Pattern formation in reaction diffusion models with spatially inhomogeneous diffusion coefficients

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 existence of spatial inhomogeneities in various biological systems, most models have only been considered in a spatially homogeneous environment. The authors consider a two-chemical reaction-diffusion mechanism in one space dimension in which one of the diffusion coefficients depends explicitly on the spatial variable. The model is analysed in the case of a step function diffusion coefficient and the insight gained for this special case is used to discuss pattern generation for smoothly varying diffusion coefficients. The results show that spatial inhomogeneity may be an important biological pattern regulator, and possible applications of the model to chondrogenesis in the vertebrate limb are suggested

Unravelling the Turing bifurcation using spatially varying diffusion coefficients

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 the authors determine the structure of this bifurcation for two coupled reaction diffusion equations on a two-dimensional square spatial domain when the diffusion coefficients have a small explicit variation in space across the domain. In the case of homogeneous diffusivities, the Turing bifurcation is highly degenerate. Using a two variable perturbation method, the authors show that the small explicit spatial inhomogeneity splits the bifurcation into two separate primary and two separate secondary bifurcations, with all solution branches distinct. This splitting of the bifurcation is more effective than that given by making the domain slightly rectangular, and shows clearly the structure of the Turing bifurcation and the way in which the! var ious solution branches collapse together as the spatial variation is reduced. The authors determine the stability of the solution branches, which indicates that several new phenomena are introduced by the spatial variation, including stable subcritical striped patterns, and the possibility that stable stripes lose stability supercritically to give stable spotted patterns

Travelling waves in wound healing

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 of healing as a function of the application of growth factors. Secondly, we present a model for scar tissue formation in deep wounds and focus on the role of key chemicals in determining the quality of healing. Thirdly, we propose a model for excessive healing disorders and investigate how abnormal healing may be controlled

The evolution of warning signals as reliable indicators of prey defense

It is widely argued that defended prey have tended to evolve conspicuous traits because predators more readily learn to avoid defended prey when they are conspicuous. However, a rival theory proposes that defended prey have evolved such characters because it allows them to be distinguished from undefended prey. Here we investigated how the attributes of defended (unprofitable) and undefended (profitable) computer-generated prey species tended to evolve when they were subject to selection by foraging humans. When cryptic forms of defended and undefended species were similar in appearance but their conspicuous forms were not, defended prey became conspicuous while undefended prey remained cryptic. Indeed, in all of our experiments, defended prey invariably evolved any trait that enabled them to be distinguished from undefended prey, even if such traits were cryptic. When conspicuous mutants of defended prey were extremely rare, they frequently overcame their initial disadvantage by chance. When Batesian mimicry of defended species was possible, defended prey evolved unique traits or characteristics that would make undefended prey vulnerable. Overall, our work supports the contention that warning signals are selected for their reliability as indicators of defense rather than to capitalize on any inherent educational biases of predators

Corneal epithelial wound healing

We propose a reaction-diffusion model of the mechanisms involved in the healing of corneal surface wounds. The model focuses on the stimulus for increased mitotic and migratory activity, specifically the role of epidermal growth factor. We determine an analytic approximation for the speed of travelling wave solutions of the model in terms of the parameters and verify the results numerically. By comparing the predicted speed with experimentally measured healing rates, we conclude that serum-derived factors can alone account for the overall features of the healing process, but that the supply of growth factors by the tear film, in the absence of serum-derived factors, is not sufficient to give the observed healing rate. Numerical solutions of the model equations also confirm the importance of both migration and mitosis for effective wound healing. By modifying the model, we obtain an analytic prediction for the healing rate of corneal surface wounds when epidermal growth factor is applied topically to the wound

Ministry emphasises quality of medical training

One proposed mechanism of tumour escape from immune surveillance is tumour up-regulation of the cell surface ligan FasL, whichcan lead to apoptosis of Fas receptor (Fas) positive lymphocytes. Based upon this `coun-- rattack', we have developed a mathematical model inelAin tumour cell--lymphocyte ineA-- ction cell surface expression of Fas/FasL,an d their secreted soluble forms. The model predicts that (a) the production of soluble forms of Fas an d FasL will lead to thedown regulation of theimmun respon --fi (b) matrix metallopr otein se (MMP)ink'PTfiA ion should lead toin'x# sed membran FasLan result in a higher rate of Fas-mediated apoptosis for lymphocytesthan for tumour cells. Recen studieson can--# patient len support for theseprediction s. TheclinP-- l implication are two-fold. Firstly, the use of broad spectrum MMPin'#x tors asan`fi-- n`fi--'` cagenP may be compromised by their adverse e#ecton tumour FasL up-regulation Also, Fas/FasL insL action may havean impact on the outcome ofnA--x`#B onA in immunBB`fiAw`P-- ic trialssin` the finA common pathway of all these approaches is thetran - duction of deathsign-- swithin the tumour cell

Efficient biometric and password based mutual authentication for consumer USB mass storage devices

A Universal Serial Bus (USB) Mass Storage Device (MSD), often termed a USB flash drive, is ubiquitously used to store important information in unencrypted binary format. This low cost consumer device is incredibly popular due to its size, large storage capacity and relatively high transfer speed. However, if the device is lost or stolen an unauthorized person can easily retrieve all the information. Therefore, it is advantageous in many applications to provide security protection so that only authorized users can access the stored information. In order to provide security protection for a USB MSD, this paper proposes a session key agreement protocol after secure user authentication. The main aim of this protocol is to establish session key negotiation through which all the information retrieved, stored and transferred to the USB MSD is encrypted. This paper not only contributes an efficient protocol, but also does not suffer from the forgery attack and the password guessing attack as compared to other protocols in the literature. This paper analyses the security of the proposed protocol through a formal analysis which proves that the information is stored confidentially and is protected offering strong resilience to relevant security attacks. The computational cost and communication cost of the proposed scheme is analyzed and compared to related work to show that the proposed scheme has an improved tradeoff for computational cost, communication cost and security

A mathematical model for collagen fibre formation during foetal and adult dermal wound healing

Adult dermal wounds, in contrast to foetal wounds, heal with the formation of scar tissue. A crucial factor in determining the nature of the healed tissue is the ratio of collagen 1 to collagen 3, which regulates the diameter of collagen fibres. We develop a mathematical model which focuses on the stimulus for collagen synthesis due to the secretion of the different isoforms of the regulatory chemical transforming growth factor $\beta$. Numerical simulations of the model lead to a value of this ratio consistent with that of healthy tissue for the foetus but corresponding to scarring in adult wound healing. We investigate the effect of topical application of TGF$\beta$ isoforms during healing and determine the key parameters which control the difference between adult and foetal repair