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In this article, the authors explore framing, a non-multiplicative technique commonly employed by students as they construct similar shapes. When students frame, they add (or subtract) a “border” of fixed width about a geometric object. Although the approach does not yield similar shapes in general, the mathematical underpinnings of framing are noteworthy. Using Interactive Geometry Software (IGS), teachers can explore mathematics behind the framing technique in greater depth while addressing student misconceptions and over- generalizations associated with the approach in classroom settings.

For the past five years, genome-wide association studies (GWAS) have identified hundreds of common variants associated with human diseases and traits, including high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C), and triglyceride (TG) levels. Approximately 95 loci associated with lipid levels have been identified primarily among populations of European ancestry. The Population Architecture using Genomics and Epidemiology (PAGE) study was established in 2008 to characterize GWAS-identified variants in diverse population-based studies. We genotyped 49 GWAS-identified SNPs associated with one or more lipid traits in at least two PAGE studies and across six racial/ethnic groups. We performed a meta-analysis testing for SNP associations with fasting HDL-C, LDL-C, and ln(TG) levels in self-identified European American (~20,000), African American (~9,000), American Indian (~6,000), Mexican American/Hispanic (~2,500), Japanese/East Asian (~690), and Pacific Islander/Native Hawaiian (~175) adults, regardless of lipid-lowering medication use. We replicated 55 of 60 (92%) SNP associations tested in European Americans at p

Genome-wide association studies (GWAS) are routinely being used to examine the genetic contribution to complex human traits, such as high-density lipoprotein cholesterol (HDL-C). Although HDL-C levels are highly heritable (h(2)∼0.7), the genetic determinants identified through GWAS contribute to a small fraction of the variance in this trait. Reasons for this discrepancy may include rare variants, structural variants, gene-environment (GxE) interactions, and gene-gene (GxG) interactions. Clinical practice-based biobanks now allow investigators to address these challenges by conducting GWAS in the context of comprehensive electronic medical records (EMRs). Here we apply an EMR-based phenotyping approach, within the context of routine care, to replicate several known associations between HDL-C and previously characterized genetic variants: CETP (rs3764261, p = 1.22e-25), LIPC (rs11855284, p = 3.92e-14), LPL (rs12678919, p = 1.99e-7), and the APOA1/C3/A4/A5 locus (rs964184, p = 1.06e-5), all adjusted for age, gender, body mass index (BMI), and smoking status. By using a novel approach which censors data based on relevant co-morbidities and lipid modifying medications to construct a more rigorous HDL-C phenotype, we identified an association between HDL-C and TRIB1, a gene which previously resisted identification in studies with larger sample sizes. Through the application of additional analytical strategies incorporating biological knowledge, we further identified 11 significant GxG interaction models in our discovery cohort, 8 of which show evidence of replication in a second biobank cohort. The strongest predictive model included a pairwise interaction between LPL (which modulates the incorporation of triglyceride into HDL) and ABCA1 (which modulates the incorporation of free cholesterol into HDL). These results demonstrate that gene-gene interactions modulate complex human traits, including HDL cholesterol.

IntroductionDopamine (DA) binds to five receptors (DAR), classified by their ability to increase (D1R-like) or decrease (D2R-like) cAMP. In humans, most DA circulates as dopamine sulfate (DA-S), which can be de-conjugated to bioactive DA by arylsulfatase A (ARSA). The objective was to examine expression of DAR and ARSA in human adipose tissue and determine whether DA regulates prolactin (PRL) and adipokine expression and release.MethodsDAR were analyzed by RT-PCR and Western blotting in explants, primary adipocytes and two human adipocyte cell lines, LS14 and SW872. ARSA expression and activity were determined by qPCR and enzymatic assay. PRL expression and release were determined by luciferase reporter and Nb2 bioassay. Analysis of cAMP, cGMP, leptin, adiponectin and interleukin 6 (IL-6) was done by ELISA. Activation of MAPK and PI3 kinase/Akt was determined by Western blotting.ResultsDAR are variably expressed at the mRNA and protein levels in adipose tissue and adipocytes during adipogenesis. ARSA activity in adipocyte increases after differentiation. DA at nM concentrations suppresses cAMP, stimulates cGMP, and activates MAPK in adipocytes. Acting via D2R-like receptors, DA and DA-S inhibit PRL gene expression and release. Acting via D1R/D5R receptors, DA suppresses leptin and stimulates adiponectin and IL-6 release.ConclusionsThis is the first report that human adipocytes express functional DAR and ARSA, suggesting a regulatory role for peripheral DA in adipose functions. We speculate that the propensity of some DAR-activating antipsychotics to increase weight and alter metabolic homeostasis is due, in part, to their direct action on adipose tissue.

