Search

The proteasome is responsible for selective degradation of proteins. It exists in mammalian cells under four main subtypes, which differ by the combination of their catalytic subunits: the standard proteasome (β1–β2–β5), the immunoproteasome (β1i–β2i–β5i) and the two intermediate proteasomes (β1–β2–β5i and β1i–β2–β5i). The efficiency of the four proteasome subtypes to degrade ubiquitinated or oxidized proteins remains unclear. Using cells expressing exclusively one proteasome subtype, we observed that ubiquitinated p21 and c-­myc were degraded at similar rates, indicating that the four 26S proteasomes degrade ubiquitinated proteins equally well. Under oxidative stress, we observed a partial dissociation of 26S into 20S proteasomes, which can degrade non-ubiquitinated oxidized proteins. Oxidized calmodulin and hemoglobin were best degraded in vitro by the three β5i-containing 20S proteasomes, while their native forms were not degraded. Circular dichroism analyses indicated that ubiquitin-independent recognition of oxidized proteins by 20S proteasomes was triggered by the disruption of their structure. Accordingly, β5i-containing 20S proteasomes degraded unoxidized naturally disordered protein tau, while 26S proteasomes did not. Our results suggest that the three β5i-containing 20S proteasomes, namely the immunoproteasome and the two intermediate proteasomes, might help cells to eliminate proteins containing disordered domains, including those induced by oxidative stress.

The interaction of insulin-degrading enzyme (IDE) with the main intracellular proteasome assemblies (i.e, 30S, 26S and 20S) was analyzed by enzymatic activity, mass spectrometry and native gel electrophoresis. IDE was mainly detected in association with assemblies with at least one free 20S end and biochemical investigations suggest that IDE competes with the 19S in vitro. IDE directly binds the 20S and affects its proteolytic activities in a bimodal fashion, very similar in human and yeast 20S, inhibiting at (IDE) 30 nM and activating at (IDE) 30 nM. Only an activating effect is observed in a yeast mutant locked in the "open" conformation (i.e., the alpha-3 Delta N 20S), envisaging a possible role of IDE as modulator of the 20S "open"-"closed" allosteric equilibrium. Protein-protein docking in silico proposes that the interaction between IDE and the 20S could involve the C-term helix of the 20S alpha-3 subunit which regulates the gate opening of the 20S.

International audience; In the present paper we prove a functional inequality of the Poincaré--Wirtinger type on some particular domains with a precise estimate of the constant as a function of the geometry of the domain. This type of inequality arises, for instance, in the analysis of finite volume (FV) numerical methods, which was our main motivation. As an illustration, our result let us prove uniform a priori bounds for the FV approximate solutions of the heat equation with Ventcell boundary conditions in the natural energy space constituted by functions in $H^1(\Omega)$ whose trace belongs to $H^1(\partial \Omega)$. The main difficulty here comes from the fact that the approximation is performed on non-polygonal control volumes since the domain is itself non polygonal.

In a recent paper we proved the non occurrence of the Lavrentiev gap between Lipschitz and Sobolev functions for functionals of the form $$\text {I}(u)={\int }_{\Omega }F(u,\nabla u) u|_{\partial {\Omega }} = \phi $$ when $\phi :\mathbb {R}^{n} \rightarrow \mathbb {R}$ is Lipschitz, Ω belongs to a wide class of open bounded sets in $\mathbb {R}^{n}$ containing Lipschitz domains, and the lagrangian F is assumed to be either convex in both variables or a sum of functions F(s, ξ) = a(s)g(ξ) + b(s) with g convex and s ↦ a(s)g(0) + b(s) satisfying a non oscillatory condition at infinity. In this survey we discuss the state of the art on the subject and give a self-contained proof of our result in the simpler case of a (strongly) star-shaped domain, for a lagrangian depending just on the gradient; in particular we point out what are the main difficulties to overcome in order to get the result without assuming growth conditions. We also formulate, and prove, a characterization of a useful class of star-shaped domains in terms of the radii function.

We consider the equation \(\text{ div}\,\mathbb{Y }=f\), with \(f\) a zero average function on the torus \(\mathbb{T }^d\). In their seminal paper, Bourgain and Brezis [J Am Math Soc 16(2):393–426, 2003 (electronic)] proved the existence of a solution \(\mathbb{Y }\in W^{1,d}\cap L^\infty \) for a datum \(f\in L^d\). We extend their result to the critical Sobolev spaces \(W^{s,p}\) with \((s+1)p=d\) and \(p\ge 2\). More generally, we prove a similar result in the scale of Triebel–Lizorkin spaces. We also consider the equation \(\text{ div} \,\mathbb{Y }=f\) in a bounded domain \(\varOmega \) subject to zero Dirichlet boundary condition.

We study the problem of minimizing \({\int_{\Omega} L(x,u(x),Du(x))\,{\rm d}x}\) over the functions \({u\in W^{1,p}(\Omega)}\) that assume given boundary values \({\phi}\) on ∂Ω. We assume that L(x, u, Du) = F(Du) + G(x, u) and that F is convex. We prove that if \({\phi}\) is continuous and Ω is convex, then any minimum u is continuous on the closure of Ω. When Ω is not convex, the result holds true if F(Du) = f(|Du|). Moreover, if \({\phi}\) is Lipschitz continuous, then u is Holder continuous.

α-Transglucosidase from Talaromycesduponti was used to synthesize different alkyl-α-d-glucosides from α(1-4) linked carbohydrate donors. The enzymatic preparation, purified by a single step, consisting of hydrophobic interaction chromatography, was sufficiently pure for very stereospecific synthesis to be achieved. Biphasic and homogeneous organic media could be compared for such purposes. Yields appeared to be two- to threefold higher in low-water biphasic media. High concentrations of the glucosyl donor were present in the aqueous phase, while water-immiscible alcohols were used as glucosyl acceptors. The high efficiency of the method was attributed to the shift of the thermodynamic equilibrium thanks to the extraction of the product from the aqueous phase, where the reaction occurs, into the organic phase. Operated in a continuous biphasic reactor, T. dupontiα-transglucosidase showed a good thermostability with a half-life of 23 days at 30 °C.