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Abstract In this paper we consider the matrix nonautonomous semidiscrete (or lattice) equation d d t U n = (2 n − 1) (U n + 1 − U n − 1) − 1 , as well as the scalar case thereof. This equation was recently derived in the context of auto-Bäcklund transformations for a matrix partial differential equation. We use asymptotic techniques to reveal a connection between this equation and the matrix (or, as appropriate, scalar) first Painlevé equation. In the matrix case, we also discuss our asymptotic analysis more generally, as well as considering a component-wise approach. In addition, Hamiltonian formulations of the matrix first and second Painlevé equations are given, as well as a discussion of classes of solutions of the matrix second Painlevé equation. Highlights • We derive Hamiltonian formulations for matrix P I & matrix P I I systems of equations. • Asymptotic reductions are used to derive P I from a semidiscrete equation. • Derivation generalized to matrix form using general and component-wise expansions. • Solutions of matrix P I I are elucidated using combinations of auto-Bäcklund Transforms. [ABSTRACT FROM AUTHOR]

Abstract: Oxidative stress adaptation, or hormesis, is an important mechanism by which cells and organisms respond to, and cope with, environmental and physiological shifts in the level of oxidative stress. Most studies of oxidative stress adaption have been limited to adaptation induced by acute stress. In contrast, many if not most environmental and physiological stresses are either repeated or chronic. In this study we find that both cultured mammalian cells and the fruit fly Drosophila melanogaster are capable of adapting to chronic or repeated stress by upregulating protective systems, such as their proteasomal proteolytic capacity to remove oxidized proteins. Repeated stress adaptation resulted in significant extension of adaptive responses. Repeated stresses must occur at sufficiently long intervals, however (12-h or more for MEF cells and 7 days or more for flies), for adaptation to be successful, and the levels of both repeated and chronic stress must be lower than is optimal for adaptation to acute stress. Regrettably, regimens of adaptation to both repeated and chronic stress that were successful for short-term survival in Drosophila nevertheless also caused significant reductions in life span for the flies. Thus, although both repeated and chronic stress can be tolerated, they may result in a shorter life. [Copyright &y& Elsevier]

Abstract: In a recent paper we gave a technique for identifying special solutions of hierarchies of ordinary differential equations (ODEs) and difference equations. In particular, we considered the phenomenon whereby members of one Painlevé hierarchy define solutions of members of a different Painlevé hierarchy, where both are related to the same (at least) bi-Hamiltonian completely integrable partial differential equation (PDE) or lattice hierarchy; we also considered the question of special integrals of further related Painlevé hierarchies. Here we consider three extensions of this approach. First of all, we consider the case of ODE hierarchies where the corresponding PDE hierarchy is only mono-Hamiltonian. Second, we show that our approach can also be extended in order to provide special solutions of PDEs. Our third extension is to the non-Hamiltonian case, where we consider hierarchies of ODEs related to the Burgers hierarchy. We also make the observation that our results can be phrased quite generally, and the systems of equations dealt with do not in fact need to be integrable. [Copyright &y& Elsevier]

The ability to adapt to acute oxidative stress (e.g. H2O2, peroxynitrite, menadione, and paraquat) through transient alterations in gene expression is an important component of cellular defense mechanisms. We show that such adaptation includes Nrf2-dependent increases in cellular capacity to degrade oxidized proteins that are attributable to increased expression of the 20 S proteasome and the Pa28αβ (11 S) proteasome regulator. Increased cellular levels of Nrf2, translocation of Nrf2 from the cytoplasm to the nucleus, and increased binding of Nrf2 to antioxidant response elements (AREs) or electrophile response elements (EpREs) in the 5'-untranslated region of the proteasome β5 subunit gene (demonstrated by chromatin immunoprecipitation (or ChIP) assay) are shown to be necessary requirements for increased proteasome/Pa28αβ levels, and for maximal increases in proteolytic capacity and stress resistance; Nrf2 siRNA and the Nrf2 inhibitor retinoic acid both block these adaptive changes and the Nrf2 inducers DL-sulforaphane, lipoic acid, and curcumin all replicate them without oxidant exposure. The immunoproteasome is also induced during oxidative stress adaptation, contributing to overall capacity to degrade oxidized proteins and stress resistance. Two of the three immunoproteasome subunit genes, however, contain no ARE/EpRE elements, and Nrf2 inducers, inhibitors, and siRNA all have minimal effects on immunoproteasome expression during adaptation to oxidative stress. Thus, immunoproteasome appears to be (at most) minimally regulated by the Nrf2 signal transduction pathway. [ABSTRACT FROM AUTHOR]

