Thermodynamics of information transfer between subunits in oligomeric enzymes and kinetic cooperativity. 2. Thermodynamics of kinetic cooperativity

The principles of structural kinetics allow one to define the thermodynamic conditions that are sufficient to generate a certain type of kinetic behavior. If subunits are loosely coupled, that is if no quaternary constraint exists between them, the kinetic behavior of the polymeric enzyme is qualitatively defined by the behavior of an ideal dimer. The nature and the extent of the kinetic cooperativity are defined by the energy of interaction, delta G rho, between two subunits. This energy of interaction is that of an ideal dimer relative to that of the A2 and B2 states. This thermodynamic formulation of a given type of cooperativity holds whatever the degree of polymerization of the enzyme. Under these conditions of loose coupling between subunits, positive kinetic cooperativity cannot be associated with any sigmoidicity of the rate curve. The range of energy coupling where positive kinetic cooperativity must, of necessity, be observed becomes more and more narrow as the number of subunit interactions is increased. This range, however, is independent of the number of subunits. The same situation is not observed for negative cooperativity which appears to be independent of both the number of subunits and the number of subunit interactions. If the subunits are tightly coupled, that is if quaternary constraints exist between them, three thermodynamic parameters, delta G' rho, delta G lambda, delta G mu, are required to define the nature of kinetic cooperativity. delta G' rho is the free energy of an ideal strained dimer relative to that of strained A2 and B2 states. delta G lambda and delta G mu represent the difference of strain energies between conformations A and B and B and B relative to that existing between conformations A and A. One may determine in the parametric space (delta G' rho, delta G lambda, delta G mu) the boundaries between the sufficient conditions that generate a certain type of cooperativity and the lack of these conditions. The kinetic parameters of the rate equation are not all independent. A number of constraint conditions exist between them which depend upon the subunit design of the polymeric enzyme. The existence of these constraint conditions may be diagnostic of a certain type of subunit interactions.     

Sigmoidicity in Allosteric Models

We show results complementary to papers by Bardsley and Waight [2, 3], Gibson and Levin [13], Goldbeter [14], and Karlin [19] on sigmoidicity as an essential feature of allosteric models, possibly leading to a criterion of choice between these. In particular, we give the explicit form for the second derivative of the saturation function in the MWC case, and also the calculation of the binding polynomial in the circular KNF case. First, we give analytical conditions of sigmoidicity for each characteristic function in the MWC and KNF allosteric models. In the MWC model, the regions of sigmoidicity are different for the state and saturation functions, and when the catalytic activities of the two conformational states are different, the area of sigmoidicity is significantly larger for the steady-state rate function than for the saturation function. Furthermore, we rigorously prove the existence of mixed kinetic cooperativity in certain conditions. In the KNF model, the state and saturation functions are the same and their sigmoidicity depends only on the degree of coupling between subunits and on the relative stability of the asymmetrically induced subunit interactions. Finally, we suggest a theoretical criterion for discrimination between allosteric models.     

Thermodynamics of information transfer between subunits in oligomeric enzymes and kinetic cooperativity. 3. Information transfer between the subunits of chloroplast fructose bisphosphatase

The theory and the methods that have been described in the two preceding papers in this journal have been used to analyze the kinetic properties of chloroplast fructose bisphosphatase. The enzyme is a tetramer made up of apparently identical subunits and displays a sigmoidal kinetics with respect to its substrate, fructose bisphosphate. The free ionic species, magnesium and fructose bisphosphate bind to the enzyme and the chelate fructose-bisphosphate-magnesium does not affect the sigmoidicity of the rate curves. The Hill coefficient with respect to free fructose bisphosphate is equal to 2.3, which is indeed incompatible with the view that the enzyme behaves as a dimer of dimers. This conclusion is confirmed by direct analysis of the rate curve. On the basis of the sum of the residuals, their sum of squares, the standard error of the kinetic parameters of the equation, the kinetic scheme associated with a dimer of dimers may be ruled out. On the basis of the same criteria, the fit of an Adair equation to the rate data cannot be retained as satisfactory. This is a direct proof that neither the Monod nor the Koshland model can correctly fit these kinetic data. In fact the model that fits these data best is a structural kinetic scheme where information transfer occurs between each subunit and its three neighbors ('tetrahedral' mode of information transfer). The fit of these models to a large number of kinetic data allows one to compute the free energy profile during the successive binding processes of the four substrate molecules to the enzyme. Whereas the first two steps are associated with an increase of free energy, all the other subsequent steps are associated with a decrease of free energy.     

