A simple mechanism decreasing free metabolite pool size in static spatial channelling

We propose a simple mechanism which enables decrease of the free pool of channelled metabolite in static spatial channelling, when the concentration of the enzyme consuming the channelled metabolite is greater than the concentration of the enzyme producing this metabolite. Spatial channelling occurs between two enzymes when the common metabolite is released to a small space between these enzymes and does not form a ternary covalent complex with them, as is the case in covalent (dynamic or static) channelling. The mechanism proposed is qualitatively independent of rate constants, metabolite concentrations as well as other kinetic properties and is quantitatively significant for all physiologically relevant conditions. Calculations show that the free metabolite pool must decrease, when the concentration of the enzyme consuming the channelled metabolite is greater than the enzyme producing it. This mechanism is much more effective than increase in the concentration (or rate constant) of the enzyme consuming the metabolite in the absence of spatial channelling.     

Defining control coefficients in non-ideal metabolic pathways

The extent to which an enzyme controls a flux has been defined as the effect on that flux of a small modulation of the activity of that enzyme divided by the magnitude of the modulation. We here show that in pathways with metabolic channelling or high enzyme concentrations and conserved moieties involving both enzymic and non-enzymic species, this definition is ambiguous; the magnitude of the corresponding flux control coefficient depends on how the enzyme activity is modulated. This is illustrated with two models of biochemically relevant pathways, one in which dynamic metabolite channelling plays a role, and one with a moiety-conserved cycle. To avoid such ambiguity, we view biochemical pathways in a more detailed manner, i.e., as a network of elemental steps. We define 'elemental control coefficients' in terms of the effect on a flux of an equal modulation of the forward and reverse rate constant of any such elemental step (which may correspond to transitions between enzyme states). This elemental control coefficient is independent of the method of modulation. We show how metabolic control analysis can proceed when formulated in terms of the elemental control coefficients and how the traditional control coefficients are related to these elemental control coefficients. An 'impact' control coefficient is defined which quantifies the effect of an activation of all elemental processes in which an enzyme is involved. It equals the sum of the corresponding elemental control coefficients. In ideal metabolic pathways this impact control coefficient reduces to the traditional flux control coefficient. Differences between the traditional control coefficients are indicative of non-ideality of a metabolic pathway, i.e. of channelling or high enzyme concentrations.     

Channelling can decrease pool size.

It is widely considered that a possible advantage of metabolite channelling, in which a product of an enzyme is transferred to the next enzyme in a metabolic pathway without being released to the 'bulk' solution, is that channelling can decrease the steady-state concentrations of 'pool' intermediates. This then spares the limited solvent capacity of the cell, and reduces the loss of pathway flux due to leakage or instability of the free intermediate. Recently, however, based on simulations of a particular model of a 'dynamic' channel, Cornish-Bowden ["Failure of channelling to maintain low concentrations of metabolic intermediates" (1991) Eur. J. Biochem. 195, 103-108] has argued that this is not in fact the case; his simulations indicated that the channel was rather ineffective at decreasing the concentration of the pool intermediate, and in some cases actually increased it. However, although his simulations were restricted to very specific thermodynamic and kinetic parameters, he generalised his conclusions, arguing that "channelling has no effect on the free concentration of a channelled intermediate in a pathway". By showing that, for a number of kinetic cases, the concentration of the pool intermediate did decrease substantially with increased channelling, we demonstrate here that the conclusion of Cornish-Bowden is not correct. In particular, if the reaction catalysed by the enzymes forming the channel has an equilibrium constant K higher than 1, and if the enzyme removing the product of the channel reaction is kinetically competent, channelling in the model system studied by Cornish-Bowden (1991) can decrease the steady-state concentration of the pool by a factor of 1000, independently of the mechanism of the terminal reaction and under conditions of essentially constant overall flux. If the channel is a 'static' channel, the decrease in the pool can be to arbitrarily low levels. This conclusion also holds for a system in which other reactions may consume the pool intermediate. Thus, channelling can maintain metabolite concentrations at low levels.     

