The double well potential in quantum mechanics: a simple, numerically exact formulation

The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important in quantum information theory. It is therefore desirable to have solutions to simple double well potentials that are accessible to the undergraduate student. We describe a method for obtaining the numerically exact eigenenergies and eigenstates for such a model, along with the energies obtained through the Wentzel-Kramers-Brillouin (WKB) approximation. The exact solution is accessible with elementary mathematics, though numerical solutions are required. We also find that the WKB approximation is remarkably accurate, not just for the ground state, but for the excited states as well.Comment: 10 pages, 4 figures; suitable for undergraduate courses in quantum mechanic

17Beta-estradiol Increases Basal But not Bradykinin-stimulated Release of Active t-PA in Young Postmenopausal Women

Angiotensin-converting enzyme inhibition potentiates basal and bradykinin-stimulated tissue-type plasminogen activator (t-PA) release to a greater extent in women than in men. This study tested the hypothesis that 17beta-estradiol enhances the effect of angiotensin-converting enzyme inhibition on t-PA release in young postmenopausal women. We conducted a double-blind, prospective, crossover study in 14 young postmenopausal women (mean age 48.2+/-2.3 years) who were randomized to receive 17beta-estradiol (1 mg/d) or matching placebo for 4 weeks. At the end of each treatment period, we measured the effect of intraarterial infusion of bradykinin, methacholine, and nitroprusside on forearm blood flow and net t-PA release, before and during intraarterial enalaprilat (0.33 microg/min/100 mL forearm volume). 17Beta-estradiol significantly reduced baseline venous plasminogen activator inhibitor-1 antigen (4.4+/-1.4 versus 10.4+/-2.5 ng/mL, P=0.001) and t-PA antigen (5.5+/-0.6 versus 7.5+/-1.3 ng/mL, P=0.022) compared with placebo. 17Beta-estradiol increased basal forearm vascular release of active t-PA compared with placebo (1.2+/-0.3 IU/mL/min versus 0.4+/-0.1 IU/mL/min respectively, P=0.032), without increasing t-PA antigen release (P=0.761). Enalaprilat significantly increased basal net t-PA antigen release (from -0.8+/-1.0 to 3.2+/-1.2 ng/min/100 mL, P=0.012), but not the release of active t-PA, during either placebo or 17beta-estradiol. Enalaprilat potentiated bradykinin-stimulated vasodilation and t-PA antigen and activity release similarly during placebo and 17beta-estradiol treatment. 17Beta-estradiol treatment does not alter the effect of angiotensin-converting enzyme inhibition on basal t-PA antigen or on bradykinin-stimulated t-PA antigen or activity release. 17Beta-estradiol increases basal release of active t-PA in young postmenopausal women, consistent with enhanced vascular fibrinolytic function

Impaired Endothelium-dependent Vasodilation in Overweight and Obese Adult Humans is Not Limited to Muscarinic Receptor Agonists

