Cross-diffusion-induced subharmonic spatial resonances in a predator-prey system.

In this paper we investigate the complex dynamics originated by a cross-diffusion-induced subharmonic destabilization of the fundamental subcritical Turing mode in a predator-prey reaction-diffusion system. The model we consider consists of a two-species Lotka-Volterra system with linear diffusion and a nonlinear cross-diffusion term in the predator equation. The taxis term in the search strategy of the predator is responsible for the onset of complex dynamics. In fact, our model does not exhibit any Hopf or wave instability, and on the basis of the linear analysis one should only expect stationary patterns; nevertheless, the presence of the nonlinear cross-diffusion term is able to induce a secondary instability: due to a subharmonic spatial resonance, the stationary primary branch bifurcates to an out-of-phase oscillating solution. Noticeably, the strong resonance between the harmonic and the subharmonic is able to generate the oscillating pattern albeit the subharmonic is below criticality. We show that, as the control parameter is varied, the oscillating solution (subT mode) can undergo a sequence of secondary instabilities, generating a transition toward chaotic dynamics. Finally, we investigate the emergence of subT-mode solutions on two-dimensional domains: when the fundamental mode describes a square pattern, subharmonic resonance originates oscillating square patterns. In the case of subcritical Turing hexagon solutions, the internal interactions with a subharmonic mode are able to generate the so-called "twinkling-eyes" pattern.

Demyelination patterns in a mathematical model of multiple sclerosis.

In this paper we derive a reaction-diffusion-chemotaxis model for the dynamics of multiple sclerosis. We focus on the early inflammatory phase of the disease characterized by activated local microglia, with the recruitment of a systemically activated immune response, and by oligodendrocyte apoptosis. The model consists of three equations describing the evolution of macrophages, cytokine and apoptotic oligodendrocytes. The main driving mechanism is the chemotactic motion of macrophages in response to a chemical gradient provided by the cytokines. Our model generalizes the system proposed by Calvez and Khonsari (Math Comput Model 47(7-8):726-742, 2008) and Khonsari and Calvez (PLos ONE 2(1):e150, 2007) to describe Baló's sclerosis, a rare and aggressive form of multiple sclerosis. We use a combination of analytical and numerical approaches to show the formation of different demyelinating patterns. In particular, a Turing instability analysis demonstrates the existence of a threshold value for the chemotactic coefficient above which stationary structures develop. In the case of subcritical transition to the patterned state, the numerical investigations performed on a 1-dimensional domain show the existence, far from the bifurcation, of complex spatio-temporal dynamics coexisting with the Turing pattern. On a 2-dimensional domain the proposed model supports the emergence of different demyelination patterns: localized areas of apoptotic oligodendrocytes, which closely fit existing MRI findings on the active MS lesion during acute relapses; concentric rings, typical of Baló's sclerosis; small clusters of activated microglia in absence of oligodendrocytes apoptosis, observed in the pathology of preactive lesions.

Turing pattern formation in the Brusselator system with nonlinear diffusion.

In this work we investigate the effect of density-dependent nonlinear diffusion on pattern formation in the Brusselator system. Through linear stability analysis of the basic solution we determine the Turing and the oscillatory instability boundaries. A comparison with the classical linear diffusion shows how nonlinear diffusion favors the occurrence of Turing pattern formation. We study the process of pattern formation both in one-dimensional and two-dimensional spatial domains. Through a weakly nonlinear multiple scales analysis we derive the equations for the amplitude of the stationary patterns. The analysis of the amplitude equations shows the occurrence of a number of different phenomena, including stable supercritical and subcritical Turing patterns with multiple branches of stable solutions leading to hysteresis. Moreover, we consider traveling patterning waves: When the domain size is large, the pattern forms sequentially and traveling wave fronts are the precursors to patterning. We derive the Ginzburg-Landau equation and describe the traveling front enveloping a pattern which invades the domain. We show the emergence of radially symmetric target patterns, and, through a matching procedure, we construct the outer amplitude equation and the inner core solution.

Nitric oxide is essential for vesicle formation and trafficking in Arabidopsis root hair growth.

The functions of nitric oxide (NO) in processes associated with root hair growth in Arabidopsis were analysed. NO is located at high concentrations in the root hair cell files at any stage of development. NO is detected inside of the vacuole in immature actively growing root hairs and, later, NO is localized in the cytoplasm when they become mature. Experiments performed by depleting NO in Arabidopsis root hairs indicate that NO is required for endocytosis, vesicle formation, and trafficking and it is not involved in nucleus migration, vacuolar development, and transvacuolar strands. The Arabidopsis G'4,3 mutant (double mutant nia1/nia2) is severely impaired in NO production and generates smaller root hairs than the wild type (WT). Root hairs from the Arabidopsis G'4,3 mutant show altered vesicular trafficking and are reminiscent of NO-depleted root hairs from the Arabidopsis WT. Interestingly, normal vesicle formation and trafficking as well as root hair growth is restored by exogenous NO application in the Arabidopsis G'4,3 mutant. All together, these results firmly support the essential role played by NO in the Arabidopsis root-hair-growing process.

Molecular cloning of hydrogenosomal ferredoxin cDNA from the anaerobic amoeboflagellate Psalteriomonas lanterna.

Anaerobic parasitic and free living protozoa and anaerobic rumen fungi often contain a characteristic organelle, the hydrogenosome. Recently obtained molecular data show that hydrogenosomes in parasitic protozoa probably use a mitochondria-like protein targeting mechanism, whereas for hydrogenosomes in fungi a microbody-like mechanism is inferred. Here we present, to our knowledge, the first sequence data of a hydrogenosomal protein in a free-living anaerobic protozoan. It is shown that ferredoxin of the amoeboflagellate Psalteriomonas lanterna is similar to hydrogenosomal ferredoxin of the parasite Trichomonas vaginalis. We suggest that the two ferredoxins use similar organelle targeting mechanisms.

A procedure for selecting mammalian cells with an impairment in oxidative phosphorylation.

The mitochondrial encephalomyopathies in man are characterized by heterogeneous defects leading to an impairment in the pathway of aerobic energy production. As a means of investigating the molecular and genetic mechanisms underlying these disorders we have developed a procedure for selecting mammalian cell lines with features resembling the human pathological phenotypes. The principle of the selection is the use of a fluorescent amphiphilic dye, 2,4-(dimethylamino)-1-styrylmethylpyridiniumiodine, a cation showing two main features. Firstly, it is accumulated by mitochondria to an extent correlated with the magnitude of the electrochemical gradient of protons across the mitochondrial inner membrane. Secondly, upon irradiation with UV light, it gives rise to formation of free radicals, which inflict damage to the cell. Mutant cells with an impairment in oxidative phosphorylation will have more chance to survive than wild type cells. The selection procedure was applied to a stock of mutagenized Chinese hamster ovary cells. After subcloning of the cells which survived the selection procedure, twenty-six independent clones were isolated. Eighteen of the clones had a partial deficiency of cytochrome c oxidase ranging from 30 to 60% of the activity in control cells. The properties of two of the clones are described. One clone has been cultured under non-selective conditions for at least 12 months with retention of the partial deficiency of cytochrome c oxidase.