Pathogenic mutations in the hydrophobic core of the human prion protein can promote structural instability and misfolding

Transmissible spongiform encephalopathies, or prion diseases, are caused by misfolding and aggregation of the prion protein PrP. These diseases can be hereditary in humans and four of the many disease-associated missense mutants of PrP are in the hydrophobic core: V180I, F198S, V203I and V210I. The T183A mutation is related to the hydrophobic core mutants as it is close to the hydrophobic core and known to cause instability. We have performed extensive molecular dynamics simulations of these five PrP mutants and compared their dynamics and conformations to wild-type PrP. The simulations highlight the changes that occur upon introduction of mutations and help to rationalize experimental findings. Changes can occur around the mutation site, but they can also be propagated over long distances. In particular, the F198S and T183A mutations lead to increased flexibility in parts of the structure that are normally stable, and the short β-sheet moves away from the rest of the protein. Mutations V180I, V210I and, to a lesser extent, V203I cause changes similar to those observed upon lowering the pH, which has been linked to misfolding. Early misfolding is observed in one V180I simulation. Overall, mutations in the hydrophobic core have a significant effect on the dynamics and stability of PrP, including the propensity to misfold, which helps to explain their role in the development of familial prion diseases

The staircase method: integrals for periodic reductions of integrable lattice equations

We show, in full generality, that the staircase method provides integrals for mappings, and correspondences, obtained as traveling wave reductions of (systems of) integrable partial difference equations. We apply the staircase method to a variety of equations, including the Korteweg-De Vries equation, the five-point Bruschi-Calogero-Droghei equation, the QD-algorithm, and the Boussinesq system. We show that, in all these cases, if the staircase method provides r integrals for an n-dimensional mapping, with 2r<n, then one can introduce q<= 2r variables, which reduce the dimension of the mapping from n to q. These dimension-reducing variables are obtained as joint invariants of k-symmetries of the mappings. Our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable. We also study reductions on other quad-graphs than the regular 2D lattice, and we prove linear growth of the multi-valuedness of iterates of high-dimensional correspondences obtained as reductions of the QD-algorithm.Comment: 40 pages, 23 Figure

Involutivity of integrals for sine-Gordon, modified KdV and potential KdV maps

Closed form expressions in terms of multi-sums of products have been given in \cite{Tranclosedform, KRQ} of integrals of sine-Gordon, modified Korteweg-de Vries and potential Korteweg-de Vries maps obtained as so-called $(p,-1)$-traveling wave reductions of the corresponding partial difference equations. We prove the involutivity of these integrals with respect to recently found symplectic structures for those maps. The proof is based on explicit formulae for the Poisson brackets between multi-sums of products.Comment: 24 page

Antimicrobial resistance conferred by OXA-48 β-lactamases:towards a detailed mechanistic understanding

OXA-48-type β-lactamases are now routinely encountered in bacterial infections caused by carbapenem-resistant Enterobacterales. These enzymes are of high and growing clinical significance due to the importance of carbapenems in treatment of health care-associated infections by Gram-negative bacteria, the wide and increasing dissemination of OXA-48 enzymes on plasmids, and the challenges posed by their detection. OXA-48 confers resistance to penicillin (which is efficiently hydrolyzed) and carbapenem antibiotics (which is more slowly broken down). In addition to the parent enzyme, a growing array of variants of OXA-48 is now emerging. The spectrum of activity of these variants varies, with some hydrolyzing expanded-spectrum oxyimino-cephalosporins. The growth in importance and diversity of the OXA-48 group has motivated increasing numbers of studies that aim to elucidate the relationship between structure and specificity and establish the mechanistic basis for β-lactam turnover in this enzyme family. In this review, we collate recently published structural, kinetic, and mechanistic information on the interactions between clinically relevant β-lactam antibiotics and inhibitors and OXA-48 β-lactamases. Collectively, these studies are starting to form a detailed picture of the underlying bases for the differences in β-lactam specificity between OXA-48 variants and the consequent differences in resistance phenotype. We focus specifically on aspects of carbapenemase and cephalosporinase activities of OXA-48 β-lactamases and discuss β-lactamase inhibitor development in this context. Throughout the review, we also outline key open research questions for future investigation