The theoretical analysis of kinetic behaviour of “hysteretic” allosteric enzymes V. Relaxation kinetics of dissociating enzyme systems

The expressions for relaxation time as a function of enzyme and specific ligand concentration are deduced for dissociating enzyme system 2p ? P (P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p). It is assumed that ligand binding sites are equivalent and independent in each oligomeric enzyme form and the equilibrium between oligomeric forms develops rather slowly in comparison with the rate of the binding of the ligand. The kinetics of relaxation of the dissociating enzyme system 2p ? P with progressive change of the rate constants for association of oligomeric form p has been analysed in graphic form. The situations when one of the oligomeric enzyme forms is not able to bind the ligand are also considered. The principles of the analysis of relaxation kinetics of dissociating enzyme systems 2p ? P are discussed.     

Quantitative characterization of homo- and heteroassociations of muscle phosphofructokinase with aldolase

Dissociation of purified phosphofructokinase accompanied with inactivation was analyzed in the absence and presence of aldolase and the data were compared with those obtained with muscle extract. The kinetics of the decrease in enzymatic activity was highly dependent on the dilution factor in both cases, but the inactivation appeared to be biphasic only with extract. The inactivation of the phosphofructokinase was impeded by addition of excess of aldolase. Time courses of kinase inactivation were fitted by alternative kinetic models to characterize the multiple equilibria of several homo- and hetero-oligomers of phosphofructokinase. The combination of modeling data obtained with purified and extract systems suggests that aldolase binds to an intermediate dimer of phosphofructokinase and within this heterocomplex the kinase is completely active. The intermediate dimer is stabilized by association with microtubules and the kinase activity decreased due to dilution can be recovered by addition of excess aldolase. In extract, the phosphofructokinase is of sigmoidal character (Hill coefficient of 2.3); the addition of excess exogenous aldolase to phosphofructokinase resulted in heterocomplex formation displaying Michaelian kinetics. The possible physiological relevance of heterocomplex formation of phosphofructokinase in muscle extract is discussed.     

Kinetic model of the action of oligomeric enzymes using phosphofructokinase as an example. II. General formulation of the hierarchical model

A general approach is suggested to describe the steady-state kinetics of the oligomeric enzymes on the base of the generalized statistical Ising model. Detailed analysis is given for the case of a oligomeric enzyme with a hierarchical supramolecular organization. A protomer of this enzyme composed of several equivalent subunits represents the quarternary level of structure. In their turn the finite or infinite number of protomers is associated into a oligomer thus creating a new "quinternary" level of the enzyme organization. The model accounts for the ligand-induced homotrophic cooperative interactions: firstly, between the neighbouring protomers and secondly, between the subunits of the same protomer. The influence of protomer conformation on the subunit state and the cooperativity induction caused by two-ligand binding are also taken into consideration. Monod-Wyman-Changeux's and Koshland's models are shown to be special limit cases of the suggested general theory.     

Effects of Cadmium and Mercury on the Upper Part of Skeletal Muscle Glycolysis in Mice

The effects of pre-incubation with mercury (Hg²⁺) and cadmium (Cd²⁺) on the activities of individual glycolytic enzymes, on the flux and on internal metabolite concentrations of the upper part of glycolysis were investigated in mouse muscle extracts. In the range of metal concentrations analysed we found that only hexokinase and phosphofructokinase, the enzymes that shared the control of the flux, were inhibited by Hg²⁺ and Cd²⁺. The concentrations of the internal metabolites glucose-6-phosphate and fructose-6-phosphate did not change significantly when Hg²⁺ and Cd²⁺ were added. A mathematical model was constructed to explore the mechanisms of inhibition of Hg²⁺ and Cd²⁺ on hexokinase and phosphofructokinase. Equations derived from detailed mechanistic models for each inhibition were fitted to the experimental data. In a concentration-dependent manner these equations describe the observed inhibition of enzyme activity. Under the conditions analysed, the integral model showed that the simultaneous inhibition of hexokinase and phosphofructokinase explains the observation that the concentrations of glucose-6-phosphate and fructose-6-phosphate did not change as the heavy metals decreased the glycolytic flux.     

