Model-based biotechnological potential analysis of Kluyveromyces marxianus central metabolism.

The non-conventional yeast Kluyveromyces marxianus is an emerging industrial producer for many biotechnological processes. Here, we show the application of a biomass-linked stoichiometric model of central metabolism that is experimentally validated, and mass and charge balanced for assessing the carbon conversion efficiency of wild type and modified K. marxianus. Pairs of substrates (lactose, glucose, inulin, xylose) and products (ethanol, acetate, lactate, glycerol, ethyl acetate, succinate, glutamate, phenylethanol and phenylalanine) are examined by various modelling and optimisation methods. Our model reveals the organism's potential for industrial application and metabolic engineering. Modelling results imply that the aeration regime can be used as a tool to optimise product yield and flux distribution in K. marxianus. Also rebalancing NADH and NADPH utilisation can be used to improve the efficiency of substrate conversion. Xylose is identified as a biotechnologically promising substrate for K. marxianus.

Challenges to be faced in the reconstruction of metabolic networks from public databases.

In the post-genomic era, the biochemical information for individual compounds, enzymes, reactions to be found within named organisms has become readily available. The well-known KEGG and BioCyc databases provide a comprehensive catalogue for this information and have thereby substantially aided the scientific community. Using these databases, the complement of enzymes present in a given organism can be determined and, in principle, used to reconstruct the metabolic network. However, such reconstructed networks contain numerous properties contradicting biological expectation. The metabolic networks for a number of organisms are reconstructed from KEGG and BioCyc databases, and features of these networks are related to properties of their originating database.

Using a mammalian cell cycle simulation to interpret differential kinase inhibition in anti-tumour pharmaceutical development.

Systems biology needs to show practical relevance to commercial biological challenges such as those of pharmaceutical development. The aim of this work is to design and validate some applications in anti-cancer therapeutic development. The test system was a group of novel cyclin-dependent kinase (CDK) inhibitors synthesised by Cyclacel Ltd. The measured in vitro IC50s of each compound were used as input data to a proprietary cell cycle model developed by Physiomics plc. The model was able to predict over three orders of magnitude the cytotoxicity of each compound without model adaptation to specific cancer cell types. This pattern matched the experimentally determined data. One class of compounds was predicted to cause an increase of the cell cycle length with a non-linear dose-response curve. Further work will use apoptosis and DNA replication simulations to look at overall cell effects.

A method for the determination of flux in elementary modes, and its application to Lactobacillus rhamnosus.

In this article we address the question of how, given information about the reaction fluxes of a system, flux values can be assigned to the elementary modes of that system. Having described a method by which this may be accomplished, we first illustrate its application to a hypothetical, in silico system, and then apply it to fermentation data from Lactobacillus rhamnosus. This reveals substantial changes in the flux values assigned to elementary modes, and thus to the internal metabolism, as the fermentation progresses. This is information that could not, to our knowledge, be obtained by existing methods. The relationship between our technique and the well-known method of Metabolic Flux Analysis is also discussed.

Applications of metabolic modelling to plant metabolism.

In this paper some of the general concepts underpinning the computer modelling of metabolic systems are introduced. The difference between kinetic and structural modelling is emphasized, and the more important techniques from both, along with the physiological implications, are described. These approaches are then illustrated by descriptions of other work, in which they have been applied to models of the Calvin cycle, sucrose metabolism in sugar cane, and starch metabolism in potatoes.

Reaction routes in biochemical reaction systems: algebraic properties, validated calculation procedure and example from nucleotide metabolism.

Elementary flux modes (direct reaction routes) are minimal sets of enzymes that can operate at steady state, with all irreversible reactions used in the appropriate direction. They can be interpreted as component pathways of a (bio)chemical reaction network. Here, two different definitions of elementary modes are given and their equivalence is proved. Several algebraic properties of elementary modes are then presented and proved. This concerns, amongst other features, the minimal number of enzymes of the network not used in an elementary mode and the situations where irreversible reactions are replaced by reversible ones. Based on these properties, a refined algorithm is presented, and it is formally proved that this algorithm will exclusively generate all the elementary flux modes of an arbitrary network containing reversible or irreversible reactions or both. The algorithm is illustrated by a biochemical example relevant in nucleotide metabolism. The computer implementation in two different programming languages is discussed.

The small world inside large metabolic networks.

The metabolic network of the catabolic, energy and biosynthetic metabolism of Escherichia coli is a paradigmatic case for the large genetic and metabolic networks that functional genomics efforts are beginning to elucidate. To analyse the structure of previously unknown networks involving hundreds or thousands of components by simple visual inspection is impossible, and quantitative approaches are needed to analyse them. We have undertaken a graph theoretical analysis of the E. coli metabolic network and find that this network is a small-world graph, a type of graph distinct from both regular and random networks and observed in a variety of seemingly unrelated areas, such as friendship networks in sociology, the structure of electrical power grids, and the nervous system of Caenorhabditis elegans. Moreover, the connectivity of the metabolites follows a power law, another unusual but by no means rare statistical distribution. This provides an objective criterion for the centrality of the tricarboxylic acid cycle to metabolism. The small-world architecture may serve to minimize transition times between metabolic states, and contains evidence about the evolutionary history of metabolism.