The distribution of lipoprotein(a) [Lp(a)] levels can differ dramatically across diverse racial/ethnic populations. The extent to which genetic variation in LPA can explain these differences is not fully understood. To explore this, 19 LPA tagSNPs were genotyped in 7,159 participants from the Third National Health and Nutrition Examination Survey (NHANES III). NHANES III is a diverse population-based survey with DNA samples linked to hundreds of quantitative traits, including serum Lp(a). Tests of association between LPA variants and transformed Lp(a) levels were performed across the three different NHANES subpopulations (non-Hispanic whites, non-Hispanic blacks, and Mexican Americans). At a significance threshold of p

Host genetic factors that modify risk of pneumococcal disease may help target future public health interventions to individuals at highest risk of disease. We linked data from population-based surveillance for invasive pneumococcal disease (IPD) with state-based newborn dried bloodspot repositories to identify biological samples from individuals who developed invasive pneumococcal disease. Genomic DNA was extracted from 366 case and 732 anonymous control samples. TagSNPs were selected in 34 candidate genes thought to be associated with host response to invasive pneumococcal disease, and a total of 326 variants were successfully genotyped. Among 543 European Americans (EA) (182 cases and 361 controls), and 166 African Americans (AA) (53 cases and 113 controls), common variants in surfactant protein D (SFTPD) are consistently underrepresented in IPD. SFTPD variants with the strongest association for IPD are intronic rs17886286 (allelic OR 0.45, 95% confidence interval (CI) [0.25, 0.82], with p = 0.007) in EA and 5' flanking rs12219080 (allelic OR 0.32, 95%CI [0.13, 0.78], with p = 0.009) in AA. Variants in CD46 and IL1R1 are also associated with IPD in both EA and AA, but with effects in different directions; FAS, IL1B, IL4, IL10, IL12B, SFTPA1, SFTPB, and PTAFR variants are associated (p≤0.05) with IPD in EA or AA. We conclude that variants in SFTPD may protect against IPD in EA and AA and genetic variation in other host response pathways may also contribute to risk of IPD. While our associations are not corrected for multiple comparisons and therefore must be replicated in additional cohorts, this pilot study underscores the feasibility of integrating public health surveillance with existing, prospectively collected, newborn dried blood spot repositories to identify host genetic factors associated with infectious diseases.

Osteoporosis, defined by low bone mineral density (BMD), is common among postmenopausal women. The distribution of BMD varies across populations and is shaped by both environmental and genetic factors. Because the candidate gene vitamin K epoxide reductase complex subunit 1 (VKORC1) generates vitamin K quinone, a cofactor for the gamma-carboxylation of bone-related proteins such as osteocalcin, we hypothesized that VKORC1 genetic variants may be associated with BMD and osteoporosis in the general population. To test this hypothesis, we genotyped six VKORC1 SNPs in 7,159 individuals from the Third National Health and Nutrition Examination Survey (NHANES III). NHANES III is a nationally representative sample linked to health and lifestyle variables including BMD, which was measured using dual energy x-ray absorptiometry (DEXA) on four regions of the proximal femur. In adjusted models stratified by race/ethnicity and sex, SNPs rs9923231 and rs9934438 were associated with increased BMD (p=0.039 and 0.024, respectively) while rs8050894 was associated with decreased BMD (p=0.016) among non-Hispanic black males (n=619). VKORC1 rs2884737 was associated with decreased BMD among Mexican-American males (n=795; p=0.004). We then tested for associations between VKORC1 SNPs and osteoporosis, but the results did not mirror the associations observed between VKORC1 and BMD, possibly due to small numbers of cases. This is the first report of VKORC1 common genetic variation associated with BMD, and one of the few reports available that investigate the genetics of BMD and osteoporosis in diverse populations.

