Erratum: Publisher Correction: Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge.

[This corrects the article DOI: 10.1007/s11858-022-01447-2.].

Relevant mathematical modelling efforts for understanding COVID-19 dynamics: an educational challenge.

The purpose of the work described in this paper is to emphasize the importance of using mathematical models and mathematical modelling in order to be able to understand and to learn possible behaviours in epidemic situations such as that of the COVID-19 pandemic, besides suggesting modelling techniques with which to evaluate certain sanitary decisions and policies which do, in fact, affect society as a whole. The mathematical tools that are used derive from nonlinear systems of difference equations (possibly viable at a high school level, using spreadsheets or adequate software) as well as nonlinear systems of ordinary differential equations (therefore using mathematical tools and software well within the reach of undergraduate students of many courses). This purpose is accomplished by motivating students and learners to study existing SIR-type models and modifying them in order to have a fully understandable translation of dynamics for infectious diseases such as COVID-19 in several different realistic scenarios, that is to say, situations that consider social distancing policies, widespread vaccination programmes, as well as possible and even probable results when in the presence of negationist postures and attitudes. Several modelling choices referring to real-life situations are shown and explored. These models are analysed and discussed, implicitly proposing similar attitudes and evaluations in learning environments. Conclusions are drawn, stimulating further work using the described mathematical tools and resources. Supplementary Information: The online version contains supplementary material available at 10.1007/s11858-022-01447-2.

Environmental enrichment influences survival rate and enhances exploration and learning but produces variable responses to the radial maze in old rats.

Wistar rats at 7 (mature), 16 (aging), and 22 (old) months of age spent 70 days in normal laboratory (Social), impoverished (Isolated) or dynamic Enrichment cages. The Enriched cage emphasized spatial re-arrangements of significant items, and the learning of new routes. Subsequently, Enriched rats at all ages entered a novel environment and escaped from a bright light with significantly shorter latencies than rats from either of the other environments. Mature, aging and some of the old Enriched rats also significantly outperformed their Isolated and Social counterparts in the radial maze. However old Enriched and Isolated animals showed significant variability in relation to the measure of the proportion reaching criterion on this task, and a significantly lower proportion than of old Social rats reached criterion. Enriched rats had a significantly higher survival rate than Social and Isolated animals. These findings are discussed in terms of learning efficiency and behaviors that conserve energy and thereby enhance survival.

On the inhibition of elastase by serum. Some distinguishing properties of alpha1-antitrypsin and alpha2-macroglobulin.

1. The influence of serum on the elastolytic and esterolytic activity of elastase has been studied. With both substrates the inhibition curves are linear. 1 ml of normal human serum inhibits the activity of 0.77 mg of pure porcine elastase. 2. Elastase binds faster with alpha2-macroglobulin (k = 3.4-10(6) M-1 S-1) than it does with alpha1-antitrypsin (k = 5-10(5) M-1 S-1). 3. The dissociation constant of the alpha-antitrypsin -elastase complex is much lower than that of the alpha2-macroglobulin-elastase complex but both complexes are very stable (Ki less than 10(-10) M). 4. Protein pi (inter-alpha-inhibitor) does not inhibit elastase.

Diet- and valproate-induced transient hyperammonemia: effect of L-carnitine.

Hyperammonemia is an adverse effect of valproate (VPA) treatment. In particular, transient hyperammonemia has been reported to occur in VPA-treated patients after protein-rich meals. This phenomenon may occur secondary to a VPA-mediated carnitine insufficiency. We sought to confirm that protein ingestion would result in transient hyperammonemia and to determine whether supplementation with L-carnitine would prevent this effect. We studied the effect of consumption of a standardized protein-rich meal (45 g protein) before (phase I) and after (phase II) administration of L-carnitine 50 mg/kg/day for 7 days in 11 epileptic children (13.3 +/- 2.3 years of age) receiving VPA. Venous blood was obtained during fasting (baseline) and at 2 and 4 hours after the protein-rich meal for analysis of ammonia (NH3), and VPA concentrations. Mean VPA trough concentrations did not differ significantly at any time. After protein ingestion, 2-hour NH3 concentration increased by 86% (P < .05) from baseline in phase I as compared with a 38% increase in phase II. In both phases I and II, 4-hour NH3 concentrations decreased toward baseline values. We conclude that (1) modest protein ingestion can result in significant transient increases in NH3 in VPA-treated children, (2) significant increases may occur in patients with normal fasting NH3 concentrations, (3) these increases can be significantly attenuated by L-carnitine supplementation, and (4) these changes do not appear to be related to changes in VPA concentration.

