Set-valued Markov chains and negative semitrajectories of discretized dynamical systems

Computer simulation of dynamical systems involves a phase space which is the finite set of machine arithmetic. Rounding state values of the continuous system to this grid yields a spatially discrete dynamical system, often with different dynamical behaviour. Discretization of an invertible smooth system gives a system with set-valued negative semitrajectories. As the grid is refined, asymptotic behaviour of the semitrajectories follows probabilistic laws which correspond to a set-valued Markov chain, whose transition probabilities can be explicitly calculated. The results are illustrated for two-dimensional dynamical systems obtained by discretization of fractional linear transformations of the unit disc in the complex plane.

Catalytically active Dengue virus NS3 protease forms aggregates that are separable by size exclusion chromatography

An active form of the Dengue virus protease NS3 (CF40.Gly.NS3pro) was expressed in Escherichia coli. This construct consists of a critical 40 amino acid cofactor domain from NS2B fused to the N-terminal 184 amino acid protease domain of NS3 via a flexible, covalent linker (Gly(4)SerGly(4)). The recombinantly produced protein is soluble and has a hexa-histidine tag engineered at the N-terminus for ease of purification using metal affinity chromatography. However, the presence of lower molecular weight impurities after affinity chromatography indicated the need for additional purification steps. The consistent appearance of these impurities suggested that they may be the products of proteolysis and/or auto-proteolysis. The latter possibility was subsequently excluded by the observation of the same impurities in a purified, catalytically inactive form of the recombinant protease (CF40.Gly.NS3pro.SA). Further analysis indicated that these impurities may represent premature translation termination products. Regardless of their origin, they were shown to form various sized aggregates with full-length CF40.Gly.NS3pro that can be separated by size exclusion chromatography, yielding fractions of active protease of sufficient purity for crystallisation trials. The ultimate goal of these studies is to obtain a crystal structure of a catalytically active form of the Dengue virus NS3 protease for structure-based drug design. (C) 2002 Elsevier Science (USA). All rights reserved.

Outcome variables for osteoarthritis clinical trials: the OMERACT-OARSI set of responder criteria

Improvement in analysis and reporting results of osteoarthritis (OA) clinical trials has been recently obtained because of harmonization and standardization of the selection of outcome variables (OMERACT 3 and OARSI). Moreover, OARSI has recently proposed the OARSI responder criteria. This composite index permits presentation of results of symptom modifying clinical trials in OA based on individual patient responses (responder yes/no). The 2 organizations (OMERACT and OARSI) established. a task force aimed at evaluating: (1) the variability of observed placebo and active treatment effects using the OARSI responder criteria; and (2) the possibility of proposing a simplified set of criteria. The conclusions of the task force were presented and discussed during the OMERACT 6 conference, where a simplified set of responder criteria (OMERACT-OARSI set of criteria) was proposed.