Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

G-Quadruplex DNA Sequences Are Evolutionarily Conserved and Associated with Distinct Genomic Features in Saccharomyces cerevisiae

G-quadruplex DNA is a four-stranded DNA structure formed by non-Watson-Crick base pairing between stacked sets of four guanines. Many possible functions have been proposed for this structure, but its in vivo role in the cell is still largely unresolved. We carried out a genome-wide survey of the evolutionary conservation of regions with the potential to form G-quadruplex DNA structures (G4 DNA motifs) across seven yeast species. We found that G4 DNA motifs were significantly more conserved than expected by chance, and the nucleotide-level conservation patterns suggested that the motif conservation was the result of the formation of G4 DNA structures. We characterized the association of conserved and non-conserved G4 DNA motifs in Saccharomyces cerevisiae with more than 40 known genome features and gene classes. Our comprehensive, integrated evolutionary and functional analysis confirmed the previously observed associations of G4 DNA motifs with promoter regions and the rDNA, and it identified several previously unrecognized associations of G4 DNA motifs with genomic features, such as mitotic and meiotic double-strand break sites (DSBs). Conserved G4 DNA motifs maintained strong associations with promoters and the rDNA, but not with DSBs. We also performed the first analysis of G4 DNA motifs in the mitochondria, and surprisingly found a tenfold higher concentration of the motifs in the AT-rich yeast mitochondrial DNA than in nuclear DNA. The evolutionary conservation of the G4 DNA motif and its association with specific genome features supports the hypothesis that G4 DNA has in vivo functions that are under evolutionary constraint

Paediatric obsessive-compulsive disorder and depressive symptoms: clinical correlates and CBT treatment outcomes.

Depression frequently co-occurs with paediatric obsessive-compulsive disorder (OCD), yet the clinical correlates and impact of depression on CBT outcomes remain unclear. The prevalence and clinical correlates of depression were examined in a paediatric specialist OCD-clinic sample (N = 295; Mean = 15 [7 - 18] years, 42 % female), using both dimensional (Beck Depression Inventory-youth; n = 261) and diagnostic (Development and Wellbeing Assessment; n = 127) measures of depression. The impact of depressive symptoms and suspected disorders on post-treatment OCD severity was examined in a sub-sample who received CBT, with or without SSRI medication (N = 100). Fifty-one per-cent of patients reported moderately or extremely elevated depressive symptoms and 26 % (95 % CI: 18 - 34) met criteria for a suspected depressive disorder. Depressive symptoms and depressive disorders were associated with worse OCD symptom severity and global functioning prior to CBT. Individuals with depression were more likely to be female, have had a psychiatric inpatient admission and less likely to be attending school (ps < 0.01). OCD and depressive symptom severity significantly decreased after CBT. Depressive symptoms and depressive disorders predicted worse post-treatment OCD severity (βs = 0.19 and 0.26, ps < 0.05) but became non-significant when controlling for pre-treatment OCD severity (βs = 0.05 and 0.13, ns). Depression is common in paediatric OCD and is associated with more severe OCD and poorer functioning. However, depression severity decreases over the course of CBT for OCD and is not independently associated with worse outcomes, supporting the recommendation for treatment as usual in the presence of depressive symptoms

The Yeast Pif1 Helicase Prevents Genomic Instability Caused by G-Quadruplex-Forming CEB1 Sequences In Vivo

In budding yeast, the Pif1 DNA helicase is involved in the maintenance of both nuclear and mitochondrial genomes, but its role in these processes is still poorly understood. Here, we provide evidence for a new Pif1 function by demonstrating that its absence promotes genetic instability of alleles of the G-rich human minisatellite CEB1 inserted in the Saccharomyces cerevisiae genome, but not of other tandem repeats. Inactivation of other DNA helicases, including Sgs1, had no effect on CEB1 stability. In vitro, we show that CEB1 repeats formed stable G-quadruplex (G4) secondary structures and the Pif1 protein unwinds these structures more efficiently than regular B-DNA. Finally, synthetic CEB1 arrays in which we mutated the potential G4-forming sequences were no longer destabilized in pif1Δ cells. Hence, we conclude that CEB1 instability in pif1Δ cells depends on the potential to form G-quadruplex structures, suggesting that Pif1 could play a role in the metabolism of G4-forming sequences

Genome-Wide Analyses of Recombination Prone Regions Predict Role of DNA Structural Motif in Recombination