Computer modelling and experimental evidence for two steady states in the photosynthetic Calvin cycle.

We present observations of photosynthetic carbon dioxide assimilation, and leaf starch content from genetically modified tobacco (Nicotiana tabacum) plants in which the activity of the Calvin cycle enzyme, sedoheptulose-1,7-bisphosphatase, is reduced by an antisense construct. The measurements were made on leaves of varying ages and used to calculate the flux control coefficients of sedoheptulose-1,7-bisphosphatase over photosynthetic assimilation and starch synthesis. These calculations suggest that control coefficients for both are negative in young leaves, and positive in mature leaves. This behaviour is compared to control coefficients obtained from a detailed computer model of the Calvin cycle. The comparison demonstrates that the experimental observations are consistent with bistable behaviour exhibited by the model, and provides the first experimental evidence that such behaviour in the Calvin cycle occurs in vivo as well as in silico.

Threonine synthesis from aspartate in Escherichia coli cell-free extracts: pathway dynamics.

We have developed an experimental model of the whole threonine pathway that allows us to study the production of threonine from aspartate under different conditions. The model consisted of a desalted crude extract of Escherichia coli to which we added the substrates and necessary cofactors of the pathway: aspartate, ATP and NADPH. In this experimental model we measured not only the production of threonine, but also the time dependence of all the intermediate metabolites and of the initial substrates, aspartate, ATP and NADPH. A stoichiometric conversion of precursors into threonine was observed. We have derived conditions in which a quasi steady state can be transiently observed and used to simulate physiological conditions of functioning of the pathway in the cell. The dependence of threonine synthesis and of the aspartate and NADPH consumption on the initial aspartate and threonine concentrations exhibits greater sensitivity to the aspartate concentration than to the threonine concentration in these non-steady-state conditions. A response to threonine is only observed in a narrow concentration range from 0.23 to 2 mM.

An integrated study of threonine-pathway enzyme kinetics in Escherichia coli.

We have determined the kinetic parameters of the individual steps of the threonine pathway from aspartate in Escherichia coli under a single set of experimental conditions chosen to be physiologically relevant. Our aim was to summarize the kinetic behaviour of each enzyme in a single tractable equation that takes into account the effect of the products as competitive inhibitors of the substrates in the forward reaction and also, when appropriate (e.g. near-equilibrium reactions), as substrates of the reverse reactions. Co-operative feedback inhibition by threonine and lysine was also included as necessary. We derived the simplest rate equations that describe the salient features of the enzymes in the physiological range of metabolite concentrations in order to incorporate them ultimately into a complete model of the threonine pathway, able to predict quantitatively the behaviour of the pathway under natural or engineered conditions.

Control of the threonine-synthesis pathway in Escherichia coli: a theoretical and experimental approach.

A computer simulation of the threonine-synthesis pathway in Escherichia coli Tir-8 has been developed based on our previous measurements of the kinetics of the pathway enzymes under near-physiological conditions. The model successfully simulates the main features of the time courses of threonine synthesis previously observed in a cell-free extract without alteration of the experimentally determined parameters, although improved quantitative fits can be obtained with small parameter adjustments. At the concentrations of enzymes, precursors and products present in cells, the model predicts a threonine-synthesis flux close to that required to support cell growth. Furthermore, the first two enzymes operate close to equilibrium, providing an example of a near-equilibrium feedback-inhibited enzyme. The predicted flux control coefficients of the pathway enzymes under physiological conditions show that the control of flux is shared between the first three enzymes: aspartate kinase, aspartate semialdehyde dehydrogenase and homoserine dehydrogenase, with no single activity dominating the control. The response of the model to the external metabolites shows that the sharing of control between the three enzymes holds across a wide range of conditions, but that the pathway flux is sensitive to the aspartate concentration. When the model was embedded in a larger model to simulate the variable demands for threonine at different growth rates, it showed the accumulation of free threonine that is typical of the Tir-8 strain at low growth rates. At low growth rates, the control of threonine flux remains largely with the pathway enzymes. As an example of the predictive power of the model, we studied the consequences of over-expressing different enzymes in the pathway.

Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells.

Although epidermal growth factor (EGF) induces transient activation of Ras and the mitogen-activated protein kinase (MAPK) cascade in PC12 cells, whereas nerve growth factor (NGF) stimulates sustained activation, the basis for these contrasting responses is not known. We have developed a computer simulation of EGF-induced MAPK cascade activation, which provides quantitative evidence that feedback inhibition of the MAPK cascade is the most important factor in determining the duration of cascade activation. Hence, we propose that the observed quantitative differences in EGF and NGF signalling can be accounted for by differential feedback regulation of the MAPK cascade.

