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Chunyan Mou,
Frederique Pitel,
David Gourichon,
Florence Vignoles,
Athanasia Tzika,
Patricia Tato,
Le Yu,
Dave W Burt,
Bertrand Bed'hom,
Michele Tixier-Boichard, Kevin J Painter,
Denis J Headon
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ABSTRACT: Vertebrate skin is characterized by its patterned array of appendages, whether feathers, hairs, or scales. In avian skin the distribution of feathers occurs on two distinct spatial levels. Grouping of feathers within discrete tracts, with bare skin lying between the tracts, is termed the macropattern, while the smaller scale periodic spacing between individual feathers is referred to as the micropattern. The degree of integration between the patterning mechanisms that operate on these two scales during development and the mechanisms underlying the remarkable evolvability of skin macropatterns are unknown. A striking example of macropattern variation is the convergent loss of neck feathering in multiple species, a trait associated with heat tolerance in both wild and domestic birds. In chicken, a mutation called Naked neck is characterized by a reduction of body feathering and completely bare neck. Here we perform genetic fine mapping of the causative region and identify a large insertion associated with the Naked neck trait. A strong candidate gene in the critical interval, BMP12/GDF7, displays markedly elevated expression in Naked neck embryonic skin due to a cis-regulatory effect of the causative mutation. BMP family members inhibit embryonic feather formation by acting in a reaction-diffusion mechanism, and we find that selective production of retinoic acid by neck skin potentiates BMP signaling, making neck skin more sensitive than body skin to suppression of feather development. This selective production of retinoic acid by neck skin constitutes a cryptic pattern as its effects on feathering are not revealed until gross BMP levels are altered. This developmental modularity of neck and body skin allows simple quantitative changes in BMP levels to produce a sparsely feathered or bare neck while maintaining robust feather patterning on the body.
PLoS Biology 03/2011; 9(3):e1001028. · 11.45 Impact Factor
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ABSTRACT: In this paper we consider a simple continuous model to describe cell invasion, incorporating the effects of both cell-cell adhesion and cell-matrix adhesion, along with cell growth and proteolysis by cells of the surrounding extracellular matrix (ECM). We demonstrate that the model is capable of supporting both noninvasive and invasive tumour growth according to the relative strength of cell-cell to cell-matrix adhesion. Specifically, for sufficiently strong cell-matrix adhesion and/or sufficiently weak cell-cell adhesion, degradation of the surrounding ECM accompanied by cell-matrix adhesion pulls the cells into the surrounding ECM. We investigate the criticality of matrix heterogeneity on shaping invasion, demonstrating that a highly heterogeneous ECM can result in a "fingering" of the invasive front, echoing observations in real-life invasion processes ranging from malignant tumour growth to neural crest migration during embryonic development.
Journal of Theoretical Biology 03/2010; 264(3):1057-67. · 2.21 Impact Factor
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ABSTRACT: A number of studies have previously demonstrated that "goodness of fit" is insufficient in reliably classifying the credibility of a biological model. Robustness and/or sensitivity analysis is commonly employed as a secondary method for evaluating the suitability of a particular model. The results of such analyses invariably depend on the particular parameter set tested, yet many parameter values for biological models are uncertain.
Here, we propose a novel robustness analysis that aims to determine the "common robustness" of the model with multiple, biologically plausible parameter sets, rather than the local robustness for a particular parameter set. Our method is applied to two published models of the Arabidopsis circadian clock (the one-loop [1] and two-loop [2] models). The results reinforce current findings suggesting the greater reliability of the two-loop model and pinpoint the crucial role of TOC1 in the circadian network.
Consistent Robustness Analysis can indicate both the relative plausibility of different models and also the critical components and processes controlling each model.
PLoS ONE 01/2010; 5(12):e15589. · 4.09 Impact Factor
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ABSTRACT: Sensitivity and robustness are essential properties of circadian clock systems, enabling them to respond to the environment but resist noisy variations. These properties should be recapitulated in computational models of the circadian clock. Highly nonlinear kinetics and multiple loops are often incorporated into models to match experimental time-series data, but these also impact on model properties for clock models.
Here, we study the consequences of complicated structure and nonlinearity using simple Goodwin-type oscillators and the complex Arabidopsis circadian clock models. Sensitivity analysis of the simple oscillators implies that an interlocked multi-loop structure reinforces sensitivity/robustness properties, enhancing the response to external and internal variations. Furthermore, we found that reducing the degree of nonlinearity could sometimes enhance the robustness of models, implying that ad hoc incorporation of nonlinearity could be detrimental to a model's perceived credibility.
The correct multi-loop structure and degree of nonlinearity are therefore critical in contributing to the desired properties of a model as well as its capacity to match experimental data.
PLoS ONE 01/2010; 5(11):e13867. · 4.09 Impact Factor
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ABSTRACT: Adhesion of cells to one another and their environment is an important regulator of many biological processes but has proved difficult to incorporate into continuum mathematical models. This paper develops further the new modelling approach proposed by Armstrong et al. (A continuum approach to modelling cell–cell adhesion, J. Theor. Biol. 243: 98–113, 2006). The models studied in the present paper use an integro-partial differential equation for cell behaviour, in which the integral represents the sensing by cells of their local environment. This enables an effective representation of cell–cell adhesion, as well as random cell movement, and cell proliferation. The authors use this modelling approach to investigate the ability of cell–cell adhesion to generate spatial patterns during cell aggregation. The model is also extended to give a new representation of cancer growth, whose solutions reflect the balance between cell–cell and cell–matrix adhesion in regulating cancer invasion. The non-local term in these models means that there is no standard theory from which one can deduce the boundedness required for biological realism: specifically, solutions for cell density must lie between zero and a positive density corresponding to close cell packing. Here the authors derive a number of conditions, each of which is sufficient for the required boundedness, and they demonstrate numerically that cell density increases above the upper bound for some parameter sets not satisfying these conditions. Finally the authors outline what they regard as the main mathematical challenges for future work on boundedness in models of this type.
Jnl of Applied Mathematics. 01/2009; 20:123-144.
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ABSTRACT: 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.
Journal of Theoretical Biology 12/2006; 243(1):98-113. · 2.21 Impact Factor
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ABSTRACT: 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.
Physical Review E 03/2004; 69(2 Pt 1):021910. · 2.26 Impact Factor
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ABSTRACT: 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.
Journal of Theoretical Biology 01/2004; 225(3):327-39. · 2.21 Impact Factor
