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Kinetic Properties of the Phosphofructokinase from Erythrocytes of Rats and Rabbits. 2. The Influence of Effectors Under Nearly Cellular Conditions
Abstract
The phosphofructokinase of the red cells of rats is exquisitely sensitive to inhibition by ATP. The apparent k 1 for ATP is decreased with lower pH values and fructose‐6‐phosphate concentrations. 2,3‐Bisphophoglycerate, which is present in the red cells of man and many mammals, inhibits the phosphofructokinase in a synergistic manner with ATP. The inhibitory effect of phospho enol pyruvate is biologically insignificant. It may be estimated that the enzyme would be practically completely inactive under cellular conditions without the action of positive effectors.
There exist a multitude of positive effectors. Significant activations under cellular conditions are exercised by AMP, glucose 1,6‐bisphosphate and inorganic phosphate. Fructose 1,6‐bisphosphate activates to a limited extent and ADP only at alkaline pH values. All positive effectors produce a decreased inhibition by ATP and increased affinity of the enzyme for fructose 6‐phosphate. AMP is the activator with the highest affinity, while glucose 1,6‐bisphosphate may be considered as a baseline activator owing to its sluggish turnover.
The data may be fitted in a qualitative manner to the model of Monod, Wyman and Changeux. It is possible that the negative anionic effectors act on the same site.
Traditionally biochemistry has been concerned with analyzing the components of living systems, and has paid less attention to how they interact. While the information available about individual entities such as proteins and nucleic acids is now immense and still growing rapidly, the task of determining how they interact to form a living system is now only beginning, especially with respect to quantitative behavior. In reviewing a recent book, Dr. J. S. King (1975), the editor of Clinical Chemistry has written “biochemistry was mainly a reductionist science; only lately has it become possible to fit together facts and observations into what is beginning to be a coherent -- and thus more interesting -- whole”.
1.1. As part of a continuing study on the regulation of aerobic fermentation in protozoans, we investigated the phosphofructokinase (PFK) of the protozoan Crithidia fasciculata.2.2. The enzyme is an allosteric protein with respect to its substrate, fructose-6-phosphate, and 5'AMP acts as a positive heterotropic modifier.3.3. It is activated by ATP in a hyperbolic manner, this activation being dependent on the concentration of Mg-ATP chelate (MA).4.4. Whenever free ATP (Af) is in excess of MA, the enzyme is inhibited.5.5. Af is a competitive inhibitor of AMP.6.6. Compounds known to be positive or negative heterotropic modifiers of PFK in other systems are without effect.7.7. Since most ATP in the cell is present as the chelate, the lack of regulation of glycolysis by PFK in this group of organisms probably is a function of its failure to respond to metabolic intermediates.
The activity of the phosphofructokinase from erythrocytes of rats and rabbits, and presumably of the enzyme from other sources depend on the presence of either K+ or NH4+ ions. Their effects are not due to ionic strength. The apparent activation constant, KD, is about 1 mM for NH4+ and 10 mM for K+. While K+ ions appear to act only as activators of the catalytic site, NH4+ ions have a double action. They act both as activators and as positive effectors which abolish the cooperativity, presumably by affecting the interaction between the subunits. They increase the affinity of the enzyme for fructose 6-phosphate and ATP as substrates, while the affinity for ATP as inhibitor is weakened. These effects are probably secondary to the changed interaction between the subunits. It is concluded that only data on the phosphofructokinase in K+ system are representative of normal intracellular conditions. In certain physiological and pathological states the effect of NH4+ ions on the allosteric properties of the enzyme is probably important.
Pi is an activator of both the K+- and the NH4+-activated enzyme, with an approximate KD of 1.6 mM. Its effect is therefore of importance under physiological and pathological conditions.
The data on the purified K+-activated enzyme are in good agreement with changes of the metabolic pattern of the intact erythrocyte.
Historical Background Introduction Measurement of Phosphofructokinase Activity Substrate Specificity The Reaction Mechanism Eucaryote Phosphofructokinase Procaryote Phosphofructokinase Allosteric Properties of Phosphofructokinase Chemical Modification of Ligand Binding Sites The Role of Phosphofructokinase in the Regulation of Glycolysis Concluding Remarks
Culture, blood and intracellular forms of Trypanosoma cruzi have a high rate of endogenous oxygen uptake and probably utilize amino acids and carbohydrates as their exogenous energy sources. It is likely that triglyceride is the main energy reserve. Oxidation of carbohydrate by all forms is probably via a glycolytic sequence and a complete tricarboxylic acid cycle. These data suggest that the substrates utilized and catabolic pathways present in mammalian forms of T. cruzi are similar to those of culture forms of the organism and are quite distinct from those of the bloodstream forms of African trypanosomes.
The time course of the rate of the glycolysis of human erythrocytes and of some metabolites were determined before and after rapid deoxygenation at constant intracellular pH. For this purpose stripped deoxygenated haemoglobin was used as a rapid oxygen acceptor. Deoxygenation causes an increase of the glycolytic rate by 26%. Glucose 6-phosphate is decreased while the adenine nucleotides and 2,3-bisphosphoglycerate remain constant. Fructose 1,6-bisphosphate and the triose phosphates decrease transiently before rising. The data can be explained by increased binding of phosphocompounds to deoxygenated as compared with oxygenated haemoglobin. Thereby the control enzymes hexokinase and phosphofructokinase are influenced. It is concluded that under physiological conditions changes in the oxygenation state of haemoglobin per se alter the glycolytic rate.
1. To investigate the mechanism of the reversible inactivation of pig spleen phosphofructokinase by ATP, the effect of order of addition of reactants (substrates, effectors and enzyme solution) was studied by preincubating the enzyme before assay with various combinations of its substrates and effectors. 2. Preincubation of the enzyme with MgATP or ATP at pH7.0 before addition of fructose 6-phosphate caused a rapid and much greater inhibition of activity than that observed when the reaction (carried out at identical substrate concentrations) was initiated with enzyme. 3. The rapid inhibition caused by preincubation with ATP, together with the sigmoidal response to fructose 6-phosphate and activation by AMP, were all blocked by prior photo-oxidation of the enzyme with Methylene Blue, which selectively destroys the inhibitory binding site for ATP [Ahlfors & Mansour (1969) J. Biol. Chem.244, 1247-1251]. 4. Fructose 6-phosphate, but not Mg(2+), protected phosphofructokinase from inhibition during preincubation with ATP in a manner that was sigmoidally dependent on the fructose 6-phosphate concentration. 5. Mg(2+), by protecting the enzyme from the inhibitory effect of preincubation at low pH (7.0) and by preventing its activation during preincubation with fructose 6-phosphate, demonstrated both a weak activating effect in the absence of the other substrates and a stronger inhibitory effect in the presence of fructose 6-phosphate. 6. Positive effectors (K(+), NH(4) (+), AMP and aspartate) protected the enzyme from inhibition during preincubation with MgATP in proportion to their potency as activators, but citrate potentiated the ATP inhibition. P(i) significantly slowed the inactivation process without itself acting as a positive effector. 7. The non-linear dependence of the initial rate of the unmodified enzyme on protein concentration (associated with increased positive homotropic co-operativity to fructose 6-phosphate) was intensified by preincubation with ATP and abolished by photo-oxidation. 8. The results are interpreted in terms of an association-dissociation model which postulates that protonation, at low pH, of a photo-oxidation-sensitive inhibitory site for ATP allows more rapid dissociation of an active tetramer to an inactive dimeric species.
Phosphofructokinases from rat erythrocytes and rabbit muscle have been compared in their kinetic behavior with respect to monovalent cation activation and ATP inhibition.
Both ammonium and potassium ions affect the muscle enzyme in a two-fold manner: they act both as activators and effectors. On the other hand only ammonium exerts the two-fold effects oil the erythrocyte enzyme, while the potassium ions activate without affecting cooperativity.
The lower ATP inhibition of muscle phosphofructokinase may be partially explained by the action of potassium ions on the cooperative behavior of the enzyme.
The differences between the phosphofructokinases from erythrocytes and muscle in the potassium type-II activation and ATP inhibition represent an organ specifity. Furthermore, the inhibition constants for 2,3-bisphosphoglycerate differ by 10-fold between the two enzymes.
A simple mathematical model for glycolysis in erythrocytes is presented which takes into account ATP synthesis and consumption. The system is described by four ordinary differential equations. Conditions in vivo are described by a stable steady state. The model predicts correctly the metabolite concentrations found in vivo. The parameters involved are in agreement with data on the separate steps. The metabolite changes found in pyruvate kinase-deficient erythrocytes and the species variations among erythrocytes from different animals are described satisfactorily. The roles of the enzymes in the control of metabolites and glycolytic flux are expressed in the form of a control matrix and control strengths [R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89-95] respectively. Erythrocytes from various species are shown to be adapted to a maximal ATP-consumption rate. The calculated eigenvalues reveal the pronounced time-hierarchy of the glycolytic reactions. Owing to the slowness of the 2,3-bisphospho-glycerate phosphatase reaction, quasi-steady states occur during the time-interval of about 0.5-2h incubation, which are defined by perturbed 2,3-bisphosphoglycerate concentrations. The theoretical predictions agree with experimental data. In the quasi-steady state the flux control is exerted almost entirely by the hexokinase-phosphofructokinase system. The model describes satisfactorily the time-dependent changes after addition of glucose to starved erythrocytes. The theoretical consequences are discussed of the conditions in vitro with lactate accumulation and the existence of a time-independent conservation quantity for the oxidized metabolites. Even in this closed system quasi-steady states occur which are characterized by approximately constant concentrations of all glycolytic metabolites except for the accumulation of lactate, fructose 1,6-bisphosphate and triose phosphate.
The interaction of phosphofructokinase with NH4+, AMP, ATP, citrate, MgATP or fructose 6-phosphate, and in part with their mixtures forming either binary or ternary complexes has been studied by means of ultraviolet difference spectroscopy and circular dichroism spectroscopy in the wavelength range 265 – 300 nm with the aim of characterizing the conformational corollaries of the ligand effects on phosphofructokinase.
The positive as well as the negative effectors change phosphofructokinase conformation in different ways, not easily interpretable in terms of one active and one inactive enzyme conformation. The spectroscopic equivalents of phosphofructokinase conformation changes resulting from catalytic activity are similar to those produced by the reaction products. The ligand concentration-dependent changes of absorption differences in the tryptophyl, tyrosyl and phenylalanyl region parallel each other, i.e. the interactions of the ligands with phosphofructokinase are not confined to specific aromatic side chains, but involve conformation changes of the large domains of the protein. ATP affinity to the enzyme shows temperature-dependent biphasic changes so that ATP binding appears to be either an entropy-driven or enthalpy-driven process. The dissociation constants of the ligands derived from spectroscopic titration of binary complex formation are comparable to those calculated from kinetic experiments. MgATP and fructose 6-phosphate each alone change phosphofructokinase conformation by binary complex formation in keeping with a random order of reaction sequence.
The influence of the positive effectors AMP, sulphate, glucose 1,6-bisphosphate and the negative effector 2,3-bisphoglycerate on rat erythrocyte phosphofructokinase has been investigated. The kinetic data have been fitted to the Monod-Wyman-Changeux model as well as to a model based on a closed association-dissociation equilibrium. The application of the fitting procedure yields for both models a good correspondence between theoretical and experimental data and equal results with respect to the action of the effectors on the enzyme. The corresponding dissociation constants for the binding of the positive effectors to the active state are: AMP 35 μM, sulphate 0.43 mM and glucose 1,6-bisphosphate 15 μM. 2,3-Bisphosphoglycerate as an inhibitor stabilizes the inactive state (dissociation constant: 1.4 mM).
A preliminary discrimination between the Monod-Wyman-Changeux model and the association-dissociation model has been attempted.
1.1. Phosphofructokinase (EC 2.7.1.11) was purified from monkey liver.2.2. The enzyme was inhibited at high concentrations of ATP. This inhibition was relieved by cyclic AMP or raised concentrations of F6P and/or MgCl2.3.3. At pH 7.0 the kinetics were found to be hyperbolic with sub-inhibitory levels of ATP, and sigmoidal with respect to F6P.4.4. Plots of activity vs MgCl2 concentration were hyperbolic at low concentrations of ATP but biphasic at a high level of ATP (2 mM).5.5. The properties of the enzyme appear to be qualitatively similar to those of other mammalian phosphofructokinases but show some quantitative differences.
Recycling of fructose 6-phosphate and fructose 1,6-bisphosphate in the rat liver under gluconeogenic and glycolytic conditions was investigated with a computer model containing representations of the kinetic properties of phosphofructokinase and fructose 1,6-bisphosphatase under realistic physiological conditions. The two enzyme submodels were constructed from data for the isolated enzymes in vitro by formal optimization. Tissue metabolite concentrations were corrected for cytosolic/mitochondrial compartmentation and effects of chelation and protonation equilibria. This model, which mostly considers the behavior of livers from starved rats, predicts negligible recycling under physiologically realistic conditions. Metabolic regulation of fructose 6-phosphate, the magnesium ion concentration and the distribution of adenine nucleotides appear to prevent operation of a 'futile cycle' in vivo. Rate-limiting chemical species were identified by sensitivity analysis.
Arginine deiminase (EC 3.5.3.6) has been shown to have regulatory properties. The activity was observed to be sigmoidal with respect to substrate concentrations. Addition of histidine to the system caused the abolition of sigmoidal responses. The regulatory properties of the enzyme as well as the desensitising action of histidine could also be demonstrated with whole cell suspensions. The pH of the system also seemed to influence modulations in the enzyme.
1. Adenosine increases the adenine nucleotide pool in rat erythrocytes. Hence, we tested the effect of the nucleoside on the glycolytic pathway in red blood cells. 2. A 2.5-fold increase in the level of fructose-1,6-bisphosphate and a 34% augmentation in lactate pool were observed in rat erythrocytes, 30 min after adenosine treatment. 3. Under conditions preventing adenosine metabolism, 1 microM nucleoside addition to isolated erythrocytes induced an 89% increase in lactate production and an increase in glucose consumption. 4. Activation of red cell phosphofructokinase (PFK) is produced by addition of microM concentrations of adenosine. Our data suggest a role for adenosine in the glycolysis flux regulation through PFK activation.
As in mammalian cells, phosphofructokinase (PFK) is of major regulatory importance in the glucose metabolism of Plasmodium berghei. The malarial enzyme shows allosteric properties similar to PFK from various sources; it is activated by fructose-6-phosphate and inhibited by ATP, but differs with respect to allosteric regulation. Enzyme activity is only marginally increased by AMP, a potent activator of many phosphofructokinases. Phosphoenolpyruvate, which is reported to inhibit PFK activity, efficiency activates the malarial enzyme. No activation by ADP was observed. Instead, ADP inhibits the enzyme non-allosterically and competitively to the substrate MgATP. Phosphate stimulates the catalytic activity of malarial PFK independently of the activation by F6P and PEP.
The regulatory properties of phosphofructokinase from rat mucosa, liver, brain and muscle were investigated. Mucosal phosphofructokinase displayed cooperativity with respect to fructose 6-phosphate at pH 7.0 and so did the muscle, brain and liver isoenzymes. All these four isoenzymes were inhibited by ATP, the mucosal isoenzyme being the least inhibited. They were also inhibited by citrate and creatine phosphate. AMP, ADP, glucose 1,6-diphosphate, fructose 2,6-bisphosphate and inorganic phosphate were all strong activators for the mucosal, brain, liver and muscle phosphofructokinase, but the mucosal isoenzyme was found to be more activated than the others, accounting for the higher rates of glycolysis observed in mucosa. The results suggest that mucosal phosphofructokinase is unique and different from all the other isoenzymes.
Hexokinase (ATP: hexose 6-phosphotransferase, E.C.2.7.1.1) and phosphofructokinase (ATP:fructose-6-phosphate 1-phosphotransferase, E.C.2.7.1.11), two key regulatory enzymes of the glycolytic pathway in vertebrate cells, have been isolated and partially purified from Trypanosoma (Schizotrypanum) cruzi epimastigotes. Both enzymes are associated with particles sedimentable at 105 000 X gav for 1 h and have a high degree of latency; they can be solubilized by sonication. Hexokinase catalyses the phosphorylation of a series of monosaccharides at the following relative rates: D-glucose (100) congruent to D-fructose (97) greater than 2-deoxy-D-glucose (72) congruent to mannose (69) greater than 2-amino-D-glucose (63) greater than 3-O-methyl-D-glucose (21). Very little or no phosphorylating activity was found for D-galactose, N-acetyl-2-amino-D-glucose or 1-alpha-methyl-D-glucose. D-Glucose phosphorylation at fixed ATP concentration follows simple Michaelis-Menten kinetics with Km = 40 microM and Vmax = 440 nmol min-1 mg-1 protein. D-Mannose, 2-deoxy-D-glucose and N-acetyl-2-amino-D-glucose act as competitive inhibitors of glucose phosphorylation, suggesting a single kinase. Mg2+-ATP is the preferred phosphoryl donor, ITP and GTP being much less effective. T. cruzi hexokinase is not inhibited by D-glucose 6-phosphate, or by any of the following compounds (2 mM):D-fructose 6-phosphate, D-fructose 1,6-diphosphate, D-glucose 1,6-diphosphate, phosphoenol pyruvate, L-malate and citrate. Phosphofructokinase displays simple Michaelis-Menten kinetics with no evidence of sigmoidicity with respect to D-fructose 6-phosphate at all ATP concentrations tested, giving a Km of 1.31 mM and Vmax = 400 nmol min-1 mg-1 protein at optimal ATP levels. With respect to ATP, the enzyme exhibits Michaelis-Menten kinetics at low concentration (less than 1 mM) of the substrate (Km = 40 microM at 5 mM MgCl2, pH 7.4). A moderate inhibition is observed at high ATP levels (70% of maximal activity at 2 mM). GTP can substitute for ATP as the phosphoryl donor (Km = 79 microM under the same conditions), but produces only very small inhibitory effects at high concentrations. 5'-AMP activates the enzyme by decreasing its Km with respect to D-fructose 6-phosphate without affecting Vm. Other well-known regulators of the activity of this enzyme in procaryote and vertebrate systems such as citrate, phosphoenol pyruvate, ammonium and phosphate ions have no effect in T. cruzi.
We have studied the erythrocyte enzyme phosphofructokinase (PFK) from two strains of Long-Evans rats with genetically determined differences in erythrocyte 2,3-diphosphoglycerate (DPG) levels. The DPG difference is due to two alleles at one locus. With one probable exception, the genotype at this locus is always associated with the hemoglobin (Hb) electrophoretic phenotype, due to a polymorphism at the III beta-globin locus. The enzyme PFK has been implicated in the DPG difference because glycolytic intermediate levels suggest that this enzyme has a higher in vivo activity in High-DPG strain rats, although the total PFK activity does not differ. We report here that partially purified erythrocyte PFK from Low-DPG strain cells is inhibited significantly more at physiological levels of DPG (P less than 0.01) than PFK from High-DPG strain erythrocytes. Citrate and adenosine triphosphate also inhibit the Low-DPG enzyme more than the High-DPG enzyme. Therefore, a structurally different PFK, with a greater sensitivity to inhibitors, may explain the lower DPG and ATP levels observed in Low-DPG strain animals. These data support a two-locus (Hb and PFK) hypothesis and provide a gene marker to study the underlying genetic and physiologic relationships of these loci.
A metabolic osmotic model of red blood cells is presented which takes into account the main reaction steps of glycolysis and the passive and active fluxes of ions across the cell membrane. Cellular energy metabolism and osmotic behaviour are linked by the ATP consumption for the active transport of cations as well as by the osmotic action of the glycolytic intermediate 2,3-diphosphoglycerate (2,3-DPG). The model is based on a system of differential equations describing the metabolic reactions and transport processes. Further, two algebraic conditions for the osmotic equilibrium and the electroneutrality of the cell are considered. Using realistic system parameters the model allows the calculation of a great number of dependent variables, among them the cell volume, the concentrations of metabolites and ions and the transmembrane potential. Only stationary states are considered. The parameter dependence of important model variables is characterized by control coefficients. The main results are: (a) The volume of erythrocytes is mainly determined by the permeabilities of the leak fluxes of cations, the content of hemoglobin and the activity of the hexokinase-phosphofructokinase system of glycolysis; (b) Changes of volume affect the glycolytic rate mainly by changing the concentration of ATP which is a regulator of glycolysis; (c) A change in the membrane area may affect the other cell properties only if it is connected with variations of the number of active and leak sites of the membrane.
According to the mathematical model, the dependence of the rate of glycolysis on the ATP concentration can be represented by the bell‐shaped curve with the descending part at the concentration of ATP close to physiological values. The existence of the descending part is a result of the strong inhibition of phosphofructokinase by ATP and hexokinase by glucose 6‐phosphate and provides stabilisation of the intracellular concentration of ATP.
Using arsenate as an uncoupler of the oxidation of glucose and ATP synthesis, the dependence of the rate of glycolysis on the ATP concentration in erythrocytes was measured. This dependence (glycolysis characteristic) is represented by a bell‐shaped curve. The normalized glycolysis characteristics are the same for all the donors investigated.
The increase of permeability of the erythrocyte membrane to monovalent cations by the polyene antibiotic levorin leads to an increase of glycolytic rate in erythrocytes (40–70%) and to a decrease in the ATP concentration (15%) and glucose 6‐phosphate (25–60%). The data obtained with levorin, and also other results on Na, K‐ATPase activation are in a good agreement with the characteristic obtained using arsenate.
In all cases, inhibition of Na ⁺ , K ⁺ ‐ATPase of erythrocytes by ouabain leads to the decrease of the rate of lactate production (10–20%) and increase of the concentration of glucose 6‐phosphate (14–40%). The ATP concentrations remains almost unchanged or is only slightly increased. The rate of glucose utilisation in erythrocytes from different donors show two types of behaviour. In the first type of erythrocyte it drops proportionally to the decrease in the lactate production rate; in the second type of erythrocyte it remains unchanged.
The experimental results presented are in qualitative agreement with the predictions of the mathematical model.
Phosphofructokinase (PFK) from Rana ridibunda erythrocytes was purified about 570-fold by column chromatography on Cibacron Blue Sepharose. The resulting enzyme preparation had a specific activity of 1.94 U/mg protein and a pH maximum of 7.6. The molecular weight as determined by HPLC chromatography was 330,000 Da. The S0.5 value for fructose-6-phosphate (F6P) was 5.6 mM and the Km for ATP 0.87 mM. The enzyme was sensitive to inhibition by ATP which was increased with lower F6P concentrations. At physiological levels of 2,3-diphosphoglycerate (0.35 mumol/ml RBC), 20% of PFK activity was inhibited. Significant activations under cellular conditions were exercised by AMP and, to a lesser extent, by Pi. Micromolar concentrations of fructose-2,6-bisphosphate and glucose-1,6-bisphosphate were also potent activators of the erythrocyte enzyme. Fructose-1,6-bisphosphate (10-50) microM activated the enzyme to a limited extent. With respect to these effects, it is suggested that PFK is a significant enzyme in regulating the glycolytic flux of Rana ridibunda red blood cells. The existence of a regulatory mechanism controlled by the energy status of the red cell, as well as the state of oxygenation of haemoglobin, is discussed, in which PFK occupies a central role.
Phosphofructokinase in rabbit skeletal muscle was assayed before and after intravenous epinephrine administration. Assays at optimal pH (8.2) and in the presence of optimal substrate concentrations showed no significant difference in enzyme activity. Muscle extracts prepared in the presence of caffeine were assayed under conditions optimal for allosteric kinetics (pH 6.9 and low substrate concentrations) and in the presence of cyclic 3′,5′-AMP. These assays showed that enzyme activity in epinephrine extracts was much higher than control activity. Under the following conditions control activity increased and activity in epinephrine extracts was not significantly changed: (a) if muscle extracts were prepared in the presence of fructose-1,6-P2; (b) when the substrate concentrations in the assay mixture were high; (c) when there was not enough coupling enzymes present to remove rapidly fructose-1,6-P2 formed; (d) when muscle extracts were prepared in the absence of caffeine. Studies on the kinetics of the enzyme at pH 6.9 showed that following epinephrine administration phosphofructokinase became less sensitive to ATP inhibition and had a higher affinity to its second substrate, fructose-6-P.
Studies on purified phosphofructokinase revealed that enzyme incubated with fructose-6-P, fructose-1,6-P2, cyclic 3′,5′-AMP or 5′-AMP could be modified to a form that was active independent of the presence of cyclic 3′,5′-AMP, and less sensitive to inhibition by ATP and caffeine. We conclude that phosphofructokinase, following epinephrine administration, is converted to a form that is more active under assay conditions that favor enzyme inhibition. Such activation appears to be mediated through a combination of hexose phosphates and adenylate nucleotides that are known to be increased by epinephrine.
The kinetic behavior of crystalline heart phosphofructokinase was studied under different conditions. At pH 8.2 the enzyme exhibited Michaelis-Menten kinetics with respect to ATP, fructose 6-phosphate, or Mg⁺⁺. The Michaelis constants for these substrates were determined. At pH 6.9, ATP inhibited the enzyme. The presence of a lag period was demonstrated when the enzyme was incubated with ATP. Analysis of the kinetic data by means of the Hill equation revealed that the apparent order of the reaction with respect to fructose-6-P was more than one. When the ATP concentration was increased, the apparent order of the reaction was also increased, up to a value of 2.5. Activators such as cyclic 3′,5′-AMP reduced the apparent Km for fructose-6-P. Cyclic 3′,5′-AMP caused a change to first order kinetics in the presence of low ATP concentrations. At higher concentrations of ATP, cyclic 3′,5′-AMP caused a significant decrease in the sigmoid shape of the saturation curves for fructose-6-P, with little change in the apparent order of the reaction. A form of phosphofructokinase was isolated in the absence of stabilizers (ATP and fructose-1,6-di-P). It was found to be more sensitive to ATP inhibition, as evidenced by a lower apparent Ki, and gave curves for fructose-6-P which were more sigmoid than those of the native enzyme.
Crystalline heart phosphofructokinase (s20,ω = 14.5) could be reversibly dissociated to a subactive protomer with an s20,ω value of 7.5 at pH 6.5. The enzyme could further be dissociated in the presence of 5 M guanidine HCl to smaller subunits with an s20,ω value of 2.75, which had no enzyme activity. The effect of different ligands on the sedimentation behavior of the enzyme at pH 6.5 was investigated. ATP was found to favor the dissociated form of the enzyme (7.5 S). Fructose 1,6-di-P favored the fully active polymerized form of the enzyme. Based on the present results and previous reports, a model for the molecular organization of phosphofructokinase is presented.
Phosphofructokinase from sheep heart was desensitized to ATP inhibition by photo-oxidation of the enzyme in the presence of methylene blue. Amino acid analyses were performed on native and photo-oxidized enzyme. The results showed that of a total of 18.2 moles of histidine per 10⁵ g of enzyme an average of 3 was lost after photo-oxidation. The total number of cysteine residues was reduced from an average of 14.0 to 6.6 moles/10⁵ g of enzyme following such treatment. No other amino acid was affected by photo-oxidation with the possible exception of methionine.
The allosteric kinetics of phosphofructokinase was studied after treatment with ethoxyformic anhydride at pH 6.1. Evidence that the reagent reacted with histidine residues came from spectrophotometric studies and from the fact that the reaction could be reversed with hydroxylamine at neutral pH. Spectrophotometric determination of the product of the reaction, N-ethoxyformyl histidine, agreed well with ¹⁴C-ethoxyformyl groups formed in the protein in the range of 0 to 4 moles of product per 10⁵ g of enzyme. At pH 8.2, the kinetics of the enzyme containing 3.5 moles of ethoxyformylated residues per 10⁵ g of protein was indistinguishable from that of the native enzyme except for a 22 to 44% decrease in Vmax. However, at pH 6.9, the kinetics of the same derivative was characterized by (a) a loss of sensitivity to inhibition by ATP, (b) a loss of cooperativity with fructose-6-P, and (c) a decrease in sensitivity to inhibition by citrate and to activation by AMP or 3',5'-cyclic AMP. The degree of loss of these regulatory properties was dependent on the extent of modification of the enzyme. Maximum desensitization occurred when 3 to 4 moles of the anhydride reacted per 10⁵ g of protein. Brief treatment of ethoxyformylated enzyme with neutral hydroxylamine resulted in enzyme indistinguishable from the native protein on the basis of catalytic activity and sensitivity to ATP inhibition. Ethoxyformylation of the enzyme was normally carried out in the presence of ATP and fructose-1,6-di-P. However, the effects of the anhydride on the enzyme were the same when the incubation was carried out in the absence of these compounds.
Incubation of ethoxyformylated phosphofructokinase in mild acid resulted in loss of activity similar to that observed with native enzyme. The behavior of ethoxyformylated phosphofructokinase on sucrose gradients was identical with that of native enzyme in the presence of ATP or fructose-6-P. However, in the absence of substrates, the ethoxyformylated protein was somewhat more aggregated than the native enzyme.
The properties of ethoxyformylated phosphofructokinase are compared to those of photo-oxidized enzyme. It is probable that alteration of histidine residues in both cases is largely responsible for the loss of the allosteric properties of the enzyme.
A relatively simple procedure was devised for the purification of phosphofructokinase from rabbit liver extracts. The enzyme was purified more than 2600-fold with a yield of close to 50%.
Liver phosphofructokinase migrates faster on zone electrophoresis than rabbit skeletal muscle phosphofructokinase. It also differs from muscle enzyme in stability, molecular weight, and kinetic properties. The liver enzyme behaves on Sepharose chromatography as a polymer of various states of aggregation with the largest aggregate having a particle weight of many millions.
A comparison of the kinetic properties of liver and muscle phosphofructokinase revealed similarities in pH optimum, cation activation, and substrate affinity at pH 8.2. On the other hand, striking differences in kinetic control properties were observed at pH 7.0. The liver enzyme was more inhibited by ATP, less sensitive to the deinhibiting action of AMP, ADP, and cyclic 3',5'-AMP, less inhibited by citrate, phosphoenolpyruvate, phosphocreatine, 2-phosphoglycerate, and 3-phosphoglycerate, and more inhibited by 2,3-diphosphoglycerate than muscle phosphofructokinase.
The results suggest that liver phosphofructokinase is less suited for anaerobic energy production than the skeletal muscle enzyme and may not be subject to the same control mechanism in vivo.
Under appropriate conditions, the activity of phosphofructokinase of skeletal muscle from frog and mouse is extremely sensitive to small changes in pH in the physiological range, a low pH decreasing the affinity of the enzyme for fructose 6-phosphate. It is concluded that shifts in intracellular pH are important in the regulation of phosphofructokinase, but that this effect makes interpretation of data from intact muscle quite difficult.
Human phosphofructokinase was partially purified from skeletal muscle and erythrocytes. Erythrocyte phosphofructokinase migrated faster on electrophoresis, showed greater affinity for DEAE-cellulose in Tris-phosphate buffer at pH 8, was more inhibited by ATP, and was less inhibited by citrate than muscle phosphofructokinase. Antibody to muscle phosphofructokinase inhibited the activity of erythrocyte phosphofructokinase less than that of the muscle enzyme, but the enzymes could not be distinguished by immunodiffusion methods.
By sucrose density gradient centrifugation, the molecular weight of muscle phosphofructokinase was estimated to be between 3.8 × 10⁵ and 4.3 × 10⁵ for the smallest active form. When larger amounts of enzyme were centrifuged, a broad peak resulted, suggesting polymerization of the enzyme. The sedimentation coefficient of erythrocyte phosphofructokinase was also concentration-dependent, but a heterogeneous peak was obtained when even small amounts of enzyme were centrifuged so that the molecular weight could not be estimated accurately.
In kinetic studies of both enzymes, Lineweaver-Burk plots yielded parallel lines when activity was measured at different fixed concentrations of the second substrate. Both Km and Vmax for either substrate were increased by raising the concentration of the other substrate. The pH maximum for both enzymes was about 8.5 and inhibition at low pH was greater with high ATP. NH4⁺ and Pi increased Vmax and decreased Km for both substrates.
A simple procedure for purification of phosphofructokinase from rabbit erythrocytes was developed. The purified enzyme yields a single band on acrylamide gel electrophoresis. A schlieren pattern obtained from ultracentrifugation of the enzyme shows an asymmetrical peak and the major component has a sedimentation coefficient of 80 S. The results of sucrose density gradient centrifugation of fresh hemolysate show that the erythrocyte phosphofructokinase has a molecular weight of about 500,000. The molecular weight of dissociated enzyme in guanidine was determined to be approximately 53,000. Amino acid composition and a tryptic peptide map of erythrocyte phosphofructokinase are considerably different from those of skeletal muscle phosphofructokinase.
Immunological reactivity of erythrocyte phosphofructokinase with antibody against muscle enzyme is less than that of muscle phosphofructokinase.
Kinetic studies reveal that erythrocyte phosphofructokinase is inhibited by 2,3-diphosphoglycerate and that this inhibition is released by inorganic phosphate but not by AMP or ADP. Possible physiological significance of these observations is discussed.
A mathematical model of glycolysis in the steady state of human erythrocytes is proposed based on an analytical treatment. Assuming a linear dependence of the enzyme velocities on the substrate concentrations, which is justified for all non-equilibrium enzymes, simple analytical expressions for all metabolites of the glycolysis could be obtained. From a consideration of the NADH/NAD-coupling between the lactate dehydrogenase and the glyceraldehyde-phosphate dehydrogenase reactions a conservation quantity for the concentrations of the oxidized metabolites is derived.
The activity of the phosphofructokinase from erythrocytes of rats and rabbits, and presumably of the enzyme from other sources depend on the presence of either K+ or NH4+ ions. Their effects are not due to ionic strength. The apparent activation constant, KD, is about 1 mM for NH4+ and 10 mM for K+. While K+ ions appear to act only as activators of the catalytic site, NH4+ ions have a double action. They act both as activators and as positive effectors which abolish the cooperativity, presumably by affecting the interaction between the subunits. They increase the affinity of the enzyme for fructose 6-phosphate and ATP as substrates, while the affinity for ATP as inhibitor is weakened. These effects are probably secondary to the changed interaction between the subunits. It is concluded that only data on the phosphofructokinase in K+ system are representative of normal intracellular conditions. In certain physiological and pathological states the effect of NH4+ ions on the allosteric properties of the enzyme is probably important.
Pi is an activator of both the K+- and the NH4+-activated enzyme, with an approximate KD of 1.6 mM. Its effect is therefore of importance under physiological and pathological conditions.
The data on the purified K+-activated enzyme are in good agreement with changes of the metabolic pattern of the intact erythrocyte.
Whole glycolysis, enzymatic activities in the Embden-Meyerhof pathway, kinetics of the penetration of orthophosphate ions, and the concentration of various intracellular fractions, i.e. orthophosphates, intermediate phosphoderivatives of glycolysis and ATP, were studied in 30 normal subjects and in 17 subjects with liereditary hypophosphatemic vitamin D-resistant rickets.A comparison of the results obtained with children treated with vitamin D, those not treated with vitamin D and untreated adults shows no significant differences among the three categories. p]The following results were obtained in our study of affected subjects: 1.1. Glycolytic activity is elevated without inducing any accumulation of the intermediates between glucose and lactate.2.2. Enzymatic activity in the Embden-Meyerhof pathway is normal, except for pyruvate kinase which is significantly increased.3.3. The concentration of the intermediate phosphoderivatives of glycolysis is normal.4.4. ATP concentration is increased (P = 0.01).5.5. Intracellular orthophosphate concentration is decreased (P = 0.002).6.6. The kinetics of the entrance of extracellular orthophosphates into red blood cells is significantly increased (P = 0.001) without affecting the final equilibrium of distribution of phosphate ions throughout all parts of the membrane.These results make one think that the hypophosphatemia seen in hereditary vitamin D-resistant rickets cannot be explained either by modification of the plasma membrane permeability to phosphorus or by alteration of glycolysis.The problem of vitamin D resistance and the resultant disturbances which it causes in the cellular transport of calcium are cited as a tentative explanation for
1.1. Glycolysis in a cell-free extract from rat diaphragm was stimulated at elevated pH in the presence of higher concentrations of ATP. A similar situation was also observed in the case of intact-cell preparations of rat diaphragm.2.2. It was found that the rate of inhibition of phosphofructokinase (ATP: D-fructose 6-phosphate 1-phosphotransferase, EC 2.7.1.11) activity by excess ATP was strictly dependent upon the pH; at pH 7.3 an increase in ATP concentration from 1 to 1.7 mM resulted in a sudden inhibition of phosphofructokinase activity, whereas at pH 7.6 such an effect was not observed until the ATP level was raised to 2–3 mM (0.05 mM fructose 6-phosphate was employed as substrate). Consequently phosphofructokinase activity was profoundly influenced by quite a minute change in pH when larger amounts of ATP were present in the glycolytic system.3.3. Since the glucose 6-phosphate which accumulated during phosphofructokinase inhibition was inhibitory to hexokinase (ATP: D-hexose 6-phosphotransferase, EC 2.7.1.1), the pH-induced stimulation of phosphofructokinase caused an exaggerated acceleration of overall glycolysis.4.4. Preincubation of the cell-free extract without substrates (aging) rendered phosphofructokinase protein unresponsive both to the stimulation on raising pH and to the inhibition by ATP. It is tentatively proposed that the affinity of the inhibitory site(s) of phosphofructokinase for ATP is affected by hydrogen ion concentration and that aging causes a change of conformation of the enzyme, thus blocking the control mechanism of phosphofructokinase.
1. 1. Glycolysis in a cell-free extract from rat diaphragm was stimulated at elevated pH in the presence of higher concentrations of ATP. A similar situation was also observed in the case of intact-cell preparations of rat diaphragm. 2. 2. It was found that the rate of inhibition of phosphofructokinase (ATP: D-fructose 6-phosphate 1-phosphotransferase, EC 2.7.1.11) activity by excess ATP was strictly dependent upon the pH; at pH 7.3 an increase in ATP concentration from 1 to 1.7 mM resulted in a sudden inhibition of phosphofructokinase activity, whereas at pH 7.6 such an effect was not observed until the ATP level was raised to 2-3 mM (0.05 mM fructose 6-phosphate was employed as substrate). Consequently phosphofructokinase activity was profoundly influenced by quite a minute change in pH when larger amounts of ATP were present in the glycolytic system. 3. 3. Since the glucose 6-phosphate which accumulated during phosphofructokinase inhibition was inhibitory to hexokinase (ATP: D-hexose 6-phosphotransferase, EC 2.7.1.1), the pH-induced stimulation of phosphofructokinase caused an exaggerated acceleration of overall glycolysis. 4. 4. Preincubation of the cell-free extract without substrates (aging) rendered phosphofructokinase protein unresponsive both to the stimulation on raising pH and to the inhibition by ATP. It is tentatively proposed that the affinity of the inhibitory site(s) of phosphofructokinase for ATP is affected by hydrogen ion concentration and that aging causes a change of conformation of the enzyme, thus blocking the control mechanism of phosphofructokinase.
1. Methods are described for the extraction, partial purification and assay of phosphofructokinase in rat epididymal adipose tissue. 2. The enzyme was inhibited by ATP at concentrations above 20mum and by citrate; the enzyme was activated by ADP, AMP, 3',5'-(cyclic)-AMP, phosphate and sulphate. 3. The enzyme lost activity on incubation at 25 degrees or during chromatography on DEAE-cellulose unless fluoride at a concentration of 4mm was present. 4. The significance of these results in relation to the role of glycolysis and citrate in lipogenesis is discussed.
Phosphofructokinase has been partially purified from Escherichia coli, and its kinetic properties investigated. It shows co-operative interactions with respect to one of its substrates, fructose-6-phosphate, but not towards the second, namely ATP. ADP and other diphosphonucleosides act as activators and phosphoenolpyruvate as an inhibitor. Both effectors decrease the homotropic interactions between fructose-6-phosphate molecules; but, whereas the activators increase the affinity of the enzyme for this substrate, the inhibitor decreases it. These ligands have no effect on the maximum velocity of the reaction, except in the case of ADP which is a competitive inhibitor of ATP.These homotropic and heterotropic interactions are qualitatively and quantitatively accounted for by the concerted transition theory proposed by Monod, Wyman & Changeux (1965), assuming the enzyme to be in equilibrium between two conformational states which differ in their dissociation constants for fructose-6-phosphate, activators and inhibitor. A convenient method of obtaining these intrinsic dissociation constants has been derived from the equations of the theory. From the kinetic data, it is also possible to obtain the value of the equilibrium constant between the two states, if it is assumed that the enzyme is a tetramer made up of four identical subunits and that the transition is perfectly concerted.