Plastid and cytosolic phosphofructokinases from the developing endosperm of ricinus communis: II. Comparison of the kinetic and regulatory properties of the isoenzymes

A steady-state kinetic analysis of plastid phosphofructokinase at pH 8.2 is consistent with the enzyme having a sequential reaction mechanism. Cytosolic phosphofructokinase probably has a similar mechanism. At pH 7.0 plastid phosphofructokinase shows cooperative binding of fructose 6-phosphate and is inhibited by higher concentrations of ATP. In contrast cytosolic phosphofructokinase shows normal kinetics at both pH 8.2 and 7.0 with respect to fructose 6-phosphate and is not inhibited by ATP. In the case of plastid phosphofructokinase the affinity for fructose 6-phosphate increases as the pH is raised from 7 to 8.2 whereas cytosolic phosphofructokinase is affected in an opposite manner. Phosphate is the principal activator of plastid phosphofructokinase since the cooperative kinetics toward fructose 6-phosphate are shifted toward Michaelis-Menten kinetics by 1 mm sodium phosphate and this concentration of phosphate relieves the inhibition by ATP. Both isoenzymes are inhibited by phosphoenolpyruvate, 2-phosphoglycerate, and 3-phosphoglycerate at pH 7.2. Plastid phosphofructokinase is most strongly inhibited by phosphoenol pyruvate with the I_0.5 value varying from 0.08 to 0.5 μm depending on substrate concentrations; phosphate reverses this inhibition. In contrast cytosolic phosphofructokinase is much less inhibited by phosphoenolpyruvate with an I_0.5 approximately 1000-fold higher. Cytosolic phosphofructokinase is powerfully inhibited by 3-phosphoglycerate with an I_0.5 value of 60 μm and this appears to be the principal regulator of this isoenzyme. The two isoenzymes of phosphofructokinase in the endosperm appear, therefore, to be regulated differently. Plastid phosphofructokinase is inhibited by phosphoenolpyruvate and ATP and is activated by phosphate; whereas the cytosolic enzyme is inhibited principally by 3-phosphoglycerate and this inhibition is only partially relieved by phosphate. Some of the differences reported previously for phosphofructokinases from different plant tissues may, therefore, be due to varying ratios of the cytosolic and plastid isoenzymes.     

Adipose-tissue phosphofructokinase. Rapid purification and regulation by phosphorylation in vitro.

A new procedure for the purification of phosphofructokinase using Blue Dextran-Sepharose is described. This allowed an approx. 1000-fold purification of phosphofructokinase from rat white and brown adipose tissue to be achieved in essentially a single step. The purified enzymes from both tissues were found to exhibit hyperbolic kinetics with fructose 6-phosphate, to be inhibited by ATP and citrate, and to be activated by 5'-AMP, phosphate and fructose 2,6-bisphosphate. The enzymes were phosphorylated by the catalytic subunit of cyclic AMP-dependent protein kinase, and phosphorylation was found to be associated with increases in activity when the enzymes were assayed under appropriate sub-optimal conditions. In particular, the phosphorylated enzymes exhibited less inhibition by ATP and the white-adipose-tissue enzyme was more sensitive to activation by fructose 2,6-bisphosphate. It is suggested that an increase in the cytoplasmic concentration of cyclic AMP in tissues other than liver may result in an increase in glycolysis through the phosphorylation of phosphofructokinase by cyclic AMP-dependent protein kinase.     

Modulation of phosphofructokinase action by macromolecular interactions. Quantitative analysis of the phosphofructokinase-aldolase-calmodulin system

The simultaneous effect of calmodulin and aldolase (D-fructose-1,6-bisphosphate D-glyceraldehyde-3-phosphate-lyase, EC 4.1.2.13) on the concentration-dependent behaviour of muscle phosphofructokinase (ATP: D-fructose-6-phosphate 1-phosphotransferase, EC 2.7.1.11) has been analysed by means of a covalently attached fluorescent probe, gel penetration experiments, and using a kinetic approach. We found that calmodulin-induced inactivation of phosphofructokinase is suspended by addition of an equimolar amount of aldolase. This effect was attributed to an apparent competition of calmodulin and aldolase for the dimeric forms of kinase. Moreover, the direct binding of aldolase to calmodulin has also been demonstrated, which resulted in a significant decrease in the kcat value of the enzyme. The quantitative analysis of these interactions in the system phosphofructokinase-calmodulin-aldolase is presented. A possible molecular model for the modulation of phosphofructokinase action by macromolecular interactions is envisaged.     

