Analysis of sucrose accumulation in the sugar cane culm on the basis of in vitro kinetic data

The Silicon Cell initiative: working towards a detailed kinetic description at the cellular level

The Silicon Cell initiative aims to understand cellular systems on the basis of the characteristics of their components. As a tool to achieve this, detailed kinetic models at the network reaction level are being constructed. Such detailed kinetic models are extremely useful for medical and biotechnological applications and form strong tools for fundamental studies. Several recently constructed detailed kinetic models on metabolism (glycolysis), signal transduction (EGF receptor), and the eukaryotic cell cycle (Saccharomyces cerevisiae) have been used to exemplify the Silicon Cell project. These models are stored and made accessible via the JWS Online Cellular Systems Modeling project, a web-based repository of kinetic models. Using a web-browser the models can be interrogated via a user-friendly graphical interface. The goal of the two projects is to combine models on parts of cellular systems and ultimately to construct detailed kinetic models at the cellular level.

Kinetic constraints for formation of steady states in biochemical networks

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. This work introduces the concept of kinetic constraints. It is shown that maximal reaction rates are appropriate constraints only for isolated enzymatic reactions. For biochemical networks, it is revealed that constraints for formation of a steady state require specific relationships between maximal reaction rates of all enzymes. The constraints for a branched network are significantly different from those for a cyclic network. Moreover, the constraints do not require Michaelis-Menten constants for most enzymes, and they only require the constants for the enzymes at the branching or cyclic point. Reversibility of reactions at system boundary or branching point may significantly impact on kinetic constraints. When enzymes are regulated, regulations may impose severe kinetic constraints for the formation of steady states. As the complexity of a network increases, kinetic constraints become more severe. In addition, it is demonstrated that kinetic constraints for networks with co-regulation can be analyzed using the approach. In general, co-regulation enhances the constraints and therefore larger fluctuations in fluxes can be accommodated in the networks with co-regulation. As a first example of the application, we derive the kinetic constraints for an actual network that describes sucrose accumulation in the sugar cane culm, and confirm their validity using numerical simulations.

Protein-level expression and localization of sucrose synthase in the sugarcane culm

No comprehensive studies on the localization of sucrose synthase (SuSy, EC 2.4.1.13) in sugarcane internodes have been reported. The expression and localization of SuSy in young (internode 3) to mature (internode 9) internodes of sugarcane (Saccharum spp. hybrids) var. N19 was investigated. Enzyme activity in the top and bottom, as well as the peripheral and core parts of the internodes suggested that SuSy is present ubiquitously but that levels can differ significantly in different parts of the internodes and with maturity. This was also confirmed by immunohistochemistry, which showed that both vascular and storage parenchyma tissues contain SuSy in young and mature internodes. The ratio of sucrose breakdown to synthesis activity increased approximately 12-fold from an average of 0.12 in internode three to 1.4 in internode nine. This indicates that different forms of SuSy are present in young and mature internodes, or that the ratios of different isoforms differ between young and mature internodes. Immunoblotting showed that at least one form of SuSy present in young tissue was absent, or present below detection limits, in mature culm tissue.

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.

A method for classifying metabolites in topological pathway analyses based on minimization of pathway number

Metabolic pathway analysis based on the concept of elementary flux mode is a valuable tool for reconstruction of bacterial metabolisms and in predicting optimal conversion yields in biotechnology. However, pathway analysis of large and highly entangled metabolic networks meets the problem of combinatorial explosion of possible routes across the networks. Here we propose a method for coping with this problem by suitably classifying metabolites as external or internal. External metabolites are considered to have buffered concentrations while internal metabolites have to fulfil a balance condition at steady state. For many substances such as nutrients and excreted products, there are biochemical reasons to classify them as external. In addition, other substances (especially at central branching points) can operationally be considered external in order to avoid combinatorial explosion. We suggest to find such a classification of metabolites that minimizes the number of elementary flux modes (pathways). This is motivated by the objectives of finding such a description of the system that reduces as much as possible the amount of necessary data and of removing the ambiguity and arbitrariness in the classification of metabolites in an automated, systematic way. For networks of moderate size, the solution to this combinatorial minimization problem can be found by exhaustive search. To tackle also larger systems, a stochastic optimization program based on the Metropolis algorithm was developed. Both methods are applied, for illustration, to several reaction schemes including a larger network representing glutathione metabolism.