Muscarinic receptor agonists have primarily been used to characterize endothelium-dependent vasodilator dysfunction with overweight/obesity. Reliance on a single class of agonist, however, yields limited, and potentially misleading, information regarding endothelial vasodilator capacity. The aims of this study were to determine 1) whether the overweight/obesity-related reduction in endothelium-dependent vasodilation extends beyond muscarinic receptor agonists and 2) whether the contribution of nitric oxide (NO) to endothelium-dependent vasodilation is reduced in overweight/obese adults. Eighty-six middle-aged and older adults were studied: 42 normal-weight (54 +/- 1 yr, 21 men and 21 women, body mass index = 23.4 +/- 0.3 kg/m(2)) and 44 overweight/obese (54 +/- 1 yr, 28 men and 16 women, body mass index = 30.3 +/- 0.6 kg/m(2)) subjects. Forearm blood flow (FBF) responses to intra-arterial infusions of acetylcholine in the absence and presence of the endothelial NO synthase inhibitor N(G)-monomethyl-l-arginine, methacholine, bradykinin, substance P, isoproterenol, and sodium nitroprusside were measured by strain-gauge plethysmography. FBF responses to each endothelial agonist were significantly blunted in the overweight/obese adults. Total FBF (area under the curve) to acetylcholine (50 +/- 5 vs. 79 +/- 4 ml/100 ml tissue), methacholine (55 +/- 4 vs. 86 +/- 5 ml/100 ml tissue), bradykinin (62 +/- 5 vs. 85 +/- 4 ml/100 ml tissue), substance P (37 +/- 4 vs. 57 +/- 5 ml/100 ml tissue), and isoproterenol (62 +/- 4 vs. 82 +/- 6 ml/100 ml tissue) were 30%-40% lower in the overweight/obese than normal-weight adults. N(G)-monomethyl-l-arginine significantly reduced the FBF response to acetylcholine to the same extent in both groups. There were no differences between the groups in the FBF responses to sodium nitroprusside. These results indicate that agonist-stimulated endothelium-dependent vasodilation is universally impaired with overweight/obesity. Moreover, this impairment appears to be independent of NO

Bradykinin Type 2 Receptor BE1 Genotype Influences Bradykinin-dependent Vasodilation During Angiotensin-converting Enzyme Inhibition

To test the hypothesis that the bradykinin receptor 2 (BDKRB2) BE1+9/-9 polymorphism affects vascular responses to bradykinin, we measured the effect of intra-arterial bradykinin on forearm blood flow and tissue-type plasminogen activator (t-PA) release in 89 normotensive, nonsmoking, white American subjects in whom degradation of bradykinin was blocked by enalaprilat. BE1 genotype frequencies were +9/+9:+9/-9:-9/-9=19:42:28. BE1 genotype was associated with systolic blood pressure (121.4+/-2.8, 113.8+/-1.8, and 110.6+/-1.8 mm Hg in +9/+9, +9/-9, and -9/-9 groups, respectively; P=0.007). In the absence of enalaprilat, bradykinin-stimulated forearm blood flow, forearm vascular resistance, and net t-PA release were similar among genotype groups. Enalaprilat increased basal forearm blood flow (P=0.002) and decreased basal forearm vascular resistance (P=0.01) without affecting blood pressure. Enalaprilat enhanced the effect of bradykinin on forearm blood flow, forearm vascular resistance, and t-PA release (all P\u3c0.001). During enalaprilat, forearm blood flow was significantly lower and forearm vascular resistance was higher in response to bradykinin in the +9/+9 compared with +9/-9 and -9/-9 genotype groups (P=0.04 for both). t-PA release tended to be decreased in response to bradykinin in the +9/+9 group (P=0.08). When analyzed separately by gender, BE1 genotype was associated with bradykinin-stimulated t-PA release in angiotensin-converting enzyme inhibitor-treated men but not women (P=0.02 and P=0.77, respectively), after controlling for body mass index. There was no effect of BE1 genotype on responses to the bradykinin type 2 receptor-independent vasodilator methacholine during enalaprilat. In conclusion, the BDKRB2 BE1 polymorphism influences bradykinin type 2 receptor-mediated vasodilation during angiotensin-converting enzyme inhibition

