Linked-function origins of cooperativity in a symmetrical dimer

The thermodynamic origins of substrate binding cooperativity in a dimeric enzyme that can bind one substrate (A) and one allosteric ligand (X) to each of two identical subunits are discussed. It is assumed that maximal activity is not subject to allosteric modification and that the substrates and allosteric ligands achieve binding equilibrium in the steady state. Each uniquely ligated form is assumed to be capable of exhibiting unique binding properties, and only the principles of thermodynamic linkage are used to constrain the system further. The explicit relationship between the Hill coefficient, the concentration of X, and the magnitudes of the relevant coupling free energies and dissociation constants is derived. In the absence of X only the homotropic coupling between substrate sites contributes to a nonhyperbolic substrate saturation profile. An allosteric ligand, X, can alter the cooperativity in two distinct ways, one mechanism being manifested when X is saturating and the only only when X is present at saturating concentrations. By evaluating the concentration of substrate required to produce half-maximal velocity as a function of [X], as well as the Hill coefficients when X is absent and fully saturating, the dissociation and coupling constants most important for understanding the mechanisms of allosteric action in an enzyme of this type can be determined.     

H/D Exchange Characterization of Silent Coupling: Entropy-Enthalpy Compensation in Allostery

The allosteric coupling constant in K-type allosteric systems is defined as a ratio of the binding of substrate in the absence of effector to the binding of the substrate in the presence of a saturating concentration of effector. As a result, the coupling constant is itself an equilibrium value comprised of a ΔH and a TΔS component. In the scenario in which TΔS completely compensates ΔH, no allosteric influence of effector binding on substrate affinity is observed. However, in this “silent coupling” scenario, the presence of effector causes a change in the ΔH associated with substrate binding. A suggestion has now been made that “silent modulators” are ideal drug leads because they can be modified to act as either allosteric activators or inhibitors. Any attempt to rationally design the effector to be an allosteric activator or inhibitor is likely to be benefitted by knowledge of the mechanism that gives rise to coupling. Hydrogen/deuterium exchange with mass spectrometry detection has now been used to identify regions of proteins that experience conformational and/or dynamic changes in the allosteric regulation. Here, we demonstrate the expected temperature dependence of the allosteric regulation of rabbit muscle pyruvate kinase by Ala to demonstrate that this effector reduces substrate (phosphoenolpyruvate) affinity at 35°C and at 10°C but is silent at intermediate temperatures. We then explore the use of hydrogen/deuterium exchange with mass spectrometry to evaluate the areas of the protein that are modified in the mechanism that gives rise to the silent coupling between Ala and phosphoenolpyruvate. Many of the peptide regions of the protein identified as changing in this silent system (Ala as the effector) were included in changes previously identified for allosteric inhibition by Phe.     

Purification and characterization of glucosamine-6-phosphate deaminase from dog kidney cortex.

Glucosamine-6-phosphate deaminase (EC 5.3.1.10) from dog kidney cortex was purified to homogeneity, as judged by several criteria of purity. The purification procedure was based on two biospecific affinity chromatography steps, one of them using N-epsilon-amino-n-hexanoyl-D-glucosamine-6-phosphate agarose, an immobilized analog of the allosteric ligand, and the other by binding the enzyme to phosphocellulose followed by substrate elution, which behaved as an active-site affinity chromatography. The enzyme is an hexameric protein of about 180 kDa composed of subunits of 30.4 kDa; its isoelectric point was 5.7. The sedimentation coefficient was 8.3S, and its frictional ratio was 1.28, indicating that dog deaminase is a globular protein. The enzyme displays positive homotropic cooperativity toward D-glucosamine-6-phosphate (Hill coefficient = 2.1, pH 8.8). Cooperativity was completely abolished by saturating concentrations of GlcNAc6P; this allosteric modulator activated the reaction with a typical K-effect. Under hyperbolic kinetics, a Km value of 0.25 +/- 0.02 mM for D-glucosamine-6-phosphate was obtained. Assuming six catalytic sites per molecule, kcat is 42 s-1. Substrate-velocity data were fitted to the Monod's allosteric model for the exclusive-binding case for both substrate and activator, with two interacting substrate sites. The Kdis for N-acetyl-D-glucosamine-6-phosphate was estimated at 14 microM.     

