Metabolic Engineering of Mannitol Production in Lactococcus lactis: Influence of Overexpression of Mannitol 1-Phosphate Dehydrogenase in Different Genetic Backgrounds

To obtain a mannitol-producing Lactococcus lactis strain, the mannitol 1-phosphate dehydrogenase gene (mtlD) from Lactobacillus plantarum was overexpressed in a wild-type strain, a lactate dehydrogenase(LDH)-deficient strain, and a strain with reduced phosphofructokinase activity. High-performance liquid chromatography and ¹³C nuclear magnetic resonance analysis revealed that small amounts (<1%) of mannitol were formed by growing cells of mtlD-overexpressing LDH-deficient and phosphofructokinase-reduced strains, whereas resting cells of the LDH-deficient transformant converted 25% of glucose into mannitol. Moreover, the formed mannitol was not reutilized upon glucose depletion. Of the metabolic-engineering strategies investigated in this work, mtlD-overexpressing LDH-deficient L. lactis seemed to be the most promising strain for mannitol production.     

Overproduction of heterologous mannitol 1-phosphatase: a key factor for engineering mannitol production by Lactococcus lactis

To achieve high mannitol production by Lactococcus lactis, the mannitol 1-phosphatase gene of Eimeria tenella and the mannitol 1-phosphate dehydrogenase gene mtlD of Lactobacillus plantarum were cloned in the nisin-dependent L. lactis NICE overexpression system. As predicted by a kinetic L. lactis glycolysis model, increase in mannitol 1-phosphate dehydrogenase and mannitol 1-phosphatase activities resulted in increased mannitol production. Overexpression of both genes in growing cells resulted in glucose-mannitol conversions of 11, 21, and 27% by the L. lactis parental strain, a strain with reduced phosphofructokinase activity, and a lactate dehydrogenase-deficient strain, respectively. Improved induction conditions and increased substrate concentrations resulted in an even higher glucose-to-mannitol conversion of 50% by the lactate dehydrogenase-deficient L. lactis strain, close to the theoretical mannitol yield of 67%. Moreover, a clear correlation between mannitol 1-phosphatase activity and mannitol production was shown, demonstrating the usefulness of this metabolic engineering approach.     

Metabolic characterization of Lactococcus lactis deficient in lactate dehydrogenase using in vivo 13C-NMR.

The metabolism of glucose by nongrowing cells of Lactococcus lactis strain FI7851, constructed from the wild-type L. lactis strain MG1363 by disruption of the lactate dehydrogenase (ldh) gene [Gasson, M.J., Benson, K., Swindel, S. & Griffin, H. (1996) Lait 76, 33-40] was studied in a noninvasive manner by 13C-NMR. The kinetics of the build-up and consumption of the pools of intracellular intermediates mannitol 1-phosphate, fructose 1,6-bisphosphate, 3-phosphoglycerate, and phosphoenolpyruvate as well as the utilization of [1-13C]glucose and formation of products (lactate, acetate, mannitol, ethanol, acetoin, 2,3-butanediol) were monitored in vivo with a time resolution of 30 s. The metabolism of glucose by the parental wild-type strain was also examined for comparison. A clear shift from typical homolactic fermentation (parental strain) to a mixed acid fermentation (lactate dehdydrogenase deficient; LDHd strain) was observed. Furthermore, high levels of mannitol were transiently produced and metabolized once glucose was depleted. Mannitol 1-phosphate accumulated intracellularly up to 76 mM concentration. Mannitol was formed from fructose 6-phosphate by the combined action of mannitol-1-phosphate dehydrogenase and phosphatase. The results show that the formation of mannitol 1-phosphate by the LDHd strain during glucose catabolism is a consequence of impairment in NADH oxidation caused by a highly reduced LDH activity, the transient production of mannitol 1-phosphate serving as a regeneration pathway for NAD+ regeneration. Oxygen availability caused a drastic change in the pattern of intermediates and end-products, reinforcing the key-role of the fulfilment of the redox balance. The flux control coefficients for the step catalysed by mannitol-1-phosphate dehydrogenase were calculated and the implications in the design of metabolic engineering strategies are discussed.     

