Modeling spatial evolution of multi-drug resistance under drug environmental gradients.

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria based on a drug-concentration rescaling approach. We show how the resistance to drugs in space, and the consequent adaptation of growth rate, is governed by a Price equation with diffusion, integrating features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Although in many evolution models, per capita growth rate is a natural surrogate for fitness, in spatially-extended, potentially heterogeneous habitats, fitness is an emergent property that potentially reflects additional complexities, from boundary conditions to the specific spatial variation of growth rates. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical metric for characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem, λ1. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits to the relative advantage of each mutant across the environment. Our approach allows one to predict the precise outcomes of selection among mutants over space, ultimately from comparing their λ1 values, which encode a critical interplay between growth functions, movement traits, habitat size and boundary conditions. Such mathematical understanding opens new avenues for multi-drug therapeutic optimization.

Modeling spatial evolution of multi-drug resistance under drug environmental gradients.

Multi-drug combinations to treat bacterial populations are at the forefront of approaches for infection control and prevention of antibiotic resistance. Although the evolution of antibiotic resistance has been theoretically studied with mathematical population dynamics models, extensions to spatial dynamics remain rare in the literature, including in particular spatial evolution of multi-drug resistance. In this study, we propose a reaction-diffusion system that describes the multi-drug evolution of bacteria, based on a rescaling approach (Gjini and Wood, 2021). We show how the resistance to drugs in space, and the consequent adaptation of growth rate is governed by a Price equation with diffusion. The covariance terms in this equation integrate features of drug interactions and collateral resistances or sensitivities to the drugs. We study spatial versions of the model where the distribution of drugs is homogeneous across space, and where the drugs vary environmentally in a piecewise-constant, linear and nonlinear manner. Applying concepts from perturbation theory and reaction-diffusion equations, we propose an analytical characterization of average mutant fitness in the spatial system based on the principal eigenvalue of our linear problem. This enables an accurate translation from drug spatial gradients and mutant antibiotic susceptibility traits, to the relative advantage of each mutant across the environment. Such a mathematical understanding allows to predict the precise outcomes of selection over space, ultimately from the fundamental balance between growth and movement traits, and their diversity in a population.

Tailoring Upconversion and Morphology of Yb/Eu Doped Y2O3 Nanostructures by Acid Composition Mediation.

The present study reports the production of upconverter nanostructures composed by a yttrium oxide host matrix co-doped with ytterbium and europium, i.e., Y2O3:Yb3+/Eu3+. These nanostructures were formed through the dissociation of yttrium, ytterbium and europium oxides using acetic, hydrochloric and nitric acids, followed by a fast hydrothermal method assisted by microwave irradiation and subsequent calcination process. Structural characterization has been carried out by X-ray diffraction (XRD), scanning transmission electron microscopy (STEM) and scanning electron microscopy (SEM) both coupled with energy dispersive X-ray spectroscopy (EDS). The acid used for dissociation of the primary oxides played a crucial role on the morphology of the nanostructures. The acetic-based nanostructures resulted in nanosheets in the micrometer range, with thickness of around 50 nm, while hydrochloric and nitric resulted in sphere-shaped nanostructures. The produced nanostructures revealed a homogeneous distribution of the doping elements. The thermal behaviour of the materials has been investigated with in situ X-Ray diffraction and differential scanning calorimetry (DSC) experiments. Moreover, the optical band gaps of all materials were determined from diffuse reflectance spectroscopy, and their photoluminescence behaviour has been accessed showing significant differences depending on the acid used, which can directly influence their upconversion performance.