New approach to analysis of deviations from hyperbolic law in enzyme kinetics

An empirical equation that describes deviations from Michaelian kinetics is proposed. The equation allows the limiting values of the Michaelis constant at v/Vmax --> 0 and v/Vmax --> 1 to be estimated (v is the rate of the enzymatic reaction and Vmax is the limiting value of v at saturating concentrations of substrate). The applicability of the equation is demonstrated for kinetic data obtained for glutamate dehydrogenases from various sources (negative kinetic cooperativity for coenzyme) and for biosynthetic threonine deaminase from pea seedlings (sharper approaching the limiting value of the enzymatic reaction rate with increasing substrate concentration in comparison with the hyperbolic law). The negative cooperativity for the function of saturation of protein by ligand is also analyzed (data on binding of spin-labeled NAD, NADH, and NADPH by beef liver glutamate dehydrogenase and binding of cupric ions by BSA are used as examples).     

Analysis of negative cooperativity for glutamate dehydrogenase

The empirical equation, which describes negative cooperativity in the enzyme kinetics, has been proposed. The equation is obtained from the Michaelis-Menten equation where the Michaelis constant is replaced by the effective Michaelis constant, which is a linear function of the v/Vmax ratio (v is the rate of the enzymatic reaction and Vmax is the limiting value of v at saturating concentrations of substrate). The equation allows the limiting values of the Michaelis constant at v/Vmax --> 0 and V/Vmax --> 1 to be estimated, K0 and Klim, respectively. The Klim/K0 ratio is considered as a quantitative characteristic of negative cooperativity. The applicability of the equation has been demonstrated for the kinetic data obtained for glutamate dehydrogenases from various sources (negative kinetic cooperativity for coenzyme). The negative cooperativity for the functions of saturation of protein by ligand is also analyzed. The data on binding of spin-labeled NAD, NADH, and NADPH by beef liver glutamate dehydrogenase are used as examples.     

Conditions for effective allosteric feedforward and feedback in metabolic pathways

Whether an allosteric feedback or feedforward modifier actually has an effect on the steady-state properties of a metabolic pathway depends not only on the allosteric modifier effect itself, but also on the control properties of the affected allosteric enzyme in the pathway of which it is part. Different modification mechanisms are analysed: mixed inhibition, allosteric inhibition and activation of the reversible Monod-Wyman-Changeux and reversible Hill models. In conclusion, it is shown that, whereas a modifier effect on substrate and product binding (specific effects) can be an effective negative feedback mechanism, it is much less effective as a positive feedforward mechanism. The prediction is that catalytic effects that change the apparent limiting velocity would be more effective in feedforward activation.     

Patterns of apparent co-operativity in a simple random non-equilibrium enzyme–substrate–modifier mechanism. Comparison with equilibrium allosteric models

It has often been claimed that random non-equilibrium mechanisms can result in apparent homotropic and heterotropic effects in steady-state kinetics of the kind more usually attributed to intersubunit allosteric interactions. However, it has never been shown whether any simple random mechanism could in fact give patterns of apparent interaction similar to those predicted by the well-known allosteric models. The patterns of apparent substrate co-operativity and affinity given by the steady-state of a standard simple random substrate-modifier mechanism in which catalytic velocity is proportional to substrate binding have been analysed mathematically and numerically. All patterns possible with this model are described. Some of them rather resemble those possible with standard allosteric models, in that there is a high-affinity and a low-affinity form at zero and infinite modifier concentrations (or vice versa) which show Michaelian behaviour, apparent co-operativity passing through a maximum or minimum at intermediate affinities. Unlike the allosteric models the family of curves is in principle not symmetrical. The random model can also give behaviour not possible with the standard allosteric models, such as higher substrate affinity at intermediate modifier concentrations than at either zero or infinite modifier, with concomitant negative apparent substrate co-operativity, or a single change of sign of apparent substrate co-operativity. The analysis uses recently discovered simplified forms of steady-state equations for random models.     

