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. Received: 1 January 2001 / Revised version: 17 December 2001 / Published online: 17 July 2002     

Behavior of various ribo- and deoxyribonucleosides, nucleoside monophosphate kinases, and nucleoside diphosphokinase on Blue Sepharose affinity columns.

A rapid and effective separation and purification of cytidylate-deoxycytidylate-uridylate kinase, adenylate kinase, and nucleoside diphosphokinase has been achieved with Blue Sepharose CL6B chromatography. When crude extracts of human crythrocytes or acute myelocytic leukemia cells were applied to the column, adenylate kinase, cytidylate-deoxycytidylate-uridylate kinase, and nucleoside diphosphokinase were retarded while guanylate kinase, cytidine kinase, uridine kinase, and deoxycytidine kinase were unabsorbed. The buffers required to elute the retarded kinases depended on the amount of sample applied to the column.     

METATOOL: for studying metabolic networks

MOTIVATION: To reconstruct metabolic pathways from biochemical and/or genome sequence data, the stoichiometric and thermodynamic feasibility of the pathways has to be tested. This is achieved by characterizing the admissible region of flux distributions in steady state. This region is spanned by what can be called a convex basis. The concept of 'elementary flux modes' provides a mathematical tool to define all metabolic routes that are feasible in a given metabolic network. In addition, we define 'enzyme subsets' to be groups of enzymes that operate together in fixed flux proportions in all steady states of the system. RESULTS: Algorithms for computing the convex basis and elementary modes developed earlier are briefly reviewed. A newly developed algorithm for detecting all enzyme subsets in a given network is presented. All of these algorithms have been implemented in a novel computer program named METATOOL, whose features are outlined here. The algorithms are illustrated by an example taken from sugar metabolism. AVAILABILITY: METATOOL is available from ftp://bmsdarwin.brookes.ac. uk/pub/software/ibmpc/metatool. SUPPLEMENTARY INFORMATION: http://www. biologie.hu-berlin.de/biophysics/Theory/tpfeiffer/metatoo l.html     

Nucleotide-metabolizing enzymes in Chlamydomonas flagella.

Nucleotides have at least two functions in eukaryotic cilia and flagella. ATP, originating in the cells, is utilized for motility by energy-transducing protein(s) called dynein, and the binding of guanine nucleotides to tubulin, and probably certain transformations of the bound nucleotides, are prerequisites for the assembly of microtubules. Besides dynein, which can be solubulized from Chlamydomonas flagella as a heterogeneous, Mg2+ or Ca2+-activated ATPase, we have purified and characterized five other flagellar enzymes involved in nucleotide transformations. A homogeneous, low molecular weight, Ca2+-specific adenosine triphosphatase was isolated, which was inhibited by Mg2+ and was not specific for ATP. This enzyme was not formed by treating purified dynein with proteases. It was absent from extracts of Tetrahymena cilia. Its function might be an auxiliary energy transducer, or in steering or tactic responses. Two species of adenylate kinase were isolated, one of which was much elevated in regenerating flagella; the latter was also present in cell bodies. A large part of flagellar nucleoside diphosphokinase activity could not be solubilized. Two soluble enzyme species were identified, one of which was also present in cell bodies. Since these enzymes are of interest because they might function in microtubule assembly, we studied the extent to which brain nucleoside diphosphokinase co-polymerizes with tubulin purified by repeated cycles of polymerization. Arginine kinase was not detected in Chlamydomonas flagellar extracts.     

Detection of activities that interfere with the enzymatic assay of deoxyribonucleoside 5'-triphosphates

Several enzymes that interfere with the enzymatic assay of deoxyribonucleoside 5'-triphosphates (dNTP's) are present as contaminants when nucleotides are extracted from HeLa cells with 60% methanol. These activities include a nuclease, nucleoside diphosphokinase, and deoxyribonucleoside monophosphokinases which phosphorylate dAMP, dGMP, and dCMP. Collectively, these enzymes are able to degrade and reutilize the DNA template which is used together with DNA polymerase for dNTP assays. This process introduces large errors when dNTP assays are performed in this manner. Attempts to block the enzymatic conversion of deoxyribonucleoside diphosphates to triphosphates by inhibition of nucleoside diphosphokinase were unsuccessful because of the inability to block completely the kinase activity. Acid extraction of nucleotides also results in the presence of an activity that interferes with the enzymatic dNTP assay. The error introduced by this interfering activity is much smaller than that arising from the enzymes present in methanol extracts. All of these interfering activities are removed when cells are first extracted with 60% methanol and the resulting extract is subsequently treated with perchloric acid.     

Effects of T4 phage infection and anaerobiosis upon nucleotide pools and mutagenesis in nucleoside diphosphokinase-defective Escherichia coli strains.