Engineering Lactococcus lactis for production of mannitol: high yields from food-grade strains deficient in lactate dehydrogenase and the mannitol transport system

Mannitol is a sugar polyol claimed to have health-promoting properties. A mannitol-producing strain of Lactococcus lactis was obtained by disruption of two genes of the phosphoenolpyruvate (PEP)-mannitol phosphotransferase system (PTS(Mtl)). Genes mtlA and mtlF were independently deleted by double-crossover recombination in strain L. lactis FI9630 (a food-grade lactate dehydrogenase-deficient strain derived from MG1363), yielding two mutant (Delta ldh Delta mtlA and Delta ldh Delta mtlF) strains. The new strains, FI10091 and FI10089, respectively, do not possess any selection marker and are suitable for use in the food industry. The metabolism of glucose in nongrowing cell suspensions of the mutant strains was characterized by in vivo (13)C-nuclear magnetic resonance. The intermediate metabolite, mannitol-1-phosphate, accumulated intracellularly to high levels (up to 76 mM). Mannitol was a major end product, one-third of glucose being converted to this hexitol. The double mutants, in contrast to the parent strain, were unable to utilize mannitol even after glucose depletion, showing that mannitol was taken up exclusively by PEP-PTS(Mtl). Disruption of this system completely blocked mannitol transport in L. lactis, as intended. In addition to mannitol, approximately equimolar amounts of ethanol, 2,3-butanediol, and lactate were produced. A mixed-acid fermentation (formate, ethanol, and acetate) was also observed during growth under controlled conditions of pH and temperature, but mannitol production was low. The reasons for the alteration in the pattern of end products under nongrowing and growing conditions are discussed, and strategies to improve mannitol production during growth are proposed.     

Some effects of mannitol on the glucose metabolism of two derivatives of a strain ofRhizobium japonicum differing in mannitol dehydrogenase

The effects of mannitol were investigated by comparing some metabolic features in colonial derivatives, I-110 and L1-110, ofRhizobium japonicum strain 3IIb110, grown either on glucose alone (G-cells) or in glucose media supplemented with mannitol (GM-cells). The polyol stimulated the synthesis of not only mannitol dehydrogenase, which is active in derivative L1-110, but also the nicotinamide adenine dinucleotide (NAD)-linked 6-phosphogluconate (6-PG) dehydrogenase (EC 1.1.1.43). As revealed by radiorespirometry, when GM-cells were allowed to metabolize glucose, they produced relatively more CO₂ from the first and sixth carbons of the sugar than G-cells did. This finding is evidence that NAD-linked 6-PG dehydrogenase might initiate an unknown pathway different from the hexose cycle and the pentose phosphate (PP) pathway. Mannitol exerted no allosteric control on the oxygen consumption and the glucose transport systems. Active uptake of the polyol was correlated with the presence of mannitol dehydrogenase (EC 1.1.1.67); it did not hinder the transport of glucose even though both systems derive their energy for active transport from a common source presumptively characterized as the energized membrane state. Mannitol, however, suppressed by two- or threefold the glucose uptake system. Addition of the polyol to the cell suspensions of both colonial types ofR. japonicum metabolizing glucose caused an immediate 40–50% drop of adenosine triphosphate (ATP) concentrations, owing in part to the mannitol kinase reaction. Type I-110 failed to overcome this reduction of ATP levels, and low growth rates could results. In contrast, type L1-110 offsets the reduction of ATP concentration by oxidizing mannitol as an additional source of energy through mannitol dehydrogenase, fructokinase, and a sequence of glycolytic reactions. The polyol also induced type L1-110 to produce extracellular slimy materials that, apparently, harbor amounts of ATP and proteins.     

Controlling substrate concentration in fed-batch candida magnoliae culture increases mannitol production

Candida magnoliae HH-01, a yeast strain that is currently used for the industrial production of mannitol, has the highest mannitol production ever reported for a mannitol-producing microorganism. However, when the fructose concentration exceeds 150 g/L, the volumetric mannitol production rate decreases because of a lag in mannitol production, and the yield decreases as a result of the formation of side products. In fed-batch culture, the volumetric production rate and mannitol yield from fructose vary substantially with the fructose concentration and are maximal at a controlled fructose concentration of 50 g/L. In continuous feeding experiments, the maximum mannitol yield was 85% (g/g) at a glucose/fructose feeding ratio of 1/20. A high glucose concentration in the production phase resulted in the formation of ethanol followed by a decrease in yield and productivity. NAD(P)H-dependent mannitol dehydrogenase was purified to homogeneity from C. magnoliae. In vitro, mannitol dehydrogenase was inhibited by increasing ethanol concentration. Mannitol product was also found to be inhibitory with a K(i) of 183 mM. Under optimum conditions, a final mannitol production of 213 g/L was obtained from 250 g fructose/L after 110 h.     