Rat liver glycine methyltransferase. Cooperative binding of S-adenosylmethionine and loss of cooperativity by removal of a short NH2-terminal segment

Rat liver glycine methyltransferase, a homotetramer, exhibits sigmoidal rate behavior with respect to S-adenosylmethionine (Ogawa, H., and Fujioka, M. (1982) J. Biol. Chem. 257, 3447-3452). The binding experiment shows that the sigmoidicity observed in initial velocity kinetics is explained by the cooperative binding of S-adenosylmethionine to the catalytic sites residing on each subunit. Limited proteolysis of glycine methyltransferase with trypsin in the presence of S-adenosylmethionine yields an enzyme lacking the NH2-terminal 8 residues. The proteolytically modified enzyme retains a tetrameric structure. The truncated enzyme shows no cooperativity with respect to S-adenosylmethionine binding and kinetics. It has values of Vmax and Km for glycine identical to those of the native enzyme, but a 3-fold lower [S]0.5 value for S-adenosylmethionine. The proteolytic modification is without effect on the circular dichroism and fluorescence spectra. Furthermore, the protein fluorescence of the modified enzyme is quenched upon addition of S-adenosylmethionine to the same extent as observed with the native enzyme. These results suggest that a short NH2-terminal segment, which lies outside the active site, is important for communication between subunits.     

The central loop of Escherichia coli glutamine synthetase is flexible and functionally passive

Bacterial glutamine synthetases (GSs) are dodecameric aggregates comprised of two face-to-face hexameric rings, which form a cylindrical aqueous channel. Available crystal structures indicate that each subunit provides a 'central loop' that protrudes into this channel. Residues on either side of this loop contribute directly to substrate or metal ion cofactor binding. Although it has been suggested that this conspicuous structural feature may be functionally important, a systematic structure-function analysis of this loop has not been done. Here, we examine the behavior of a cysteine mutant, E165C, which yields inter-subunit disulfide bonds connecting the central loops. The inter-subunit disulfide bonds are readily detected by electrospray ionization mass spectrometry. Based on molecular models, the disulfide bonds would form only if the engineered cysteines on adjacent subunits moved approximately 5 A. Surprisingly, inter-subunit disulfide bonds between the central loops caused no detectable changes in the KMs for glutamate or ATP, nor the KD for either ATP or the transition state analog (L)-methionine sulfoximine (MSOX). Furthermore, covalent and quantitative adduction of the E165C mutant with iodo-acetamido-pyrene yielded nearly fully active enzyme bearing fluorescent pyrene excimers. The relative contribution of pyrene monomers to excimers in the steady state fluorescence is temperature dependent, suggesting thermal equilibrium between loop conformational states. However, the monomer-excimer ratio is independent of ligands such as MSOX, glutamate, or Mn2+. These results validate the suspected flexibility of the central loop, but raise significant doubt about its direct functional role in GS catalysis via conformational switching, including the proposed regulation of GS via ADP-ribosylation within this loop.     

Differential scanning calorimetric studies of E. coli aspartate transcarbamylase. III. The denaturational thermodynamics of the holoenzyme with single-site mutations in the catalytic chain

Aspartate transcarbamylase (EC 2.1.3.2) from E. coli is a multimeric enzyme consisting of two catalytic subunits and three regulatory subunits whose activity is regulated by subunit interactions. Differential scanning calorimetric (DSC) scans of the wild-type enzyme consist of two peaks, each comprised of at least two components, corresponding to denaturation of the catalytic and regulatory subunits within the intact holoenzyme (Vickers et al., J. Biol. Chem. 253 (1978) 8493; Edge et al., Biochemistry 27 (1988) 8081). We have examined the effects of nine single-site mutations in the catalytic chains. Three of the mutations (Asp-100-Gly, Glu-86-Gln, and Arg-269-Gly) are at sites at the C1: C2 interface between c chains within the catalytic subunit. These mutations disrupt salt linkages present in both the T and R states of the molecule (Honzatko et al., J. Mol. Biol. 160 (1982) 219; Krause et al., J. Mol. Biol. 193 (1987) 527). The remainder (Lys-164-Ile, Tyr-165-Phe, Glu-239-Gln, Glu-239-Ala, Tyr-240-Phe and Asp-271-Ser) are at the C1: C4 interface between catalytic subunits and are involved in interactions which stabilize either the T or R state. DSC scans of all of the mutants except Asp-100-Gly and Arg-269-Gly consisted of two peaks. At intermediate concentrations, Asp-100-Gly and Arg-269-Gly had only a single peak near the Tm of the regulatory subunit transition in the holoenzyme, although their denaturational profiles were more complex at high and low protein concentrations. The catalytic subunits of Glu-86-Gln, Lys-164-Ile and Asp-271-Ser appear to be significantly destabilized relative to wild-type protein while Tyr-165-Phe and Tyr-240-Phe appear to be stabilized. Values of delta delta G degree cr, the difference between the subunit interaction energy of wild-type and mutant proteins, evaluated as suggested by Brandts et al. (Biochemistry 28 (1989) 8588) range from -3.7 kcal mol-1 for Glu-86-Gln to 2.4 kcal mol-1 for Tyr-165-Phe.     

