We consider the time-optimal control by magnetic fields of a spin 1/2 particle in a dissipative environment. This system is used as an illustrative example to show the role of singular extremals in the control of quantum systems. We analyze a simple case where the control law is explicitly determined. We experimentally implement the optimal control using techniques of nuclear magnetic resonance. To our knowledge, this is the first experimental demonstration of singular extremals in quantum systems with bounded control amplitudes.

No abstract

SummaryFhuA in the outer membrane of Escherichia coli serves as a transporter for ferrichrome, the antibiotics albomycin and rifamycin CGP4832, colicin M, and as receptor for phages T1, T5 and f80. The previously determined crystal structure reveals that residues 160±714 of the mature protein form a b-barrel that is closed from the periplasmic side by the globular Nproximal fragment, residues 1±159, designated the cork. In this study, deletion of the cork resulted in a stable protein, FhuAD5-160, that was incorporated in the outer membrane. Cells that synthesized FhuAD5-160 displayed a higher sensitivity to large antibiotics such as erythromycin, rifamycin, bacitracin and vancomycin, and grew on maltotetraose and maltopentaose in the absence of LamB. Higher concentrations of ferrichrome supported growth of a tonB mutant that synthesized FhuAD5-160. These results demonstrate non-speci®c diffusion of compounds across the outer membrane of cells that synthesize FhuAD5-160. However, growth of a FhuAD5-160 tonB wildtype strain occurred at low ferrichrome concentrations, and ferrichrome was transported at about 45% of the FhuA wild-type rate despite the lack of ferrichrome binding sites provided by the cork. FhuAD5-160 conferred sensitivity to the phages and colicin M at levels similar to that of wild-type FhuA, and to albomycin and rifamycin CGP 4832. The activity of FhuAD5-160 depended on TonB, although the mutant lacks the TonB box (residues 7±11) previously implicated in the interaction of FhuA with TonB. CCCP inhibited tonB-dependent transport of ferrichrome through FhuAD5-160. FhuAD5-160 still functions as a speci®c transporter, and sites in addition to the TonB box are involved in the TonB-mediated response of FhuA to the proton gradient of the cytoplasmic membrane. It is proposed that TonB interacts with the TonB box

The FhuA outer membrane protein of Escherichia coli actively transports ferrichrome, albomycin, and rifamycin CGP 4832, and confers sensitivity to microcin J25, colicin M, and the phages T1, T5, and 80. Guided by the FhuA crystal structure and derived predictions on how FhuA might function, mutants were isolated in the cork domain (residues 1 to 160) and in the ␤-barrel domain (residues 161 to 714). Deletion of the TonB box (residues 7 to 11) completely inactivated all TonB-dependent functions of FhuA. Fixation of the cork to turn 7 of the barrel through a disulfide bridge between introduced C27 and C533 residues abolished ferrichrome transport, which was restored by reduction of the disulfide bond. Deletion of residues 24 to 31, including the switch helix (residues 24 to 29), which upon binding of ferrichrome to FhuA undergoes a large structural transition (17 Å) and exposes the N terminus of FhuA (TonB box) to the periplasm, reduced FhuA transport activity (79% of the wild-type activity) but conferred full sensitivity to colicin M and the phages. Duplication of residues 23 to 30 or deletion of residues 13 to 20 resulted in FhuA derivatives with properties similar to those of FhuA with a deletion of residues 24 to 31. However, a frameshift mutation that changed QSEA at positions 18 to 21 to KKAP abolished almost completely most of FhuA's activities. The conserved residues R93 and R133 among energy-coupled outer membrane transporters are thought to fix the cork to the ␤-barrel by forming salt bridges to the conserved residues E522 and E571 of the ␤-barrel. Proteins with the E522R and E571R mutations were inactive, but inactivity was not caused by repulsion of R93 by R522 and R571 and of R133 by R571. Point mutations in the cork at sites that move or do not move upon the binding of ferrichrome had no effect or conferred only slightly reduced activities. It is concluded that the TonB box is essential for FhuA activity. The TonB box region has to be flexible, but its distance from the cork domain can greatly vary. The removal of salt bridges between the cork and the barrel affects the structure but not the function of FhuA.

Bacteria solve the iron supply problem caused by the insolubility of Fe 3+ by synthesizing iron-complexing compounds, called siderophores, and by using iron sources of their hosts, such as heme and iron bound to transferrin and lactoferrin. Escherichia coli, as an example of Gram-negative bacteria, forms sophisticated Fe 3+^s iderophore and heme transport systems across the outer membrane. The crystal structures of three outer membrane transport proteins now allow insights into energy-coupled transport mechanisms. These involve large longrange structural transitions in the transport proteins in response to substrate binding, including substrate gating. Energy is provided by the proton motive force of the cytoplasmic membrane through the activity of a protein complex that is inserted in the cytoplasmic membrane and that contacts the outer membrane transporters. Certain transport proteins also function in siderophore-mediated signaling cascades that start at the cell surface and £ow to the cytoplasm to initiate transcription of genes encoding proteins for transport and siderophore biosynthesis. ß