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Journal ArticleDOI

Spatial pattern formation in biology: I. Dermal wound healing. II. Bacterial patterns

TL;DR: A model is described for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data, and the results from the model compare well with experiment.
Abstract: Although the development of spatial pattern and form is a central issue in biology the mechanisms which generate them are generally unknown. The interdisciplinary modelling challenge is to construct realistic mechanisms which capture the key biological processes and show how they are orchestrated to create the observed pattern. We discuss two specific patterning problems of current widespread interest in biomedicine. In the first, possible mechanisms of dermal wound healing are reviewed with a discussion of what is needed of realistic models for studying wound healing. We then list a series of open problems. In the second problem we describe a model for the complex patterns formed by bacterial colonies, specifically Escherichia coli, and derive and analyse a model firmly based on experimental data. The results from the model compare well with experiment. Mathematically, the class of models discussed gives rise to novel systems of partial differential equations which pose challenging problems, both analytical and numerical. The models have provided the experimentalist with insight as to how such patterns might be formed and have suggested possible experiments to elucidate the underlying biological processes.
Citations
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DOI
14 Dec 2015
TL;DR: In this paper, the authors acknowledge EPSRC Grant No. EP/H008403/1 awarded to Professor Brian J. Howard (Oxford University), the Centre for Public Engagement (Queen Mary, University of London) for funding, and Lis Carter for help in the recording.
Abstract: We acknowledge EPSRC Grant No. EP/H008403/1 awarded to Professor Brian J. Howard (Oxford University), the Centre for Public Engagement (Queen Mary, University of London) for funding, and Lis Carter for help in the recording.

111 citations

Journal ArticleDOI
TL;DR: In this 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.

91 citations

Journal ArticleDOI
21 Apr 2016-Cell
TL;DR: This analysis revealed a collective space-sensing mechanism, which entails sequential actions of an integral feedback loop and an incoherent feedforward loop that emphasizes a role of timing control in achieving robust pattern scaling and provides a new perspective in examining the phenomenon in natural systems.

84 citations


Cites methods from "Spatial pattern formation in biolog..."

  • ...In deriving the above equations, we made the following assumptions: (1) Cells are assumed to perform an unbiased random walk and their movement is modeled as diffusion (Kenkre, 2004; Maini, 2004; Murray et al., 1998)....

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Journal ArticleDOI
TL;DR: Two modelling frameworks for studying dynamic anistropy in connective tissue are presented, motivated by the problem of fibre alignment in wound healing and it is shown that the first model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population.
Abstract: We present two modelling frameworks for studying dynamic anistropy in connective tissue, motivated by the problem of fibre alignment in wound healing. The first model is a system of partial differential equations operating on a macroscopic scale. We show that a model consisting of a single extracellular matrix material aligned by fibroblasts via flux and stress exhibits behaviour that is incompatible with experimental observations. We extend the model to two matrix types and show that the results of this extended model are robust and consistent with experiment. The second model represents cells as discrete objects in a continuum of ECM. We show that this model predicts patterns of alignment on macroscopic length scales that are lost in a continuum model of the cell population.

60 citations

Journal ArticleDOI
28 Mar 2014-PLOS ONE
TL;DR: There is feedback between the level of cell contraction and the tissue regenerated in the wound, and this model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution.
Abstract: Wound healing is a process driven by cells. The ability of cells to sense mechanical stimuli from the extracellular matrix that surrounds them is used to regulate the forces that cells exert on the tissue. Stresses exerted by cells play a central role in wound contraction and have been broadly modelled. Traditionally, these stresses are assumed to be dependent on variables such as the extracellular matrix and cell or collagen densities. However, we postulate that cells are able to regulate the healing process through a mechanosensing mechanism regulated by the contraction that they exert. We propose that cells adjust the contraction level to determine the tissue functions regulating all main activities, such as proliferation, differentiation and matrix production. Hence, a closed-regulatory feedback loop is proposed between contraction and tissue formation. The model consists of a system of partial differential equations that simulates the evolution of fibroblasts, myofibroblasts, collagen and a generic growth factor, as well as the deformation of the extracellular matrix. This model is able to predict the wound healing outcome without requiring the addition of phenomenological laws to describe the time-dependent contraction evolution. We have reproduced two in vivo experiments to evaluate the predictive capacity of the model, and we conclude that there is feedback between the level of cell contraction and the tissue regenerated in the wound.

