Biomedical subjects

Kevin J Painter

Publications and source records attributed to Kevin J Painter.

3 recordsLinked to original sources

PubMed2006

A continuum approach to modelling cell-cell adhesion.

Cells adhere to each other through the binding of cell adhesion molecules at the cell surface. This process, known as cell-cell adhesion, is fundamental in many areas of biology, including early embryo development, tissue homeostasis and tumour growth. In this paper we develop a new continuous mathematical model of this phenomenon by considering the movement of cells in response to the adhesive forces generated through binding. We demonstrate that our model predicts the aggregation behaviour of a disassociated adhesive cell population. Further, when the model is extended to represent the interactions between multiple populations, we demonstrate that it is capable of replicating the different types of cell sorting behaviour observed experimentally. The resulting pattern formation is a direct consequence of the relative strengths of self-population and cross-population adhesive bonds in the model. While cell sorting behaviour has been captured previously with discrete approaches, it has not, until now, been observed with a fully continuous model.

Animals↗

PubMed2004

From a discrete to a continuous model of biological cell movement.

The process by which one may take a discrete model of a biophysical process and construct a continuous model based upon it is of mathematical interest as well as being of practical use. In this work, we take the extended Potts model applied to biological cell movement to its continuous limit. Beginning with a single cell moving in one dimension on a lattice and obeying Potts model rules of movement we develop an expression for the diffusion coefficient of a collection of noninteracting cells which depends explicitly on the Potts model parameters. We show how this coefficient varies when the Potts parameters for cell membrane elasticity and cell-medium adhesion are varied, and perform computer simulations which support our theoretical result. We explain the relationship between the probability of occupancy of lattice points and the density profile in the continuous limit, and extend our analysis by including interactions between the cells. In so doing we are able to develop a set of coupled ordinary differential equations showing the evolution of a density profile in the presence of significant cell-cell adhesion, and show how increases in the strength of this adhesion modulates diffusion. In so doing we develop some insights into how continuous models of physical systems can be based upon discrete models which describe the same system.

Animals↗

PubMed2003

Modelling the movement of interacting cell populations.

Mathematical modelling of cell movement has traditionally focussed on a single population of cells, often moving in response to various chemical and environmental cues. In this paper, we consider models for movement in two or more interacting cell populations. We begin by discussing intuitive ideas underlying the extension of models for a single-cell population to two interacting populations. We then consider more formal model development using transition probability methods, and we discuss how the same equations can be obtained as the limiting form of a velocity-jump process. We illustrate the models we have developed via two examples. The first of these is a generic model for competing cell populations, and the second concerns aggregation in cell populations moving in response to chemical gradients.

Animals↗