The enzyme activity allosteric regulation model based on the composite nature of catalytic and regulatory sites concept

A new kinetic model of enzymatic catalysis is proposed, which postulates that enzyme solutions are equilibrium systems of oligomers differing in the number of subunits and in the mode of their assembly. It is suggested that the catalytic and regulatory sites of allosteric enzymes are of composite nature and appear as a result of subunits joining. Two possible joining modes are postulated at each oligomerization step. Catalytic site may arise on oligomer formed only by one of these modes. Effector acts by fastening together components of certain oligomeric form and increases the life time of this form. It leads to a shift of oligomer equilibrium and increases a proportion of effector-binding oligomers. Effectors-activators bind the oligomers carrying composite catalytic sites and effectors-inhibitors bind the oligomers, which do not carry active catalytic sites. Thus, catalytic activity control in such system is explained by effector-induced changes of a catalytic sites number, but not of a catalytic site activity caused by changes of subunit's tertiary structure. The postulates of the model do not contradict available experimental data and lead to a new type of general rate equation, which allows to describe and understand the specific kinetic behavior of allosteric enzymes as well as Michaelis type enzymes. All known rate equations of allosteric The equation was tested by modeling the kinetics of human erythrocyte phosphofructokinase. It enabled to reproduce quantitatively the 66 kinetic curves experimentally obtained for this enzyme under different reaction conditions.     

Computer modeling of muscle phosphofructokinase kinetics

The kinetics of the phosphofructokinase reaction were studied by computer modeling. A general random order, two-state allosteric model, of which the Monod--Wyman--Changeux model is a limiting case, was found to most accurately reproduce the experimental observations of Pettigrew & Frieden (1979 a,b). A simplified model with Hill coefficients was found to fit almost as well. In these models substrates bind preferentially to and stabilize the enzyme in the R state, and ATPH3-, the inhibitory species, binds preferentially to and stabilizes the enzyme in the T state. Enzymatic activity is regulated by conversion from the R to the T state, which is effected by protonation, especially of the uncomplexed enzyme, but the experimental data are inadequate for accurate estimation of the pKa of the enzyme. Random order binding of substrates is an important cause of sigmoidal kinetics. Additional experiments that would aid in the discrimination among rival models are described.     

Structures of S. pombe phosphofructokinase in the F6P-bound and ATP-bound states

Phosphofructokinase (Pfk1; EC 2.7.1.11) is the third enzyme of the glycolytic pathway catalyzing the formation of fructose-1,6-bisphosphate from fructose-6-phosphate (F6P) and ATP. Schizosaccharomyces pombe Pfk1 is a homo-octameric enzyme of 800 kDa molecular weight, distinct from its yeast counterparts which are mostly hetero-octameric enzymes composed of two different subunits. Having an "open" conformation and a tendency to aggregate into higher oligomeric structures, the S. pombe enzyme shows similarities to the mammalian muscle Pfk1. It has been proposed that due to the distinct N-terminal region of the S. pombe subunit, the oligomeric organization of subunits in this enzyme is different from other yeast phosphofructokinases. Electron microscopy studies were carried out to reveal the quaternary structure of the homo-octameric Pfk1 from S. pombe in the F6P-bound and in the ATP-bound state. Random conical tilt data sets have been collected from deep stain preparations of the enzyme in both states. The 0 degrees tilt images have been separated into different classes and a 3D reconstruction has been calculated for each class from the high tilt images. Our results confirm the presence of a variety of views of the particle, most of which can be interpreted as views of the molecule rotating around its long axis. Despite the biochemical differences, the structure of phosphofructokinase from S. pombe in the presence of either F6P or ATP is similar to the hetero-octameric structure of phosphofructokinase from Saccharomyces cerevisiae. The molecule can be described as composed of two subdomains, connected by two well-defined densities. We have been able to establish a correlation between the kinetic behavior and the structural conformation of Pfk1.     