Abstract: Proteins are sensitive to oxidation, and oxidized proteins are excellent substrates for degradation by proteolytic enzymes such as the proteasome and the mitochondrial Lon protease. Protein labeling is required for studies of protein turnover. Unfortunately, most labeling techniques involve 3H or 14C methylation, which is expensive, exposes researchers to radioactivity, generates large amounts of radioactive waste, and allows only single-point assays because samples require acid precipitation. Alternative labeling methods have largely proven unsuitable, either because the probe itself is modified by the oxidant(s) being studied or because the alternative labeling techniques are too complex or too costly for routine use. What is needed is a simple, quick, and cheap labeling technique that uses a non-radioactive marker, binds strongly to proteins, is resistant to oxidative modification, and emits a strong signal. We have devised a new reductive method for labeling free carboxyl groups of proteins with the small fluorophore 7-amino-4-methycoumarin (AMC). When bound to target proteins, AMC fluoresces very weakly but when AMC is released by proteinases, proteases, or peptidases, it fluoresces strongly. Thus, without acid precipitation, the proteolysis of any target protein can be studied continuously, in multiwell plates. In direct comparisons, 3H-labeled proteins and AMC-labeled proteins exhibited essentially identical degradation patterns during incubation with trypsin, cell extracts, and purified proteasome. AMC-labeled proteins are well suited to studying increased proteolytic susceptibility after protein modification, because the AMC–protein bond is resistant to oxidizing agents such as hydrogen peroxide and peroxynitrite and is stable over time and to extremes of pH, temperature (even boiling), freeze–thaw, mercaptoethanol, and methanol. [Copyright &y& Elsevier]

Abstract: In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula. [Copyright &y& Elsevier]

It is well-known that the first Painleve´ equation arises as a coalescence limit of each of the other five Painleve´ equations. This result is important because it shows that, since the solution of the first Painleve´ equation cannot be expressed in terms of known functions, then neither can the solutions of the other five Painleve´ equations (except possibly for special values of their parameters). Here we derive analogous results for three recently derived higher order ordinary differential equations believed to define new transcendental functions. We show that each of the equations considered has as a coalescence limit a member of the first Painleve´ hierarchy. We thus reduce the problem of showing that the solutions of these three cannot be expressed in terms of known functions to that of showing that the same is true for the corresponding first Painleve´ equations. This represents the first extension of coalescence results for the Painleve´ equations to their higher order analogues. [Copyright &y& Elsevier]

With this volume, "Knowledge and Society" changes its editors, its subtitle and, to some extent, its general focus. Previously edited by Henrika Kuklick at the University of Pennsylvania, the series is now based in the Department of Sociology at the University of Illinois, and edited by Lowell Hargens, Robert Alun Jones and Andrew Pickering. The subtitle has been altered to refer more specifically to the sociology of science, and the focus of the series will naturally reflect the interests and commitments of its new editors, including the sociological study of scientific communities, the sociology of scientific knowledge and practice, and the history and sociology of the social sciences.

The existence of auto-Bäcklund transformations is generally understood as being a characteristic feature of integrable equations. The nature of such transformations changes depending on whether the equation under consideration is a partial differential equation (PDE) or an ordinary differential equation (ODE). We show in this paper how certain properties of completely integrable systems such as Hamiltonian structures and Miura maps can be used in order to derive ODE-type auto-Bäcklund transformations for a certain class of PDEs. We apply this method to two integrable equations which are nonisospectral extensions of the integrated modified inverse Korteweg–de Vries equation and of the integrated modified inverse Broer–Kaup system, and show that ODE-type auto-Bäcklund transformations exist for both of them. These auto-Bäcklund transformations involve shifts on the functions appearing as coefficients in the equations and they mimic the auto-Bäcklund transformations for the second and fourth Painlevé equations. We believe these ODE-type auto-Bäckund transformations for PDEs to be new. Our derivation is in fact valid for a wide class of equations that includes both integrable and nonintegrable ODEs and PDEs. [Copyright &y& Elsevier]

Abstract: We report an entirely new role for the HSP70 chaperone in dissociating 26S proteasome complexes (into free 20S proteasomes and bound 19S regulators), preserving 19S regulators, and reconstituting 26S proteasomes in the first 1–3h after mild oxidative stress. These responses, coupled with direct 20S proteasome activation by poly(ADP ribose) polymerase in the nucleus and by PA28αβ in the cytoplasm, instantly provide cells with increased capacity to degrade oxidatively damaged proteins and to survive the initial effects of stress exposure. Subsequent adaptive (hormetic) processes (3–24h after stress exposure), mediated by several signal transduction pathways and involving increased transcription/translation of 20S proteasomes, immunoproteasomes, and PA28αβ, abrogate the need for 26S proteasome dissociation. During this adaptive period, HSP70 releases its bound 19S regulators, 26S proteasomes are reconstituted, and ATP-stimulated proteolysis is restored. The 26S proteasome-dependent, and ATP-stimulated, turnover of ubiquitinylated proteins is essential for normal cell metabolism, and its restoration is required for successful stress adaptation. [Copyright &y& Elsevier]