Diffusion-aggregation processes with mono-stable reaction terms

This paper analyses front propagation of the equation $u_\tau=[D(u)v_x]_x +f(v) \;\;\; \tau < 0, x \in \mathbb{R}$ where $f$ is a monostable (ie Fisher-type) nonlinear reaction term and $D(v)$ changes its sign once, from positive to negative values,in the interval $v \in[0,1]$ where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density $v$ at time $\tau$ and position $x$. The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both

Aggregative movement and front propagation for bi-stable population models

Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation

Reptile scale paradigm: Evo-Devo, pattern formation and regeneration

The purpose of this perspective is to highlight the merit of the reptile integument as an experimental model. Reptiles represent the first amniotes. From stem reptiles, extant reptiles, birds and mammals have evolved. Mammal hairs and feathers evolved from Therapsid and Sauropsid reptiles, respectively. The early reptilian integument had to adapt to the challenges of terrestrial life, developing a multi-layered stratum corneum capable of barrier function and ultraviolet protection. For better mechanical protection, diverse reptilian scale types have evolved. The evolution of endothermy has driven the convergent evolution of hair and feather follicles: both form multiple localized growth units with stem cells and transient amplifying cells protected in the proximal follicle. This topological arrangement allows them to elongate, molt and regenerate without structural constraints. Another unique feature of reptile skin is the exquisite arrangement of scales and pigment patterns, making them testable models for mechanisms of pattern formation. Since they face the constant threat of damage on land, different strategies were developed to accommodate skin homeostasis and regeneration. Temporally, they can be under continuous renewal or sloughing cycles. Spatially, they can be diffuse or form discrete localized growth units (follicles). To understand how gene regulatory networks evolved to produce increasingly complex ectodermal organs, we have to study how prototypic scale-forming pathways in reptiles are modulated to produce appendage novelties. Despite the fact that there are numerous studies of reptile scales, molecular analyses have lagged behind. Here, we underscore how further development of this novel experimental model will be valuable in filling the gaps of our understanding of the Evo-Devo of amniote integuments

A two-compartment mechanochemical model of the roles of\ud transforming growth factor β and tissue tension in dermal wound healing

The repair of dermal tissue is a complex process of interconnected phenomena, where cellular, chemical and mechanical aspects all play a role, both in an autocrine and in a paracrine fashion. Recent experimental results have shown that transforming growth factor−β (TGFβ) and tissue mechanics play roles in regulating cell proliferation, differentiation and the production of extracellular materials. We have developed a 1D mathematical model that considers the interaction between the cellular, chemical and mechanical phenomena, allowing the combination of TGFβ and tissue stress to inform the activation of fibroblasts to myofibroblasts. Additionally, our model incorporates the observed feature of residual stress by considering the changing zero-stress state in the formulation for effective strain. Using this model, we predict that the continued presence of TGFβ in dermal wounds will produce contractures due to the persistence of myofibroblasts; in contrast, early elimination of TGFβ significantly reduces the myofibroblast numbers resulting in an increase in wound size. Similar results were obtained by varying the rate at which fibroblasts differentiate to myofibroblasts and by changing the myofibroblast apoptotic rate. Taken together, the implication is that elevated levels of myofibroblasts is the key factor behind wounds healing with excessive contraction, suggesting that clinical strategies which aim to reduce the myofibroblast density may reduce the appearance of contractures

A fibrocontractive mechanochemical model of dermal wound\ud closure incorporating realistic growth factor kinetics

Fibroblasts and their activated phenotype, myofibroblasts, are the primary cell types involved in the contraction associated with dermal wound healing. Recent experimental evidence indicates that the transformation from fibroblasts to myofibroblasts involves two distinct processes: the cells are stimulated to change phenotype by the combined actions of transforming growth factor β (TGFβ) and mechanical tension. This observation indicates a need for a detailed exploration of the effect of the strong interactions between the mechanical changes and growth factors in dermal wound healing. We review the experimental findings in detail and develop a model of dermal wound healing that incorporates these phenomena. Our model includes the interactions between TGFβ and collagenase, providing a more biologically realistic form for the growth factor kinetics than those included in previous mechanochemical descriptions. A comparison is made between the model predictions and experimental data on human dermal wound healing and all the essential features are well matched

Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios

We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before

Blockade of Immunosuppressive Cytokines Restores NK Cell Antiviral Function in Chronic Hepatitis B Virus Infection

NK cells are enriched in the liver, constituting around a third of intrahepatic lymphocytes. We have previously demonstrated that they upregulate the death ligand TRAIL in patients with chronic hepatitis B virus infection (CHB), allowing them to kill hepatocytes bearing TRAIL receptors. In this study we investigated whether, in addition to their pathogenic role, NK cells have antiviral potential in CHB. We characterised NK cell subsets and effector function in 64 patients with CHB compared to 31 healthy controls. We found that, in contrast to their upregulated TRAIL expression and maintenance of cytolytic function, NK cells had a markedly impaired capacity to produce IFN-gamma in CHB. This functional dichotomy of NK cells could be recapitulated in vitro by exposure to the immunosuppressive cytokine IL-10, which was induced in patients with active CHB. IL-10 selectively suppressed NK cell IFN-gamma production without altering cytotoxicity or death ligand expression. Potent antiviral therapy reduced TRAIL-expressing CD56 bright NK cells, consistent with the reduction in liver inflammation it induced; however, it was not able to normalise IL-10 levels or the capacity of NK cells to produce the antiviral cytokine IFN-gamma. Blockade of IL-10 +/- TGF-beta restored the capacity of NK cells from both the periphery and liver of patients with CHB to produce IFN-gamma, thereby enhancing their non-cytolytic antiviral capacity. In conclusion, NK cells may be driven to a state of partial functional tolerance by the immunosuppressive cytokine environment in CHB. Their defective capacity to produce the antiviral cytokine IFN-gamma persists in patients on antiviral therapy but can be corrected in vitro by IL-10+/- TGF-beta blockade

Spatial patterning in modified Turing systems: Application to pigmentation patterns on marine fish

In this paper we extend the study of Turing models to investigate the rôle of boundary conditions, parameter modulation, domain growth, and coupling of models. Our numerical simulations show that such modifications lead to patterns that cannot be reproduced by the standard model. By comparing our results with pigmentation patterning on marine fish we conclude that such models may have wider application than originally imagined

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation

Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains

By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth