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.     

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.     

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.     

The rationalization of high enzyme concentration in metabolic pathways such as glycolysis

The cellular concentration of enzymes of some major metabolic pathways, such as glycolysis, can approach millimolarity. This concentration of enzyme can catalyze in vitro rates which are 100-fold higher than maximum pathway flux. In an attempt to understand the need for such high enzyme concentration, an artificial metabolic pathway of five enzymes (apropos the central enzymes of glycolysis) has been modeled. Numerical methods were then used to determine the effect of enzyme concentration on: (1) the change in total free metabolite concentration as the pathway changes from low flux to high flux, (2) the time lag (transient time) in the rate of final product formation upon the transition from low flux to high flux. Both the changes in metabolite pool size and the transient time decreased with increased enzyme concentrations. When all enzymatic reactions were assigned Keq of unity, a concentration for each enzyme of 25 microM is sufficient to provide a transient time of 1 sec. When Keq different from unity are introduced, more enzyme is required to provide comparably short transient times. Under the latter condition, a pathway of sufficiently low transient time would require all the enzyme available in mammalian muscle. It is shown that there is little scope for further increases in either enzyme concentration or of catalytic efficiency of independent enzymes. Therefore, an alternative method of increasing efficiency is considered in which enzyme-bound metabolites can serve directly as substrates for subsequent enzymes in a metabolic pathway.     

Optimizing the sensitivity of enzyme systems to perturbations from equilibrium

Algebraic derivations and numerical examples illustrate how metabolite pool sizes and enzyme rate constants influence the rate at which a multireactant enzyme system, initially poised in a near-equilibrium steady state, responds to small perturbations in the concentrations of the reactants. Certain enzymes, such as those employing the ordered bi bi catalytic mechanism, become relatively insensitive to perturbations when the reactants are all present at high concentrations. Other enzymes, such as those employing the ping-pong bi bi mechanism, are most sensitive to perturbations at high reactant concentrations. The ratio of the reactant concentrations to one another significantly alters sensitivity to perturbations; equations are presented for calculation of the reactant concentrations yielding maximal sensitivity to perturbations. Natural selection could choose metabolite pool sizes and enzyme rate constants which would optimize the performance of these systems, but changing metabolic loads (naturally or experimentally imposed) constantly alter the sensitivity of these systems to perturbations, changing the relative strengths of various connections in metabolic control networks.     

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.     

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.     

Regulation of the formation of protease byBacillus megaterium

The formation of protease takes place in washed cells ofBacillus megaterium incubated in a nitrogen-free medium. The rate of enzyme synthesis is decreased much less than that of cell proteins as compared with growing cells. The synthesis of protease in a nitrogen-free medium requires the presence of glucose. The omission of glucose results in stopping of the enzyme formation and substantial decrease of the rate of protein synthesis. Protease is not synthesized when the washed cells are incubated in a phosphate, free medium. The incubation of the cells in a nitrogen-free medium results in a decrease of the concentration of amino acids in the pool. In a phosphate-free medium the content of free amino acids increases temporarily and decreases again later. When the culture grown in the medium containing threonine or threonine and isoleucine in addition to NH₄ ions is transferred into the medium without amino acids, no protease formation is found during derepression of enzymes synthesizing both amino acids. The cells grown in a medium containing casamino acids begin to form the enzyme after a short lag period when transferred into the medium containing NH₄ as a sole nitrogen source or into a nitrogen-free medium.     

Structural and functional organization of Complex I in the mitochondrial respiratory chain

Metabolic flux control analysis of NADH oxidation in bovine heart submitochondrial particles revealed high flux control coefficients for both Complex I and Complex III, suggesting that the two enzymes are functionally associated as a single enzyme, with channelling of the common substrate, Coenzyme Q. This is in contrast with the more accepted view of a mobile diffusable Coenzyme Q pool between these enzymes. Dilution with phospholipids of a mitochondrial fraction enriched in Complexes I and III, with consequent increased theoretical distance between complexes, determines adherence to pool behavior for Coenzyme Q, but only at dilution higher than 1:5 (protein:phospholipids), whereas, at lower phospholipid content, the turnover of NADH cytochrome c reductase is higher than expected by the pool equation.     

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.     