On the relationship between the Hill coefficients for steady-state and transient kinetic data: A criterion for concerted transitions in allosteric proteins

A frequently used measure for the extent of cooperativity in ligand binding by allosteric proteins is the Hill coefficient. Hill coefficients can be measured for steady-state kinetic data and also for transient kinetic data. Here, the relationship between the two types of Hill coefficients is analysed. It is shown that a value of 1 for the ratio of the two Hill coefficients is a test for a concerted ligand-induced transition between two conformations of the protein, in accordance with the Monod-Wyman-Changeux model. A value of 1 for this ratio has recently been observed for a series of chaperonin GroEL mutants suggesting that ATP-induced allosteric transitions in this protein are concerted.     

Compartmented coupling of chicken heart mitochondrial creatine kinase to the nucleotide translocase requires the outer mitochondrial membrane

The kinetic coupling of mitochondrial creatine kinase (MiMi-CK) to ADP/ATP translocase in chicken heart mitochondrial preparations is demonstrated. Measuring the MiMi-CK apparent Km value for MgATP2- (at saturating creatine) gives a value of 36 microM when MiMi-CK is coupled to oxidative phosphorylation. This Km value is threefold lower than the Km for enzyme bound to mitoplasts or free in solution. The nucleotide translocase Km value for ADP decreases from 20 to 10 microM in the presence of 50 mM creatine only with intact mitochondria. Similar experiments with mitoplasts do not give decreased Km values. The observed Km differences can be used to calculate the concentration of ATP and ADP under steady-state conditions showing that the observed differences in the kinetic constants accurately reflect the enzyme activities of MiMi-CK under the different conditions. The behavior of the Km values provides evidence for what we term compartmented coupling. Therefore, like the rabbit heart system (S. Erickson-Viitanen, P. Viitanen, P. J. Geiger, W. C. T. Yang, and S. P. Bessman (1982) J. Biol. Chem. 257, 14395-14404) compartmented coupling requires an intact outer mitochondrial membrane. The apparent Km values for normal or compartmentally coupled systems can be used to calculate steady-state values of ATP and ADP by coupling enzyme theory. Hence, the overall kinetic parameters accurately reflect the behavior of the enzymes whether free in solution or in the intermembrane space.     

MgATP and fructose 6-phosphate interactions with phosphofructokinase from Escherichia coli.

A thermodynamic linked-function analysis is presented of the interactions of MgATP and fructose 6-phosphate (Fru-6-P) with phosphofructokinase (PFK) from Escherichia coli in the absence of allosteric effectors. MgATP and Fru-6-P are shown to bind in random fashion by product inhibition of the back-reaction as well as by the kinetically competent binding of each ligand individually as monitored by the consequent changes in the intrinsic fluorescence of E. coli PFK. When Fru-6-P is saturating, the dissociation of MgATP is sufficiently slow that it cannot achieve a binding equilibrium in the steady state, causing the observed Km (49 microM) to significantly exceed the Kd (1.7 microM) deduced from a thermodynamic linkage analysis. The following features distinguish the interactions of MgATP and Fru-6-P with E. coli PFK: MgATP and Fru-6-P antagonize each other's binding to the enzyme in a saturable manner with an overall apparent coupling free energy equal to +2.5 kcal/mol at 25 degrees C; MgATP induces positive cooperativity in the Fru-6-P binding profile, with the Hill coefficient calculated from the Fru-6-P binding curves reaching a maximum of 3.6 when MgATP is saturating; and MgATP exhibits substrate inhibition at low concentrations of Fru-6-P. Simulations based upon the rate equation pertaining to a two-active-site, two-substrate dimer indicate that these features can all result from two independent couplings: an antagonistic MgATP-Fru-6-P coupling extending at least in part between active sites and a MgATP-induced Fru-6-P-Fru-6-P coupling.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetic linked-function analysis of the multiligand interactions on Mg(2+)-activated yeast pyruvate kinase.

