Fernando Oliveira

On the generic existence of homoclinic points

This work is concerned with the generic existence of homoclinic points for area preserving diffeomorphisms of compact orientable surfaces. We give a shorter proof of Pixtons theorem that shows that, C r -generically, an area preserving diffeomorphism of the two sphere has the property that every hyperbolic periodic point has transverse homoclinic points. Then, we extend Pixtons result to the torus and investigate certain generic aspects of the accumulation of the invariant manifolds all over themselves in the case of symplectic diffeomorphisms of compact manifolds.

Thiamine deficiency during pregnancy leads to cerebellar neuronal death in rat offspring: role of voltage-dependent K+ channels.

Oxidative stress, selective neuronal loss, and diminished activity of thiamine-dependent enzymes play a role in many neurodegenerative diseases, including Alzheimers disease, Parkinsons disease and Huntingtons disease. To further understand the major implications of thiamine deficiency (TD) in neuronal death, we induced TD during pregnancy and evaluated the effects on the offspring. The body and brain weights of pups from thiamine-deficient dams were significantly smaller than normal. Loss of neuronal viability was examined by trypan blue exclusion assay, and demonstrated increased cytotoxicity in primary cultures of TD neurons. Additionally, cerebellar cultures were exposed to thiamine-free cell culture medium to better explore the effects of thiamine withdrawal. Alterations in potassium current has previously been associated with the development of cell death. In this study, we examined the TD effects on delayed rectifier and A-type K+ channels, two well-known voltage-activated K+ channels involved in the regulation of action potential firing in cerebellar granule neurons. Current recordings were performed in cultured rat cerebellar granule neurons at day 7, using the whole-cell voltage-clamp technique. Our data demonstrate that thiamine deficiency provoked a significant decrease in the voltage-dependent K+ membrane conductance. Finally, TD markedly depressed the transient A-type K+ currents.

Resurgent Na+ current: a new avenue to neuronal excitability control.

Integrative and firing properties are important characteristics of neuronal circuits and these responses are determined in large part by the repertoire of ion channels they express, which can vary considerably between cell types. Recently, a new mode of operation of voltage dependent sodium channels has been described that generates a so-called resurgent Na+ current. Accumulating evidence suggests resurgent Na current participates in the generation of sub-threshold inward Na+ current causing membrane depolarization which provides the necessary drive to fire high-frequency action potentials. Recent studies indicate that resurgent Na+ current could be a more widespread feature than previously thought.

On the Cinfty genericity of homoclinic orbits

We show that the existence of a transverse homoclinic orbit to a given periodic one is a C generic property, for most homotopy classes of area-preserving diffeomorphisms of compact surfaces. An application to the C genericity of area-preserving diffeomorphisms with positive topological entropy is given.

Angiotensin II increases evoked release at the frog neuromuscular junction through a receptor sensitive to A779.

Receptor mediated presynaptic modulation is a ubiquitous mechanism involved in synaptic plasticity. Here we show that angiotensin II increased quantal content at the frog neuromuscular junction. This presynaptic effect of angiotensin II was insensitive to losartan and PD123319, but was antagonized by a more potent partial agonist of the amphibian angiotensin receptor, L162313. In addition, A779, a blocker of the angiotensin-[1-7] receptor, also abolished the effect of angiotensin II. These results indicate that the effect of angiotensin II on evoked release is mediated through an angiotensin receptor. L162313 alone increased quantal content, and A779 also antagonized this effect of L162313. We conclude that the neuromuscular junction possesses angiotensin receptors involved in presynaptic modulation.

Minimal non-ergodic C^1-diffeomorphisms of the circle

We construct, for each irrational number α, a minimal C 1 -diffeomorphism of the circle with rotation number α which is not ergodic with respect to the Lebesgue measure.

Thiamine deficiency in vitro accelerates A-type potassium current inactivation in cerebellar granule neurons

Thiamine deficiency during embryonic or early postnatal development causes deficits in cerebellum-dependent activities including motor control and procedural memory. Here, we give a detailed description of the changes to A-type current in cultured cerebellar granule neurons exposed to thiamine deficiency in vitro. A-type current in treated neurons was reduced to 51% of that in controls. The remaining A-type current in treated neurons exhibited normal activation kinetics and voltage dependence whereas inactivation was markedly faster. These effects were selective because the delayed-rectifier potassium current density and kinetics were unchanged in thiamine-deficient neurons. A computational model of the cerebellar granule neuron was used to test the impact of these alterations and predicts an increase in excitability that is especially pronounced for synaptic activation. Our results suggest that the loss of A-type potassium conductance leads to hyperactivity in cerebellar granule neurons and may contribute to cell death observed in the granule layer of cerebellum during thiamine-deficiency in vivo.

Energy Metabolism in Huntington’s Disease

Neurodegenerative diseases are pathological processes characterized by neuronal death and morbid evolution leading to occupational injury and serious neuropsychiatric disorders. The natural course of neurodegenerative diseases does not show regression of symptoms or cure and current treatments are far from producing a real improvement in the quality of patient’s life. Several studies have been conducted in an attempt to find causes of cellular disturbances focusing new pharmacological targets priming to successful therapeutic interventions. Studies have been directed to investigate possible changes in energy metabolism pathways. Indeed, some disturbances in glycolytic pathway and mitochondrial dysfunctions have been associated with Huntington’s Disease and other neurodegenerative diseases and are often related to the events of cell death. In this section, an overview of the energy metabolism pathways will be presented and the particular aspects of energetic metabolism in Huntington’s Disease will be discussed.

Extending Circle Mappings to the Annulus

We show that any monotone degree one C∞ mapping of the circle can be realized as the induced mapping on the boundary by a C∞ area preserving diffeomorphism of the open annulus. The circle mapping may have critical points, allowing the possibility of Denjoy behavior on the boundary.