Kinetic modeling can describe in vivo glycolysis in Entamoeba histolytica

Glycolysis in the human parasite Entamoeba histolytica is characterized by the absence of cooperative modulation and the prevalence of pyrophosphate-dependent (over ATP-dependent) enzymes. To determine the flux-control distribution of glycolysis and understand its underlying control mechanisms, a kinetic model of the pathway was constructed by using the software gepasi. The model was based on the kinetic parameters determined in the purified recombinant enzymes, and the enzyme activities, and steady-state fluxes and metabolite concentrations determined in amoebal trophozoites. The model predicted, with a high degree of accuracy, the flux and metabolite concentrations found in trophozoites, but only when the pyrophosphate concentration was held constant; at variable pyrophosphate, the model was not able to completely account for the ATP production/consumption balance, indicating the importance of the pyrophosphate homeostasis for amoebal glycolysis. Control analysis by the model revealed that hexokinase exerted the highest flux control (73%), as a result of its low cellular activity and strong AMP inhibition. 3-Phosphoglycerate mutase also exhibited significant flux control (65%) whereas the other pathway enzymes showed little or no control. The control of the ATP concentration was also mainly exerted by ATP consuming processes and 3-phosphoglycerate mutase and hexokinase (in the producing block). The model also indicated that, in order to diminish the amoebal glycolytic flux by 50%, it was required to decrease hexokinase or 3-phosphoglycerate mutase by 24% and 55%, respectively, or by 18% for both enzymes. By contrast, to attain the same reduction in flux by inhibiting the pyrophosphate-dependent enzymes pyrophosphate-phosphofructokinase and pyruvate phosphate dikinase, they should be decreased > 70%. On the basis of metabolic control analysis, steps whose inhibition would have stronger negative effects on the energy metabolism of this parasite were identified, thus becoming alternative targets for drug design.     

Inhibition by aphidicolin and dideoxythymidine triphosphate of a multienzyme complex of DNA synthesis from human cells

A multienzyme complex consisting of DNA polymerase and several DNA precursor-synthesizing enzymes was solubilized by gentle lysis of cultured human cells. This complex channelled the distal precursor [3H]dTMP into DNA. The patterns of inhibition of the complex by aphidicolin and dideoxythymidine triphosphate (ddTTP) suggested that the complex contained the replicative DNA polymerase, polymerase alpha. Inhibition by ddTTP was competitive with dTTP. This was exploited to estimate the effective concentration of [3H]dTTP at the site of DNA synthesis during channelling of [3H]dTMP into DNA. The estimated concentration (about 50 microM) was so high as to suggest that the solubilized complex was able to functionally compartmentalize DNA precursors.     

On the role of enzyme kinetic parameters in determining the effectiveness with which channelling can decrease the size of a metabolite pool

Recently, it has been argued that the phenomenon of direct transfer of intermediate metabolites between adjacent enzymes, also known as metabolic channelling, would not decrease the concentration of those intermediates in the bulk solution. However, this conclusion has been drawn by extrapolation from the results of simulations with a rather restricted set of parameters. We show that, for a number of kinetic cases, the existence of metabolic channelling can decrease the size of the soluble pool of intermediates. When the enzyme(s) downstream of the channel have a catalytic capacity that is large relative to the enzymes upstream of the channel, the decrease of concentration can be substantial (3 orders of magnitude).     

Purification and covalent coupling of calf brain prolidase

We have investigated methods of stabilizing prolidase by chemical modification and covalent coupling to various supports, for use in protein hydrolysis and possible use in enzyme replacement therapy. Purified acetone powder of calf brain prolidase was further purified by gel filtration on Sephadex G-200 and chromatography on DEAE-Sephadex A25. Polyacrylamide gel electrophoresis showed that the number of bands was reduced from 11 to 2. Since yields were low, the purified (NH₄)₂SO₄ fraction was used in all experiments. Thiolation of the enzyme reduced the amount of protein coupled to AH-or CH-Sepharose 4B. Activities were highest when the protein was linked through its carboxyl groups. The coupled enzyme showed much greater thermal stability than its free counterpart. Of the bound preparations, the thiolated was less stable than the untreated. Untreated and thiolated enzymes bound to either matrix showed higher activity at low pH and less at high pH than the free material. Thiolation shifted the pH maximum from 6.8 to 7.5. The free thiolated enzyme and that bound to activated SH-Sepharose 4B showed greater thermal stability and a broader pH range of optimal activity than the bound untreated enzyme. These results show that prolidase can be immobilized by coupling to an insoluble matrix through various types of covalent bonds with retention of activity and increased stability.     

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.     

Fractionation and purification of the enzymes stored in the latex of Carica papaya

The latex of the tropical species Carica papaya is well known for being a rich source of the four cysteine endopeptidases papain, chymopapain, glycyl endopeptidase and caricain. Altogether, these enzymes are present in the laticifers at a concentration higher than 1 mM. The proteinases are synthesized as inactive precursors that convert into mature enzymes within 2 min after wounding the plant when the latex is abruptly expelled. Papaya latex also contains other enzymes as minor constituents. Several of these enzymes namely a class-II and a class-III chitinase, an inhibitor of serine proteinases and a glutaminyl cyclotransferase have already been purified up to apparent homogeneity and characterized. The presence of a beta-1,3-glucanase and of a cystatin is also suspected but they have not yet been isolated. Purification of these papaya enzymes calls on the use of ion-exchange supports (such as SP-Sepharose Fast Flow) and hydrophobic supports [such as Fractogel TSK Butyl 650(M), Fractogel EMD Propyl 650(S) or Thiophilic gels]. The use of covalent or affinity gels is recommended to provide preparations of cysteine endopeptidases with a high free thiol content (ideally 1 mol of essential free thiol function per mol of enzyme). The selective grafting of activated methoxypoly(ethylene glycol) chains (with M(r) of 5000) on the free thiol functions of the proteinases provides an interesting alternative to the use of covalent and affinity chromatographies especially in the case of enzymes such as chymopapain that contains, in its native state, two thiol functions.     

