Topology, vorticity, and limit cycle in a stabilized Kuramoto-Sivashinsky equation.

A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex-like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.

Global potential, topology, and pattern selection in a noisy stabilized Kuramoto-Sivashinsky equation.

We formulate a general method to extend the decomposition of stochastic dynamics developed by Ao et al. [J. Phys. Math. Gen. 37, L25-L30 (2004)] to nonlinear partial differential equations which are nonvariational in nature and construct the global potential or Lyapunov functional for a noisy stabilized Kuramoto-Sivashinsky equation. For values of the control parameter where singly periodic stationary solutions exist, we find a topological network of a web of saddle points of stationary states interconnected by unstable eigenmodes flowing between them. With this topology, a global landscape of the steady states is found. We show how to predict the noise-selected pattern which agrees with those from stochastic simulations. Our formalism and the topology might offer an approach to explore similar systems, such as the Navier Stokes equation.

Performing protein crosslinking using gas-phase cleavable chemical crosslinkers and liquid chromatography-tandem mass spectrometry.

In this article, we describe our methods and protocols using collision-induced dissociative chemical crosslinking-tandem mass spectrometry (CID-CXL-MS/MS) analysis and the practical considerations when implementing these reagents and methodology for protein crosslinking studies. The synthesis of our novel chemical crosslinkers is described as well as their use for effectively labeling protein and protein complexes. Several sample preparation methods for liquid chromatography-tandem mass spectrometry are provided including the enrichment of interpeptide crosslinks. For identification of CID-CXL-MS/MS crosslinks, details regarding MS acquisition parameters and the utilization of various mass spectrometers are addressed along with post-data acquisition analysis to identify interpeptide crosslinks. Once the CID-CXL-MS/MS approach is optimized for a protein target or a set of targets, it can be used as a tool for biological research for studying protein structure when integrated with data obtained using other techniques, such as NMR, X-ray crystallography, and cryo-electron microscopy, or extended to the study of protein-protein interactions in physiological environments.

Mitochondrial inhibitor models of Huntington's disease and Parkinson's disease induce zinc accumulation and are attenuated by inhibition of zinc neurotoxicity in vitro or in vivo.

BACKGROUND: Inhibition of mitochondrial function occurs in many neurodegenerative diseases, and inhibitors of mitochondrial complexes I and II are used to model them. The complex II inhibitor, 3-nitroproprionic acid (3-NPA), kills the striatal neurons susceptible in Huntington's disease. The complex I inhibitor N-methyl-4-phenylpyridium (MPP(+)) and 6-hydroxydopamine (6-OHDA) are used to model Parkinson's disease. Zinc (Zn(2+)) accumulates after 3-NPA, 6-OHDA and MPP(+) in situ or in vivo. OBJECTIVE: We will investigate the role of Zn(2+) neurotoxicity in 3-NPA, 6-OHDA and MPP(+). METHODS: Murine striatal/midbrain tyrosine hydroxylase positive, or near-pure cortical neuronal cultures, or animals were exposed to 3-NPA or MPP(+) and 6-OHDA with or without neuroprotective compounds. Intracellular zinc ([Zn(2+)](i)), nicotinamide adenine dinucleotide (NAD(+)), NADH, glycolytic intermediates and neurotoxicity were measured. RESULTS: We showed that compounds or genetics which restore NAD(+) and attenuate Zn(2+) neurotoxicity (pyruvate, nicotinamide, NAD(+), increased NAD(+) synthesis, sirtuin inhibition or Zn(2+) chelation) attenuated the neuronal death induced by these toxins. The increase in [Zn(2+)](i) preceded a reduction in the NAD(+)/NADH ratio that caused a reversible glycolytic inhibition. Pyruvate, nicotinamide and NAD(+) reversed the reductions in the NAD(+)/NADH ratio, glycolysis and neuronal death after challenge with 3-NPA, 6-OHDA or MPP(+), as was previously shown for exogenous Zn(2+). To test efficacy in vivo, we injected 3-NPA into the striatum of rats and systemically into mice, with or without pyruvate. We observed early striatal Zn(2+) fluorescence, and pyruvate significantly attenuated the 3-NPA-induced lesion and restored behavioral scores. CONCLUSIONS: Together, these studies suggest that Zn(2+) accumulation caused by MPP(+) and 3-NPA is a novel preventable mechanism of the resultant neurotoxicity.

