The role of initial geometry in experimental models of wound closing

Wound healing assays are commonly used to study how populations of cells, initialised on a two-dimensional surface, act to close an artificial wound space. While real wounds have different shapes, standard wound healing assays often deal with just one simple wound shape, and it is unclear whether varying the wound shape might impact how we interpret results from these experiments. In this work, we describe a new kind of wound healing assay, called a sticker assay, that allows us to examine the role of wound shape in a series of wound healing assays performed with fibroblast cells. In particular, we show how to use the sticker assay to examine wound healing with square, circular and triangular shaped wounds. We take a standard approach and report measurements of the size of the wound as a function of time. This shows that the rate of wound closure depends on the initial wound shape. This result is interesting because the only aspect of the assay that we change is the initial wound shape, and the reason for the different rate of wound closure is unclear. To provide more insight into the experimental observations we describe our results quantitatively by calibrating a mathematical model, describing the relevant transport phenomena, to match our experimental data. Overall, our results suggest that the rates of cell motility and cell proliferation from different initial wound shapes are approximately the same, implying that the differences we observe in the wound closure rate are consistent with a fairly typical mathematical model of wound healing. Our results imply that parameter estimates obtained from an experiment performed with one particular wound shape could be used to describe an experiment performed with a different shape. This fundamental result is important because this assumption is often invoked, but never tested

The Source of Alabama’s Abundance of Arbitration Cases: Alabama’s Bizarre Law of Damages for Mental Anguish

This Article gives an overview of arbitration litigation in Alabama, including the evolution of mental anguish jurisprudence in contract cases, especially with regard to the automobile and home industries; a proposal to bring Alabama law in line with controlling authorities through substantive and procedural reforms; and an appendix listing a decade of arbitration cases decided by Alabama appellate courts

Breast cancer risk and imprinting methylation in blood

Date of Acceptance: 17/08/2015 Acknowledgements This study was supported by the Breast Cancer Campaign (2008MayPR46) and Fraserburgh Moonlight Prowl Breast Cancer Charity. PH, GH and GWH acknowledge the support of the Scottish Government. We would like to thank Val Bain and Michela Donnarumma for help with the data and sample collection.Peer reviewedPublisher PD

Survival, extinction, and interface stability in a two--phase moving boundary model of biological invasion

We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two populations: each population undergoes linear diffusion and logistic growth, and the boundary between the two populations evolves according to a two--phase Stefan condition. This mathematical model describes situations where one population invades into regions occupied by the other population, such as the spreading of a malignant tumour into surrounding tissues. Full time--dependent numerical solutions are obtained using a level--set numerical method. We use these numerical solutions to explore several properties of the model including: (i) survival and extinction of one population initially surrounded by the other; and (ii) linear stability of the moving front boundary in the context of a travelling wave solution subjected to transverse perturbations. Overall, we show that many features of the well--studied one--phase single population analogue of this model can be very different in the more realistic two--phase setting. These results are important because realistic examples of biological invasion involve interactions between multiple populations and so great care should be taken when extrapolating predictions from a one--phase single population model to cases for which multiple populations are present. Open source Julia--based software is available on GitHub to replicate all results in this study.Comment: 31 pages. 9 figure

Discrete and continuous mathematical models of sharp-fronted collective cell migration and invasion

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction-diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion, however these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically-inspired mechanisms and then deriving the reaction-diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, that we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two--dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provides a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp frontsComment: 47 Pages, 8 Figure