HapMap findings reveal surprisingly asymmetric distribution of recombinogenic regions. Short recombinogenic regions (hotspots) are interspersed between large relatively non-recombinogenic regions. This raises the interesting possibility of DNA sequence and/or other cis- elements as determinants of recombination. We hypothesized the involvement of non-canonical sequences that can result in local non-B DNA structures and tested this using the G-quadruplex DNA as a model. G-quadruplex or G4 DNA is a unique form of four-stranded non-B DNA structure that engages certain G-rich sequences, presence of such motifs has been noted within telomeres. In support of this hypothesis, genome-wide computational analyses presented here reveal enrichment of potential G4 (PG4) DNA forming sequences within 25618 human hotspots relative to 9290 coldspots (p<0.0001). Furthermore, co-occurrence of PG4 DNA within several short sequence elements that are associated with recombinogenic regions was found to be significantly more than randomly expected. Interestingly, analyses of more than 50 DNA binding factors revealed that co-occurrence of PG4 DNA with target DNA binding sites of transcription factors c-Rel, NF-kappa B (p50 and p65) and Evi-1 was significantly enriched in recombination-prone regions. These observations support involvement of G4 DNA in recombination, predicting a functional model that is consistent with duplex-strand separation induced by formation of G4 motifs in supercoiled DNA and/or when assisted by other cellular factors

Intramolecular Folding in Human ILPR Fragment with Three C-Rich Repeats

Enrichment of four tandem repeats of guanine (G) rich and cytosine (C) rich sequences in functionally important regions of human genome forebodes the biological implications of four-stranded DNA structures, such as G-quadruplex and i-motif, that can form in these sequences. However, there have been few reports on the intramolecular formation of non-B DNA structures in less than four tandem repeats of G or C rich sequences. Here, using mechanical unfolding at the single-molecule level, electrophoretic mobility shift assay (EMSA), circular dichroism (CD), and ultraviolet (UV) spectroscopy, we report an intramolecularly folded non-B DNA structure in three tandem cytosine rich repeats, 5'-TGTC4ACAC4TGTC4ACA (ILPR-I3), in the human insulin linked polymorphic region (ILPR). The thermal denaturation analyses of the sequences with systematic C to T mutations have suggested that the structure is linchpinned by a stack of hemiprotonated cytosine pairs between two terminal C4 tracts. Mechanical unfolding and Br2 footprinting experiments on a mixture of the ILPR-I3 and a 5′-C4TGT fragment have further indicated that the structure serves as a building block for intermolecular i-motif formation. The existence of such a conformation under acidic or neutral pH complies with the strand-by-strand folding pathway of ILPR i-motif structures

Laboratory layered latte

Inducing thermal gradients in fluid systems with initial, well-defined density gradients results in the formation of distinct layered patterns, such as those observed in the ocean due to double-diffusive convection. In contrast, layered composite fluids are sometimes observed in confined systems of rather chaotic initial states, for example, lattes formed by pouring espresso into a glass of warm milk. Here, we report controlled experiments injecting a fluid into a miscible phase and show that, above a critical injection velocity, layering emerges over a time scale of minutes. We identify critical conditions to produce the layering, and relate the results quantitatively to double-diffusive convection. Based on this understanding, we show how to employ this single-step process to produce layered structures in soft materials, where the local elastic properties vary step-wise along the length of the material

The genomic features that affect the lengths of 5’ untranslated regions in multicellular eukaryotes