Studies on the structure of yeast phosphofructokinase

In this paper, we describe an efficient procedure for the purification of yeast phosphofructokinase. This procedure eliminates any time delay and enables to obtain an enzyme with minimum proteolytic alterations. The molecular weights of the oligomeric enzyme and of its constitutive subunits were both evaluated by means of several independent methods. However, the accuracy of each measurement was not sufficient to discriminate between an hexameric and an octameric structure of the enzyme oligomer. On the other hand, crosslinking experiments demonstrated the octameric structure of yeast phosphofructokinase. Obviously, some methods of molecular weight determination have led to erroneous results. In particular, our experiments show that the reliability of molecular weight determinations performed by gel filtration of native proteins must be considered with caution.     

The Enzyme Activity Allosteric Regulation Model Based on the Composite Nature of Catalytic and Regulatory Sites Concept

Abstract

A new kinetic model of enzymatic catalysis is proposed, which postulates that enzyme solutions are equilibrium systems of oligomers differing in the number of subunits and in the mode of their assembly. It is suggested that the catalytic and regulatory sites of allosteric enzymes are of composite nature and appear as a result of subunits joining. Two possible joining modes are postulated at each oligomerization step. Catalytic site may arise on oligomer formed only by one of these modes. Effector acts by fastening together components of certain oligomeric form and increases the life time of this form. It leads to a shift of oligomer equilibrium and increases a proportion of effector-binding oligomers. Effectors-activators bind the oligomers carrying composite catalytic sites and effectors-inhibitors bind the oligomers, which do not carry active catalytic sites. Thus, catalytic activity control in such system is explained by effector-induced changes of a catalytic sites number, but not of a catalytic site activity caused by changes of subunit's tertiary structure.

The postulates of the model do not contradict available experimental data and lead to a new type of general rate equation, which allows to describe and understand the specific kinetic behavior of allosteric enzymes as well as Michaelis type enzymes. All known rate equations of allosteric

The equation was tested by modeling the kinetics of human erythrocyte phosphofructokinase. It enabled to reproduce quantitatively the 66 kinetic curves experimentally obtained for this enzyme under different reaction conditions.     

Phosphofructokinase from lycopersicon esculentum fruits-II. Changes in the regulatory properties with dissociation

The regulatory properties of PFK. from the tomato are discussed in relation to the dissociation of the oligomeric form of the enzyme. Both the oligomeric and monomeric forms of PFK were inhibited by citrate, malate, PEP, 2-phosphoglycerate, phosphoglycolate and ammonium sulphate. PEP was the most potent inhibitor of PFK activity with 9 and 10 μn PEP causing 50%, inhibition of the oligomeric and monomeric forms of PFK respectively. The inhibition by all these metabolites of the oligomeric form of PFK was sigmoidal while their inhibition of the monomeric form was hyperbolic. The magnitude of inhibition by these metabolites is affected by the levels of Mg²⁺. The oligomeric form of the enzyme is more resistant to citrate inhibition than the monomeric form. In the presence of citrate or ammonium sulphate, the kinetics of the oligomeric form of PFK with F6P yielded positive cooperativity while in their absence, the kinetics revealed negative cooperative interactions. Phosphoenolpyruvate had no effect on the nature of the kinetics with F6P. ADP is stimulatory to the oligomeric form while it is slightly inhibitory to the monomeric form. The significance of these properties and their relation with the regulation of PFK activity in vivo are discussed.     

Mouse (C57BL/KsJ) liver phosphofructokinase. Allosteric kinetics and age-related changes in the genetically diabetic state

The regulatory kinetic properties of phosphofructokinase partially purified from the livers of C57BL/KsJ mice were studied. The fructose 6-phosphate saturation curves were highly pH dependent. At a fixed MgATP concentration (1 mM), allosteric kinetics was observed in the range of pH studied (7.3 to 8.3) and the S0.5 values for fructose 6-phosphate decreased by about 0.2 to 0.3 mM for each 0.1-unit increment in pH. Allosteric effects on the sigmoidal response to fructose 6-phosphate: activation by AMP, NH4+, and glucose 1,6-bisphosphate, inhibition by MgATP2-, and synergistic inhibition between ATP and citrate, were all present at pH 8.0 to 8.2. Comparative kinetic studies with liver phosphofructokinase isolated from both the normal (C57BL/KsJ) and the genetically diabetic (C57BL/KsJ-db) mice of 9 to 10 and 15 to 16 weeks of age showed that the enzyme from the livers of diabetic mice exhibited decreased activity at subsaturating concentrations of fructose 6-phosphate. However, phosphofructokinase isolated from the livers of normal and genetically diabetic mice of 4 to 5 weeks of age showed no difference in kinetic properties. Thus, there appears to be a correlation between the change in properties of liver phosphofructokinase and the expression of hyperglycemia and obesity in the genetically diabetic mice. The decreased activity of liver phosphofructokinase in the older diabetic animals may well be one of the causes of the increased blood glucose levels. The results are also discussed in a general context with regard to the possible role of phosphofructokinase in the regulation of hepatic gluconeogenesis.     