Modelling photosynthesis and its control.

The dynamic and steady-state behaviour of a computer simulation of the Calvin cycle reactions of the chloroplast, including starch synthesis and degradation, and triose phosphate export have been investigated. A major difference compared with previous models is that none of the reversible reactions are assumed to be at equilibrium. The model can exhibit alternate steady states of low or high carbon assimilation flux, with hysteresis in the transitions between the steady states induced by environmental factors such as phosphate and light intensity. The enzymes which have the greatest influence on the flux have been investigated by calculation of their flux control coefficients. Different patterns of control are exhibited over the assimilation flux, the flux to starch and the flux to cytosolic triose phosphate. The assimilation flux is mostly sensitive to sedoheptulose bisphosphatase and Rubisco, with the exact distribution depending on their relative activities. Other enzymes, particularly the triose phosphate translocator, become more influential when other fluxes are considered. These results are shown to be broadly consistent with observations on transgenic plants.

A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks.

A set of linear pathways often does not capture the full range of behaviors of a metabolic network. The concept of 'elementary flux modes' provides a mathematical tool to define and comprehensively describe all metabolic routes that are both stoichiometrically and thermodynamically feasible for a group of enzymes. We have used this concept to analyze the interplay between the pentose phosphate pathway (PPP) and glycolysis. The set of elementary modes for this system involves conventional glycolysis, a futile cycle, all the modes of PPP function described in biochemistry textbooks, and additional modes that are a priori equally entitled to pathway status. Applications include maximizing product yield in amino acid and antibiotic synthesis, reconstruction and consistency checks of metabolism from genome data, analysis of enzyme deficiencies, and drug target identification in metabolic networks.

Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering.

Rational metabolic engineering requires powerful theoretical methods such as pathway analysis, in which the topology of metabolic networks is considered. All metabolic capabilities in steady states are composed of elementary flux modes, which are minimal sets of enzymes that can each generate valid steady states. The modes of the fructose-2,6-bisphosphate cycle, the combined tricarboxylic-acid-glyoxylate-shunt system and tryptophan synthesis are used here for illustration. This approach can be used for many biotechnological applications such as increasing the yield of a product, channelling a product into desired pathways and in functional reconstruction from genomic data.

A control analysis exploration of the role of ATP utilisation in glycolytic-flux control and glycolytic-metabolite-concentration regulation.

A theoretical metabolic-control-analysis approach has been used to study aspects of glycolytic-flux control and carbon-metabolite regulation, particularly the role of ATP demand (ATPase), in order to determine what general features of the regulation of energy metabolism would be consistent with good carbon-metabolite homeostasis in the face of large changes in carbon flux. On the basis of a semi-quantitative control-analysis model, incorporating estimates of substrate, product and effector actions on the enzymes, the experimentally observed characteristics of glycolytic-flux changes prove to impose constraints on the feasible ranges of these estimates. This leads to the identification of several features of energy metabolism, each of which is necessary but not sufficient to explain the observations; although most of these have been advocated previously (such as AMP activation of phosphofructokinase (PFK), ADP inhibition of ATPase and the role of energy charge or ATP/ADP ratio), our analysis allows their relative importance to be assessed. In the model, the distribution of flux control depends primarily on ADP inhibition of ATPase, and on the activation of PFK by AMP; increase in ADP inhibition of ATPase increases the control on PFK; increase in AMP activation of PFK increases control on ATPase. PFK exerts greater flux control than does ATPase over approximately 50% of the ranges (parameter space) studied, but its control is sufficiently high to achieve sizeable flux increases over less than 20% of the space. Furthermore, control by alteration in PFK activity is shown to result in poor glycolytic metabolite homeostasis over the entire parameter space studied. However, over a large proportion of the parameter space, control by activation of ATPase can lead to large flux changes, i.e. high flux control, coupled with excellent glycolytic-metabolite homeostasis, similar to that observed in working muscle. As well as altering the relative degrees of flux control invested in PFK and ATPase, ADP inhibition of ATPase and AMP activation of PFK have pronounced effects on the homeostatic properties of the system. Stronger ADP inhibition of ATPase results in improved homeostasis of glycolytic metabolites, ATP and ADP in response to PFK activation, whereas stronger activation of PFK by AMP improves the homeostasis of these three quantities in response to ATPase activation. The results are further evidence of the potential for physiological ATP demand to exert control over glycolytic flux, but additionally show that the known effector interactions, in addition to their previously known role in ATP regulation, could contribute to the remarkable homeostasis of glycolytic-metabolite levels observed in vivo. They further indicate that quantitative characterisation of likely domains of behaviour of metabolic systems can be achieved by an algebraic analysis that is not highly dependent on a full and precise knowledge of the molecular details of the kinetic/regulatory properties of the enzymes, but that still allows an assessment of whether hypotheses regarding the system are feasible and sufficient to account for the observations.