Balancing access to antibiotics with control of antibiotic resistance is a global public health priority. Currently, antibiotic stewardship is informed by a 'use it and lose it' principle, in which population antibiotic use is linearly related to resistance rates. However, theoretical and mathematical models suggest use-resistance relationships are non-linear. One explanation is that resistance genes are commonly associated with 'fitness costs', impairing pathogen replication or transmissibility. Therefore, resistant genes and pathogens may only gain a survival advantage where antibiotic selection pressures exceed critical thresholds. These thresholds may provide quantitative targets for stewardship: optimising control of resistance while avoiding over-restriction of antibiotics. We evaluated the generalisability of a nonlinear time-series analysis approach for identifying thresholds using historical prescribing and microbiological data from five populations in Europe. We identified minimum thresholds in temporal relationships between use of selected antibiotics and rates of carbapenem-resistant Acinetobacter baumannii (in Hungary), extended spectrum β-lactamase producing Escherichia coli (Spain), cefepime-resistant Escherichia coli (Spain), gentamicin-resistant Pseudomonas aeruginosa (France), and methicillin-resistant Staphylococcus aureus (Northern Ireland) in different epidemiological phases. Using routinely generated data, our approach can identify context-specific quantitative targets for rationalising population antibiotic use and controlling resistance. Prospective intervention studies restricting antibiotic consumption are needed to validate Results Identifying non-linear temporal relationships: from experiment to applicationIn a Monte Carlo experiment we compared the ability of linear and non-linear time-series analysis (Multivariate Adaptive Regression Splines, MARS) to identify pre-defined relationships between simulated explanatory and outcome time-series (Supplementary Figure 1). Non-linear time-series analysis (NL-TSA) accurately identified both truly linear and nonlinear associations. However, linear time-series analysis provided biased estimations and overall poorer data-fit if relationships were non-linear. NL-TSA models applied to retrospective time-series data from five European study populations (examples 1-5), frequently identified minimum thresholds in antibiotic useresistance relationships, (figures 1-5 and Supplementary Table 1). 'Ceiling effects', in which further increases in explanatory variables did not affect resistance rates, were found at highlevels of use of some antibiotics and hand hygiene. Non-linearities in autoregression and population interaction terms further indicated the complexity of transmission dynamics within and between clinical populations. Example 1: Carbapenem-resistant Acinetobacter baumannii (Debrecen, Hungary) We examined ecological determinants of carbapenem-resistant A. baumannii (CRAb) in a tertiary hospital population in Debrecen, Hungary (figure 1). Betwee...

The mechanism of a chemical reaction can be characterized in terms of chemical events that take place during the reaction. These events are bond weakening/breaking and/or bond strengthening/forming. The reaction electronic flux (REF), a concept that identifies and rationalizes the electronic activity taking place along the reaction coordinate, has emerged recently as a powerful tool for characterizing the mechanism of chemical reactions. A quantitative theory introducing new descriptors for characterizing reaction mechanisms is presented in detail and three illustrative examples are revisited. In nucleophilic substitution reactions the REF indicates that bond breaking or forming events may be leading the electronic activity whereas in the methanol decomposition reaction by copper oxide, the REF allows to discover that consecutive electronic reductions of copper together with bond breaking processes control the course of the reaction. reaction mechanisms, chemical potential, conceptual DFT, reaction electronic flux (REF)

A theoretical study of methanol decomposition using a model representing the initial step of the reaction CH₃OH + CuO → CH₂O + H₂O + Cu is presented. Theoretical calculations using B3LYP/6-31 G along with Lanl2DZ pseudopotentials on metallic centers were performed and the results discussed within the framework of the reaction force analysis. It has been found that the reaction takes place following a stepwise mechanism: first, copper reduction (Cu⁺² → Cu⁺) accompanies the oxygen transposition and then a second reduction takes place (Cu⁺ → Cu₀) together with a proton transfer that produce formaldehyde and release a water molecule.

Fukui functions (FF) are chemical descriptors useful to explain the reactivity of systems towards electron transfer. Whereas they have been widely employed for molecules, their application to extended systems is scarce. One of the reasons for the limited devel-1 opment of such analysis in solids is the improper evaluation of FF in the usual computational approaches based on density functional theory and periodic boundary conditions.In this work we compare the available approaches and propose a new method, based on the interpolation of partially charged systems, that mitigates some of the problems encountered. We discuss the reactivity of alkaline earth oxides (MgO, CaO, SrO and BaO) in terms of the FF analysis, providing a robust way to account for the higher reactivity of surface oxygen sites compared to bulk sites.