55 citations

References
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Journal ArticleDOI
TL;DR: In this article, it is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis.
Abstract: It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances. Such reaction-diffusion systems are considered in some detail in the case of an isolated ring of cells, a mathematically convenient, though biologically unusual system. The investigation is chiefly concerned with the onset of instability. It is found that there are six essentially different forms which this may take. In the most interesting form stationary waves appear on the ring. It is suggested that this might account, for instance, for the tentacle patterns on Hydra and for whorled leaves. A system of reactions and diffusion on a sphere is also considered. Such a system appears to account for gastrulation. Another reaction system in two dimensions gives rise to patterns reminiscent of dappling. It is also suggested that stationary waves in two dimensions could account for the phenomena of phyllotaxis. The purpose of this paper is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism. The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts. The full understanding of the paper requires a good knowledge of mathematics, some biology, and some elementary chemistry. Since readers cannot be expected to be experts in all of these subjects, a number of elementary facts are explained, which can be found in text-books, but whose omission would make the paper difficult reading.

9,015 citations

Book
01 Jul 1981
TL;DR: This chapter discusses the mechanics of Erythrocytes, Leukocytes, and Other Cells, and their role in Bone and Cartilage, and the properties of Bioviscoelastic Fluids, which are a by-product of these cells.
Abstract: Prefaces. 1. Introduction: A sketch of the History and Scope of the Field. 2. The Meaning of the Constitutive Equation. 3. The Flow Properties of Blood. 4. Mechanics of Erythrocytes, Leukocytes, and Other Cells. 5. Interaction of Red Blood Cells with Vessel Wall, and Wall Shear with Endothelium. 6 Bioviscoelastic Fluids. Bioviscoelastic Solids. 8. Mechanical Properties and Active Remodeling of Blood Vessels. 9. Skeletal Muscle. 10. Heart Muscle. 11. Smooth Muscles. 12. Bone and Cartilage. Indices

6,027 citations

Journal ArticleDOI
TL;DR: In this article, the authors present a sketch of the history and scope of the field of bio-physiology and discuss the meaning of the Constitutive Equation and the flow properties of blood.
Abstract: Prefaces. 1. Introduction: A sketch of the History and Scope of the Field. 2. The Meaning of the Constitutive Equation. 3. The Flow Properties of Blood. 4. Mechanics of Erythrocytes, Leukocytes, and Other Cells. 5. Interaction of Red Blood Cells with Vessel Wall, and Wall Shear with Endothelium. 6 Bioviscoelastic Fluids. Bioviscoelastic Solids. 8. Mechanical Properties and Active Remodeling of Blood Vessels. 9. Skeletal Muscle. 10. Heart Muscle. 11. Smooth Muscles. 12. Bone and Cartilage. Indices

3,670 citations

Book
01 Jan 1983
TL;DR: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know.
Abstract: This book is a lucid, straightforward introduction to the concepts and techniques of statistical physics that students of biology, biochemistry, and biophysics must know. It provides a sound basis for understanding random motions of molecules, subcellular particles, or cells, or of processes that depend on such motion or are markedly affected by it. Readers do not need to understand thermodynamics in order to acquire a knowledge of the physics involved in diffusion, sedimentation, electrophoresis, chromatography, and cell motility--subjects that become lively and immediate when the author discusses them in terms of random walks of individual particles.

3,041 citations

Journal ArticleDOI
11 Apr 1980-Science
TL;DR: When tissue cells are cultured on very thin sheets of cross-linked silicone fluid, the traction forces the cells exert are made visible as elastic distortion and wrinkling of this substratum.
Abstract: When tissue cells are cultured on very thin sheets of cross-linked silicone fluid, the traction forces the cells exert are made visible as elastic distortion and wrinkling of this substratum. Around explants this pattern of wrinkling closely resembles the "center effects" long observed in plasma clots and traditionally attributed to dehydration shrinkage.

1,377 citations