Search

In a recent paper by one of the authors and collaborators, motivated by the Olive Quick Decline Syndrome (OQDS) outbreak, which has been ongoing in Southern Italy since 2013, a simple epidemiological model describing this epidemic was presented. Beside the bacterium Xylella fastidiosa, the main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model was based on a system of ordinary differential equations, the analysis of which provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. Although the model presented there was mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within an integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed, numerical simulations support the outcomes of the mathematical analysis, according to which the removal of a suitable amount of weed biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted in the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen. In this paper for a more realistic description and a clearer interpretation of the proposed control measures, a spatial structure of the epidemic system has been included, but, in order to keep mathematical technicalities to a minimum, only two players have been described in a dynamical way, trees and insects, while the weed biomass is taken to be a given quantity. The control measures have been introduced only on a subregion of the whole habitat, in order to contain costs of intervention. We show that such a practice can lead to the eradication of an epidemic outbreak. Numerical simulations confirm both the results of the previous paper and the theoretical results of the model with a spatial structure, though subject to regional control only.

In this study, the formation of the adult sea urchin shape is rationalized within the Turing's theory paradigm. The emergence of protrusions from the expanding underlying surface is described through a reaction-diffusion model with Gray-Scott kinetics on a growing oblate spheroid. The case of slow exponential isotropic growth is considered. The model is first studied in terms of the spatially homogenous equilibria and of the bifurcations involved. Turing diffusion-driven instability is shown to occur and the impact of the slow exponential growth on the resulting Turing regions adequately discussed. Numerical investigations validate the theoretical results showing that the combination between an inhibitor and an activator can result in a distribution of spot concentrations that underlies the development of ambulacral tentacles in the sea urchin's adult stage. Our findings pave the way for a model-driven experimentation that could improve the current biological understanding of the gene control networks involved in patterning.

This paper deals with the numerical (finite volume) approximation of reaction–diffusion systems with relaxation, among which the hyperbolic extension of the Allen–Cahn equation – given by τ ∂ t t u + ( 1 − τ f ′ ( u ) ) ∂ t u − μ ∂ x x u = f ( u ) , where τ , μ > 0 and f is a cubic-like function with three zeros – represents a notable prototype. Appropriate discretizations are constructed starting from the kinetic interpretation of the model as a particular case of reactive jump process, given by the substitution of the Fourier's law with the Maxwell–Cattaneo's law. A corresponding pseudo-kinetic scheme is also proposed for the Guyer–Krumhansl's law. For the Maxwell–Cattaneo case, numerical experiments 1 are provided for exemplifying the theoretical analysis (previously developed by the same authors) concerning the stability of traveling waves under a sign condition on the damping term g : = 1 − τ f ′ . Moreover, important evidence of the validity of those results beyond the formal hypotheses g ( u ) > 0 for any u is numerically established.

Nonlinear reaction-diffusion problems are ubiquitous in science, ranging from physics to engineering, from economy to biology. In particular, in this paper two-dimensional problems with generic Dirichlet boundary conditions or homogeneous Neumann boundary conditions are focused on. To simulate this class of mathematical problems, a quite simple generalized collocation method is proposed and developed. Moreover, a test case and an application to the Schnakenberg model are described, in order to show the efficiency of the simulation method and the goodness of the numerical results.

We study an individual-based model in which two spatially-distributed species, characterized by different diffusivities, compete for resources. We consider three different ecological settings. In the first, diffusing faster has a cost in terms of reproduction rate. In the second case, resources are not uniformly distributed in space. In the third case, the two species are transported by a fluid flow. In all these cases, at varying the parameters, we observe a transition from a regime in which diffusing faster confers an effective selective advantage to one in which it constitutes a disadvantage. We analytically estimate the magnitude of this advantage (or disadvantage) and test it by measuring fixation probabilities in simulations of the individual-based model. Our results provide a framework to quantify evolutionary pressure for increased or decreased dispersal in a given environment., 11 pages, 6 figures, accepted for publication in J. Theo. Biol

Este artículo contiene 7 páginas, 4 figuras., The study of spatial patterns in the distribution of organisms is a central issue in ecology. Here we address the question of whether predator–prey interactions can induce nonuniform distributions. We study how diffusion affects the stability of predator– prey coexistence equilibria and show a new difference between ratio- and prey-dependent models. Recently, Peter Abrams and Lev Ginzburg reviewed the controversial issue of what kind of function better describes the rate of prey consumption by an average predator, the so-called ‘‘predator functional response.’’ Here, we focus on reaction-diffusion predator– prey models with and without predator dependence in the functional response. We show that classical prey-dependent models cannot give rise to spatial structures through diffusiondriven instabilities; however, predator-dependent models with the same degree of complexity can. The origin of predator dependence in the rate of prey consumption is the mutual interference between predators. Therefore, we show that this mechanism can generate patchiness in a homogeneous environment under certain conditions of trophic interaction and predator–prey relative diffusion, This work has been supported by CIRIT grants 1999FI 00524 UPC APMARN to D. Alonso and 1997FI 00296 UB APMARN to F. Bartumeus from the Catalan autonomous government.