Fermentation of glucose, lactose, galactose, mannitol, and xylose by bifidobacteria

For six strains of Bifidobacterium bifidum (Lactobacillus bifidus), fermentation balances of glucose, lactose, galactose, mannitol, and xylose were determined. Products formed were acetate, l(+)-lactate, ethyl alcohol, and formate. l(+)-Lactate dehydrogenase of all strains studied was found to have an absolute requirement for fructose-1,6-diphosphate. The phosphoroclastic enzyme could not be demonstrated in cell-free extracts. Cell suspensions fermented pyruvate to equimolar amounts of acetate and formate. Alcohol dehydrogenase was shown in cell-free extracts. Possible explanations have been suggested for the differences in fermentation balances found for different strains and carbon sources. By enzyme determinations, it was shown that bifidobacteria convert mannitol to fructose-6-phosphate by an inducible polyol dehydrogenase and fructokinase. For one strain of B. bifidum, molar growth yields of glucose, lactose, galactose, and mannitol were determined. The mean value of Y (ATP), calculated from molar growth yields and fermentation balances, was 11.3.     

Degradation of endogenous fructose during catabolism of sucrose and mannitol in halophilic archaebacteria

Metabolism of fructose arising endogenously from sucrose or mannitol was studied in halophilic archaebacteria Haloarcula vallismortis and Haloferax mediterranei. Activities of the enzymes of Embden-Meyerhof-Parnas (EMP) pathway, Entner-Doudoroff (ED) pathway and Pentose Phosphate (PP) pathway were examined in extracts of cells grown on sucrose or mannitol and compared to those grown on fructose and glucose. Sucrase and NAD-specific mannitol dehydrogenase were induced only when sucrose or mannitol respectively were the growth substrates. Endogenously arising fructose was metabolised in a manner similar to that for exogenously supplied fructose i.e. a modified EMP pathway initiated by ketohexokinase. While the enzymes for modified EMP pathway viz. ketohexokinase, 1-phosphofructokinase and fructose 1,6-bisphosphate aldolase were present under all growth conditions, their levels were elevated in presence of fructose. Besides, though fructose 1,6-bisphosphatase, phosphohexoseisomerase and glucose 6-phosphate dehydrogenase were present, the absence of 6-phosphogluconate dehydratase precluded routing of fructose through ED pathway, or through PP pathway directly as 6-phosphogluconate dehydrogenase was lacking. Fructose 1,6-bisphosphatase plays the unusual role of a catabolic enzyme in supporting the non-oxidative part of PP pathway. However the presence of constitutive levels of glucose dehydrogenase and 2-keto 3-deoxy 6-phosphogluconate aldolase when glucose or sucrose were growth substrates suggested that glucose breakdown took place via the modified ED pathway.Abbreviations EMP Embden Meyerhof Parnas - ED Entner Doudoroff - PP pentose phosphate - KHK ketohexokinase - 1-PFK 1-phosphofructokinase - PEP-PTS phosphoenolpyruvate phosphotransferase - 6-PFK 6-phosphofructokinase - FBPase fructose 1,6-bisphosphatase - PHI phosphohexoseisomerase - G6P-DH glucose 6-phosphate dehydrogenase - 6PG-DH 6-phosphogluconate dehydrogenase - GAPDH glyceraldehyde 3-phosphate dehydrogenase - FIP fructose 1-phosphate - GSH reduced glutathione - 2-ME -mercaptoethanol - FBP fructose 1,6-bisphosphate - KDPG 2-keto 3-deoxy 6-phosphogluconate - F6P fructose 6-phosphatez     

Engineering of the metabolism of Saccharomyces cerevisiae for anaerobic production of mannitol