Aging and Endothelial Progenitor Cell Telomere Length in Healthy Men

BACKGROUND: Telomere length declines with age in mature endothelial cells and is thought to contribute to endothelial dysfunction and atherogenesis. Bone marrow-derived circulating endothelial progenitor cells (EPCs) are critical to vascular health as they contribute to both reendothelialization and neovascularization. We tested the hypothesis that EPC telomere length decreases with age in healthy adult humans.METHODS: Peripheral blood samples were collected from 40 healthy, non-obese, sedentary men: 12 young (age 21-34 years), 12 middle-aged (43-55 years) and 16 older (57-68 years). Putative EPCs were isolated from peripheral blood mononuclear cells and telomere length was determined using genomic DNA preparation and Southern hybridization techniques.RESULTS: EPC telomere length (base pairs) was approximately 20% (p=0.01) lower in the older (8492+523 bp) compared to the middle-aged (10,565+572 bp) and young (10,205+501 bp) men. Of note, there was no difference in EPC telomere length between the middle-aged and young men.CONCLUSIONS: These results demonstrate that EPC telomere length declines with age in healthy, sedentary men. Interestingly, telomere length was well preserved in the middle-aged compared to young men, suggesting that EPC telomere shortening occurs after the age of 55 years

Aging and Endothelial Progenitor Cell Telomere Length in Healthy Men

BACKGROUND: Telomere length declines with age in mature endothelial cells and is thought to contribute to endothelial dysfunction and atherogenesis. Bone marrow-derived circulating endothelial progenitor cells (EPCs) are critical to vascular health as they contribute to both reendothelialization and neovascularization. We tested the hypothesis that EPC telomere length decreases with age in healthy adult humans. METHODS: Peripheral blood samples were collected from 40 healthy, non-obese, sedentary men: 12 young (age 21-34 years), 12 middle-aged (43-55 years) and 16 older (57-68 years). Putative EPCs were isolated from peripheral blood mononuclear cells and telomere length was determined using genomic DNA preparation and Southern hybridization techniques. RESULTS: EPC telomere length (base pairs) was approximately 20% (p=0.01) lower in the older (8492+523 bp) compared to the middle-aged (10,565+572 bp) and young (10,205+501 bp) men. Of note, there was no difference in EPC telomere length between the middle-aged and young men. CONCLUSIONS: These results demonstrate that EPC telomere length declines with age in healthy, sedentary men. Interestingly, telomere length was well preserved in the middle-aged compared to young men, suggesting that EPC telomere shortening occurs after the age of 55 years

Individualization of piperacillin dosing for critically ill patients: Dosing software to optimize antimicrobial therapy

Piperacillin-tazobactam is frequently used for empirical and targeted therapy of infections in critically ill patients. Considerable pharmacokinetic (PK) variability is observed in critically ill patients. By estimating an individual's PK, dosage optimization Bayesian estimation techniques can be used to calculate the appropriate piperacillin regimen to achieve desired drug exposure targets. The aim of this study was to establish a population PK model for piperacillin in critically ill patients and then analyze the performance of the model in the dose optimization software program BestDose. Linear, with estimated creatinine clearance and weight as covariates, Michaelis-Menten (MM) and parallel linear/MM structural models were fitted to the data from 146 critically ill patients with nosocomial infection. Piperacillin concentrations measured in the first dosing interval, from each of 8 additional individuals, combined with the population model were embedded into the dose optimization software. The impact of the number of observations was assessed. Precision was assessed by (i) the predicted piperacillin dosage and by (ii) linear regression of the observed-versus-predicted piperacillin concentrations from the second 24 h of treatment. We found that a linear clearance model with creatinine clearance and weight as covariates for drug clearance and volume of distribution, respectively, best described the observed data. When there were at least two observed piperacillin concentrations, the dose optimization software predicted a mean piperacillin dosage of 4.02 g in the 8 patients administered piperacillin doses of 4.00 g. Linear regression of the observed-versus-predicted piperacillin concentrations for 8 individuals after 24 h of piperacillin dosing demonstrated an r2 of > 0.89. In conclusion, for most critically ill patients, individualized piperacillin regimens delivering a target serum piperacillin concentration is achievable. Further validation of the dosage optimization software in a clinical trial is required. Copyrigh