Sucrose cycling in heterotrophic plant cell metabolism: first step towards an experimental model

Sucrose is the cornerstone of higher plant metabolism. Produced by photosynthesis, sucrose is the main substrate for respiration and biosynthesis. The emerging idea is that sucrose may act as regulator of its own metabolism, characterized in particular by a permanent process of degradation and formation. This sucrose turnover may control several important physiological functions. Of particular concern is an energy dependent cycle involving the hexokinase. This report presents an experimental approach to define quantitatively physiological states of suspension-cultured plant cells wih reference to their sucrose content and respiration rate. Sucrose depletion of normal cells incubated in a medium devoid of sugar is measured in vivo using 13C and respiration is simultaneously recorded. Results obtained with sucrose-storing cells and Arabidopsis thaliana show that respiration rate is closely linked to the available sucrose. Sucrose-depleted cells offer a stable model to study the bioenergetics of the process.

Calculating as many fluxes as possible in underdetermined metabolic networks

A frequently occurring problem in Metabolic Flux Analysis is that the linear equation systems are underdetermined. A procedure for determining which reaction velocities can be calculated in underdetermined metabolic systems from measured rates and computing these velocities is given. The method is based on the null-space matrix to the stoichiometry matrix corresponding to the reactions with unknown velocities. Moreover, an elementary representation of the null-space is presented. This representation enables one to find those sets of measurable velocities that allow calculation of a certain non-measurable rate. The approach is illustrated by an example from monosaccharide metabolism.

Identification of a novel sugar transporter homologue strongly expressed in maturing stem vascular tissues of sugarcane by expressed sequence tag and microarray analysis

The ability of sugarcane to accumulate sucrose provides an experimental system for the study of gene expression determining carbohydrate partitioning and metabolism. A sequence survey of 7242 ESTs derived from the sucrose-accumulating, maturing stem revealed that transcripts for carbohydrate metabolism gene sequences (CMGs) are relatively rare in this tissue. However, within the CMG group, putative sugar transporter ESTs form one of the most abundant classes observed. A combination of EST analysis and microarray and northern hybridization revealed that one of the putative sugar transporter types, designated PST type 2a, was the most abundant and most strongly differentially expressed CMG in maturing stem tissue. PST type 2a is homologous to members of the major facilitator super-family of transporters, possessing 12 predicted transmembrane domains and a sugar transport conserved domain, interrupted by a large cytoplasmic loop. Its transcript was localized to phloem companion cells and associated parenchyma in maturing stem, suggesting a role in sugar translocation rather than storage. In addition, other categories of CMGs show evidence of coordinated expression, such as enzymes involved in sucrose synthesis and cleavage, and a majority of enzymes involved in glycolysis and the pentose phosphate pathway. This study demonstrates the utility of genomic approaches using large-scale EST acquisition and microarray hybridization techniques for studies of the developmental regulation of metabolic enzymes and potential transporters in sugarcane.

Two approaches for metabolic pathway analysis?

Metabolic pathway analysis is becoming increasingly important for assessing inherent network properties in (reconstructed) biochemical reaction networks. Of the two most promising concepts for pathway analysis, one relies on elementary flux modes and the other on extreme pathways. These concepts are closely related because extreme pathways are a subset of elementary modes. Here, the common features, differences and applicability of these concepts are discussed. Assessing metabolic systems by the set of extreme pathways can, in general, give misleading results owing to the exclusion of possibly important routes. However, in certain network topologies, the sets of elementary modes and extreme pathways coincide. This is quite often the case in realistic applications. In our opinion, the unification of both approaches into one common framework for metabolic pathway analysis is necessary and achievable.

