Biomedical subjects

Jonathan A Sherratt

Publications and source records attributed to Jonathan A Sherratt.

14 recordsLinked to original sources

PubMed2006

Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments.

In many semi-arid environments, vegetation is self-organised into spatial patterns. The most striking examples of this are on gentle slopes, where striped patterns are typical, running parallel to the contours. Previously, Klausmeier [1999. Regular and irregular patterns in semiarid vegetation. Science 284, 1826-1828.] has proposed a model for vegetation stripes based on competition for water. Here, we present a detailed study of the patterned solutions in the full nonlinear model, using numerical bifurcation analysis of both the pattern odes and the model pdes. We show that patterns exist for a wide range of rainfall levels, and in particular for much lower rainfall than have been considered by previous authors. Moreover, we show that for many rainfall levels, patterns with a variety of different wavelengths are stable, with mode selection dependent on initial conditions. This raises the possibility of hysteresis, and in numerical solutions of the model we show that pattern selection depends on rainfall history in a relatively simple way.

Demography↗

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↗

PubMed2006

Delayed density-dependent season length alone can lead to rodent population cycles.

Studies of cyclic microtine populations (voles and lemmings) have suggested a relationship between the previous year's population density and the subsequent timing of the onset of reproduction by overwintered breeding females. No studies have explored the importance of this relationship in the generation of population cycles. Here we mathematically examine the implications of variation in reproductive season length caused by delayed density-dependent changes in its start date. We demonstrate that when reproductive season length is a function of past population densities, it is possible to get realistic population cycles without invoking any changes in birth rates or survival. When parameterized for field voles (Microtus agrestis) in Kielder Forest (northern England), our most realistic model predicts population cycles of similar periodicity to the Kielder populations. Our study highlights the potential importance of density-dependent reproductive timing in microtine population cycles and calls for investigations into the mechanism(s) underlying this phenomenon.

Animals↗

PubMed2006

Macrophage dynamics in diabetic wound dealing.

Wound healing in diabetes is a complex process, characterised by a chronic inflammation phase. The exact mechanism by which this occurs is not fully understood, and whilst several treatments for healing diabetic wounds exist, very little research has been conducted towards the causes of the extended inflammation phase. We describe a mathematical model which offers a possible explanation for diabetic wound healing in terms of the distribution of macrophage phenotypes being altered in the diabetic patient compared to normal wound repair. As a consequence of this, we put forward a suggestion for treatment based on rectifying the macrophage phenotype imbalance.

Algorithms↗

PubMed2005

An analysis of vegetation stripe formation in semi-arid landscapes.

Vegetation stripes ("tiger bush") are a characteristic feature of semi-arid environments. The stripes typically lie along the contours of gentle slopes, and some authors report a gradual uphill migration. A previous mathematical model (Klausmeier, Science, 284:1826, 1999) has shown that this phenomenon can be explained relatively simply by the downhill flow of rainwater coupled with the diffusive spread of the plant population. This paper presents a detailed analysis of pattern formation in the Klausmeier model. The author derives formulae for the wavelength and migration speed of the predicted patterns, and systematically investigates how these depend on model parameters. The results make new predictions and suggest possible approaches to testing the model.

Desert Climate↗

PubMed2004

Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFbeta.

The process of cancer invasion involves a complex interplay between cell-cell and cell-medium adhesion, proteolytic enzyme secretion, cell birth and death processes, random and directed motility, and immune response, as well as many other factors. The growth factor TGF beta is known to have a complex effect on this process. It inhibits mitosis and promotes apoptosis in a concentration-dependent manner in vitro, and it is for this reason that its secretion is thought to be helpful in inhibiting tumour growth. However, recent in vitro and in vivo results have shown a significant effect of this growth factor in promoting the sensitivity of malignantly transformed cells to gradients of extracellular matrix proteins--an effect which tends to increase invasiveness. The drug tamoxifen has been demonstrated to be therapeutically effective in the treatment of patients with breast cancer; however, it is known also that many patients become resistant to the effect of this drug after a few years, and the reasons for this remain controversial. In this work we take our established model of cancer invasion (J. Theor. Biol. 216(1) (2002) 85), and extend it to include the effect of TGF beta. In so doing we demonstrate that a tamoxifen-stimulated upregulation of the secretion of TGF beta may give rise to a tumour which has a smaller number of cells but which has a greater invasiveness, greater metastatic potential, and a tumour histology which is known to correlate with a poorer prognosis. These data suggest that tamoxifen-stimulated secretion of TGF beta might explain treatment failure in some patients.

Anticarcinogenic Agents↗

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↗

PubMed2003

Control of epidermal stem cell clusters by Notch-mediated lateral induction.

Stem cells in the basal layer of human interfollicular epidermis form clusters that can be reconstituted in vitro. In order to supply the interfollicular epidermis with differentiated cells, the size of these clusters must be controlled. Evidence suggests that control is regulated via differentiation of stem cells on the periphery of the clusters. Moreover, there is growing evidence that this regulation is mediated by the Notch signalling pathway. In this paper, we develop theoretical arguments, in conjunction with computer simulations of a model of the basal layer, to show that regulation of differentiation is the most likely mechanism for cluster control. In addition, we show that stem cells must adhere more strongly to each other than they do to differentiated cells. Developing our model further we show that lateral-induction, mediated by the Notch signalling pathway, is a natural mechanism for cluster control. It can not only indicate to cells the size of the cluster they are in and their position within it, but it can also control the cluster size. This can only be achieved by postulating a secondary, cluster wide, differentiation signal, and cells with high Delta expression being deaf to this signal.