Temporal analysis of metabolic systems and its application to metabolite channelling

When a metabolic system undergoes a transition between steady states, the lag or transition time of the system is determined by the aggregated lifetimes of the metabolite pools. This allows the transition time, and hence the temporal responsiveness of the system, to be estimated from a knowledge of the starting and finishing steady states and obviates the need for dynamic measurements. The analysis of temporal response in metabolic systems may be integrated with the general field of metabolic control analysis by the definition of a temporal control coefficient (C) in terms of flux and concentration control coefficients. The temporal control coefficient exhibits summation and other properties analogous to the flux and concentration control coefficients. For systems in which static metabolite channels exits, the major kinetic advantage of channelling is a reduction in pool sizes and, as a result, a more rapid system response reflected in a reduced transition time. The extent of the channelling advantage may therefore be assessed from a knowledge of the system transition time. This reveals that no channelling advantage is achieved at high enzyme concentration (i.e., comparable to K_m) or, in the case of ‘leaky’ channels, where rapid equilibrium kinetic mechanisms obtain. In the case of a perfect channel with no leakage and direct transfer of metabolite between adjacent enzyme active sites, the transition time is minimized and equal to the lifetime of the enzyme–substrate complex.     

Failure of channelling to maintain low concentrations of metabolic intermediates

Computer modelling has been used to investigate the effect of direct transfer of metabolites between consecutive enzymes (channelling) on the free concentrations of the channelled metabolites. When a channelled intermediate cannot participate in any other reactions, any increase in channelling tends to increase its free concentration, albeit very slightly, unless the increase in net flux brought about by the channel is compensated for by a simultaneous decrease in the activity of the route through the free intermediate, in which case channelling has no effect at all on the free steady-state concentration of the channelled intermediate. If the free intermediate is capable of participating in side reactions, channelling can decrease these side reactions, but only slightly unless virtually all of the final product results from flux through the channel and the rate constants for the direct pathway are virtually zero. In general, channelling appears not to provide a useful mechanism for maintaining intermediate concentrations at low levels.     

Channelling and formation of 'active' formaldehyde in dimethylglycine oxidase

Here we report crystal structures of dimethylglycine oxidase (DMGO) from the bacterium Arthrobacter globiformis, a bifunctional enzyme that catalyzes the oxidation of N,N-dimethyl glycine and the formation of 5,10-methylene tetrahydrofolate. The N-terminal region binds FAD covalently and oxidizes dimethylglycine to a labile iminium intermediate. The C-terminal region binds tetrahydrofolate, comprises three domains arranged in a ring-like structure and is related to the T-protein of the glycine cleavage system. The complex with folinic acid indicates that this enzyme selectively activates the N10 amino group for initial attack on the substrate. Dead-end reactions with oxidized folate are avoided by the strict stereochemical constraints imposed by the folate-binding funnel. The active sites in DMGO are approximately 40 A apart, connected by a large irregular internal cavity. The tetrahydrofolate-binding funnel serves as a transient entry-exit port, and access to the internal cavity is controlled kinetically by tetrahydrofolate binding. The internal cavity enables sequestration of the reactive iminium intermediate prior to reaction with tetrahydrofolate and avoids formation of toxic formaldehyde. This mode of channelling in DMGO is distinct from other channelling mechanisms.     

Binding of malate dehydrogenase and NADH channelling to complex I

As previously reported, mitochondrial malate dehydrogenase (MDH) binds to purified complex I of the electron transport system. With conditions used in previous reports, MDH binds even more extensively, but probably predominantly non-specifically, to the matrix side of the inner mitochondrial membrane of submitochodrial particles (SMP). Herein we report experimental conditions for highly specific binding of malate dehydrogenase to complex I within SMP. These conditions permit us to demonstrate NADH channelling from malate dehydrogenase to complex I using the completing reaction test. This test, though not ideal for all situations, has several advantages over the enzyme buffering test previously used. These advantages should facilitate further studies elucidating NADH channeling to complex I from MDH and other dehydrogenases. Independent evidence of NADH channelling to the electron transport chain and the potential advantages of substrate channelling in general are also discussed. Substrate channelling from MDH in particular may be especially beneficial because of the unfavourable equilibrium and kinetics of this enzyme reaction.     