Treatment of multifunctional enzymes in metabolic pathway analysis

In metabolic pathway analysis, it should be considered that many enzymes operate with low specificity (e.g. nucleoside diphosphokinase, uridine kinase, transketolase, aldolase), so that various substrates and products can be converted. Here, we analyze the effect of enzymes with low substrate specificity on the elementary flux modes (pathways). We also study the benefits of two different approaches to describing multifunctional enzymes. The usual description is in terms of (overall) enzymatic reactions. At a more detailed level, the reaction steps (half-reactions, hemi-reactions) of the formation and conversion of enzyme-substrate complexes are considered. Multifunctional enzymes operate according to various mechanisms. This is illustrated here by the reaction schemes for the different enzyme mechanisms of bifunctional enzymes. For enzymes with two or more functions, it is important to consider only linearly independent functions, because otherwise cyclic elementary modes would occur which do not perform any net transformation. However, the choice of linearly independent functions is not a priori unique. We give a method for making this choice unique by considering the extreme pathways of the hemi-reactions system. A formal application of the algorithm for computing elementary flux modes (pathways) yields the result that the number of such modes sometimes depend on the level of description if some reactions are reversible and the products of the multifunctional enzymes are external metabolites or some multifunctional enzymes partly share the same metabolites. However, this problem can be solved by appropriate interpretation of the definition of elementary modes and the correct choice of independent functions of multifunctional enzymes. The analysis is illustrated by a biochemical example taken from nucleotide metabolism, comparing the two ways of description for nucleoside diphosphokinase and adenylate kinase, and by several smaller examples.

Metabolic control analysis of glycerol synthesis in Saccharomyces cerevisiae

Glycerol, a major by-product of ethanol fermentation by Saccharomyces cerevisiae, is of significant importance to the wine, beer, and ethanol production industries. To gain a clearer understanding of and to quantify the extent to which parameters of the pathway affect glycerol flux in S. cerevisiae, a kinetic model of the glycerol synthesis pathway has been constructed. Kinetic parameters were collected from published values. Maximal enzyme activities and intracellular effector concentrations were determined experimentally. The model was validated by comparing experimental results on the rate of glycerol production to the rate calculated by the model. Values calculated by the model agreed well with those measured in independent experiments. The model also mimics the changes in the rate of glycerol synthesis at different phases of growth. Metabolic control analysis values calculated by the model indicate that the NAD(+)-dependent glycerol 3-phosphate dehydrogenase-catalyzed reaction has a flux control coefficient (C(J)v1) of approximately 0.85 and exercises the majority of the control of flux through the pathway. Response coefficients of parameter metabolites indicate that flux through the pathway is most responsive to dihydroxyacetone phosphate concentration (R(J)DHAP= 0.48 to 0.69), followed by ATP concentration (R(J)ATP = -0.21 to -0.50). Interestingly, the pathway responds weakly to NADH concentration (R(J)NADH = 0.03 to 0.08). The model indicates that the best strategy to increase flux through the pathway is not to increase enzyme activity, substrate concentration, or coenzyme concentration alone but to increase all of these parameters in conjunction with each other.

The role of stoichiometric analysis in studies of metabolism: an example

Stoichiometric analysis uses matrix algebra to deduce the constraints implicit in metabolic networks. When applied to simple networks, it can often give the impression of being an unnecessarily complicated way of arriving at information that is obvious from inspection, for example, that the sum of the concentrations of the adenine nucleotides is constant. Applied to a more complicated example, that of glycolysis in Trypanosoma brucei, it yields information that is far from obvious and may have importance for developing therapeutic ways of eliminating this parasite. Even in simplified form, the network contains nine reactions or transport steps involving 11 metabolites. This immediately shows that there must be at least two stoichiometric constraints, and indeed two can be recognized by inspection: conservation of adenine nucleotides and conservation of the two forms of NAD. There is, however, a third, which involves eight different phosphorylated intermediates in non-obvious combinations and is very difficult to recognize by inspection. It is also difficult to recognize by inspection that no fourth stoichiometric constraint exists. Gaussian elimination provides a systematic way of analysing a network in such a way that all the stoichiometric relationships that it contains emerge automatically.