On the controllability of distributed systems

To “control” a system is to make it behave (hopefully) according to our “wishes,” in a way compatible with safety and ethics, at the least possible cost. The systems considered here are distributed—i.e., governed (modeled) by partial differential equations (PDEs) of evolution. Our “wish” is to drive the system in a given time, by an adequate choice of the controls, from a given initial state to a final given state, which is the target. If this can be achieved (respectively, if we can reach any “neighborhood” of the target) the system, with the controls at our disposal, is exactly (respectively, approximately) controllable. A very general (and fuzzy) idea is that the more a system is “unstable” (chaotic, turbulent) the “simplest,” or the “cheapest,” it is to achieve exact or approximate controllability. When the PDEs are the Navier–Stokes equations, it leads to conjectures, which are presented and explained. Recent results, reported in this expository paper, essentially prove the conjectures in two space dimensions. In three space dimensions, a large number of new questions arise, some new results support (without proving) the conjectures, such as generic controllability and cases of decrease of cost of control when the instability increases. Short comments are made on models arising in climatology, thermoelasticity, non-Newtonian fluids, and molecular chemistry. The Introduction of the paper and the first part of all sections are not technical. Many open questions are mentioned in the text.

On the acidity and reactivity of HNO in aqueous solution and biological systems

The gas phase and aqueous thermochemistry and reactivity of nitroxyl (nitrosyl hydride, HNO) were elucidated with multiconfigurational self-consistent field and hybrid density functional theory calculations and continuum solvation methods. The pKa of HNO is predicted to be 7.2 ± 1.0, considerably different from the value of 4.7 reported from pulse radiolysis experiments. The ground-state triplet nature of NO− affects the rates of acid-base chemistry of the HNO/NO− couple. HNO is highly reactive toward dimerization and addition of soft nucleophiles but is predicted to undergo negligible hydration (Keq = 6.9 × 10−5). HNO is predicted to exist as a discrete species in solution and is a viable participant in the chemical biology of nitric oxide and derivatives.

Selenoprotein oxidoreductase with specificity for thioredoxin and glutathione systems

Thioredoxin (Trx) and glutathione (GSH) systems are considered to be two major redox systems in animal cells. They are reduced by NADPH via Trx reductase (TR) or oxidized GSH (GSSG) reductase and further supply electrons for deoxyribonucleotide synthesis, antioxidant defense, and redox regulation of signal transduction, transcription, cell growth, and apoptosis. We cloned and characterized a pyridine nucleotide disulfide oxidoreductase, Trx and GSSG reductase (TGR), that exhibits specificity for both redox systems. This enzyme contains a selenocysteine residue encoded by the TGA codon. TGR can reduce Trx, GSSG, and a GSH-linked disulfide in in vitro assays. This unusual substrate specificity is achieved by an evolutionary conserved fusion of the TR and glutaredoxin domains. These observations, together with the biochemical probing and molecular modeling of the TGR structure, suggest a mechanism whereby the C-terminal selenotetrapeptide serves a role of a protein-linked GSSG and shuttles electrons from the disulfide center within the TR domain to either the glutaredoxin domain or Trx.