Bacteriophage T4 encodes nearly all of its own enzymes for synthesizing DNA and its precursors. An exception is nucleoside diphosphokinase (ndk gene product), which catalyzes the synthesis of ribonucleoside triphosphates and deoxyribonucleoside triphosphates (dNTPs) from the corresponding diphosphates. Surprisingly, an Escherichia coli ndk deletion strain grows normally and supports T4 infection. As shown elsewhere, these ndk mutant cells display both a mutator phenotype and deoxyribonucleotide pool abnormalities. However, after T4 infection, both dNTP pools and spontaneous mutation frequencies are near normal. An E. coli strain carrying deletions in ndk and pyrA and pyrF, the structural genes for both pyruvate kinases, also grows and supports T4 infection. We examined anaerobic E. coli cultures because of reports that in anaerobiosis, pyruvate kinase represents the major route for nucleoside triphosphate synthesis in the absence of nucleoside diphosphokinase. The dNTP pool imbalances and the mutator phenotype are less pronounced in the anaerobic than in the corresponding aerobic ndk mutant strains. Anaerobic dNTP pool data, which have not been reported before, reveal a disproportionate reduction in dGTP, relative to the other pools, when aerobic and anaerobic conditions are compared. The finding that mutagenesis and pool imbalances are mitigated in both anaerobic and T4-infected cultures provides strong, if circumstantial, evidence that the mutator phenotype of ndk mutant cells is a result of the dNTP imbalance. Also, the viability of these cells indicates the existence of a second enzyme system in addition to nucleoside diphosphokinase for nucleoside triphosphate synthesis.     

The polysome as a terminal for the creatine phosphate energy shuttle

The role of the creatine phosphate shuttle in the energetics of muscle protein synthesis in isolated polysomes, from rat hindlimb muscle, was studied. Triton X-100-treated polysomes, following their centrifugation through a 1 M sucrose gradient, contained 38 mU/mg RNA of bound creatine kinase. In the presence of pH 5 enzyme (obtained from rat liver), 0.5 mM ATP, and 1 microM GTP, amino acid (leucine) incorporation by polysomes in the presence of 8 mM creatine phosphate was twice that in the presence of an exogenous ATP regenerating system of 10 mM phospho(enol)pyruvate and 10 U/ml pyruvate kinase. Since added creatine kinase had no effect on incorporation supported by creatine phosphate it is clear that endogenous creatine kinase allows sufficient regeneration of ATP. These data also suggest that nucleoside diphosphokinase must have been associated with the polysome for phosphate was transferred to GTP from [33P]creatine phosphate, and the specific activities of ATP and GTP increased at equal rates, reaching the specific activity of creatine phosphate at 8 min. We conclude that skeletal muscle polysomes have bound creatine kinase activity and they act as terminals for the creatine phosphate energy shuttle. Creatine phosphate regenerates GTP, probably through an intermediate reaction catalyzed by nucleoside diphosphokinase. This provided an added support for the hypothesis of compartmentation of enzymes and substrates and that the transport form of energy between the mitochondria and energy utilizing sites in muscle is creatine phosphate rather than ATP, which extends the general role of the creatine phosphate energy shuttle.     

Maximum activities and effects of fructose bisphosphate on pyruvate kinase from muscles of vertebrates and invertebrates in relation to the control of glycolysis

1. Comparison of the maximum activities of pyruvate kinase with those of phosphofructokinase in a large number of muscles from invertebrates and vertebrates indicates that, in general, in any individual muscle, the activity of pyruvate kinase is only severalfold higher than that of phosphofructokinase. This is consistent with the suggestion, based on mass-action ratio data, that the pyruvate kinase reaction is non-equilibrium in muscle. However, the range of activities of pyruvate kinase in these muscles is considerably larger than that of phosphofructokinase. This difference almost disappears if the enzyme activities from muscles that are known to possess an anaerobic ;succinate pathway' are excluded. It is suggested that, in these muscles, phosphofructokinase provides glycolytic residues for both pyruvate kinase (i.e. glycolysis) and phosphoenolpyruvate carboxykinase (i.e. the succinate pathway). This is supported by a negative correlation between the activity ratio, pyruvate kinase/phosphofructokinase, and the activities of nucleoside diphosphokinase in these muscles, since high activities of nucleoside diphosphokinase are considered to indicate the presence of the succinate pathway. 2. The effect of fructose bisphosphate on the activities of pyruvate kinase from many different muscles was studied. The stimulatory effect of fructose bisphosphate appears to be lost whenever an efficient system for supply of oxygen to the muscles is developed (e.g. insects, squids, birds and mammals). This suggests that activation of pyruvate kinase is important in the co-ordinated regulation of glycolysis in anaerobic or hypoxic conditions, when the change in glycolytic flux during the transition from rest to activity needs to be large in order to provide sufficient energy for the contractile activity. However, lack of this effect in the anaerobic muscles of the birds and mammals suggests that another metabolic control may exist for avian and mammalian pyruvate kinase in these muscles.     