Structural organization of the mitochondrial respiratory chain

Two models exist of the mitochondrial respiratory chain: the model of a random organization of the individual respiratory enzyme complexes and that of a super-complex assembly formed by stable association between the individual complexes. Recently Sch?gger, using digitonin solubilization and Blue Native PAGE produced new evidence of preferential associations, in particular a Complex I monomer with a Complex III dimer, and suggested a model of the respiratory chain (the respirasome) based on direct electron channelling between complexes. Discrimination between the two models is amenable to kinetic testing using flux control analysis. Experimental evidence obtained in beef heart SMP, according to the extension of the Metabolic Control Theory for pathways with metabolic channelling, showed that enzyme associations involving Complex I and Complex III take place in the respiratory chain while Complex IV seems to be randomly distributed, with cytochrome c behaving as a mobile component. Flux control analysis at anyone of the respiratory complexes involved in aerobic succinate oxidation indicated that Complex II and III are not functionally associated in a stable supercomplex. A critical appraisal of the solid-state model of the mitochondrial respiratory chain requires its reconciliation with previous biophysical and kinetic evidence that CoQ behaves as a homogeneous diffusible pool between all reducing enzyme and all oxidizing enzymes: the hypothesis can be advanced that both models (CoQ pool and supercomplexes) are true, by postulating that supercomplexes physiologically exist in equilibrium with isolated complexes depending on metabolic conditions of the cell.     

Enzyme-enzyme interactions and control analysis. 2. The case of non-independence: heterologous associations

The association of different enzymes into a complex may induce changes in the kinetic parameters of its component enzymes. This implies that they cannot be treated as independent catalysts. It will affect the formulations and theorems of control analysis and necessitates the introduction of additional elasticities reflecting the effect of one enzyme on the rate of another. We show how this is achieved as an extension of the classical treatment. We present modified summation and connectivity theorems incorporating both homologous and heterologous interactions. The case of channelling of metabolites in such complexes is considered and an experimental method for its detection is suggested.     

Altered photosynthetic electron channelling into cyclic electron flow and nitrite assimilation in a mutant of ferredoxin:NADP(H) reductase

The mechanism by which plants regulate channelling of photosynthetically derived electrons into different areas of chloroplast metabolism remains obscure. Possible fates of such electrons include use in carbon assimilation, nitrogen assimilation and redox signalling pathways, or return to the plastoquinone pool through cyclic electron flow. In higher plants, these electrons are made accessible to stromal enzymes, or for cyclic electron flow, as reduced ferredoxin (Fd), or NADPH. We investigated how knockout of an Arabidopsis ( Arabidopsis thaliana ) ferredoxin:NADPH reductase (FNR) isoprotein and the loss of strong thylakoid binding by the remaining FNR in this mutant affected the channelling of photosynthetic electrons into NADPH- and Fd-dependent metabolism. Chlorophyll fluorescence data show that these mutants have complex variation in cyclic electron flow, dependent on light conditions. Measurements of electron transport in isolated thylakoid and chloroplast systems demonstrated perturbed channelling to NADPH-dependent carbon and Fd-dependent nitrogen assimilating metabolism, with greater competition in the mutant. Moreover, mutants accumulate greater biomass than the wild type under low nitrate growth conditions, indicating that such altered chloroplast electron channelling has profound physiological effects. Taken together, our results demonstrate the integral role played by FNR isoform and location in the partitioning of photosynthetic reducing power.     

Subtleties in control by metabolic channelling and enzyme organization

Because of its importance to cell function, the free-energy metabolism of the living cell is subtly and homeostatically controlled. Metabolic control analysis enables a quantitative determination of what controls the relevant fluxes. However, the original metabolic control analysis was developed for idealized metabolic systems, which were assumed to lack enzyme-enzyme association and direct metabolite transfer between enzymes (channelling). We here review the recently developed molecular control analysis, which makes it possible to study non-ideal (channelled, organized) systems quantitatively in terms of what controls the fluxes, concentrations, and transit times. We show that in real, non-ideal pathways, the central control laws, such as the summation theorem for flux control, are richer than in ideal systems: the sum of the control of the enzymes participating in a non-ideal pathway may well exceed one (the number expected in the ideal pathways), but may also drop to values below one. Precise expressions indicate how total control is determined by non-ideal phenomena such as ternary complex formation (two enzymes, one metabolite), and enzyme sequestration. The bacterial phosphotransferase system (PTS), which catalyses the uptake and concomitant phosphorylation of glucose (and also regulates catabolite repression) is analyzed as an experimental example of a non-ideal pathway. Here, the phosphoryl group is channelled between enzymes, which could increase the sum of the enzyme control coefficients to two, whereas the formation of ternary complexes could decrease the sum of the enzyme control coefficients to below one. Experimental studies have recently confirmed this identification, as well as theoretically predicted values for the total control. Macromolecular crowding was shown to be a major candidate for the factor that modulates the non-ideal behaviour of the PTS pathway and the sum of the enzyme control coefficients.     

