Conservation laws and unidentifiability of rate expressions in biochemical models.

New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis.

Microaerobic glycerol formation in Saccharomyces cerevisiae.

The yeast Saccharomyces cerevisiae produces large amounts of glycerol as an osmoregulator during hyperosmotic stress and as a redox sink at low oxygen availability. NAD(+)-dependent glycerol-3-phosphate dehydrogenase in S. cerevisiae is present in two isoforms, coded for by two different genes, GPD1 and GPD2. Mutants for either one or both of these genes were investigated under carefully controlled static and dynamic conditions in continuous cultures at low oxygen transfer rates. Our results show that S. cerevisiae controls the production of glycerol in response to hypoxic conditions by regulating the expression of several genes. At high demand for NADH reoxidation, a strong induction was seen not only of the GPD2 gene, but also of GPP1, encoding one of the molecular forms of glycerol-3-phosphatase. Induction of the GPP1 gene appears to play a decisive role at elevated growth rates. At low demand for NADH reoxidation via glycerol formation, the GPD1, GPD2, GPP1, and GPP2 genes were all expressed at basal levels. The dynamics of the gene induction and the glycerol formation at low demand for NADH reoxidation point to an important role of the Gpd1p; deletion of the GPD1 gene strongly altered the expression patterns of the GPD2 and GPP1 genes under such conditions. Furthermore, our results indicate that GCY1 and DAK1, tentatively encoding glycerol dehydrogenase and dihydroxyacetone kinase, respectively, may be involved in the redox regulation of S. cerevisiae.

A new method for studying microaerobic fermentations. II. An experimental investigation of xylose fermentation.

A new experimental technique, called oxygen programmed fermentation (OPF), was used to study microbial cultures of the years Pichia stipitis and Candida utilis growing on xylose as carbon and energy source. In the oxygen programmed fermentation, the inlet oxygen mole fraction was continuously changed to scan through a wide range of oxygen uptake rates in a continuous culture. The largest ethanol yields and productivities of P. stipitis were found at oxygen transfer rates below 1.5 mmol L(-1) h(-1). It was found that the ratio between the culture fluorescence and near-IR absorbance increased at oxygen transfer rates lower than 1.5 mmol L(-1) h(-1). Small amounts of ethanol were produced also by C. utilis when the oxygen transfer rate was between 0 and 3 mmol L(-1) h(-1). It is suggested that OPF will form a nice complement to ordinary, microaerobic chemostat experiments, by making the identification of interesting regions of oxygen transfer rates possible in an efficient and time-saving initial experiment. (c) 1994 John Wiley & Sons, Inc.