Soil temperature and diapause maintenance in eggs of the spittlebug, Deois flavopicta (Hemiptera: Cercopidae).

Diapausing eggs of the neotropical pasture pest, Deois flavopicta (Stal) (Hemiptera: Cercopidae), were exposed to low overnight temperatures that simulated field conditions during the dry season (23/12, 23/15 and 23/18 degrees C day/night), for different periods (0-60 days). After treatment, eggs were kept at 28 degrees C and contact water (100% humidity) until hatching. A group of diapausing eggs were kept all the time under this last condition as a control treatment. Time for hatching (in degree-days) was reduced with decrease in low overnight temperature and increase of exposure time to these cold shocks, although there was no interaction between the factors. Regression of exposure time to cold shock influencing the expected mean hatching time produced independent equations for temperatures below 18 degrees C and 15 degrees C. We constructed a model that simulates the expected proportion of the population hatching after the beginning of rainy season based on regression equations to mean hatching time and associated standard deviation. The simulation generated for the model correlated significantly with nymphal population observed in the field. These results showed that overnight soil temperatures below 18 degrees C, as occurs in Central and South-eastern Brazil between May and August, shorten the period of diapause, increase quiescent eggs in the soil, and may have synchronize population hatching.

[Non-invasive diagnosis of pulmonary hypertension: ESC/ERS Guidelines with commentary of the Cologne Consensus Conference 2010]. / Nicht-invasive Diagnostik der pulmonalen Hypertonie: ESC/ERS-Leitlinien mit Kommentierung der Kölner Konsensus-Konferenz 2010.

The 2009 European Guidelines on Diagnosis and Treatment of Pulmonary Hypertension have been adopted for Germany. The guidelines contain detailed recommendations for the diagnosis of pulmonary hypertension. However, the practical implementation of the European Guidelines in Germany requires the consideration of several country-specific issues and already existing novel data. This requires a detailed commentary to the guidelines, and in some aspects an update y appears necessary. In June 2010, a Consensus Conference organized by the PH working groups of the German Society of Cardiology (DGK), the German Society of Respiratory Medicine (DGP) and the German Society of Pediatric Cardiology (DGPK) was held in Cologne, Germany. This conference aimed to solve practical and controversial issues surrounding the implementation of the European Guidelines in Germany. To this end, a number of working groups was initiated, one of which was specifically dedicated to non-invasive diagnosis of PH. This commentary summarizes the results and recommendations of the working group on treatment of PAH.

Characterization of aminoglycoside 6'-N-acetyltransferases [AAC(6')] from gram-negative bacteria and Streptomyces kanamyceticus.

Aminoglycoside-6'-N-acetyltransferase [AAC(6') enzymes] from several Gram-negative bacteria and Streptomyces kanamyceticus were purified by affinity and ion exchange chromatography. The different enzymes were characterized by their biochemical properties including molecular weights, isoelectric points, substrate ranges, and pH-optima. These biochemical characteristics were compared to the data for 6'-N-acetyltransferases from other Gram-negative and Gram-positive bacteria. All data indicated that the group of AAC(6') enzymes is rather heterogeneous from the biochemical point of view and led us to a new proposal for classification of subgroups.

Temperature and pH dependence of the association rate constant of elastase with alpha 2-macroglobulin.

Binding kinetics of porcine pancreatic elastase to human alpha 2-macroglobulin was monitored by measuring the enzymatic activity of alpha 2-macroglobulin-bound elastase on succinyltrialanine p-nitroanilide after inhibition of free elastase by alpha 1-proteinase inhibitor. The association of the two proteins follows second-order kinetics with a rate constant ka = 4.4 X 10(6) M-1 S-1 at pH 8.0 and 25 degrees C. The rate of association strongly increases between pH 5.0 and 8.0, suggesting that the rate-limiting step of binding is the proteolytic cleavage at the bait region of the macroglobulin. The study of the temperature dependence of ka shows that the binding of elastase to alpha 2-macroglobulin is characterized by a positive entropy of activation (delta S* = +35.3 e.u. at 25 degrees C).

Role of transposition and homologous recombination in the rearrangement of plasmid DNA.

The multi-resistance plasmid pBP16 was used to analyse the variability of R-factors from clinical isolates and the molecular structures and processes involved. The observed rearrangement in pBP16 and its derivatives included inversion, deletion, replicon fusion and dissociation, and transposition. All these events could be traced to the presence and activity of multiple copies of the IS-element IS160 within pBP16. Since IS-elements are common in R-factors, it is likely that they are one of the main reasons for plasmid instability and that they are involved in a major way in plasmid evolution.