Cell Adhesion↗

PubMed2002

Intercellular adhesion and cancer invasion: a discrete simulation using the extended Potts model.

We develop a discrete model of malignant invasion using a thermodynamic argument. An extension of the Potts model is used to simulate a population of malignant cells experiencing interactions due to both homotypic and heterotypic adhesion while also secreting proteolytic enzymes and experiencing a haptotactic gradient. In this way we investigate the influence of changes in cell-cell adhesion on the invasion process. We demonstrate that the morphology of the invading front is influenced by changes in the adhesiveness parameters, and detail how the invasiveness of the tumour is related to adhesion. We show that cell-cell adhesion has less of an influence on invasion compared with cell-medium adhesion, and that increases in both proteolytic enzyme secretion rate and the coefficient of haptotaxis act in synergy to promote invasion. We extend the simulation by including proliferation, and, following experimental evidence, develop an algorithm for cell division in which the mitotic rate is explicitly related to changes in the relative magnitudes of homotypic and heterotypic adhesiveness. We show that although an increased proliferation rate usually results in an increased depth of invasion into the extracellular matrix, it does not invariably do so, and may, indeed, cause invasiveness to be reduced.

Algorithms↗

PubMed2002

Mathematical modelling of nitric oxide regulation of rete peg formation in psoriasis.

Recent experiments have shown that in patients with psoriasis, highly elevated levels of nitric oxide (NO) are released at the surface of psoriatic plaques. Nitric oxide is a central biological regulator of many aspects of physiology, and it is a natural possibility that the high nitric oxide levels in psoriasis play a causal role in the onset of the disease. Here, we use mathematical modelling to investigate this possibility. We begin by discussing a simple model consisting of a single equation for nitric oxide concentration, which enables nitric oxide secretion rates in the basal epidermis to be calculated from the observed NO release rates at the skin surface. Using this key parameter value, we then develop an extended model that tests the hypothesis that nitric oxide regulates the formation of the extended rete pegs seen in psoriatic plaques. This occurs via the peroxynitrite-dependent activation of the collagenase MMP-8, which is produced by neutrophils present at high levels in psoriatic plaques. The plausibility of the hypothesis is demonstrated and specific testable quantitative predictions about the roles of the various cell types and signalling molecules are made.

Epidermis↗

PubMed2002

Modelling blood flow regulation by nitric oxide in psoriatic plaques.

Psoriasis is a common skin disease, with a clinical appearance of red, scaly lesions, known as plaques. Recent experimental research has shown that the ubiquitous cell-signalling molecule nitric oxide (NO) is actively synthesized within these plaques by the iNOS enzyme. In contrast, NO production from normal, healthy skin is a byproduct of the reduction of nitrite in sweat. Measurement of NO release rates at the skin surface are 100 times greater from psoriatic lesions than normal skin. We propose a mathematical model for the dynamics of NO within psoriatic plaques, that incorporates diffusion, production in the basal epidermis, decay within the plaque, and active scavenging by red blood cell haemoglobin; this last effect introduces a key nonlinearity into the model. We present numerical simulations of the model in two space dimensions, and then describe an approximation that reduces the model to two coupled ordinary differential equations. This reduced system can be solved exactly, giving an approximation for the NO release rate as an explicit function of model parameters. We use this approximation to explain some recent, surprising experimental results.

Computer Simulation↗

PubMed2002

Theoretical models of wound healing: past successes and future challenges.

The complex biology of wound healing is an area in which theoretical modelling has already made a significant impact. In this review article, the authors describe the key features of wound healing biology, divided into four components: epidermal wound healing, remodelling of the dermal extracellular matrix, wound contraction, and angiogenesis. Within each of these categories, previous modelling work is described, and the authors identify what they regard as the main challenges for future theoretical work.

Epidermis↗

PubMedDate not supplied

Cells behaving badly: a theoretical model for the Fas/FasL system in tumour immunology.

One proposed mechanism of tumour escape from immune surveillance is tumour up-regulation of the cell surface ligand FasL, which can lead to apoptosis of Fas receptor (Fas) positive lymphocytes. Based upon this 'counterattack', we have developed a mathematical model involving tumour cell-lymphocyte interaction, cell surface expression of Fas/FasL, and their secreted soluble forms. The model predicts that (a) the production of soluble forms of Fas and FasL will lead to the down-regulation of the immune response; (b) matrix metalloproteinase (MMP) inactivation should lead to increased membrane FasL and result in a higher rate of Fas-mediated apoptosis for lymphocytes than for tumour cells. Recent studies on cancer patients lend support for these predictions. The clinical implications are two-fold. Firstly, the use of broad spectrum MMP inhibitors as anti-angiogenic agents may be compromised by their adverse effect on tumour FasL up-regulation. Also, Fas/FasL interactions may have an impact on the outcome of numerous ongoing immunotherapeutic trials since the final common pathway of all these approaches is the transduction of death signals within the tumour cell.

Apoptosis↗