Biomedical subjects

Markus R Owen

Publications and source records attributed to Markus R Owen.

4 recordsLinked to original sources

PubMed2004

Intra-membrane ligand diffusion and cell shape modulate juxtacrine patterning.

A key problem in developmental biology is how pattern and planar polarity are transmitted in epithelial structures. Examples include Drosophila neuronal differentiation, ommatidia formation in the compound eye, and wing hair polarization. A key component for the generation of such patterns is direct cell-cell signalling by transmembrane ligands, called juxtacrine signalling. Previous models for this mode of communication have considered homogeneous distributions in the cell membrane, and the role of polarity has been largely ignored. In this paper we determine the role of inhomogeneous protein and receptor distributions in juxtacrine signalling. We explicitly include individual membrane segments, diffusive transport of proteins and receptors between these segments, and production terms with a combination of local and global responses to ligand binding. Our analysis shows that intra-membrane ligand transport is vital for the generation of long wavelength patterns. Moreover, with no ligand transport, there is no pattern formation for lateral induction, a process in which receptor activation up-regulates ligand production. Biased production of ligand also modulates patterning bifurcations and predicted wavelengths. In addition, biased ligand and receptor trafficking can lead to regular polarity across a lattice, in which each cell has the same orientation-directly analogous to patterns of hairs in the Drosophila wing. We confirm the trends in pattern wavelengths previously observed for patterns with cellular homogeneity-lateral inhibition tends to give short-range patterns, while lateral induction can give patterns with much longer wavelengths. Moreover, the original model can be recovered if intra-membrane bound receptor diffusion is included and rapid equilibriation between the sides is considered. Finally, we consider the role of irregular cell shapes and waves in such networks, including wave propagation past clones of non-signalling cells.

Animals↗

PubMed2004

A new interpretation of the Keller-Segel model based on multiphase modelling.

In this paper an alternative derivation and interpretation are presented of the classical Keller-Segel model of cell migration due to random motion and chemotaxis. A multiphase modelling approach is used to describe how a population of cells moves through a fluid containing a diffusible chemical to which the cells are attracted. The cells and fluid are viewed as distinct components of a two-phase mixture. The principles of mass and momentum balance are applied to each phase, and appropriate constitutive laws imposed to close the resulting equations. A key assumption here is that the stress in the cell phase is influenced by the concentration of the diffusible chemical. By restricting attention to one-dimensional cartesian geometry we show how the model reduces to a pair of nonlinear coupled partial differential equations for the cell density and the chemical concentration. These equations may be written in the form of the Patlak-Keller-Segel model, naturally including density-dependent nonlinearities in the cell motility coefficients. There is a direct relationship between the random motility and chemotaxis coefficients, both depending in an inter-related manner on the chemical concentration. We suggest that this may explain why many chemicals appear to stimulate both chemotactic and chemokinetic responses in cell populations. After specialising our model to describe slime mold we then show how the functional form of the chemical potential that drives cell locomotion influences the ability of the system to generate spatial patterns. The paper concludes with a summary of the key results and a discussion of avenues for future research.

Body Patterning↗

PubMed2004

Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites.

Poor drug delivery and low rates of cell proliferation are two factors associated with hypoxia that diminish the efficacy of many chemotherapeutic drugs. Since macrophages are known to migrate specifically towards, and localize within, hypoxic tumour regions, a promising resolution to these problems involves genetically engineering macrophages to perform such anti-tumour functions as inducing cell lysis and inhibiting angiogenesis. In this paper we outline a modelling approach to characterize macrophage infiltration into early avascular solid tumours, and extensions to study the interaction of these cells with macrophages already present within the tumour. We investigate the role of chemotaxis and chemokine production, and the efficacy of macrophages as vehicles for drug delivery to hypoxic tumour sites. The model is based upon a growing avascular tumour spheroid, in which volume is filled by tumour cells, macrophages and extracellular material, and tumour cell proliferation and death is regulated by nutrient diffusion. Crucially, macrophages occupy volume, and hence contribute to the volume balance and hence the size of the tumour. We also include oxygen-dependent production of macrophage chemokines, which can lead to accumulations in the hypoxic region of the tumour. We find that the macrophage chemotactic sensitivity is a key determinant of macrophage infiltration and tumour size. Although increased infiltration should be beneficial from the point of view of macrophage-based therapies, such infiltration in fact leads to increased tumour sizes. Finally, we include terms representing the induced death of tumour cells by hypoxic engineered macrophages. We demonstrate that reductions in tumour size can be achieved, but predict that a combination of therapies would be required for complete eradication. We also highlight some counter-intuitive predictions-for example, absolute and relative measures of tumour burden lead to different conclusions about prognosis. In summary, this paper illustrates how mathematical models may be used to investigate promising macrophage-based therapies.

Cell Death↗

PubMed2003

Oscillations and patterns in spatially discrete models for developmental intercellular signalling.

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.

Algorithms↗