Under anaerobic conditions, Saccharomyces cerevisiae uses NADH-dependent glycerol-3-phosphate dehydrogenase (Gpd1p and Gpd2p) to re-oxidize excess NADH, yielding substantial amounts of glycerol. In a Deltagpd1 Deltagpd2 double-null mutant, the necessary NAD+ regeneration through glycerol production is no longer possible, and this mutant does not grow under anaerobic conditions. The excess NADH formed can potentially be used to drive other NADH-dependent reactions or pathways. To investigate this possibility, a double-null mutant was transformed with a heterologous gene (mtlD) from Escherichia coli, coding for NADH-dependent mannitol-1-phosphate dehydrogenase. Expression of this gene in S. cerevisiae should result in NADH oxidation by the NADH-requiring formation of mannitol-1-phosphate from fructose-6-phosphate. The strain was characterized using step-change experiments, in which, during the exponential growth phase, the inlet gas was changed from air to nitrogen. It was found that the mutant produced mannitol only under anaerobic conditions. However, anaerobic growth was not regained, which was probably due to the excessive accumulation of mannitol in the cells.     

A thermostable mannitol-1-phosphate dehydrogenase is required in mannitol metabolism of the thermophilic acetogenic bacterium Thermoanaerobacter kivui

Acetogenic bacteria recently attracted attention because they reduce carbon dioxide (CO₂) with hydrogen (H₂) to acetate or to other products such as ethanol. Besides gases, acetogens use a broad range of substrates, but conversion of the sugar alcohol mannitol has rarely been reported. We found that the thermophilic acetogenic bacterium Thermoanaerobacter kivui grew on mannitol with a specific growth rate of 0.33 h⁻¹ to a final optical density (OD₆₀₀) of 2.2. Acetate was the major product formed. A lag phase was observed only in cultures pre-grown on glucose, not in those pre-grown on mannitol, indicating that mannitol metabolism is regulated. Mannitol-1-phosphate dehydrogenase (MtlD) activity was observed in cell-free extracts of cells grown on mannitol only. A gene cluster (TKV_c02830–TKV_c02860) for mannitol uptake and conversion was identified in the T. kivui genome, and its involvement was confirmed by deleting the mtlD gene (TKV_c02860) encoding the key enzyme MtlD. Finally, we overexpressed mtlD, and the recombinant MtlD carried out the reduction of fructose-6-phosphate with NADH, at a high V_MAX of 1235 U mg⁻¹ at 65°C. The enzyme was thermostable for 40 min at 75°C, thereby representing the first characterized MtlD from a thermophile.     

Regulation of product formation during glucose or lactose limitation in nongrowing cells of Streptococcus lactis

Nongrowing cells of Streptococcus lactis in a pH-stat were dosed with sugar to allow fermentation at the maximum rate or were fed a continuous supply of sugar at rates less than the maximum. Under anaerobic conditions, rapid fermentation of either glucose or lactose was essentially homolactic. However, with strain ML3, limiting the fermentation rate diverted approximately half of the pyruvate to formate, acetate, and ethanol. At limiting glucose fermentation rates, cells contained lower concentrations of lactate dehydrogenase activator (fructose 1,6-diphosphate) and pyruvate formate-lyase inhibitors (triose phosphates). As a result, pyruvate formate-lyase and pyruvate dehydrogenase play a greater role in pyruvate metabolism. In contrast to strain ML3, strain ML8 did not give the same diversion of products under anaerobic conditions, and cells retained higher concentrations of the above effector compounds. Lactose metabolism under aerobic conditions resulted in pyruvate excretion by both S. lactis ML3 and ML8. At 7% of the maximum utilization rate, pyruvate accounted for 69 and 35% of the lactose metabolized by ML3 and ML8, respectively. Acetate was also a major product, especially with ML8. The data suggest that NADH oxidase is involved in coenzyme recycling in the presence of oxygen and that pyruvate formate-lyase is inactivated, but the pyruvate dehydrogenase complex still functions.     

Regulation of product formation during glucose or lactose limitation in nongrowing cells of Streptococcus lactis.