The multiligand interactions governing the allosteric response of Mg(2+)-activated yeast pyruvate kinase (YPK) during steady-state turnover were quantitated by kinetic linked-function analysis. The substrate, PEP, the enzyme-bound divalent metal, Mg(2+), and the allosteric effector, FBP, positively influence each other's interaction with the enzyme in the presence of saturating concentrations of the second substrate, MgADP. The presence of Mg(2+) enhances the interaction of PEP and of FBP with YPK by -2.0 and -1.0 kcal/mol, respectively. The simultaneous interaction of PEP, Mg(2+), and FBP with YPK is favored by -4.1 kcal/mol over the sum of their independent binding free energies. The coupling free energies measured for Mg(2+)-activated YPK are weaker than the corresponding coupling free energies measured for Mn(2+)-activated YPK [Mesecar, A., and Nowak, T. (1997) Biochemistry 36, 6792, 6803], but are consistent with results of thermodynamic measurements with the Mg(2+)-YPK complex [Bollenbach, T. J., and Nowak, T. (2001) Biochemistry 36, 13088-13096]. A comparison of ligand binding data measured by kinetic and thermodynamic linked-function analyses reveals that the MgADP complex modulates both the binding of the other three ligands and the two- and three-ligand coupling interactions between the other three ligands. Enzyme-bound Mg(2+) does not influence the homotropic cooperativity in PEP binding to YPK. It is the MgADP complex that induces homotropic cooperativity in PEP binding. It is the enzyme-bound Mn(2+) that induces homotropic binding of PEP with Mn(2+)-activated YPK. These results lend support to the hypothesis that divalent metals modulate the interactions of ligands on YPK and that divalent metals play a role in regulation of the glycolytic pathway.     

Involvement of a divalent cation in the binding of fructose 6-phosphate to Trypanosoma cruzi phosphofructokinase: kinetic and magnetic resonance studies

When Mg2+ ions were replaced by Mn2+ in the assay of Trypanosoma (Schizotrypanum) cruzi phosphofructokinase (ATP:D-fructose-6-phosphate 1-phosphotransferase, EC 2.7.1.11) the Km for D-fructose 6-phosphate (F6P) was reduced threefold while the corresponding constant for ATP was essentially unaffected. A detailed kinetic investigation showed that the apparent Km for F6P decreased monotonically with increasing free Mn2+ concentrations, from a limiting value of 5.7 mM in its absence to a limiting value of 1.1 mM in the presence of saturating concentrations of the ion; the Vmax of the enzyme was, on the other hand, not affected by the concentration of Mn2+. Conversely, it was shown that the apparent Km for Mn2+ at fixed MnATP concentrations decreased with increasing F6P concentrations, from a limiting value of 30 microM in the absence of the sugar phosphate to 9 microM at saturating concentrations of the substrate, while the apparent Vmax increased monotonically from zero to its limiting value. Both electron paramagnetic resonance and water proton longitudinal relaxation studies showed binding of one Mn2+ ion per 18,000 Da catalytic subunit of enzyme in the absence of F6P, with a dissociation constant of 57 +/- 4 microM, comparable to the apparent Km for the ion in the absence of F6P. The presence of saturating level of F6P decreases the value of the dissociation constant of Mn2+ to a limiting value of 7.9 microM in agreement with the results of the kinetic analysis. The substrate F6P decreases the enhancement of the water proton longitudinal relaxation rate in a saturable fashion, suggesting displacement of water molecules coordinated to the enzyme-bound Mn2+ ion by the sugar phosphate. Computer fitting of the several dissociation constants and relaxation enhancements for binary and ternary complexes gives a value of 7.9 mM for the dissociation constant of the enzyme-F6P complex in the absence of Mn2+ and 1.1 mM in the presence of saturating concentrations of the ion, in excellent agreement with the respective Km values of F6P extrapolated to zero and saturating Mn2+, respectively. Studies of the frequency dependence of the water proton longitudinal relaxation rate enhancements in the presence of both binary (enzyme-Mn2+) and ternary (enzyme-Mn2(+)-F6P) complexes, are most simply explained by assuming two exchangeable water molecules in the coordination sphere of the enzyme-bound Mn2+ in the binary complex, while in the ternary complex the data are consistent with the displacement of one of the water molecule from the coordination sphere with no significant alteration of the correlation time. Overall, the kinetic and binding data are consistent with the formation of an enzyme-metal-F6P bridge complex at the active site of T. cruzi phosphofructokinase, a coordination scheme which is unique among the phosphofructokinases.     