<p>Abstract</p> <p>Background</p> <p>The lengths of 5’UTRs of multicellular eukaryotes have been suggested to be subject to stochastic changes, with upstream start codons (uAUGs) as the major constraint to suppress 5’UTR elongation. However, this stochastic model cannot fully explain the variations in 5’UTR length. We hypothesize that the selection pressure on a combination of genomic features is also important for 5’UTR evolution. The ignorance of these features may have limited the explanatory power of the stochastic model. Furthermore, different selective constraints between vertebrates and invertebrates may lead to differences in the determinants of 5’UTR length, which have not been systematically analyzed.</p> <p>Methods</p> <p>Here we use a multiple linear regression model to delineate the correlation between 5’UTR length and the combination of a series of genomic features (G+C content, observed-to-expected (OE) ratios of uAUGs, upstream stop codons (uSTOPs), methylation-related CG/UG dinucleotides, and mRNA-destabilizing UU/UA dinucleotides) in six vertebrates (human, mouse, rat, chicken, African clawed frog, and zebrafish) and four invertebrates (fruit fly, mosquito, sea squirt, and nematode). The relative contributions of each feature to the variation of 5’UTR length were also evaluated.</p> <p>Results</p> <p>We found that 14%~33% of the 5’UTR length variations can be explained by a linear combination of the analyzed genomic features. The most important genomic features are the OE ratios of uSTOPs and G+C content. The surprisingly large weightings of uSTOPs highlight the importance of selection on upstream open reading frames (which include both uAUGs and uSTOPs), rather than on uAUGs <it>per se</it>. Furthermore, G+C content is the most important determinants for most invertebrates, but for vertebrates its effect is second to uSTOPs. We also found that shorter 5’UTRs are affected more by the stochastic process, whereas longer 5’UTRs are affected more by selection pressure on genomic features.</p> <p>Conclusions</p> <p>Our results suggest that upstream open reading frames may be the real target of selection, rather than uAUGs. We also show that the selective constraints on genomic features of 5’UTRs differ between vertebrates and invertebrates, and between longer and shorter 5’UTRs. A more comprehensive model that takes these findings into consideration is needed to better explain 5’UTR length evolution.</p

Measuring patient-perceived continuity of care for patients with long-term conditions in primary care

Background: Continuity of care is widely acknowledged as important for patients with multi-morbidity but simple, service-orientated indices cannot capture the full impact of continuity in complex care delivery systems. The patient's perspective is important to assess outcomes fully and this is challenging because generic measures of patient-perceived continuity are lacking. We investigate the Chao Perception of Continuity (Chao PC) scale to determine its suitability as a measure of continuity of care for patients with a long-term condition (stroke), and co-morbidity, in a primary care setting. Methods: Design and Setting: A questionnaire study embedded in a prospective observational cohort study of outcomes for patients following acute stroke. Participants: 168 community dwelling patients (58% male) mean age 68 years a minimum one year post-stroke. Functional status: Barthel Index mean =16. Intervention: A 23-item questionnaire, the Chao Perception of Continuity (Chao PC) scale, sent by post to their place of residence or administered face to face as part of the final cohort study assessment. Results: 310 patients were invited to participate; 168 (54%) completed a questionnaire. All 23 questionnaire items were entered into a Principal Component Analysis. Emergent factors from the exploratory analysis were (1) inter-personal trust (relational continuity); (2) interpersonal knowledge and information (informational and relational continuity) and (3) the process of care (managerial continuity). The strongest of these was inter-personal trust. Conclusion: The context-specific items in the Chao PC scale are difficult for respondents to interpret in a United Kingdom Primary Care setting resulting in missing data and low response rates. The Chao-PC therefore cannot be recommended for wider application as a general measure of continuity of care without significant modification. Our findings reflect the acknowledged dimensions of continuity and support the concept of continuity of care as a multi-dimensional construct. We demonstrate the overlapping boundaries across the dimensions in the factor structure derived. Trust and interpersonal knowledge are clearly identified as valuable components of any patient-perceived measure of continuity of care

Post-Mortem diagnosis of dementia by informant interview

Abstract The diagnosis of normal cognition or dementia in the Brazilian Brain Bank of the Aging Brain Study Group (BBBABSG) has relied on postmortem interview with an informant. Objectives: To ascertain the sensitivity and specificity of postmortem diagnosis based on informant interview compared against the diagnosis established at a memory clinic. Methods: A prospective study was conducted at the BBBABSG and at the Reference Center for Cognitive Disorders (RCCD), a specialized memory clinic of the Hospital das Clínicas, University of São Paulo Medical School. Control subjects and cognitively impaired subjects were referred from the Hospital das Clínicas to the RCCD where subjects and their informants were assessed. The same informant was then interviewed at the BBBABSG. Specialists' panel consensus, in each group, determined the final diagnosis of the case, blind to other center's diagnosis. Data was compared for frequency of diagnostic equivalence. For this study, the diagnosis established at the RCCD was accepted as the gold standard. Sensitivity and specificity were computed. Results: Ninety individuals were included, 45 with dementia and 45 without dementia (26 cognitively normal and 19 cognitively impaired but non-demented). The informant interview at the BBBABSG had a sensitivity of 86.6% and specificity of 84.4% for the diagnosis of dementia, and a sensitivity of 65.3% and specificity of 93.7% for the diagnosis of normal cognition. Conclusions: The informant interview used at the BBBABSG has a high specificity and sensitivity for the diagnosis of dementia as well as a high specificity for the diagnosis of normal cognition