Quantification of metabolism in Saccharomyces cerevisiae under hyperosmotic conditions using elementary mode analysis

Yeast metabolism under hyperosmotic stress conditions was quantified using elementary mode analysis to obtain insights into the metabolic status of the cell. The fluxes of elementary modes were determined as solutions to a linear program that used the stoichiometry of the elementary modes as constraints. The analysis demonstrated that distinctly different sets of elementary modes operate under normal and hyperosmotic conditions. During the adaptation phase, elementary modes that only produce glycerol are active, while elementary modes that yield biomass, ethanol, and glycerol become active after the adaptive phase. The flux distribution in the metabolic network, calculated using the fluxes in the elementary modes, was employed to obtain the flux ratio at key nodes. At the glucose 6-phosphate (G6P) node, 25% of the carbon influx was diverted towards the pentose phosphate pathway under normal growth conditions, while only 0.3% of the carbon flux was diverted towards the pentose phosphate pathway during growth at 1?M NaCl, indicating that cell growth is arrested under hyperosmotic conditions. Further, objective functions were used in the linear program to obtain optimal solution spaces corresponding to the different accumulation rates. The analysis demonstrated that while biomass formation was optimal under normal growth conditions, glycerol synthesis was closer to optimal during adaptation to osmotic shock.     

The yeast Cdc8 exhibits both deoxythymidine monophosphate and diphosphate kinase activities

The existence of multifunctional enzymes in the nucleotide biosynthesis pathways is believed to be one of the important mechanisms to facilitate the synthesis and the efficient supply of deoxyribonucleotides for DNA replication. Here, we used the bacterially expressed yeast thymidylate kinase (encoded by the CDC8 gene) to demonstrate that the purified Cdc8 protein possessed thymidylate-specific nucleoside diphosphate kinase activity in addition to thymidylate kinase activity. The yeast endogenous nucleoside diphosphate kinase is encoded by YNK1, which appears to be non-essential. Our results suggest that Cdc8 has dual enzyme activities and could duplicate the function of Ynk1 in thymidylate synthesis. We also discuss the importance of the coordinated expression of CDC8 during the cell cycle progression in yeast.     

A kinetically important phosphoryl-enzyme intermediary in the intrinsic purine nucleoside-5'-diphosphokinase activity of Escherichia coli acetate kinase.

Initial rate studies of the intrinsic purine nucleoside-5′-diphosphokinase activity of Escherichia coli acetate kinase suggest that the kinetic reaction pathway is a ping-pong (or double-displacement) mechanism. Further evidence to support this mechanistic assignment was obtained through the use of the alternative substrate approach with ITP and GTP and by competitive inhibition studies with CrGTP and CrADP. That this diphosphokinase activity is intrinsic to the acetate kinase was demonstrated by the concomitant loss of the two activities when the phosphorylated form of acetate kinase was treated with 1 m hydroxylamine at pH 8. These data are fully consistent with the participation of an acyl-P intermediary in the acetate kinase and nucleoside diphosphokinase activities. The kinetic parameters suggest that the acetate kinase is a competent purine nucleoside-5′-diphosphokinase, but the metabolic significance of this function remains unassessed.     

Analyzing molecular reaction networks

Pathways are typically the central concept in the analysis of biochemical reaction networks. A pathway can be interpreted as a chain of enzymatical reactions performing a specific biological function. A common way to study metabolic networks are minimal pathways that can operate at steady state called elementary modes. The theory of chemical organizations has recently been used to decompose biochemical networks into algebraically closed and self-maintaining subnetworks termed organizations. The aim of this paper is to elucidate the relation between these two concepts. Whereas elementary modes represent the boundaries of the potential behavior of the network, organizations define metabolite compositions that are likely to be present in biological feasible situations. Hence, steady state organizations consist of combinations of elementary modes. On the other hand, it is possible to assign a unique (and possibly empty) set of organizations to each elementary mode, indicating the metabolites accompanying the active pathway in a feasible steady state.     

Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase. A theoretical study using elementary flux modes

This article is devoted to the study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. However, the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. So far, this route has not been analysed in detail. Using the concept of elementary flux modes, we investigate theoretically which salvage pathways exist in erythrocytes, which enzymes belong to each of these and what relative fluxes these enzymes carry. Here, we compute the net overall stoichiometry of ATP build-up from the recycled substrates and show that the network has considerable redundancy. For example, four different pathways of adenine salvage and 12 different pathways of adenosine salvage are obtained. They give different ATP/glucose yields, the highest being 3:10 for adenine salvage and 2:3 for adenosine salvage provided that adenosine is not used as an energy source. Implications for enzyme deficiencies are discussed.     

