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In this paper some of the relationships between optimal control and statistics are examined. We produce generalized, smoothing splines by solving an optimal control problem for linear control systems, minimizing the 2 -norm of the control signal, while driving the scalar output of the control system close to given, prespecified interpolation points. We then prove a convergence result for the smoothing splines, using results from the theory of numerical quadrature. Finally, we show, in simulations, that our approach works in practice as well as in theory.

The budC gene coding for a new meso-2,3-butanediol dehydrogenase (BDH) from Serratia marcescens H30 was cloned and expressed in Escherichia coli BL21(DE3), purified, and characterized for its properties. The recombinant BDH with a molecular weight of 27.4 kDa exhibited a reversible transformation between acetoin and 2,3-butanediol. In the presence of NADH, BDH could catalyze the reduction of diacetyl and (3R)-acetoin to (3S)-acetoin and meso-2,3-butanediol, respectively, while (3S)-acetoin as a substrate could be further transformed into (2S, 3S)-2,3-butanediol at pH 9.0. For diol oxidation reactions, (3R)-acetoin and (3S)-acetoin were obtained when meso-2,3-butanediol and (2S,3S)-2,3-butanediol were used as the substrates with BDH and NAD(+). (2R,3R)-2,3-butanediol was not a substrate for the BDH at all. The low K m value (4.1 mM) in meso-2,3-butanediol oxidation reaction and no activity for diacetyl, acetoin, and 2,3-butanediol as the substrates with NADP(+)/NADPH suggested that the budC gene product belongs to a NAD(H)-dependent meso-2,3-BDH. Maximum activities for diacetyl and (3S/3R)-acetoin reduction were observed at pH 8.0 and pH 5.0 while for meso-2,3-butanediol oxidation it was pH 8.0. However, the optimum temperature for oxidation and reduction reactions was about 40 °C. In addition, the BDH activity for meso-2,3-butanediol oxidation was enhanced in the presence of Fe(2+) and for diacetyl and (3S/3R)-acetoin reduction in the presence of Mg(2+) and Mn(2+), while several metal ions inhibited its activity, particularly Fe(3+) for reduction of diacetyl and acetoin. Sequence analysis showed that the BDH from S. marcescens H30 possessed two conserved sequences including the coenzyme binding motif (GxxxGxG) and the active-site motif (YxxxK), which are present in the short-chain dehydrogenase/reductase superfamily.

Quorum sensing (QS), or the control of gene expression in response to cell density, is used by both gram-negative and gram-positive bacteria to regulate a variety of physiological functions. Increasing evidence implies that certain eukaryotes produce QS-inhibitory compounds. In this work, we tested Tremella fuciformis for their ability to inhibit QS-regulated behaviors. T. fuciformis fruiting bodies were dried and extracted using 75% (v/v) aqueous methanol. The crude extract was redissolved in appropriate concentrations of dimethyl sulfoxide (DMSO), sterilized by filtration through a 0.45-microm membrane filter and added to Chromobacterium violaceum CV026 cultures, which was used to monitor QS inhibition. Inhibitory activity was measured by quantifying violacein production using a microplate reader. The results have revealed that the DMSO-soluble compounds extracted from T. fuciformis could inhibit violacein production, a QS-regulated behavior in C. violaceum. The results suggest an attractive tool to control and handle detrimental infections caused by human, animal, and plant pathogens. Further studies are required to isolate specific substances from T. fuciformis extract acting as QS inhibitors.

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