Nongrowing cells of Streptococcus lactis in a pH-stat were dosed with sugar to allow fermentation at the maximum rate or were fed a continuous supply of sugar at rates less than the maximum. Under anaerobic conditions, rapid fermentation of either glucose or lactose was essentially homolactic. However, with strain ML3, limiting the fermentation rate diverted approximately half of the pyruvate to formate, acetate, and ethanol. At limiting glucose fermentation rates, cells contained lower concentrations of lactate dehydrogenase activator (fructose 1,6-diphosphate) and pyruvate formate-lyase inhibitors (triose phosphates). As a result, pyruvate formate-lyase and pyruvate dehydrogenase play a greater role in pyruvate metabolism. In contrast to strain ML3, strain ML8 did not give the same diversion of products under anaerobic conditions, and cells retained higher concentrations of the above effector compounds. Lactose metabolism under aerobic conditions resulted in pyruvate excretion by both S. lactis ML3 and ML8. At 7% of the maximum utilization rate, pyruvate accounted for 69 and 35% of the lactose metabolized by ML3 and ML8, respectively. Acetate was also a major product, especially with ML8. The data suggest that NADH oxidase is involved in coenzyme recycling in the presence of oxygen and that pyruvate formate-lyase is inactivated, but the pyruvate dehydrogenase complex still functions.     

Characterization of mannitol metabolism in the mangrove red algaCaloglossa leprieurii (Montagne) J.Agardh

A metabolic pathway, known as the mannitol cycle in fungi, has been identified as a new entity in the eulittoral mangrove red algaCaloglossa leprieurii (Montagne) J. Agardh. Three specific enzymes, mannitol-1-phosphate dehydrogenase (Mt1PDH; EC 1.1.1.17), mannitol-1-phosphatase (MtlPase; EC 3.1.3.22), mannitol dehydrogenase (MtDH; EC 1.1.1.67) and one nonspecific hexokinase (HK; EC 2.7.1.1) were determined and biochemically characterized in cell-free extracts. Mannitol-1-phosphate dehydrogenase showed activity maxima at pH 7.0 [fructose-6-phosphate (F6P) reduction] and pH 8.5 [oxidation of mannitol-1-phosphate (Mt1P)], and a very high specificity for both carbohydrate substrates. TheK _m values were 1.4 mM for F6P, 0.09 mM for MOP, 0.020 mM for NADH and 0.023 mM for NAD⁺. For the dephosphorylation of MOP, MtlPase exhibited a pH optimum at 7.2, aK _m value of 1.2 mM and a high requirement of Mg²⁺ for activation. Mannitol dehydrogenase had activity maxima at pH 7.0 (fructose reduction) and pH 9.8 (mannitol oxidation), and was less substrate-specific than Mt1PDH and MtlPase, i.e. it also catalyzed reactions in the oxidative direction with arabitol (64.9%), sorbitol (31%) and xylitol (24.8%). This enzyme showedK _m values of 39 mM for fructose, 7.9 mM for mannitol, 0.14 mM for NADH and 0.075 mM for NAD⁺. For the non-specific HK, only theK _m values for fructose (0.19 mM) and glucose (7.5 mM) were determined. The activities of the anabolic enzymes Mt1PDH and MtlPase were always at least two orders of magnitude higher than those of the degradative enzymes, indicating a net carbon flow towards a high intracellular mannitol pool. The function of mannitol metabolism inC. leprieurii as a biochemical adaptation to the environmental extremes in the mangrove habitat is discussed.Abbreviations F6P fructose-6-phosphate - HK hexokinase - Mt1P mannitol-1-phosphate - Mt1PDH mannitol-1-phosphate dehydrogenase - Mt1Pase mannitol-1-phosphatase - MtDH mannitol dehydrogenase     

Biotechnological production of mannitol and its applications

Mannitol, a naturally occurring polyol (sugar alcohol), is widely used in the food, pharmaceutical, medical, and chemical industries. The production of mannitol by fermentation has become attractive because of the problems associated with its production chemically. A number of homo- and heterofermentative lactic acid bacteria (LAB), yeasts, and filamentous fungi are known to produce mannitol. In particular, several heterofermentative LAB are excellent producers of mannitol from fructose. These bacteria convert fructose to mannitol with 100% yields from a mixture of glucose and fructose (1:2). Glucose is converted to lactic acid and acetic acid, and fructose is converted to mannitol. The enzyme responsible for conversion of fructose to mannitol is NADPH- or NADH-dependent mannitol dehydrogenase (MDH). Fructose can also be converted to mannitol by using MDH in the presence of the cofactor NADPH or NADH. A two enzyme system can be used for cofactor regeneration with simultaneous conversion of two substrates into two products. Mannitol at 180 g l⁻¹ can be crystallized out from the fermentation broth by cooling crystallization. This paper reviews progress to date in the production of mannitol by fermentation and using enzyme technology, downstream processing, and applications of mannitol.     