pH dependence of the reverse reaction catalyzed by phosphofructokinase I from Escherichia coli: implications for the role of Asp 127.

The kinetics of the reverse reaction catalyzed by Escherichia coli phosphofructokinase, i.e., the synthesis of ATP and fructose-6-phosphate from ADP and fructose-1,6-bisphosphate, have been studied at different pH values, from pH 6 to pH 9.2. Hyperbolic saturations of the enzyme are observed for both substrates. The affinity for fructose-1,6-bisphosphate decreases with pH following the ionization of a group with a pK of 6.6, whereas the catalytic rate constant and perhaps the affinity for ADP are controlled by the ionization of a group with a pK of 6. Several arguments show that the pK of 6.6 is probably that of the carboxyl group of Asp 127, whereas the pK of 6 is tentatively attributed to the carboxyl group of Asp 103. The pK of 6.6 is assigned to the carboxyl group of Asp 127 in the free enzyme, and a simple model suggests that the same group would have an abnormally high pK, above 9.6, in the complex between phosphofructokinase and fructose-1,6-bisphosphate. It is proposed that the large pK shift of more than 3 pH units upon binding of fructose-1,6-bisphosphate is due to an electrostatic repulsion that could exist between the 1-phosphate group and the carboxyl group of Asp 127, which are close to each other in the crystal structure of phosphofructokinase (Shirakihara, Y. & Evans, P.R., 1988, J. Mol. Biol. 204, 973-994). The same interpretation would also explain the much higher affinity of the enzyme for fructose-1,6-bisphosphate when Asp 127 is protonated.(ABSTRACT TRUNCATED AT 250 WORDS)     

Binding of MgATP to yeast phosphofructokinase.

Binding of MgATP to yeast phosphofructokinase was investigated by the gel filtration equilibrium dialysis technique. Per subunit of yeast phosphofructokinase two molecules of MgATP are bound in the absence of fructose-6-phosphate, one to a high-affinity and one to a low-affinity site. The experimental data were compared with a kinetic model of yeast phosphofructokinase as described by Freyer et al. [3].     

Expression of matrilin-2 in oval cells during rat liver regeneration.

The matrilins represent a new family of oligomeric proteins that are assumed to act as adapter molecules connecting other proteins and proteoglycans in the extracellular matrix. Matrilin-2, the largest member of the family, displays a broad tissue distribution. It incorporates into loose and dense connective tissue and becomes associated with some basement membranes. The aim of our study was to analyse the expression of matrilin-2 in two liver regeneration models and to identify its cellular origin. Liver regeneration was induced in rats by partial hepatectomy (PH) and by the 2-acetylaminofluorene (AAF)/partial hepatectomy (PH) experimental models. Formalin fixed, paraffin embedded tissue sections were used for immunohistochemistry applying a rabbit matrilin-2 polyclonal antibody. Matrilin-2 was detected in normal rat liver and partially hepatectomized liver in the portal area, but could not be demonstrated in the acini. Matrilin-2 mRNA expression was analysed by RT-PCR and in situ hybridization. In the AAF/PH model the oval cells but not the hepatocytes produced matrilin-2 mRNA. Increase in protein level in the AAF/PH regenerating liver model was demonstrated by Western blotting. The protein was present in the basement membrane zone around the tubules formed by oval cells. Our data show that hepatic oval cells produce matrilin-2, a novel ECM protein, suggesting that matrilin-2 is an important component of ECM during stem cell-driven liver regeneration.