Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type

We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system

From Classical Trajectories to Quantum Commutation Relations

In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian description because of the Noether theorem and because they are the starting point for the quantization. As a matter of fact many ambiguities arise in each step of such a reconstruction which must be solved by the ingenuity of the theoretician. In the present work we describe geometric structures emerging in Lagrangian, Hamiltonian and Quantum description of a dynamical system underlining how many of them are not really fixed only by the trajectories observed by the experimentalist.Comment: 25 pages. Comments are welcome

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

Fractional Dynamics of Relativistic Particle

Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to a non-potential four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u_{\mu} u^{\mu}+c^2=0, where c is a speed of light in vacuum. In the general case, the fractional dynamics of relativistic particle is described as non-Hamiltonian and dissipative. Conditions for fractional relativistic particle to be a Hamiltonian system are considered

Expression of Nestin by Neural Cells in the Adult Rat and Human Brain

Neurons and glial cells in the developing brain arise from neural progenitor cells (NPCs). Nestin, an intermediate filament protein, is thought to be expressed exclusively by NPCs in the normal brain, and is replaced by the expression of proteins specific for neurons or glia in differentiated cells. Nestin expressing NPCs are found in the adult brain in the subventricular zone (SVZ) of the lateral ventricle and the subgranular zone (SGZ) of the dentate gyrus. While significant attention has been paid to studying NPCs in the SVZ and SGZ in the adult brain, relatively little attention has been paid to determining whether nestin-expressing neural cells (NECs) exist outside of the SVZ and SGZ. We therefore stained sections immunocytochemically from the adult rat and human brain for NECs, observed four distinct classes of these cells, and present here the first comprehensive report on these cells. Class I cells are among the smallest neural cells in the brain and are widely distributed. Class II cells are located in the walls of the aqueduct and third ventricle. Class IV cells are found throughout the forebrain and typically reside immediately adjacent to a neuron. Class III cells are observed only in the basal forebrain and closely related areas such as the hippocampus and corpus striatum. Class III cells resemble neurons structurally and co-express markers associated exclusively with neurons. Cell proliferation experiments demonstrate that Class III cells are not recently born. Instead, these cells appear to be mature neurons in the adult brain that express nestin. Neurons that express nestin are not supposed to exist in the brain at any stage of development. That these unique neurons are found only in brain regions involved in higher order cognitive function suggests that they may be remodeling their cytoskeleton in supporting the neural plasticity required for these functions

Global profiling of co- and post-translationally N-myristoylated proteomes in human cells

Protein N-myristoylation is a ubiquitous co- and post-translational modification that has been implicated in the development and progression of a range of human diseases. Here, we report the global N-myristoylated proteome in human cells determined using quantitative chemical proteomics combined with potent and specific human N-myristoyltransferase (NMT) inhibition. Global quantification of N-myristoylation during normal growth or apoptosis allowed the identification of >100 N-myristoylated proteins, >95% of which are identified for the first time at endogenous levels. Furthermore, quantitative dose response for inhibition of N-myristoylation is determined for >70 substrates simultaneously across the proteome. Small-molecule inhibition through a conserved substrate-binding pocket is also demonstrated by solving the crystal structures of inhibitor-bound NMT1 and NMT2. The presented data substantially expand the known repertoire of co- and post-translational N-myristoylation in addition to validating tools for the pharmacological inhibition of NMT in living cells

Epigallocatechin 3-gallate suppresses interleukin-1β-induced inflammatory responses in intervertebral disc cells in vitro and reduces radiculopathic pain in rats

Intervertebral disc (IVD) disease, which is characterised by age-related changes in the adult disc, is the most common cause of disc failure and low back pain. The purpose of this study was to analyse the potential of the biologically active polyphenol epigallocatechin 3-gallate (EGCG) for the treatment of painful IVD disease by identifying and explaining its anti-inflammatory and anti-catabolic activity. Human IVD cells were isolated from patients undergoing surgery due to degenerative disc disease (n = 34) and cultured in 2D or 3D. An inflammatory response was activated by IL-1β, EGCG was added, and the expression/activity of inflammatory mediators and pathways was measured by qRT-PCR, western blotting, ELISA, immunofluorescence and transcription factor assay. The small molecule inhibitor SB203580 was used to investigate the involvement of the p38 pathway in the observed effects. The analgesic properties of EGCG were analysed by the von Frey filament test in Sprague-Dawley rats (n = 60). EGCG significantly inhibited the expression of pro-inflammatory mediators and matrix metalloproteinases in vitro, as well as radiculopathic pain in vivo, most probably by modulation of the activity of IRAK-1 and its downstream effectors p38, JNK and NF-κB

An inflammatory nucleus pulposus tissue culture model to test molecular regenerative therapies: validation with Epigallocatechin 3-Gallate

Organ cultures are practical tools to investigate regenerative strategies for the intervertebral disc. However, most existing organ culture systems induce severe tissue degradation with only limited representation of the in vivo processes. The objective of this study was to develop a space- and cost-efficient tissue culture model, which represents degenerative processes of the nucleus pulposus (NP). Intact bovine NPs were cultured in a previously developed system using Dyneema jackets. Degenerative changes in the NP tissue were induced either by the direct injection of chondroitinase ABC (1-20 U/mL) or by the diffusion of interleukin-1 beta (IL-1β) and tumor necrosis factor alpha (TNF-α) (both 100 ng/mL) from the culture media. Extracellular matrix composition (collagens, proteoglycans, water, and DNA) and the expression of inflammatory and catabolic genes were analyzed. The anti-inflammatory and anti-catabolic compound epigallocatechin 3-gallate (EGCG, 10 µM) was employed to assess the relevance of the degenerative NP model. Although a single injection of chondroitinase ABC reduced the proteoglycan content in the NPs, it did not activate cellular responses. On the other hand, IL-1β and TNF-α significantly increased the mRNA expression of inflammatory mediators IL-6, IL-8, inducible nitric oxide synthase (iNOS), prostaglandin-endoperoxide synthase 2 (PTGS2) and matrix metalloproteinases (MMP1, MMP3, and MMP13). The cytokine-induced gene expression in the NPs was ameliorated with EGCG. This study provides a proof of concept that inflammatory NP cultures, with appropriate containment, can be useful for the discovery and evaluation of molecular therapeutic strategies against early degenerative disc disease