Time-resolved fluorescence studies of heterotropic ligand binding to cytochrome P450 3A4

Cytochrome P450 3A4 (CYP3A4) is a major enzymatic determinant of drug and xenobiotic metabolism that demonstrates remarkable substrate diversity and complex kinetic properties. The complex kinetics may result, in some cases, from multiple binding of ligands within the large active site or from an effector molecule acting at a distal allosteric site. Here, the fluorescent probe TNS (2-p-toluidinylnaphthalene-6-sulfonic acid) was characterized as an active site fluorescent ligand. UV-vis difference spectroscopy revealed a TNS-induced low-spin heme absorbance spectrum with an apparent K(d) of 25.4 +/- 2 microM. Catalytic turnover using 7-benzyloxyquinoline (7-BQ) as a substrate demonstrated TNS-dependent inhibition with an IC(50) of 9.9 +/- 0.1 microM. These results suggest that TNS binds in the CYP3A4 active site. The steady-state fluorescence of TNS increased upon binding to CYP3A4, and fluorescence titrations yielded a K(d) of 22.8 +/- 1 microM. Time-resolved frequency-domain measurement of TNS fluorescence lifetimes indicates a testosterone (TST)-dependent decrease in the excited-state lifetime of TNS, concomitant with a decrease in the steady-state fluorescence intensity. In contrast, the substrate erythromycin (ERY) had no effect on TNS lifetime, while it decreased the steady-state fluorescence intensity. Together, the results suggest that TNS binds in the active site of CYP3A4, while the first equivalent of TST binds at a distant allosteric effector site. Furthermore, the results are the first to indicate that TST bound to the effector site can modulate the environment of the heterotropic ligand.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

Hill coefficient ratios give binding ratios of allosteric enzyme effectors; inhibition, activation, and squatting in deoxycytidylate aminohydrolase (EC 3.5.4.12)

The ratio of the steady-state kinetic Hill coefficients of two different effectors equals (under some rather weak general assumptions) the ratio in which the effectors displace each other from an enzyme. This principle can make implications of experimental allosteric enzyme kinetic data immediately apparent. We can use it to find that one molecule of the allosteric inhibitor of dCMP aminohydrolase, at moderately high effector concentrations, displaces one molecule of substrate, or one molecule of activator, whereas at very high concentrations, one molecule of inhibitor displaces two of substrate. Further use of the principle suggests that substrate, at high concentrations, binds binds to activator sites. However, ratios of substrate, activator, and inhibitor Hill coefficients are incompatible with a simple model of activation in which substrate and activator are bound to the same conformation.     

Biphasic effect of fructose 2,6-bisphosphate on the liver fructose-1,6-bisphosphatase: mechanistic and physiological implications

Fructose 2,6-bisphosphate has been claimed to be both a substrate analogue and an allosteric inhibitor of fructose-1,6-bisphosphatase. The results reported here show that fructose 2,6-bisphosphate can be both an inhibitor and an activator of the enzyme, depending on the substrate concentration. This biphasic behaviour at saturating concentrations of substrate can only be due to an allosteric effect. In addition to the mechanistic implication it is possible that this finding may have physiological meaning.     

