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

Repair rather than segregation of damage is the optimal unicellular aging strategy

BACKGROUND: How aging, being unfavourable for the individual, can evolve is one of the fundamental problems of biology. Evidence for aging in unicellular organisms is far from conclusive. Some studies found aging even in symmetrically dividing unicellular species; others did not find aging in the same, or in different, unicellular species, or only under stress. Mathematical models suggested that segregation of non-genetic damage, as an aging strategy, would increase fitness. However, these models failed to consider repair as an alternative strategy or did not properly account for the benefits of repair. We used a new and improved individual-based model to examine rigorously the effect of a range of aging strategies on fitness in various environments. RESULTS: Repair of damage emerges as the best strategy despite its fitness costs, since it immediately increases growth rate. There is an optimal investment in repair that outperforms damage segregation in well-mixed, lasting and benign environments over a wide range of parameter values. Damage segregation becomes beneficial, and only in combination with repair, when three factors are combined: (i) the rate of damage accumulation is high, (ii) damage is toxic and (iii) efficiency of repair is low. In contrast to previous models, our model predicts that unicellular organisms should have active mechanisms to repair damage rather than age by segregating damage. Indeed, as predicted, all organisms have evolved active mechanisms of repair whilst aging in unicellular organisms is absent or minimal under benign conditions, apart from microorganisms with a different ecology, inhabiting short-lived environments strongly favouring early reproduction rather than longevity. CONCLUSIONS: Aging confers no fitness advantage for unicellular organisms in lasting environments under benign conditions, since repair of non-genetic damage is better than damage segregation. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12915-014-0052-x) contains supplementary material, which is available to authorized users