Increasing evidence highlights the importance of context-specific understanding of the impacts of climate change and the need to move beyond generalized assumptions regarding the nature and utility of adaptive capacity in facilitating adaptation. The household level of impact and response is an under-researched context, despite influential decisions affecting local and system vulnerability being made at this scale. Assessments of household adaptive capacity currently assess the influences of adaptive capacity or the influences on adaptive capacity in isolation. We argue that comprehensive assessments need to examine these influences in combination to capture a dynamic and integrated view of households that better reflects their positioning and role(s) in broader social-political contexts. To transition assessments away from examining households as discrete units to recognizing their role within a larger governance context, we outline four themes focused on: (1) analysis of governance contexts, (2) determination of adaptive capacity sources, (3) assessment of cross-scalar trade-offs, and (4) integrated goal setting to facilitate boundary critiques. By considering these themes, the relationships between capacities and actions are highlighted, and the simultaneous outcomes of adaptive choices at individual and broader system scales can be evaluated. We argue that such boundary critique has the potential to yield a more comprehensive assessment of adaptive capacity focused upon cross-scalar influences and impacts.

SARS-CoV-2 has caused symptomatic COVID-19 and widespread death across the globe. We sought to determine genetic variants contributing to COVID-19 susceptibility and hospitalization in a large biobank linked to a national United States health system. We identified 19,168 (3.7%) lab-confirmed COVID-19 cases among Million Veteran Program participants between March 1, 2020, and February 2, 2021, including 11,778 Whites, 4,893 Blacks, and 2,497 Hispanics. A multi-population genome-wide association study (GWAS) for COVID-19 outcomes identified four independent genetic variants (rs8176719, rs73062389, rs60870724, and rs73910904) contributing to COVID-19 positivity, including one novel locus found exclusively among Hispanics. We replicated eight of nine previously reported genetic associations at an alpha of 0.05 in at least one population-specific or the multi-population meta-analysis for one of the four MVP COVID-19 outcomes. We used rs8176719 and three additional variants to accurately infer ABO blood types. We found that A, AB, and B blood types were associated with testing positive for COVID-19 compared with O blood type with the highest risk for the A blood group. We did not observe any genome-wide significant associations for COVID-19 severity outcomes among those testing positive. Our study replicates prior GWAS findings associated with testing positive for COVID-19 among mostly White samples and extends findings at three loci to Black and Hispanic individuals. We also report a new locus among Hispanics requiring further investigation. These findings may aid in the identification of novel therapeutic agents to decrease the morbidity and mortality of COVID-19 across all major ancestral populations.

BackgroundPatients with chronic inflammatory disease (CID) treated with immunosuppressive medications have increased risk for severe COVID-19. Although mRNA-based SARS-CoV-2 vaccination provides protection in immunocompetent persons, immunogenicity in immunosuppressed patients with CID is unclear.ObjectiveTo determine the immunogenicity of mRNA-based SARS-CoV-2 vaccines in patients with CID.DesignProspective observational cohort study.SettingTwo U.S. CID referral centers.ParticipantsVolunteer sample of adults with confirmed CID eligible for early COVID-19 vaccination, including hospital employees of any age and patients older than 65 years. Immunocompetent participants were recruited separately from hospital employees. All participants received 2 doses of mRNA vaccine against SARS-CoV-2 between 10 December 2020 and 20 March 2021. Participants were assessed within 2 weeks before vaccination and 20 days after final vaccination.MeasurementsAnti-SARS-CoV-2 spike (S) IgG+ binding in all participants, and neutralizing antibody titers and circulating S-specific plasmablasts in a subset to assess humoral response after vaccination.ResultsMost of the 133 participants with CID (88.7%) and all 53 immunocompetent participants developed antibodies in response to mRNA-based SARS-CoV-2 vaccination, although some with CID developed numerically lower titers of anti-S IgG. Anti-S IgG antibody titers after vaccination were lower in participants with CID receiving glucocorticoids (n = 17) than in those not receiving them; the geometric mean of anti-S IgG antibodies was 357 (95% CI, 96 to 1324) for participants receiving prednisone versus 2190 (CI, 1598 to 3002) for those not receiving it. Anti-S IgG antibody titers were also lower in those receiving B-cell depletion therapy (BCDT) (n = 10). Measures of immunogenicity differed numerically between those who were and those who were not receiving antimetabolites (n = 48), tumor necrosis factor inhibitors (n = 39), and Janus kinase inhibitors (n = 11); however, 95% CIs were wide and overlapped. Neutralization titers seemed generally consistent with anti-S IgG results. Results were not adjusted for differences in baseline clinical factors, including other immunosuppressant therapies.LimitationsSmall sample that lacked demographic diversity, and residual confounding.ConclusionCompared with nonusers, patients with CID treated with glucocorticoids and BCDT seem to have lower SARS-CoV-2 vaccine-induced antibody responses. These preliminary findings require confirmation in a larger study.Primary funding sourceThe Leona M. and Harry B. Helmsley Charitable Trust, Marcus Program in Precision Medicine Innovation, National Center for Advancing Translational Sciences, and National Institute of Arthritis and Musculoskeletal and Skin Diseases.

