Nonlinear Analysis of Juxtacrine Patterns (2008)
Helen J. Wearing, Jonathan A. Sherratt
We investigate a discrete mathematical model for a type of cell-cell communication in early development which has the potential to generate a wide range of spatial patterns. Our previous work on this...
Abstract. 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...
ORIGINAL ARTICLE Macrophage Dynamics in Diabetic Wound Healing (2008)
Helen V. Waugh, Jonathan A. Sherratt
Abstract 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...
Helen J. Wearing, Jonathan A. Sherratt
Keratinocyte growth factor signalling: a mathematical model
Extracellular matrix-mediated chemotaxis can impede cell migration (2008)
Abbey J. Perumpanani, David L. Simmons, Karen M. Miller, George Ward, John Norbury, ...
Cells use a combination of changes in adhesion, proteolysis and motility (directed and random) during the process of migration. Proteolysis of the extracellular matrix (ECM) results in the creation...
Periodic travelling waves are an important solution form in oscillatory reaction–diffusion equations. I have shown previously that such waves arise naturally near a boundary at which a Dirichlet...
on Modelling Blood Flow Regulation by Nitric Oxide in (2007)
Psoriatic Plaques, Jonathan A. Sherratt, Richard Weller, Nicholas J. Savill
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 cellsignalling molecule nitric oxide...
Alison L. Kay, Jonathan A. Sherratt
Many systems in biology and chemistry are oscillatory, with a stable, spatially homogeneous steady state which consists of periodic temporal oscillations in the interacting species, and such systems...
Control of epidermal stem cell clusters by Notch-mediated (2007)
Lateral Induction Nicholas, Nicholas J. Savill, Jonathan A. Sherratt
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...
Multinodularity In Benign, Abbey J Perumpanani, Jonathan A Sherratt, John Norbury
Tumours that grow locally, but do not invade the surrounding tissue are called benign. Such benign tumours are characterized by the presence of a surrounding band of connective tissue called a...
J. Smith, Jonathan A. Sherratt, J. Armstrong
effects of obstacle size on periodic travelling
Nicola J. Armstrong, Kevin J. Painter, Jonathan A. Sherratt
Abstract Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development. They are one of the first instances of a periodic pattern,...
Nicola J. Armstrong, Kevin J. Painter, Jonathan A. Sherratt
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...
Jonathan A. Sherratt, Gabriel J. Lord
Nonlinear dynamics and pattern bifurcations in a model for vegetation
Tamoxifen treatment failure in cancer and the nonlinear dynamics of TGFβ (2004)
Stephen Turner, Jonathan A. Sherratt, David Cameron
Th process of cancer invasion involves a complex interplay between cell--cell and cell--mediumadhl--med proteolytic enzyme secretion, cellbirth anddeath processes, random and directed motility, and...
Sherratt / Journal of Theoretical Biology 225 (2003) 327–339 339 (2003)
Kevin J. Painter, Jonathan A. Sherratt
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...
Stephen Turner, Jonathan A. Sherratt
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...
Lateral induction by juxtacrine signalling is a new mechanism for pattern formation (2000)
Markus R. Owen, Jonathan A. Sherratt, Helen J. Wearing
Many signaling molecules in epithelia are now known to function in a membrane-bound form, binding to receptors on immediately neighbouring cells. This “juxtacrine ” mode of communication has been...
Traveling wave solutions of a mathematical model for tumor encapsulation (1999)
Abstract. The formation of a capsule of dense, fibrous extracellular matrix around a solid tumor is a key prognostic indicator in a wide range of cancers. However, the cellular mechanisms underlying...
John C. Dallon, Jonathan A. Sherratt, K. Maini
Matrix orientation plays a crucial role in determining the severity of scar tissue after dermal wounding. We present a model framework which allows us to examine the interaction of many of the...
How far can a juxtacrine signal travel (1999)
Markus R. Owen, Jonathan A. Sherratt, Simon R. Myers
Juxtacrine signalling is the process of cell communication in which ligand and receptors are both anchored in the cell membrane. We develop three mathematical models for this process, involving...
Unravelling the Turing bifurcation using spatially varying diffusion coefficients (1998)
Debbie L. Benson, Philip K. Maini, Jonathan A. Sherratt
Abstract. The Turing bifurcation is the basic bifurcation generating spatial pattern, and lies at the heart of almost all mathematical models for patterning in biology and chemistry. In this paper...