Differential effects of beta 1 and beta 2 subunits on BK channel activity

High conductance, calcium- and voltage-activated potassium (BK) channels are widely expressed in mammals. In some tissues, the biophysical properties of BK channels are highly affected by coexpression of regulatory (beta) subunits. beta1 and beta2 subunits increase apparent channel calcium sensitivity. The beta1 subunit also decreases the voltage sensitivity of the channel and the beta2 subunit produces an N-type inactivation of BK currents. We further characterized the effects of the beta1 and beta2 subunits on the calcium and voltage sensitivity of the channel, analyzing the data in the context of an allosteric model for BK channel activation by calcium and voltage (Horrigan and Aldrich, 2002). In this study, we used a beta2 subunit without its N-type inactivation domain (beta2IR). The results indicate that the beta2IR subunit, like the beta1 subunit, has a small effect on the calcium binding affinity of the channel. Unlike the beta1 subunit, the beta2IR subunit also has no effect on the voltage sensitivity of the channel. The limiting voltage dependence for steady-state channel activation, unrelated to voltage sensor movements, is unaffected by any of the studied beta subunits. The same is observed for the limiting voltage dependence of the deactivation time constant. Thus, the beta1 subunit must affect the voltage sensitivity by altering the function of the voltage sensors of the channel. Both beta subunits reduce the intrinsic equilibrium constant for channel opening (L0). In the allosteric activation model, the reduction of the voltage dependence for the activation of the voltage sensors accounts for most of the macroscopic steady-state effects of the beta1 subunit, including the increase of the apparent calcium sensitivity of the BK channel. All allosteric coupling factors need to be increased in order to explain the observed effects when the alpha subunit is coexpressed with the beta2IR subunit.     

Heart phosphofructokinase: allosteric kinetics with fructose 6-sulfate.

The allosteric regulation of heart phosphofructokinase was studied at pH 6.9 with an alternative substrate, fructose 6-sulfate. The alternative substrate allowed kinetic studies to be carried out at high enzyme concentrations (0.1 mg/ml) where the effect of allosteric ligands on enzyme physical structure has been studied. A Km for ATP binding (8-10 muM) in the presence of saturating AMP concentrations was found which agreed well with the value obtained at pH 8.2, ATP inhibitory effects closely followed saturation of its substrate site. Hill plots for ATP inhibition gave an interaction coefficient of 3.5 indicating cooperatively between at least four enzyme subunits. Neither AMP nor fructose 6-sulfate affected the cooperativity between the ATP inhibitory sites but only increased the inhibitory threshold. As the ATP concentration was increased from suboptimal to inhibitory levels, interaction coefficients for AMP and fructose 6-sulfate changed from 1 to 2. Increasing citrate concentration resulted in an increase in the interaction coefficient for fructose 6-sulfate to a value of 1.9. Citrate inhibition was synergistic with ATP inhibition with an interaction coefficient of 2. The data indicate that allosteric kinetics of the enzyme can be shown at high enzyme concentrations with the alternative substrate. ATP inhibition appears to involve interaction between at least four subunits, while citrate, AMP, and fructose 6-sulfate interact minimally with two subunits.     

Substrate antagonism in the kinetic mechanism of E. coli phosphofructokinase-1.

In the presence of its allosteric activator GDP, the major phosphofructokinase-1 from Escherichia coli K12 follows Michaelis—Menten kinetics. The kinetic behavior observed at steady-state using different concentrations of the substrates ATP and fructose-6-phosphate and the pattern of inhibition by the substrate analogs adenylyl-(β,γ-methylene)-diphosphonate and D-arabinose-5-phosphate are consistent with a random sequential mechanism in rapid equilibrium, rather than with an ordered binding as was suggested earlier. However, ATP and fructose-6-phosphate do not bind independently to the same active site, since the apparent affinity for one substrate is decreased about 20-fold when the other substrate is already bound. The antagonism between ATP and fructose-6-phosphate shows that a negative interaction occurs during the reaction with E. coli phosphofructokinase-1 which must be considered in addition to its allosteric properties.