The life cycle of Caulobacter crescentus is of interest because of the asymmetric nature of cell division that gives rise to progeny that have distinct morphology and function. One daughter called the stalked cell is sessile and capable of DNA replication, while the second daughter called the swarmer cell is motile but quiescent. Advances in microscopy combined with molecular biology techniques have revealed that macromolecules are localized in a non-homogeneous fashion in the cell cytoplasm, and that dynamic localization of proteins is critical for cell cycle progression and asymmetry. However, the molecular-level mechanisms that govern protein localization, and enable the cell to exploit subcellular localization towards orchestrating an asymmetric life cycle remain obscure. There are also instances of researchers using intuitive reasoning to develop very different verbal explanations of the same biological process. To provide a complementary view of the molecular mechanism controlling the asymmetric division cycle of Caulobacter, we have developed a mathematical model of the cell cycle regulatory network. Our reaction-diffusion models provide additional insight into specific mechanism regulating different aspects of the cell cycle. We describe a molecular mechanism by which the bifunctional histidine kinase PleC exhibits bistable transitions between phosphatase and kinase forms. We demonstrate that the kinase form of PleC is crucial for both swarmer-to-stalked cell morphogenesis, and for replicative asymmetry in the predivisional cell. We propose that localization of the scaffolding protein PopZ can be explained by a Turing-type mechanism. Finally, we discuss a preliminary model of ParA- dependent chromosome segregation. Our model simulations are in agreement with experimentally observed protein distributions in wild-type and mutant cells. In addition to predicting novel mutants that can be tested in the laboratory, we use our models to reconcile competing hypotheses and provide a unified view of the regulatory mechanisms that direct the Caulobacter cell cycle. Ph. D.

Phosphorylation and dephosphorylation of proteins are mechanisms of activation and deactivation which regulate many cellular processes. Both mechanisms have been usually described in well mixed environments. MARCKS is a protein which binds to the membrane by electrostatic interaction. It is translocated from the membrane and phosphorylated by Protein Kinase C. Back in the cytoplasm the translocated MARCKS proteins are dephosphorylated by the enzyme phosphatase and can reattach to the membrane. These three processes (membrane binding, translocation, dephosphorylation) give rise to a cyclic dynamics known as the myristoyl-electrostatic switch. Methods We employ a reaction-diffusion model for the concentrations of MARCKS and PKC in the cell in a circular domain. Results Herein, we start from a reaction-diffusion model taking into account mass conservation of the MARCKS proteins. Then, we extend the model by including the dynamics of binding and unbinding of PKC enzymes, which are in turn activated by spikes of calcium. Furthermore, we show that the model fits previous experimental results well and predicts, in addition, the formation of domains with high concentration of MARCKS proteins at the membrane. Conclusions We have developed a simple model of binding, phosphorylation and desphosphorylation for MARCKS protein. The main prediction emerging from numerical simulations of the model is the spontaneous appearance of domains of high concentration of membrane proteins.

Injections of neural tracers into many mammalian neocortical areas reveal a common patchy motif of clustered axonal projections. We studied in simulation a mathematical model for neuronal development in order to investigate how this patchy connectivity could arise in layer II/III of the neocortex. In our model, individual neurons of this layer expressed the activator–inhibitor components of a Gierer–Meinhardt reaction–diffusion system. The resultant steady-state reaction–diffusion pattern across the neuronal population was approximately hexagonal. Growth cones at the tips of extending axons used the various morphogens secreted by intrapatch neurons as guidance cues to direct their growth and invoke axonal arborization, so yielding a patchy distribution of arborization across the entire layer II/III. We found that adjustment of a single parameter yields the intriguing linear relationship between average patch diameter and interpatch spacing that has been observed experimentally over many cortical areas and species. We conclude that a simple Gierer–Meinhardt system expressed by the neurons of the developing neocortex is sufficient to explain the patterns of clustered connectivity observed experimentally., Cerebral Cortex, 24 (2), ISSN:1047-3211, ISSN:1460-2199