The kinetic behavior of crystalline heart phosphofructokinase was studied under different conditions. At pH 8.2 the enzyme
exhibited Michaelis-Menten kinetics with respect to ATP, fructose 6-phosphate, or Mg++. The Michaelis constants for these substrates were determined. At pH 6.9, ATP inhibited the enzyme. The presence of a lag
period was demonstrated when the enzyme was incubated with ATP. Analysis of the kinetic data by means of the Hill equation
revealed that the apparent order of the reaction with respect to fructose-6-P was more than one. When the ATP concentration
was increased, the apparent order of the reaction was also increased, up to a value of 2.5. Activators such as cyclic 3',5'-AMP
reduced the apparent Km for fructose-6-P. Cyclic 3',5'-AMP caused a change to first order kinetics in the presence of low ATP concentrations. At
higher concentrations of ATP, cyclic 3',5'-AMP caused a significant decrease in the sigmoid shape of the saturation curves
for fructose-6-P, with little change in the apparent order of the reaction. A form of phosphofructokinase was isolated in
the absence of stabilizers (ATP and fructose-1,6-di-P). It was found to be more sensitive to ATP inhibition, as evidenced
by a lower apparent Ki, and gave curves for fructose-6-P which were more sigmoid than those of the native enzyme.
Crystalline heart phosphofructokinase (s20,ω = 14.5) could be reversibly dissociated to a subactive protomer with an s20,ω value of 7.5 at pH 6.5. The enzyme could further be dissociated in the presence of 5 m guanidine HCl to smaller subunits with an s20,ω value of 2.75, which had no enzyme activity. The effect of different ligands on the sedimentation behavior of the enzyme
at pH 6.5 was investigated. ATP was found to favor the dissociated form of the enzyme (7.5 S). Fructose 1,6-di-P favored the
fully active polymerized form of the enzyme. Based on the present results and previous reports, a model for the molecular
organization of phosphofructokinase is presented.
We have studied the effects of physiological concentrations of 2,3-DPG on most of the enzymatic steps of the glycolytic and related pathways and have found that it is a potent inhibitor of hexokinase, phosphofructokinase (PFK), aldolase, glyceraldehyde phosphate dehydrogenase (GAPD) and phos-phoglucomutase (PGM). Because the inhibition is competitive in most of these cases it is not evident in standard assay systems.
The intracellular distribution of ATP, 2,3-bisphosphoglycerate(P2-glycerate) and Mg2+ was calculated for the oxygenated and deoxygenated human erythrocyte for the normal range and that of pathophysiological variations based on the association constants of the relevant complexes.
The data indicate that about 20% of ATP is bound both in the oxygenated and deoxygenated cells, while 39 and 73% of P2-glycerate is bound under these conditions. An increase of the free Mg2+ concentration from 0.7 to 1.1 mM is produced by complete deoxygenation of haemoglobin.
The calculations would indicate that during deoxygenation of haemoglobin the hexokinase reacts to the increased concentration of the activator Mg2+ and the decline of the inhibitor P2-glycerate with an elevation of its activity which corresponds to experimental data on intact erythrocytes.
The P2-glycerate formation rate in deoxygenated cells is stimulated about 2.5 times in comparison to oxygenated cells as estimated from the free concentration of P2-glycerate and the kinetic constants of bisphosphoglycerate mutase.
An assessment of the possible influence of other anions including bicarbonate shows that the distribution of the species of ATP, P2-glycerate and Mg2+ are changed by less than 20%.
Together with the data presented in the accompanying paper, the results given here indicate that the constants and estimates are approximately valid for intracellular conditions.
Phosphofructokinase from sheep heart was desensitized to ATP inhibition by photo-oxidation of the enzyme in the presence of
methylene blue. Amino acid analyses were performed on native and photo-oxidized enzyme. The results showed that of a total
of 18.2 moles of histidine per 105 g of enzyme an average of 3 was lost after photo-oxidation. The total number of cysteine residues was reduced from an average
of 14.0 to 6.6 moles/105 g of enzyme following such treatment. No other amino acid was affected by photo-oxidation with the possible exception of
methionine.
The allosteric kinetics of phosphofructokinase was studied after treatment with ethoxyformic anhydride at pH 6.1. Evidence
that the reagent reacted with histidine residues came from spectrophotometric studies and from the fact that the reaction
could be reversed with hydroxylamine at neutral pH. Spectrophotometric determination of the product of the reaction, N-ethoxyformyl histidine, agreed well with 14C-ethoxyformyl groups formed in the protein in the range of 0 to 4 moles of product per 105 g of enzyme. At pH 8.2, the kinetics of the enzyme containing 3.5 moles of ethoxyformylated residues per 105 g of protein was indistinguishable from that of the native enzyme except for a 22 to 44% decrease in Vmax. However, at pH 6.9, the kinetics of the same derivative was characterized by (a) a loss of sensitivity to inhibition by ATP, (b) a loss of cooperativity with fructose-6-P, and (c) a decrease in sensitivity to inhibition by citrate and to activation by AMP or 3',5'-cyclic AMP. The degree of loss of these
regulatory properties was dependent on the extent of modification of the enzyme. Maximum desensitization occurred when 3 to
4 moles of the anhydride reacted per 105 g of protein. Brief treatment of ethoxyformylated enzyme with neutral hydroxylamine resulted in enzyme indistinguishable
from the native protein on the basis of catalytic activity and sensitivity to ATP inhibition. Ethoxyformylation of the enzyme
was normally carried out in the presence of ATP and fructose-1,6-di-P. However, the effects of the anhydride on the enzyme
were the same when the incubation was carried out in the absence of these compounds.
Incubation of ethoxyformylated phosphofructokinase in mild acid resulted in loss of activity similar to that observed with
native enzyme. The behavior of ethoxyformylated phosphofructokinase on sucrose gradients was identical with that of native
enzyme in the presence of ATP or fructose-6-P. However, in the absence of substrates, the ethoxyformylated protein was somewhat
more aggregated than the native enzyme.
The properties of ethoxyformylated phosphofructokinase are compared to those of photo-oxidized enzyme. It is probable that
alteration of histidine residues in both cases is largely responsible for the loss of the allosteric properties of the enzyme.
A relatively simple procedure was devised for the purification of phosphofructokinase from rabbit liver extracts. The enzyme
was purified more than 2600-fold with a yield of close to 50%.
Liver phosphofructokinase migrates faster on zone electrophoresis than rabbit skeletal muscle phosphofructokinase. It also
differs from muscle enzyme in stability, molecular weight, and kinetic properties. The liver enzyme behaves on Sepharose chromatography
as a polymer of various states of aggregation with the largest aggregate having a particle weight of many millions.
A comparison of the kinetic properties of liver and muscle phosphofructokinase revealed similarities in pH optimum, cation
activation, and substrate affinity at pH 8.2. On the other hand, striking differences in kinetic control properties were observed
at pH 7.0. The liver enzyme was more inhibited by ATP, less sensitive to the deinhibiting action of AMP, ADP, and cyclic 3',5'-AMP,
less inhibited by citrate, phosphoenolpyruvate, phosphocreatine, 2-phosphoglycerate, and 3-phosphoglycerate, and more inhibited
by 2,3-diphosphoglycerate than muscle phosphofructokinase.