Progesterone and the metabolic control of the lactose biosynthetic pathway during lactogenesis in the rat

1. Lactogenesis was initiated in pregnant rats by ovariectomy, thereby causing progesterone withdrawal, after which the mammary tissue was analysed for contents of enzymes and metabolites concerned with the biosynthesis of lactose. 2. Lactose synthesis increased about 126-fold with little or no accompanying change in the contents of most metabolic intermediates or in the adenine nucleotide energy charge. 3. Comparison of mass-action ratios with equilibrium constants showed that phosphoglucomutase (EC 2.7.5.1), UDP-glucose pyrophosphorylase (EC 2.7.7.9) and UDP-glucose epimerase (EC 5.1.3.2.) catalysed reactions close to equilibrium. Nucleoside diphosphokinase (EC 2.7.4.6.) activity was very high and probably equilibrates the UTP-UDP and ATP-ADP couples. Lactose synthetase and hexokinase (EC 2.7.1.1) appeared to catalyse rate-limiting reactions. 4. Large increases were seen of UDP-glucose pyrophosphorylase (5-fold), lactose synthetase A protein (3.8-fold) and alpha-lactalbumin (28-fold), but not of hexokinase, phosphoglucomutase, UDP-glucose epimerase, nucleoside diphosphokinase or glucose 6-phosphate dehydrogenase (EC 1.1.1.49) activities. 5. It appeared that the increased lactose synthesis was largely accounted for by the increased lactose synthetase A protein activity and alpha-lactalbumin.     

Understanding specificity in metabolic pathways—Structural biology of human nucleotide metabolism

Interactions are the foundation of life at the molecular level. In the plethora of activities in the cell, the evolution of enzyme specificity requires the balancing of appropriate substrate affinity with a negative selection, in order to minimize interactions with other potential substrates in the cell. To understand the structural basis for enzyme specificity, the comparison of structural and biochemical data between enzymes within pathways using similar substrates and effectors is valuable.Nucleotide metabolism is one of the largest metabolic pathways in the human cell and is of outstanding therapeutic importance since it activates and catabolises nucleoside based anti-proliferative drugs and serves as a direct target for anti-proliferative drugs. In recent years the structural coverage of the enzymes involved in human nucleotide metabolism has been dramatically improved and is approaching completion. An important factor has been the contribution from the Structural Genomics Consortium (SGC) at Karolinska Institutet, which recently has solved 33 novel structures of enzymes and enzyme domains in human nucleotide metabolism pathways and homologs thereof. In this review we will discuss some of the principles for substrate specificity of enzymes in human nucleotide metabolism illustrated by a selected set of enzyme families where a detailed understanding of the structural determinants for specificity is now emerging.     

Tubulin-associated nucleoside diphosphokinase.

Microtubule protein, prepared by cycles of polymerisation and dissociation, contained a nucleoside diphosphokinase (NDP kinase) activity (EC 2.7.4.6). This activity was not intrinsic to the tubulin dimer or the so-called microtubule-associated proteins. The NDP kinase had the following properties. (1) The enzyme existed in a low-molecular-weight form and in association with the complex of microtubule-associated proteins and tubulin (i.e. multimeric tubulin). (2) The low-molecular-weight species was also formed by dissociation of multimeric tubulin by salt or by removal of microtubule-associated proteins on phosphocellulose. (3) GDP bound to the exchangeable site of multimeric tubulin and also GDP derived from the E site of the tubulin dimer was a substrate for the NDP kinase. (4) The NDP kinase showed a 7-fold increase in activity during ATP-dependent microtubule assembly. On the basis of these properties, it is proposed that microtubule protein contains an NDP kinase specifically associated with tubulin and its functions.     

Analysis of optimal phenotypic space using elementary modes as applied to Corynebacterium glutamicum

Background  

Quantification of the metabolic network of an organism offers insights into possible ways of developing mutant strain for better productivity of an extracellular metabolite. The first step in this quantification is the enumeration of stoichiometries of all reactions occurring in a metabolic network. The structural details of the network in combination with experimentally observed accumulation rates of external metabolites can yield flux distribution at steady state. One such methodology for quantification is the use of elementary modes, which are minimal set of enzymes connecting external metabolites. Here, we have used a linear objective function subject to elementary modes as constraint to determine the fluxes in the metabolic network of Corynebacterium glutamicum. The feasible phenotypic space was evaluated at various combinations of oxygen and ammonia uptake rates.