Impacts of climate change on aquaculture

• Aquaculture is a significant industry in UK coastal waters, with annual turnover valued at more than £1.8bn. It particularly important in western and northern Scotland. • Aquaculture is sensitive to the marine environment and changes therein. • The dominant contribution of a single species (Atlantic salmon) to production tonnage and value potentially increases vulnerability to climate change. • Temperature increase is expected to increase growth rates for most species farmed. • Increased problems associated with some diseases and parasites, notably sea lice and gill disease (which has emerged as a serious problem), are likely to increase in the short term and to get worse in the longer term. Impacts may be synergistic. • Harmful Algal Blooms (HABs) and jellyfish swarms/invasions may also get worse, however complex ecosystem interactions make responses uncertain. • The situation for shellfish is similar to finfish, although they are additionally at risk of accumulation of toxins from HABs, and recruitment failure, and, in the longer term, to sea-level rises and ocean acidification. • Technical and management changes in the rapidly evolving aquaculture industry make long-term impacts of climate change difficult to forecast

Prehypertension and Endothelial Progenitor Cell Function.

Prehypertension is associated with significant damage to the coronary vasculature and increased rates of adverse cardiovascular events. Circulating endothelial progenitor cells (EPCs) are critical to vascular repair and the formation of new blood vessels. We tested the hypothesis that prehypertension is associated with EPC dysfunction. Peripheral blood samples were collected from 83 middle-aged and older adults (51 M/32 F): 40 normotensive (age 53±2 yr; BP 111/74±1/1 mmHg) and 43 prehypertensive (54±2; 128/77±1/1 mmHg). EPCs were isolated from peripheral blood and EPC colony-forming capacity (colony-forming unit assay), migratory activity (Boyden chamber) and apoptotic susceptibility (active caspase-3 concentrations) were determined. There were no significant differences in either the number of EPC CFUs (10±2 vs. 9±1), EPC migration (1165±82 vs. 1120±84 fluorescent units), or active intracellular caspase-3 concentrations (2.7±0.3 vs. 2.3±0.2 ng/mL) between the normotensive and prehypertensive groups. When groups were stratified into low prehypertension (n=27; systolic BP: 120–129 mmHg) and high prehypertension (n=16; 130–139 mmHg), it was found that EPCs from the high prehypertensive group produced fewer (~65%, P\u3c0.05) CFUs compared with the low prehypertensive (4±1 vs. 12±2) and normotensive adults. In conclusion, EPC colonyforming capacity is impaired only in prehypertensive adults with systolic BP greater than 130 mmHg. Prehypertension is not associated with migratory dysfunction or enhanced apoptosis of EPCs

Basal Endothelial Nitric Oxide Release is Preserved in Overweight and Obese Adults

OBJECTIVE: Impaired basal nitric oxide release is associated with a number of cardiovascular disorders including hypertension, arterial spasm, and myocardial infarction. We determined whether basal endothelial nitric oxide release is reduced in otherwise healthy overweight and obese adult humans.RESEARCH METHODS AND PROCEDURES: Seventy sedentary adults were studied: 32 normal weight (BMI/m(2)), 24 overweight (BMI \u3e or = 25 \u3c 30 kg/m(2)), and 14 obese (BMI \u3e or = 30 kg/m(2)). Forearm blood flow (FBF) responses to intra-arterial infusions of N(g)-monomethyl-L-arginine (5 mg/min), a nitric oxide synthase inhibitor, were used as an index of basal nitric oxide release.RESULTS: N(g)-monomethyl-L-arginine elicited significant reductions in FBF in the normal weight (from 4.1 +/- 0.2 to 2.7 +/- 0.2 mL/100 mL tissue/min), overweight (4.1 +/- 0.1 to 2.8 +/- 0.2 mL/100 mL tissue/min), and obese (3.9 +/- 0.3 to 2.7 +/- 0.2 mL/100 mL tissue/min) subjects. Importantly, the magnitude of reduction in FBF (approximately 30%) was similar among the groups.DISCUSSION: These results indicate that the capacity of the endothelium to release nitric oxide under basal conditions is not compromised in overweight and obese adults