The results suggest that liver phosphofructokinase is less suited for anaerobic energy production than the skeletal muscle
enzyme and may not be subject to the same control mechanism in vivo.
1.1. Human erythrocyte phosphofructokinase (ATP:d-fructose 6-phosphate 1-phosphotransferase, EC 2.7.1.11) was purified 15 000-fold by (NH4)2SO4 precipitation, heating and column chromatography on Sepharose 6-B. The resulting enzyme preparation had a specific activity of 60 μmoles Fru-1,6-P2 formed per min per mg protein at 25 °C.2.2. With cellulose-acetate electrophoresis only one band was observed after detection of the enzyme activity with the fluorescent technique.3.3. Citrate and 2,3-diphosphoglycerate do not inhibit. The inhibition by ATP is pH dependent. Cyclic AMP is able to reverse the inhibition by ATP to some extent.4.4. With GTP, ITP and UTP no inhibition is observed. At saturating concentrations of GTP, ATP still inhibits phosphofructokinase.5.5. The variation of the activity of phosphofructokinase at various ATP and Fru-6-P concentrations was studied. In the reaction mechanism a ternary complex is involved.
Phosphofructokinase catalyzes the conversion of
fructose-6-phosphate to fructose-1,6-diphosphate.
Control of glycolysis is usually explained in terms of
the properties of three enzymes: hexokinase, phosphofructokinase
and pyruvate kinase. Recently Beutler
reported that phosphofructokinase (PFK) of
human erythrocytes is inhibited by 2,3-DPG. It is
known that the concentration of 2,3-DPG in erythrocytes
is very high. In view of control of glycolysis the
finding by Beutler is very important. However, our results are in disagreement with those of Beutler.
Under simulated intracellular conditions (pH 7.2, 37 °C, 130 mM KCl, 20 mM NaCl and haemoglobin concentrations > 1.5 mM) the conditional association constants for the binding of ATP and 2,3-bisphosphoglycerate (P2-glycerate) to deoxygenated and oxygenated haemoglobin (Hb and HbO2, respectively) and the influence of Mg2+ on the binding of phosphocompounds were determined by means of a cation-sensitive electrode and ultrafiltration.
The K′ass for the binding of ATP to Hb is 2.6 mM−1 and 0.36 mM−1 for HbO2. P2-glycerate is bound to Hb with K′ass of 5 mM−1 and to HbO2 with a K′ass of 0.25 mM−1. The anions compete with each other in binding. Mg2+ is not bound to haemoglobin but it reduces the binding of the phosphocompounds by complexing with them. It decreases the shift of the oxygen binding curve produced by ATP. MgATP is weakly bound to Hb with a K′ass of 0.14 mM−′ and to HbO2 with a K′ass of 0.039 mM−1. Binding of the Mg ·P2-glycerate complex to haemoglobin was not established.
The calculated values for the dependence of p50 (the partial pressure of oxygen at half-saturation of haemoglobin) on the free concentration of P2-glycerate, based on the K′ass of Hb and HbO2 complexes, agree well with the experimental data on erythrolysates and intact human red blood cells. The K′ass are furthermore an appropriate basis for the estimation of the intraerythrocatic state of Mg2+ and the metabolites.
A theoretical analysis of the crossover theorem is presented based on a linear approximation. Cases are considered in which the simple crossover theorem may lead to erroneus conclusions. Among them are the following: more than one interaction site of an effector with the enzymatic chain; influx and efflux of metabolites regulated by outer metabolic processes; existence of inner effectors; conservation equations for metabolite concentrations; and changes of the state of complexes with the metabolites. It is shown that the action of an effector does not always produce a crossover at the affected enzyme. On the other hand, examples are given where “pseudo-crossovers” occur at unaffected enzymes. It is concluded that for real systems the identification of the interaction sites of an effector with an enzymatic chain cannot be achieved by the simple crossover theorem. Furthermore, even the identification of “rate controlling” or “regulatory important” enzymes by means of crossovers must be done with great caution.A simple and general procedure for the identification of interaction sites of an outer effector with an enzymatic chain is proposed. It requires the determination of the flux through the chain, the concentrations of the substrates and products of the enzymatic step under consideration and the rate law by which an inner effector, if present, influences the reaction rate of this step.
A strategy suitable for computer programming is presented which permits the estimation of kinetic parameters and of their range of statistical variation from initial‐rate measurements or from binding data. It can be used for steady‐state rate equations, rapid‐equilibrium mechanisms, binding kinetics, descriptive models such as Adair's or Hill's equations, and for the study of more complicated allosteric models. The desired kinetic equation is addressed from a model catalogue.
The strategy consists of four main steps: (1) formulation of a goodness‐of‐fit criterion using the concept of the distance between observed and predicted behaviour of the model, avoiding assumptions about the statistical structure; (2) localization of the best fit, i.e. of the parameter point of minimum distance from the data by a search algorithm derived from Marquardt's method; (3) exclusion of discrepancies between model and data by testing the randomness of the vector of residual deviations and the structure of the information matrix; (4) exploration of the parameter variability based on a linear approximation of the fit criterion.
Input to the programme are ligand concentrations and measured‐response data, a code number of the desired model, and a guessed starting point of the parameters which, in contrast to older methods, need not be precise. The output is either a set of parameter values with a respective region of variation, supplemented by tables and graphs of the fit obtained, or the rejection of the data with comments on the reason of failure. The possible reasons include statistical fluctuation or systematic trends in the data, lack of required information (poor experimental design), and inappropriate model (non‐unique or inconsistent kinetic model).
Tests on isosteric and allosteric kinetic data lead to the conclusion that the convergence of the strategy is very good when the fit surface is well defined (good data and correct model).
1. Phosphofructokinase from rat liver has been partially purified by ammonium sulphate precipitation so as to remove enzymes that interfere in one assay for phosphofructokinase. The properties of this enzyme were found to be similar to those of the same enzyme from other tissues (e.g. cardiac muscle, skeletal muscle and brain) that were previously investigated by other workers. 2. Low concentrations of ATP inhibited phosphofructokinase activity by decreasing the affinity of the enzyme for the other substrate, fructose 6-phosphate. Citrate, and other intermediates of the tricarboxylic acid cycle, also inhibited the activity of phosphofructokinase. 3. This inhibition was relieved by either AMP or fructose 1,6-diphosphate; however, higher concentrations of ATP decreased and finally removed the effect of these activators. 4. Ammonium sulphate protected the enzyme from inactivation, and increased the activity by relieving the inhibition due to ATP. The latter effect was similar to that of AMP. 5. Phosphofructokinase was found in the same cellular compartment as fructose 1,6-diphosphatase, namely the soluble cytoplasm. 6. The properties of phosphofructokinase and fructose 1,6-diphosphatase are compared and a theory is proposed that affords dual control of both enzymes in the liver. The relation of this to the control of glycolysis and gluconeogenesis is discussed.
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