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.

A global two component signal transduction system that integrates the control of photosynthesis, carbon dioxide assimilation, and nitrogen fixation

Photosynthesis, biological nitrogen fixation, and carbon dioxide assimilation are three fundamental biological processes catalyzed by photosynthetic bacteria. In the present study, it is shown that mutant strains of the nonsulfur purple photosynthetic bacteria Rhodospirillum rubrum and Rhodobacter sphaeroides, containing a blockage in the primary CO2 assimilatory pathway, derepress the synthesis of components of the nitrogen fixation enzyme complex and abrogate normal control mechanisms. The absence of the Calvin–Benson–Bassham (CBB) reductive pentose phosphate CO2 fixation pathway removes an important route for the dissipation of excess reducing power. Thus, the mutant strains develop alternative means to remove these reducing equivalents, resulting in the synthesis of large amounts of nitrogenase even in the presence of ammonia. This response is under the control of a global two-component signal transduction system previously found to regulate photosystem biosynthesis and the transcription of genes required for CO2 fixation through the CBB pathway and alternative routes. In addition, this two-component system directly controls the ability of these bacteria to grow under nitrogen-fixing conditions. These results indicate that there is a molecular link between the CBB and nitrogen fixation process, allowing the cell to overcome powerful control mechanisms to remove excess reducing power generated by photosynthesis and carbon metabolism. Furthermore, these results suggest that the two-component system integrates the expression of genes required for the three processes of photosynthesis, nitrogen fixation, and carbon dioxide fixation.