We conducted a preregistered multilaboratory project (k = 36; N = 3,531) to assess the size and robustness of ego-depletion effects using a novel replication method, termed the paradigmatic replication approach. Each laboratory implemented one of two procedures that was intended to manipulate self-control and tested performance on a subsequent measure of self-control. Confirmatory tests found a nonsignificant result (d = 0.06). Confirmatory Bayesian meta-analyses using an informed-prior hypothesis (δ = 0.30, SD = 0.15) found that the data were 4 times more likely under the null than the alternative hypothesis. Hence, preregistered analyses did not find evidence for a depletion effect. Exploratory analyses on the full sample (i.e., ignoring exclusion criteria) found a statistically significant effect (d = 0.08); Bayesian analyses showed that the data were about equally likely under the null and informed-prior hypotheses. Exploratory moderator tests suggested that the depletion effect was larger for participants who reported more fatigue but was not moderated by trait self-control, willpower beliefs, or action orientation.

BackgroundWe previously developed an African-ancestry-specific polygenic hazard score (PHS46+African) that substantially improved prostate cancer risk stratification in men with African ancestry. The model consists of 46 SNPs identified in Europeans and 3 SNPs from 8q24 shown to improve model performance in Africans. Herein, we used principal component (PC) analysis to uncover subpopulations of men with African ancestry for whom the utility of PHS46+African may differ.Materials and methodsGenotypic data were obtained from the PRACTICAL consortium for 6253 men with African genetic ancestry. Genetic variation in a window spanning 3 African-specific 8q24 SNPs was estimated using 93 PCs. A Cox proportional hazards framework was used to identify the pair of PCs most strongly associated with the performance of PHS46+African. A calibration factor (CF) was formulated using Cox coefficients to quantify the extent to which the performance of PHS46+African varies with PC.ResultsCF of PHS46+African was strongly associated with the first and twentieth PCs. Predicted CF ranged from 0.41 to 2.94, suggesting that PHS46+African may be up to 7 times more beneficial to some African men than others. The explained relative risk for PHS46+African varied from 3.6% to 9.9% for individuals with low and high CF values, respectively. By cross-referencing our data set with 1000 Genomes, we identified significant associations between continental and calibration groupings.ConclusionWe identified PCs within 8q24 that were strongly associated with the performance of PHS46+African. Further research to improve the clinical utility of polygenic risk scores (or models) is needed to improve health outcomes for men of African ancestry.

Adaptation is a key feature of sustainable social-ecological systems. As societies traverse various temporal and spatial scales, they are exposed to differing contexts and precursors for adaptation. A cursory view of the response to these differing contexts and precursors suggests the particular ability of persistent societies to adapt to changing circumstances. Yet a closer examination into the meaning of adaptation and its relationship to concepts of resilience, vulnerability, and sustainability illustrates that, in many cases, societies actually manipulate their social-ecological contexts rather than adapt to them. It could be argued that manipulative behaviors are a subset of a broader suite of adaptive behaviors; however, this paper suggests that manipulative behaviors have fundamentally different intentions and outcomes. Specifically, adaptive behaviors are respectful of the intrinsic integrity of social-ecological systems and change is directed toward internal or self-regulating modification. By way of contrast, manipulative behaviors tend to disregard the integrity of social-ecological systems and focus on external change or manipulating the broader system with the aim of making self-regulation unnecessary. It is argued that adaptive behaviors represent long-term strategies for building resilience, whereas manipulative behaviors represent short-term strategies with uncertain consequences for resilience, vulnerability, and the sustainability of social-ecological systems. Of greatest significance; however, is that manipulative strategies have the potential to avoid authentic experiences of system dynamics, obscure valuable learning opportunities, create adverse path dependencies, and lessen the likelihood of effective adaptation in future contexts.