Role of glucose in the bioconversion of fructose into mannitol by Candida magnoliae

The most efficient substrate for mannitol production by Candida magnoliae HH-01 is fructose; glucose and sucrose can also be converted into mannitol but with lower conversion yields. Mannitol dehydrogenase was purified and characterized; it had the highest activity with fructose as the substrate and used only NADPH. In fed-batch fermentation with glucose, the production of mannitol from fructose ceased when the glucose was exhausted but it was reinitiated with the addition of glucose, implying that glucose plays an important role in NADPH regeneration.     

Identification of a Cryptococcus neoformans gene that directs expression of the cryptic Saccharomyces cerevisiae mannitol dehydrogenase gene.

The Mtl gene from Cryptococcus neoformans, which confers the ability of Saccharomyces cerevisiae Sc4l YJO to grow on mannitol with substantial NAD-dependent mannitol dehydrogenase activity, was identified. Purifications and characterizations of this enzyme show that it is found in polyploid strain BB1, and the peptide sequence of the enzyme helped identify the saccharomyces gene encoding this mannitol dehydrogenase activity. On the other hand, the Mtl gene of C. neoformans encodes a 346-amino-acid protein which is not mannitol dehydrogenase but a regulatory element which is active in a heterologous fungus.     

Purification of NAD-dependent mannitol dehydrogenase from celery suspension cultures.

Mannitol dehydrogenase, a mannitol:mannose 1-oxidoreductase, constitutes the first enzymatic step in the catabolism of mannitol in nonphotosynthetic tissues of celery (Apium graveolens L.). Endogenous regulation on the enzyme activity in response to environmental cues is critical in modulating tissue concentration of mannitol, which, importantly, contribute to stress tolerance of celery. The enzyme was purified to homogeneity from celery suspension cultures grown on D-mannitol as the carbon source. Mannitol dehydrogenase was purified 589-fold to a specific activity of 365 mumol h-1 mg-1 protein with a 37% yield of enzyme activity present in the crude extract. A highly efficient and simple purification protocol was developed involving polyethylene glycol fractionation, diethylaminoethyl-anion-exchange chromatography, and NAD-agarose affinity chromatography using NAD gradient elution. Sodium dodecylsulfate gel electrophoresis of the final preparation revealed a single 40-kD protein. The molecular mass of the native protein was determined to be approximately 43 kD, indicating that the enzyme is a monomer. Polyclonal antibodies raised against the enzyme inhibited enzymatic activity of purified mannitol dehydrogenase. Immunoblots of crude protein extracts from mannitol-grown celery cells and sink tissues of celery, celeriac, and parsley subjected to sodium dodecyl sulfate gel electrophoresis showed a single major immuno-reactive 40-kD protein.     

Overproducton of mannitol dehydrogenase in Rhodobacter sphaeroides

Mannitol dehydrogenase (MDH) from Rhodobacter sphaeroides Si4 was overproduced by constructing a strain that overexpresses the MDH gene and by producing high cell concentrations via fed-batch cultivation in a bioreactor. With the gene of mannitol dehydrogenase (mtlK) cloned into the expression vector pKK223-3 expression of MDH in Escherichia coli was obtained, but the specific enzyme activity was lower than in R. sphaeroides Si4. In order to overexpress mtlK in R. sphaeroides, plasmid pAK82 was constructed by cloning a DNA fragment carrying mtlK into the broad-host-range expression vector pRK415. When pAK82 was introduced into R. sphaeroides Si4 the specific mannitol dehydrogenase activity in the strain obtained was 0.48 unit (U)mg^–1, 3.4-fold higher thain in the wild type. In this way the enzyme yield from cultivation in a bioreactor could be improved from 110 Ul^–1 to 350 Ul^–1. A further increase in productivity was obtained by fed-batch cultivation of R. sphaeroides Si4 [pAK82]. Using this cultivation method can optical density of 27.6 was reached in the bioreactor, corresponding to a dry mass of 16.6 g l^–1. Since MDH formation correlated with biomass production, the MDH yield could be raised to 918 Ul^–1, an 8.3-fold increase in comparison to batch cultivation of the wild-type strain.Dedicated to Prof. Fritz Wagner on the occasion of his 65th birthday.