Insertions of resistance genes into Tn21-like transposons.

The evolution of Tn21 and related multiresistance transposons of natural and artificial origin is described. Variations resulting from insertions and deletions in these transposons indicate the presence of specific recombination sites. There is evidence that these 'hot spots' are flanking several resistance genes. We examined these structures on the basis of the aadA gene, mediating resistance to spectinomycin and streptomycin. Comparison of the DNA sequences of Tn21, Tn7 and pSa indicate the wide spread of these recombination sites.

Tn2440, a composite tetracycline resistance transposon with direct repeated copies of IS160 at its flanks.

The tetracycline resistance region of the multi-resistance plasmid pBP16 is flanked by direct repeats of the insertion sequence IS160. The tetracycline resistance region plus the flanking IS elements can transpose as a discrete unit. The composite transposon, designated Tn2440, has a size of 4.0 kb.

Amikacin resistance mediated by multiresistance transposon Tn2424.

Tn2424, a multiresistance transposon 25 kilobases long, was isolated from IncFII plasmid NR79. Tn2424 transposed resistance to sulfonamides, streptomycin and spectinomycin, mercuric chloride, chloramphenicol, and amikacin with a frequency of 6 X 10(-5). Resistance to amikacin was mediated by a 6'-N-acetyltransferase, which conferred higher levels of resistance in Pseudomonas aeruginosa than in Escherichia coli. A restriction analysis and cloning experiments resulted in a physical and functional map of Tn2424. Comparison by a heteroduplex technique revealed that Tn2424 includes the total sequence of Tn21 and two additional DNA fragments that are 1.8 and 4 kilobases long.

The relationship of pulmonary artery wedge pressure to the posterior aortic wall echocardiogram in patients free of obstructive mitral valve disease.

Aortic wall echocardiograms were obtained simultaneously with pulmonary artery wedge pressures (PAWP) in 21 patients free of obstructive mitral valve disease. There was a significant (p < 0.001) negative correlation between the fraction of passive posterior aortic wall motion occurring in the first third of diastole (the atrial emptying index--AEI) and the pulmonary artery wedge pressure (r = -0.91). The AEI for patients with normal PAWP (less than or equal to 12 mm. Hg) was 0.94 +/- 0.06 (mean +/- S.D.) compared with 0.61 +/- 0.20 for those with abnormal PAWP (> 12 mm. Hg). No patient with a normal PAWP had an AEI < 0.80, and no patient with a PAWP > 18 mm. Hg had an AEI > 0.66. These data suggest that analogous to the reported use of the AEI to estimate severity of mitral obstruction, the index provides a noninvasive measure of left ventricular filling pressure when the mitral valve is normal.

Cardiac pacemakers: current concepts.

Cardiac pacemakers are generally used in conditions where bradyarrhythmia is a major problem, such as advanced heart block, sick sinus syndrome and bundle branch block. Temporary or permanent pacing may be needed to control certain tachyarrhythmias refractory to medical therapy. Temporary pacing may be of value in the diagnosis of sinus node dysfunction and preexcitation syndrome, and may be used expectantly in some patients with acute myocardial infarction.

Evolution of plasmid-coded resistance to broad-spectrum cephalosporins.

A clinical isolate of Klebsiella ozaenae with transferable resistance to broad-spectrum cephalosporins produces a beta-lactamase determined by plasmid pBP60. The beta-lactamase had the same isoelectric point as SHV-1 (7.6). From heteroduplex analysis, an extensive homology between the two bla genes could be deduced; therefore, the new beta-lactamase was designated SHV-2. Enzymatic studies revealed that SHV-2 was able to hydrolyze broad-spectrum cephalosporins due to an increased affinity of these compounds for the enzyme. The assumption that SHV-2 is a natural mutant of SHV-1 was strongly supported by the isolation of a laboratory mutant of SHV-1 that showed activities similar to those of SHV-2.

Systolic mitral flutter, an echocardiographic clue to the diagnosis of ruptured chordae tendineae.

A new finding of fine systolic fluttering of the mitral leaflet is described in two patients with ruptured chordae tendinease and severe mitral regurgitation. The flutter is caused by the action of high-velocity blood flow upon the leaflet margin that has lost its support. The jet stream of blood evokes a high-frequency vibratory motion of the tensed leaflet as opposed to the previously described, lower frequency, less specific, diastolic flutter. This finding was not seen in the echocardiograms of 75 patients with other forms of mitral regurgitation. Systolic flutter appears to be specific for ruptured chordae tendineae.