Mitochondrial creatine kinase - a square protein

The recently determined structure of octameric mitochondrial creatine kinase has provided new insights into the functioning of this enzyme and its role in channelling energy from the mitochondria to the cytoplasm. Creatine kinase, a member of the family of guanidino kinases, is structurally similar to glutamine synthetase, suggesting a possible evolutionary link between both protein families     

Studies on the effects of structure on the behavior of enzyme systems

The effects of structural features on various properties of enzyme systems are studied. Some of the effects are: in a homogeneous reaction, enzyme compartmentalization decreases the rate; in a heterogeneous reaction, compartmentalization increases the rate. The steady-state concentration of intermediates is larger in a non-uniform than in uniform systems. Periodicities do not generally occur in the common kinetic systems; they do occur in autocatalytic systems, but compartmentalization reduces their probability of occurrence. The conditions for overshoot are different for uniform and non-uniform systems. Multiple stable steady states are not a common occurrence among biologically typical reactions; they do occur in combined autocatalytic and surface systems (a mechanism for the gener position effect is suggested by this property). The local pH is affected by the enzyme aggregation as well as by the geometry of the enzyme structure. A 2-step system can give rise to the characteristic rate vs. pH curve, where the optimum is not necessarily at isoelectric point. The expression for the osmotic pressure inside a spherical particle is deduced. The pressure is shown to be dependent on the radius. The rate inside a cell particle is shown to be determined by the shape of the particle.     

Multiple glucose 6-phosphate pools or channelling of flux in diverse pathways?

Glucose 6-phosphate is an intermediate of pathways of glucose utilization and production as well as a regulator of enzyme activity and gene expression. Studies on the latter functions are in part based on measurement of the glucose 6-phosphate content in a whole-cell extract. Several studies have suggested that there are multiple subcellular pools of glucose 6-phosphate. It is proposed that this data can be interpreted in terms of channelling of metabolic intermediates through multiple pathways of glucose metabolism with leakage of glucose 6-phosphate from the channels into a single free pool. It is also proposed that measurement of total tissue content of glucose 6-phosphate approximates the free pool.     

A novel gamma-N-methylaminobutyrate demethylating oxidase involved in catabolism of the tobacco alkaloid nicotine by Arthrobacter nicotinovorans pAO1.

Nicotine catabolism, linked in Arthrobacter nicotinovorans to the presence of the megaplasmid pAO1, leads to the formation of gamma-N-methylaminobutyrate from the pyrrolidine ring of the alkaloid. Until now the metabolic fate of gamma-N-methylaminobutyrate has been unknown. pAO1 carries a cluster of ORFs with similarity to sarcosine and dimethylglycine dehydrogenases and oxidases, to the bifunctional enzyme methylenetetrahydrofolate dehydrogenase/cyclohydrolase and to formyltetrahydrofolate deformylase. We cloned and expressed the gene carrying the sarcosine dehydrogenase-like ORF and showed, by enzyme activity, spectrophotometric methods and identification of the reaction product as gamma-aminobutyrate, that the predicted 89 395 Da flavoprotein is a demethylating gamma-N-methylaminobutyrate oxidase. Site-directed mutagenesis identified His67 as the site of covalent attachment of FAD and confirmed Trp66 as essential for FAD binding, for enzyme activity and for the spectral properties of the wild-type enzyme. A Km of 140 microm and a kcat of 800 s(-1) was determined when gamma-N-methylaminobutyrate was used as the substrate. Sarcosine was also turned over by the enzyme, but at a rate 200-fold slower than gamma-N-methylaminobutyrate. This novel enzyme activity revealed that the first step in channelling the gamma-N-methylaminobutyrate generated from nicotine into the cell metabolism proceeds by its oxidative demethylation.     

