NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

Tempol ameliorates murine viral encephalomyelitis by preserving the blood-brain barrier, reducing viral load, and lessening inflammation

Multiple sclerosis (MS) is a progressive inflammatory and/or demyelinating disease of the human central nervous system (CNS). Most of the knowledge about the pathogenesis of MS has been derived from murine models, such as experimental autoimmune encephalomyelitis and vital encephalomyelitis. Here, we infected female C57BL/6 mice with a neurotropic strain of the mouse hepatitis virus (MHV-59A) to evaluate whether treatment with the multifunctional antioxidant tempol (4-hydroxy-2,2,6,6-tetramethyl-1-piperidinyloxy) affects the ensuing encephalomyelitis. In untreated animals, neurological symptoms developed quickly: 90% of infected mice died 10 days after virus inoculation and the few survivors presented neurological deficits. Treatment with tempol (24 mg/kg, ip, two doses on the first day and daily doses for 7 days plus 2 mM tempol in the drinking water ad libitum) profoundly altered the disease outcome: neurological symptoms were attenuated, mouse survival increased up to 70%, and half of the survivors behaved as normal mice. Not Surprisingly, tempol substantially preserved the integrity of the CNS, including the blood-brain barrier. Furthermore, treatment with tempol decreased CNS vital titers, macrophage and T lymphocyte infiltration, and levels of markers of inflammation, such as expression of inducible nitric oxide synthase, transcription of tumor necrosis factor-alpha and interferon-gamma, and protein nitration. The results indicate that tempol ameliorates murine viral encephalomyelitis by altering the redox status of the infectious environment that contributes to an attenuated CNS inflammatory response. overall, our study supports the development of therapeutic strategies based on nitroxides to manage neuroinflammatory diseases, including MS. (C) 2009 Elsevier Inc. All rights reserved.