Ecological problem solving requires a flexible social infrastructure that can incorporate scientific insights and adapt to changing conditions. As applied to watershed management, social infrastructure includes mechanisms to design, carry out, evaluate, and modify plans for resource protection or restoration. Efforts to apply the best science will not bring anticipated results without the appropriate social infrastructure. For the Long Tom Watershed Council, social infrastructure includes a management structure, membership, vision, priorities, partners, resources, and the acquisition of scientific knowledge, as well as the communication with and education of people associated with and affected by actions to protect and restore the watershed. Key to integrating science and practice is keeping science in the loop, using data collection as an outreach tool, and the Long Tom Watershed Council's subwatershed enhancement program approach. Resulting from these methods are ecological leadership, restoration projects, and partnerships that catalyze landscape-level change.

Ghrelin exerts key effects on islet hormone secretion to regulate blood glucose levels. Here, we sought to determine whether ghrelin's effects on islets extend to the alteration of islet size and [beta] cell mass. We demonstrate that reducing ghrelin - by ghrelin gene knockout (GKO), conditional ghrelin cell ablation, or high-fat diet (HFD) feeding - was associated with increased mean islet size (up to 62%), percentage of large islets (up to 854%), and [beta] cell cross-sectional area (up to 51%). In GKO mice, these effects were more apparent in 10- to 12-week-old mice than in 4-week-old mice. Higher [beta] cell numbers from decreased [beta] cell apoptosis drove the increase in [beta] cell cross-sectional area. Conditional ghrelin cell ablation in adult mice increased the [beta] cell number per islet by 40% within 4 weeks. A negative correlation between islet size and plasma ghrelin in HFD-fed plus chow-fed WT mice, together with even larger islet sizes in HFD-fed GKO mice than in HFD-fed WT mice, suggests that reduced ghrelin was not solely responsible for diet-induced obesity-associated islet enlargement. Single-cell transcriptomics revealed changes in gene expression in several GKO islet cell types, including upregulation of Manf, Dnajc3, and Gnas expression in [beta] cells, which supports decreased [beta] cell apoptosis and/or increased [beta] cell proliferation. These effects of ghrelin reduction on islet morphology might prove useful when designing new therapies for diabetes., Introduction Ghrelin is secreted primarily by gastric ghrelin cells (1). It is mainly via binding to CNS and pituitary growth hormone secretagogue receptors (GHSRs) that ghrelin's actions to increase GH [...]

Polygenic hazard score (PHS) models are associated with age at diagnosis of prostate cancer. Our model developed in Europeans (PHS46) showed reduced performance in men with African genetic ancestry. We used a cross-validated search to identify single nucleotide polymorphisms (SNPs) that might improve performance in this population. Anonymized genotypic data were obtained from the PRACTICAL consortium for 6253 men with African genetic ancestry. Ten iterations of a 10-fold cross-validation search were conducted to select SNPs that would be included in the final PHS46+African model. The coefficients of PHS46+African were estimated in a Cox proportional hazards framework using age at diagnosis as the dependent variable and PHS46, and selected SNPs as predictors. The performance of PHS46 and PHS46+African was compared using the same cross-validated approach. Three SNPs (rs76229939, rs74421890 and rs5013678) were selected for inclusion in PHS46+African. All three SNPs are located on chromosome 8q24. PHS46+African showed substantial improvements in all performance metrics measured, including a 75% increase in the relative hazard of those in the upper 20% compared to the bottom 20% (2.47-4.34) and a 20% reduction in the relative hazard of those in the bottom 20% compared to the middle 40% (0.65-0.53). In conclusion, we identified three SNPs that substantially improved the association of PHS46 with age at diagnosis of prostate cancer in men with African genetic ancestry to levels comparable to Europeans.