Dietary zinc reduction, pyruvate supplementation, or zinc transporter 5 knockout attenuates ß-cell death in nonobese diabetic mice, islets, and insulinoma cells.

Pancreatic zinc (Zn(2+)) concentrations are linked to diabetes and pancreatic dysfunction, but Zn(2+) is also required for insulin processing and packaging. Zn(2+) released with insulin increases ß-cell pancreatic death after streptozotocin toxin exposure in vitro and in vivo. Triosephosphate accumulation, caused by NAD(+) loss and glycolytic enzyme dysfunction, occur in type-1 diabetics (T1DM) and animal models. We previously showed these mechanisms are also involved in Zn(2+) neurotoxicity and are attenuated by nicotinamide- or pyruvate-induced restoration of NAD(+) concentrations, Zn(2+) restriction, or inhibition of Sir2 proteins. We tested the hypothesis that similar Zn(2+)- and NAD(+)-mediated mechanisms are involved in ß-cell toxicity in models of ongoing T1DM using mouse insulinoma cells, islets, and nonobese diabetic (NOD) mice. Zn(2+), streptozotocin, and cytokines caused NAD(+) loss and death in insulinoma cells and islets, which were attenuated by Zn(2+) restriction, pyruvate, nicotinamide, NAD(+), and inhibitors of Sir2 proteins. We measured diabetes incidence and mortality in NOD mice and demonstrated that pyruvate supplementation, or genetic or dietary Zn(2+) reduction, attenuated these measures. T-lymphocyte infiltration, punctate Zn(2+) staining, and ß-cell loss increased with time in islets of NOD mice. Dietary Zn(2+) restriction or Zn(2+) transporter 5 knockout reduced pancreatic Zn(2+) staining and increased ß-cell mass, glucose homeostasis, and survival in NOD mice, whereas Zn(2+) supplementation had the opposite effects. Pancreatic Zn(2+) reduction or NAD(+) restoration (pyruvate or nicotinamide supplementation) are suggested as novel targets for attenuating T1DM.

Serum or target deprivation-induced neuronal death causes oxidative neuronal accumulation of Zn2+ and loss of NAD+.

Trophic deprivation-mediated neuronal death is important during development, after acute brain or nerve trauma, and in neurodegeneration. Serum deprivation (SD) approximates trophic deprivation in vitro, and an in vivo model is provided by neuronal death in the mouse dorsal lateral geniculate nucleus (LGNd) after ablation of the visual cortex (VCA). Oxidant-induced intracellular Zn(2+) release ([Zn(2+) ](i) ) from metallothionein-3 (MT-III), mitochondria or 'protein Zn(2+) ', was implicated in trophic deprivation neurotoxicity. We have previously shown that neurotoxicity of extracellular Zn(2+) required entry, increased [Zn(2+) ](i) , and reduction of NAD(+) and ATP levels causing inhibition of glycolysis and cellular metabolism. Exogenous NAD(+) and sirtuin inhibition attenuated Zn(2+) neurotoxicity. Here we show that: (1) Zn(2+) is released intracellularly after oxidant and SD injuries, and that sensitivity to these injuries is proportional to neuronal Zn(2+) content; (2) NAD(+) loss is involved - restoration of NAD(+) using exogenous NAD(+) , pyruvate or nicotinamide attenuated these injuries, and potentiation of NAD(+) loss potentiated injury; (3) neurons from genetically modified mouse strains which reduce intracellular Zn(2+) content (MT-III knockout), reduce NAD(+) catabolism (PARP-1 knockout) or increase expression of an NAD(+) synthetic enzyme (Wld(s) ) each had attenuated SD and oxidant neurotoxicities; (4) sirtuin inhibitors attenuated and sirtuin activators potentiated these neurotoxicities; (5) visual cortex ablation (VCA) induces Zn(2+) staining and death only in ipsilateral LGNd neurons, and a 1 mg/kg Zn(2+) diet attenuated injury; and finally (6) NAD(+) synthesis and levels are involved given that LGNd neuronal death after VCA was dramatically reduced in Wld(s) animals, and by intraperitoneal pyruvate or nicotinamide. Zn(2+) toxicity is involved in serum and trophic deprivation-induced neuronal death.