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Metabolism is one of the best studied fields of biochemistry, but its regulation involves processes on many different levels, some of which are still not understood well enough to allow for quantitative modeling and prediction. Glycolysis in yeast is a good example: although high-quality quantitative data are available, well-established mathematical models typically only cover direct regulation of the involved enzymes by metabolite binding. The effect of various metabolites on the enzyme kinetics is summarized in carefully developed mathematical formulae. However, this approach implicitly assumes that the enzyme concentrations themselves are constant, thus neglecting other regulatory levels--e.g. transcriptional and translational regulation--involved in the regulation of enzyme activities. It is believed, however, that different experimental conditions result in different enzyme activities regulated by the above mechanisms. Detailed modeling of all regulatory levels is still out of reach since some of the necessary data--e.g. quantitative large scale enzyme concentration data sets--are lacking or rare. Nevertheless, a viable approach is to include the regulation of enzyme concentrations into an established model and to investigate whether this improves the predictive capabilities. Proteome data are usually hard to obtain, but levels of mRNA transcripts may be used instead as clues for changes in enzyme concentrations. Here we investigate whether including mRNA data into an established model of yeast glycolysis allows to predict the steady state metabolic concentrations for different experimental conditions. To this end, we modified an established ODE model for the glycolytic pathway of yeast to include changes of enzyme concentrations. Presumable changes were inferred from mRNA transcript level measurement data. We investigate how this approach can be used to predict metabolite concentrations for steady-state yeast cultures at five different oxygen levels ranging from anaerobic to fully aerobic conditions. We were partly able to reproduce the experimental data and present a number of changes that were necessary to improve the modeling result.

We demonstrate an approach to automatically generating kinetic models of metabolic networks. In a first step, the metabolic network is characterised by its stoichiometric structure. Then to each reaction a kinetic equation is associated describing the metabolic flux. For the kinetics we use a formula that is universally applicable to reactions with arbitrary numbers of substrates and products. Last, the kinetics of the reactions are assigned parameters. The resulting model in SBML format can be fed into standard simulation tools. The approach is applied to the sulphur-glutathione-pathway in Saccharomyces cerevisiae.

Values of enzyme kinetic parameters are a key requisite for the kinetic modelling of biochemical systems. For most kinetic parameters, however, not even an order of magnitude is known, so the estimation of model parameters from experimental data remains a major task in systems biology. We propose a statistical approach to infer values for kinetic parameters across species and enzymes making use of parameter values that have been measured under various conditions and that are nowadays stored in databases. We fit the data by a statistical regression model in which the substrate, the combination enzyme-substrate and the combination organism-substrate have a linear effect on the logarithmic parameter value. As a result, we obtain predictions and error ranges for unknown enzyme parameters. We apply our method to decadic logarithmic Michaelis-Menten constants from the BRENDA database and confirm the results with leave-one-out crossvalidation, in which we mask one value at a time and predict it from the remaining data. For a set of 8 metabolites we obtain a standard prediction error of 1.01 for the deviation of the predicted values from the true values, while the standard deviation of the experimental values is 1.16. The method is applicable to other types of kinetic parameters for which many experimental data are available.

Expression of metabolic enzymes increases the metabolic capabilities of the cell, but it also consumes resources, and the gene regulatory systems of cells have to handle this tradeoff. To study whether gene expression patterns reflect the varying metabolic needs of the cell, we translated gene expression profiles into sets of active biochemical reactions, which constitute the expressed metabolic subnetworks. The metabolic capacity of a carbon source denotes the number of metabolites that can be produced from this carbon source and some inorganic nutrients. We studied the metabolic subnetworks that are expressed during diauxic shift in yeast and found that the capacities of different carbon sources tend to decrease during the diauxic shift. The subnetwork expressed in the initial glucose environment shows a high capacity of glucose, much higher than networks of the same size arising in later stages of the diauxic shift or from a random selection of reactions. The same holds for the essential capacity, the number of important, constitutive compounds that can be produced from glucose. These findings indicate that gene regulation increases the range of essential compounds that can be obtained from the available nutrients, while minimising the number of expressed enzymes and therefore the burden of protein synthesis.

The Systems Biology Markup Language (SBML) is an XML-based format for representing mathematical models of biochemical reaction networks, and it is likely to become a main standard in the systems biology community. As published mathematical models in cell biology are growing in number and size, modular modelling approaches will gain additional importance. The main issue to be addressed in computer-assisted model combination is the specification and handling of model semantics. The software SBMLmerge assists the user in combining models of biological subsystems to larger biochemical networks. First, the program helps the user in annotating all model elements with unique identifiers pointing to databases such as KEGG or Gene Ontology. Second, during merging, SBMLmerge detects and resolves various syntactic and semantic problems. Typical problems are conflicting variable names, elements which appear in more than one input model, and mathematical problems arising from the combination of equations. If the input models make contradicting statements about a biochemical quantity, the user is asked to choose between them. In the end the merging process results in a new, valid SBML model.

Functional properties of biochemical networks depend on both the network structure and the kinetic parameters. Extensive data on metabolic network topologies have been collected in databases, but much less information is available about the kinetic constants or metabolite concentrations. Depending on the values of these parameters, metabolic fluxes and control coefficients may vary within a wide range. Nevertheless, some of the parameters may have little influence on the observables of interest. We address the question whether, despite uncertainty about kinetic parameters, probabilistic statements can be made about dynamic network features. To this end, we perform a variability analysis of the parameters: assuming that the parameters follow statistical distributions, we compute the resulting distributions of the network properties like metabolic fluxes, concentrations, or control coefficients by Monte Carlo simulation. In this manner, we study systematically the possible distributions arising from typical topologies of biochemical networks such as linear chains, branched networks, and signaling and gene expression cascades. This analysis reveals how much information about dynamic behavior can be drawn from structural knowledge.