Continuous monitoring of adenosine 5'-triphosphate in the microenvironment of immobilized enzymes by firefly luciferase

The study of enzymes sequestered in artificial or biological systems is generally conducted by indirect methodology with macroscopic measurements of reactants in the bulk medium. This paper describes a new approach with firefly luciferase to monitor ATP concentration directly in the microenvironment of enzymes producing or consuming ATP. Upon addition of ATP to immobilized firefly luciferase, the onset of light production is slower than that observed with the soluble enzyme, due to a slower diffusion of ATP to the immobilized enzyme. With immobilized pyruvate kinase, a relative accumulation of ATP inside the beads is demonstrated, as measured with coimmobilized firefly luciferase. The accumulation of product (ATP) is enhanced when the bead suspension is not stirred. This ATP in the beads is relatively inaccessible to soluble hexokinase added to the bulk medium. Similarly, a rapid ATP depletion in the microenvironment of immobilized hexokinase is demonstrated. This microscopic event is kinetically distinguishable from the slower macroscopic depletion of substrate in the bulk medium. The rate of depletion in the microenvironment depends on the local activity of the immobilized enzyme but not on the total amount of enzyme in suspension, as does the macroscopic phenomenon. The theoretical principles for the interaction of diffusion and catalysis in these systems are briefly summarized and discussed. These results are relevant to various molecular mechanisms proposed for membrane-bound enzyme action and regulation, derived from macroscopic kinetic measurements assuming a negligible diffusion control.     

Authenticity and reconstitution of immobilized enzymes: characterization and denaturation/renaturation of glucoamylase II.

Glucoamylase II (GA II) immobilized to Eupergit C and CIZ as a porous and nonporous matrix shows enzymatic characteristics indistinguishable from those of the free enzyme, except for reduced specific activity. Since this decrease is equally observed for both matrices, it has to be ascribed to nonproductive fixation of the enzyme or steric hindrance rather that perturbations caused by "inner diffusion" effects. Authenticity refers to the optimum pH for catalytic activity, Michaelis constants for starch and maltoheptaose, as well as identical stability toward temperature, pH, and guanidinium chloride (GdmCl). On the basis of these data, the two-state mechanism observed for the equilibrium transitions of the free enzyme may be assumed to hold also for the immobilized enzyme. Renaturation after preceding denaturation in 6.4 and 7 M GdmCl leads to widely differing yields depending on the conditions. Shifting the denaturant concentration stepwise back to nondenaturing GdmCl concentrations leads to a broad range of "hysteresis" accompanied by aggregation. Rapid dilution of the free and immobilized enzymes at pH greater than 6 and sufficiently low protein concentration leads to reactivation yields of 80 and 45%, respectively. For the free enzyme, reconstitution at lower pH is determined by the kinetic competition of folding and aggregation. In the case of the immobilized enzyme, "entangling" of the matrix with the unfolded polypeptide chain competes with renaturation.     

Effect of acetate and octanoate on tricarboxylic acid cycle metabolite disposal during propionate oxidation in the perfused rat heart

Tricarboxylic acid cycle pool size is determined by anaplerosis and metabolite disposal. The regulation of the latter during propionate metabolism was studied in isolated perfused rat hearts in the light of the characteristics of NADP-linked malic enzyme, which is inhibited by acetyl-CoA. The acetyl-CoA concentration was varied by infusions of acetate and octanoate, and the rate of metabolite disposal was calculated from a metabolic balance sheet compiled from the relevant metabolic fluxes. Propionate addition increased the tricarboxylic acid cycle pool size 4-fold and co-infusion of acetate or octanoate did not change it further. Propionate caused a decrease in the CoA-SH concentration and a 10-fold increase in the propionyl-CoA concentration. A paradoxical increase in the CoA-SH concentration was observed upon co-infusion of acetate in the presence of propionate, an effect probably caused by competitive inhibition of propionate activation. A more pronounced decline in the propionyl-CoA concentration was observed upon the co-infusion of octanoate. In a metabolic steady state, acetate and octanoate reduced propionate disposal only slightly, but did not increase the tricarboxylic acid cycle pool size. The results are in accord with the notion that the tricarboxylic acid pool size is mainly regulated by the anaplerotic mechanisms.     

Cellular concentrations of enzymes and their substrates

The activity of crude and pure enzyme preparations as well as the molecular weight of these enzymes were obtained from the literature for several organisms. From these data enzyme concentrations were calculated and compared to the concentration(s) of their substrates in the same organism. The data are expressed as molar ratios of metabolite concentration to enzyme site concentration. Of the 140 ratios calculated, 88% were one or greater, indicating that in general substrates exceed their cognate enzyme concentrations. Of the 17 cases where enzyme exceeds metabolite concentration, 16 were in glycolysis. The data in general justify the use of enzyme kinetic mechanisms determined in vitro in the construction of dynamic models which simulate in vivo metabolism.