially serve as clinically useful diagnostic markers of UCC.</p

Statistically significant differences between controls and bladder cancer patient sub-cohorts with data normalization to the sum of all endogenous hexoses or HexNAcs.

<p>Statistically significant differences between controls and bladder cancer patient sub-cohorts with data normalization to the sum of all endogenous hexoses or HexNAcs.</p

Correlation of CRP and glycan nodes.

<p>Log of CRP concentration vs. (a) α2–6 sialylation; r = 0.34 and (b) β1–6 branching; r = 0.38 are plotted. Both correlations are statistically significant (Pearson correlation; <i>p</i> < 0.001).</p

Molecular overview of the glycan “node” analysis procedure.

<p>For glycans from blood plasma and other biofluids, O-linked glycans are released during permethylation, while N-linked glycans and glycolipids are released during acid hydrolysis. The unique pattern of methylation and acetylation in the final partially methylated alditol acetates (PMAAs) corresponds to the unique “glycan node” in the original glycan polymer and provides the molecular basis for separation and quantification by GC-MS. Figure adapted with permission from Borges CR et al. Anal. Chem. 2013, 85(5):2927–2936. Copyright 2013 American Chemical Society.</p