Chloride-ion stimulation of the tonoplast H+-translocating ATPase from Hevea brasiliensis (rubber tree) latex. A dual mechanism.

The effect of Cl- and other anions on the tonoplast H+-translocating ATPase (H+-ATPase) from Hevea brasiliensis (rubber tree) latex was investigated. Cl- and other anions stimulated the ATPase activity of tightly sealed vesicles prepared from Hevea tonoplast, with the following decreasing order of effectiveness: Cl- greater than Br- greater than SO4(2-) greater than NO3-. As indicated by the changes of the protonmotive potential difference, anion stimulation of tonoplast H+-ATPase was caused in part by the ability of these anions to dissipate the electrical potential. This interpretation assumes not a channelling of these anions against a membrane potential, negative-inside, but a modification of the permeability of these ions through the tonoplast membrane. In addition, Cl- and the other anions stimulated the ATPase activity solubilized from the tonoplast membrane. Consequently, the tonoplast H+-pumping ATPase can be considered as an anion-stimulated enzyme. These results are discussed in relation to various models described in the literature for the microsomal H+-ATPase systems claimed as tonoplast entities.     

Control in channelled pathways. A matrix method calculating the enzyme control coefficients

The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.     

Quantitative studies of enzyme-substrate compartmentation,functional coupling and metabolic channelling in muscle cells

Some historical aspects of development of the concepts of functional coupling, metabolic channelling, compartmentation and energy transfer networks are reviewed. Different quantitative approaches, including kinetic and mathematical modeling of energy metabolism, intracellular energy transfer and metabolic regulation of energy production and fluxes in the cells in vivo are analyzed. As an example of the system with metabolic channelling, thermodynamic aspects of the functioning the mitochondrial creatine kinase functionally coupled to the oxidative phosphorylation are considered. The internal thermodynamics of the mitochondrial creatine kinase reaction is similar to that for other isoenzymes of creatine kinase, and the oxidative phosphorylation process specifically influences steps of association and dissociation of MgATP with the enzyme due to channelling of ATP from adenine nucleotide translocase. A new paradigm of muscle bioenergetics - the paradigm of energy transfer and feedback signaling networks based on analysis of compartmentation phenomena and structural and functional interactions in the cell is described. Analysis of the results of mathematical modeling of the compartmentalized energy transfer leads to conclusion that both calcium and ADP, which concentration changes synchronously in contraction cycle, may simultaneously activate oxidative phosphorylation in the muscle cells in vivo. The importance of the phosphocreatine circuit among other pathways of intracellular energy transfer network is discussed on the basis of the recent data published in the literature, with some experimental demonstration. The results of studies of perfused rat hearts with completely inhibited creatine kinase show significantly decreased work capacity and respectively, energy fluxes, in these hearts in spite of significant activation of adenylate kinase system (Dzeja et al. this volume). These results, combined with those of mathematical analysis of the energy metabolism of hearts of transgenic mice with switched off creatine kinase isoenzymes confirm the importance of phosphocreatine pathway for energy transfer for cell function and energetics in mature heart and many other types of cells, as one of major parts of intracellular energy transfer network and metabolic regulation.     

On the pseudo-steady-state approximation and Tikhonov theorem for general enzyme systems

The effectiveness of the Tikhonov theorem for justifying the so-called pseudo-steady-state approximation (PSSA) in general closed enzyme systems is proved under a widely satisfied sufficient condition on the ligand stoichiometry, which also allows us to state that all slow variables of the degenerate system are driven by a single scalar function (the pseudo- steady-state rate equation). Finally, remarks on the perturbative small parameter and open enzyme systems are made.     

Thiol dependent oxidation of enzymes: The last chance against oxidative stress

• 1.1. A survey of known effects of oxidized thiols on enzyme activity reveals a potential concerted action on metabolic pathways determining an impairment of anabolic reduction processes and an activation of the oxidative arm of the hexose monophosphate shunt. Thus it appears that, following oxidative stress, the increase of disulphides may act in restoring a reduced state in the cell by specifically channelling the metabolic energy flux.