Modelling Cognitive Decline in the Hypertension in the Very Elderly Trial [HYVET] and Proposed Risk Tables for Population Use

Although, on average, cognition declines with age, cognition in older adults is a dynamic process. Hypertension is associated with greater decline in cognition with age, but whether treatment of hypertension affects this is uncertain. Here, we modelled dynamics of cognition in relation to the treatment of hypertension, to see if treatment effects might better be discerned by a model that included baseline measures of cognition and consequent mortalityThis is a secondary analysis of the Hypertension in the Very Elderly Trial (HYVET), a double blind, placebo controlled trial of indapamide, with or without perindopril, in people aged 80+ years at enrollment. Cognitive states were defined in relation to errors on the Mini-Mental State Examination, with more errors signifying worse cognition. Change in cognitive state was evaluated using a dynamic model of cognitive transition. In the model, the probabilities of transitions between cognitive states is represented by a Poisson distribution, with the Poisson mean dependent on the baseline cognitive state. The dynamic model of cognitive transition was good (R(2) = 0.74) both for those on placebo and (0.86) for those on active treatment. The probability of maintaining cognitive function, based on baseline function, was slightly higher in the actively treated group (e.g., for those with the fewest baseline errors, the chance of staying in that state was 63% for those on treatment, compared with 60% for those on placebo). Outcomes at two and four years could be predicted based on the initial state and treatment.A dynamic model of cognition that allows all outcomes (cognitive worsening, stability improvement or death) to be categorized simultaneously detected small but consistent differences between treatment and control groups (in favour of treatment) amongst very elderly people treated for hypertension. The model showed good fit, and suggests that most change in cognition in very elderly people is small, and depends on their baseline state and on treatment. Additional work is needed to understand whether this modelling approach is well suited to the valuation of small effects, especially in the face of mortality differences between treatment groups.ClinicalTrials.gov NCT0012281

The flow of a DAE near a singular equilibrium

We extend the differential-algebraic equation (DAE) taxonomy by assuming that the linearization of a DAE about a singular equilibrium has a particular index-2 Kronecker normal form. A Lyapunov-Schmidt procedure is used to reduce the DAE to a quasilinear normal form which is shown to posses quasi-invariant manifolds which intersect the singularity. In turn, this provides solutions of the DAE which pass through the singularity

Trajectories of a DAE near a pseudo-equilibrium

We consider a class of differential-algebraic equations (DAEs) defined by analytic nonlinearities and study its singular solutions. The main assumption used is that the linearization of the DAE represents a Kronecker index-2 matrix pencil and that the constraint manifold has a quadratic fold along its singularity. From these assumptions we obtain a normal form for the DAE where the presence of the singularity and its effects on the dynamics of the problem are made explicit in the form of a quasi-linear differential equation. Subsequently, two distinct types of singular points are identified through which there pass exactly two analytic solutions: pseudo-nodes and pseudo-saddles. We also demonstrate that a singular point called a pseudo-node supports an uncountable infinity of solutions which are not analytic in general. Moreover, akin to known results in the literature for DAEs with singular equilibria, a degenerate singularity is found through which there passes one analytic solution such that the singular point in question is contained within a quasi-invariant manifold of solutions. We call this type of singularity a pseudo-centre and it provides not only a manifold of solutions which intersects the singularity, but also a local flow on that manifold which solves the DAE

Evolution of drug-resistant and virulent small colonies in phenotypically diverse populations of the human fungal pathogen Candida glabrata

Antimicrobial resistance frequently carries a fitness cost to a pathogen, measured as a reduction in growth rate compared to the sensitive wild-type, in the absence of antibiotics. Existing empirical evidence points to the following relationship between cost of resistance and virulence. If a resistant pathogen suffers a fitness cost in terms of reduced growth rate it commonly has lower virulence compared to the sensitive wild-type. If this cost is absent so is the reduction in virulence. Here we show, using experimental evolution of drug resistance in the fungal human pathogen Candida glabrata, that reduced growth rate of resistant strains need not result in reduced virulence. Phenotypically heterogeneous populations were evolved in parallel containing highly resistant sub-population small colony variants (SCVs) alongside sensitive sub-populations. Despite their low growth rate in the absence of an antifungal drug, the SCVs did not suffer a marked alteration in virulence compared with the wild-type ancestral strain, or their co-isolated sensitive strains. This contrasts with classical theory that assumes growth rate to positively correlate with virulence. Our work thus highlights the complexity of the relationship between resistance, basic life-history traits and virulence.</p

Data from: Temporal variation in antibiotic environments slows down resistance evolution in pathogenic Pseudomonas aeruginosa

Antibiotic resistance is a growing concern to public health. New treatment strategies may alleviate the situation by slowing down the evolution of resistance. Here, we evaluated sequential treatment protocols using two fully independent laboratory-controlled evolution experiments with the human pathogen Pseudomonas aeruginosa PA14 and two pairs of clinically relevant antibiotics (doripenem/ciprofloxacin and cefsulodin/gentamicin). Our results consistently show that the sequential application of two antibiotics decelerates resistance evolution relative to monotherapy. Sequential treatment enhanced population extinction although we applied antibiotics at sub-lethal dosage. In both experiments, we identified an order-effect of the antibiotics used in the sequential protocol, leading to significant variation in the long-term efficacy of the tested protocols. These variations appear to be caused by asymmetric evolutionary constraints, whereby adaptation to one drug slowed down adaptation to the other drug, but not vice versa. An understanding of such asymmetric constraints may help future development of evolutionary robust treatments against infectious disease

Data for dose response curves

This file contains the data for the dose-response curves as shown in supplementary Fig. S2 of the paper. The columns indicate the following: $date: the data was collected on two days;$treatment: specifies antibiotic treatment; $ID: a number from "0" to "10" that serves as ID for the ascending antibiotic concentrations;$conc_ng_ml: concentration of antibiotic in ng/ml; $replicate: name of technical replicate;$od_600: optical density at 600 nm read after 12h of incubation at 37°C