On the transition from initial data to travelling waves in the Fisher-KPP equation (1998)
Abstract. The Fisher-KIT equation u, = u, + u ( 1- u) has a travelling wave solution for all speeds> 2. Initial data that decrease monotonically from 1 to 0 on- co < x < a, with u (x, 0) =...
Modelling the macrophage invasion of tumours: Effects on growth and composition (1998)
OWEN, MARKUS R., SHERRATT, JONATHAN A.
Even in the early stages of their development, tumours are not simply a homogeneous grouping of mutant cells; rather, they develop in tandem with normal tissue cells, and also recruit other cell...
Markus R. Owen, Jonathan A. Sherratt, Cval U. K
Solid tumours do not develop as a homogeneous mass of mutant cells, rather, they grow in tandem with normal tissue cells initially present, and may also recruit other cell types including lymphatic...
Jonathan A. Sherratt, Barry T. Eagan, Mark A. Lewis
A constant dilemma in theoretical ecology is knowing whether model predictions correspond to real phenomena or whether they are artifacts of the modelling framework. The frequent absence of detailed...
OLSEN, LUKE, SHERRATT, JONATHAN A., MAINI, PHILIP K., ARNOLD, FRANK
Angiogenesis, the process by which new blood capillaries grow into a tissue from surrounding parent vessels, is a key event in dermal wound healing, malignant-tumour growth, and other pathologic...
SHERRATT, JONATHAN A., MARCHANT, BEN P.
Wavefront solutions of scalar reaction-diffusion equations have been intensively studied for many years. There are two basic cases, typified by quadratic and cubic kinetics. An intermediate case is...
Luke Olsen, Jonathan A. Sherratt, Philip K. Maini
The healing of adult mammalian skin wounds involves a complex sequence of spatially and temporally coordinated processes. Wound contraction, by reducing the size of the injury, is an intrinsic...
Review Forma, 10,205222,1995 Travelling Waves in Wound Healing (1995)
Paul D. Dales, Luke Olsen, Philip K. Maini, Jonathan A. Sherratt
Abstract. We illustrate the role of travelling waves in wound healing by considering three different cases. Firstly, we review a model for surface wound healing in the cornea and focus on the speed...
Phase differences in reaction-diffusion-advection systems and applications to morphogenesis (1995)
PERUMPANANI, ABBEY J., SHERRATT, JONATHAN A., MAINI, PHILIP K.
The authors study the effect of advection on reaction-diffusion patterns. It is shown that the addition of advection to a two-variable reaction–diffusion system with periodic boundary conditions...
λ–;ω systems are a class of simple examples of two coupled reaction-diffusion equations whose kinetics have a stable limit cycle. The author considers the evolution of such systems from simple...
Mathematical models of wound healing in embryonic and adult epidermis (1992)
SHERRATT, JONATHAN A., MARTIN, PAUL, MURRAY, J. D., LEWIS, JULIAN
Epidermal wound healing occurs by quite different mechanisms in embryos and adults. In the latter case, it has long been known that cells crawl inwards via lamellipodia to close the defect. In the...
MAINI, PHILIP K., BENSON, DEBBIE L., SHERRATT, JONATHAN A.
Reaction-diffusion models for biological pattern formation have been studied extensively in a variety of embryonic and ecological contexts. However, despite experimental evidence pointing to the...
A Perturbation Problem Arising from a Mechanical Model for Epithelial Morphogenesis (1991)
In this paper, the author applies the mechanical model of Murray and Oster (1984) for epithelial morphogenesis to the behaviour of an epithelial sheet after a section of the sheet has been removed....
Abstract. Periodic travelling waves are a fundamental solution form in oscillatory reactiondiffusion equations. Here I discuss the generation of periodic travelling waves in a reaction-diffusion...
Disease effects on reproduction can cause population cycles in seasonal environments
Smith, Matthew J, White, Andrew, Sherratt, Jonathan A, Telfer, Sandra, Begon, Michael, Lambin, Xavier
Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share...
Periodic travelling waves in cyclic populations: field studies and reaction–diffusion models
Sherratt, Jonathan A, Smith, Matthew J
Periodic travelling waves have been reported in a number of recent spatio-temporal field studies of populations undergoing multi-year cycles. Mathematical modelling has a major role to play in...
Locating the transition from periodic oscillations to spatiotemporal chaos in the wake of invasion
Sherratt, Jonathan A., Smith, Matthew J., Rademacher, Jens D. M.
In systems with cyclic dynamics, invasions often generate periodic spatiotemporal oscillations, which undergo a subsequent transition to chaos. The periodic oscillations have the form of a wavetrain...