Generalized Voronoi Tessellation as a Model of Two-dimensional Cell Tissue Dynamics

Voronoi tessellations have been used to model the geometric arrangement of cells in morphogenetic or cancerous tissues, however so far only with flat hypersurfaces as cell-cell contact borders. In order to reproduce the experimentally observed piecewise spherical boundary shapes, we develop a consistent theoretical framework of multiplicatively weighted distance functions, defining generalized finite Voronoi neighborhoods around cell bodies of varying radius, which serve as heterogeneous generators of the resulting model tissue. The interactions between cells are represented by adhesive and repelling force densities on the cell contact borders. In addition, protrusive locomotion forces are implemented along the cell boundaries at the tissue margin, and stochastic perturbations allow for non-deterministic motility effects. Simulations of the emerging system of stochastic differential equations for position and velocity of cell centers show the feasibility of this Voronoi method generating realistic cell shapes. In the limiting case of a single cell pair in brief contact, the dynamical nonlinear Ornstein-Uhlenbeck process is analytically investigated. In general, topologically distinct tissue conformations are observed, exhibiting stability on different time scales, and tissue coherence is quantified by suitable characteristics. Finally, an argument is derived pointing to a tradeoff in natural tissues between cell size heterogeneity and the extension of cellular lamellae.Comment: v1: 34 pages, 19 figures v2: reformatted 43 pages, 21 figures, 1 table; minor clarifications, extended supplementary materia

Geometric mean extension for data sets with zeros

There are numerous examples in different research fields where the use of the geometric mean is more appropriate than the arithmetic mean. However, the geometric mean has a serious limitation in comparison with the arithmetic mean. Means are used to summarize the information in a large set of values in a single number; yet, the geometric mean of a data set with at least one zero is always zero. As a result, the geometric mean does not capture any information about the non-zero values. The purpose of this short contribution is to review solutions proposed in the literature that enable the computation of the geometric mean of data sets containing zeros and to show that they do not fulfil the `recovery' or `monotonicity' conditions that we define. The standard geometric mean should be recovered from the modified geometric mean if the data set does not contain any zeros (recovery condition). Also, if the values of an ordered data set are greater one by one than the values of another data set then the modified geometric mean of the first data set must be greater than the modified geometric mean of the second data set (monotonicity condition). We then formulate a modified version of the geometric mean that can handle zeros while satisfying both desired conditions

The role of mathematical modelling in understanding prokaryotic predation

With increasing levels of antimicrobial resistance impacting both human and animal health, novel means of treating resistant infections are urgently needed. Bacteriophages and predatory bacteria such as Bdellovibrio bacteriovorus have been proposed as suitable candidates for this role. Microbes also play a key environmental role as producers or recyclers of nutrients such as carbon and nitrogen, and predators have the capacity to be keystone species within microbial communities. To date, many studies have looked at the mechanisms of action of prokaryotic predators, their safety in in vivo models and their role and effectiveness under specific conditions. Mathematical models however allow researchers to investigate a wider range of scenarios, including aspects of predation that would be difficult, expensive, or time-consuming to investigate experimentally. We review here a history of modelling in prokaryote predation, from simple Lotka-Volterra models, through increasing levels of complexity, including multiple prey and predator species, and environmental and spatial factors. We consider how models have helped address questions around the mechanisms of action of predators and have allowed researchers to make predictions of the dynamics of predator–prey systems. We examine what models can tell us about qualitative and quantitative commonalities or differences between bacterial predators and bacteriophage or protists. We also highlight how models can address real-world situations such as the likely effectiveness of predators in removing prey species and their potential effects in shaping ecosystems. Finally, we look at research questions that are still to be addressed where models could be of benefit

New, rapid method to measure dissolved silver concentration in silver nanoparticle suspensions by aggregation combined with centrifugation

It is unclear whether the antimicrobial activities of silver nanoparticles (AgNPs) are exclusively mediated by the release of silver ions (Ag(+)) or, instead, are due to combined nanoparticle and silver ion effects. Therefore, it is essential to quantify dissolved Ag in nanosilver suspensions for investigations of nanoparticle toxicity. We developed a method to measure dissolved Ag in Ag(+)/AgNPs mixtures by combining aggregation of AgNPs with centrifugation. We also describe the reproducible synthesis of stable, uncoated AgNPs. Uncoated AgNPs were quickly aggregated by 2 mM Ca(2+), forming large clusters that could be sedimented in a low-speed centrifuge. At 20,100g, the sedimentation time of AgNPs was markedly reduced to 30 min due to Ca(2+)-mediated aggregation, confirmed by the measurements of Ag content in supernatants with graphite furnace atomic absorption spectrometry. No AgNPs were detected in the supernatant by UV–Vis absorption spectra after centrifuging the aggregates. Our approach provides a convenient and inexpensive way to separate dissolved Ag from AgNPs, avoiding long ultracentrifugation times or Ag(+) adsorption to ultrafiltration membranes. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1007/s11051-016-3565-0) contains supplementary material, which is available to authorized users

Mapping the scarcity of data on antibiotics in natural and engineered water environments across India

Antimicrobial resistance is a growing public health concern, increasingly recognized as a silent pandemic across the globe. Therefore, it is important to monitor all factors that could contribute to the emergence, maintenance and spread of antimicrobial resistance. Environmental antibiotic pollution is thought to be one of the contributing factors. India is one of the world’s largest consumers and producers of antibiotics. Hence, antibiotics have been detected in different environments across India, sometimes at very high concentrations due to their extensive use in humans and agriculture or due to manufacturing. We summarize the current state of knowledge on the occurrence and transport pathways of antibiotics in Indian water environments, including sewage or wastewater and treatment plants, surface waters such as rivers, lakes, and reservoirs as well as groundwater and drinking water. The factors influencing the distribution of antibiotics in the water environment, such as rainfall, population density and variations in sewage treatment are discussed, followed by existing regulations and policies aimed at the mitigation of environmental antimicrobial resistance in India, which will have global benefits. Then, we recommend directions for future research, development of standardized methods for monitoring antibiotics in water, ecological risk assessment, and exploration of strategies to prevent antibiotics from entering the environment. Finally, we provide an evaluation of how scarce the data is, and how a systematic understanding of the occurrence and concentrations of antibiotics in the water environment in India could be achieved. Overall, we highlight the urgent need for sustainable solutions to monitor and mitigate the impact of antibiotics on environmental, animal, and public health