Steady state and pre-steady state kinetic properties of rat liver selenium-glutathione peroxidase.

The kinetic properties of partially purified rat liver selenium-glutathione peroxidase were studied under various conditions. Steady state kinetic measurements show sigmoidal saturation curves, parabolic double reciprocal plots, and Hill coefficients greater than unity. Although these kinetic results appear to show cooperative interactions between subunits, they more reflect the presence of several oxidation-reduction forms of the catalytic site. A substrate-induced transition between enzyme forms was evidence by the occurrence of a lag in the attainment of the final steady state velocity under certain preincubation conditions. This hysteretic behavior was evident only when the enzyme was incubated in the absence of reduced glutathione, the donor substrate. Thus, reduced glutathione induces the transition to the fully active form of the enzyme, a slow process requiring about 0.5 min after addition of glutathione, depending on conditions. The length, tau, of the lag period is dependent on the concentrations of enzyme and glutathione, but to a first approximation, this lag period is independent of the concentration of the hydroperoxide acceptor substrate. The lag period is also relatively independent of the nature of the hydroperoxide species. A model for the transition process that is compatible with these observations and with the possible oxidation-reduction properties of the selenium moiety of the enzyme is suggested.     

Gamma–epsilon Interactions Regulate the Chloroplast ATP Synthase

Current literature on the structure and function of the chloroplast ATP synthase is reviewed with an emphasis on the roles of the gamma and epsilon subunits. Together these two subunits are thought to couple, via rotation, the proton motive force to nucleotide synthesis and hydrolysis by the catalytic F(1) segment of the enzyme. These two subunits are also responsible for inducing the latent state of the enzyme that is necessary to prevent futile hydrolysis of ATP in the dark when electron transfer and ATP synthesis are inactive. A model is presented to explain how gamma and epsilon interact to achieve the transition between the active and latent states.     

Subunit coupling and kinetic co-operativity of polymeric enzymes. Amplification, attenuation and inversion effects

The principles of structural kinetics, as applied to dimeric enzymes, allow us to understand how the strength of subunit coupling controls both substrate-binding co-operativity, under equilibrium conditions, and kinetic co-operativity, under steady state conditions. When subunits are loosely coupled, positive substrate-binding co-operativity may result in either an inhibition by excess substrate or a positive kinetic co-operativity. Alternatively, negative substrate-binding co-operativity is of necessity accompanied by negative kinetic co-operativity. Whereas the extent of negative kinetic co-operativity is attenuated with respect to the corresponding substrate-binding co-operativity, the positive kinetic co-operativity is amplified with respect to that of the substrate-binding co-operativity. Strong kinetic co-operativity cannot be generated by a loose coupling of subunits. If subunit is propagated to the other, the dimeric enzyme may display apparently surprising co-operativity effects. If the strain of the active sites generated by subunit coupling is relieved in the non-liganded and fully-liganded states, both substrate-binding co-operativity and kinetic co-operativity cannot be negative. If the strain of the active sites however, is not relieved in these states, negative substrate-binding co-operativity is accompanied by either a positive or a negative co-operativity. The possible occurrence of a reversal of kinetic co-operativity, with respect to substrate-binding co-operativity, is the direct consequence of quaternary constraints in the dimeric enzyme. Moreover, tight coupling between subunits may generate a positive kinetic co-operativity which is not associated with any substrate-binding co-operativity. In other words a dimeric enzyme may well bind the substrate in a non co-operative fashion and display a positive kinetic co-operativity generated by the strain of the active sites.     

Evolution of regulatory enzymes towards functional simplicity

The potential kinetic complexity of polymeric regulatory enzymes does not seem to be often expressed in nature. Most of these enzymes exhibit in fact a rather simple kinetic behaviour. This functional simplicity is probably the consequence of constraints between rate constants or of blocking of some reaction steps. Functional simplicity is believed to have emerged in the course of neo-Darwinian evolution as a consequence of a trend towards an improved functional efficiency. Functional efficiency may be reached, in polymeric regulatory enzymes, when either of the two sets of conditions are met. The first set of conditions implies the occurrence of the unicity of enzyme conformation in any transition state, a loose coupling between subunits and an exact balance of the driving forces exerted by the enzyme in the forward and backward directions of the catalytic step. This situation results in constraints between rate constants which allow degenerescence of the steady state rate equation. The second set of conditions involves again the unicity of enzyme conformation in any of the transition states, associated with a tight coupling of subunits, and a driving force exerted by the enzyme much strongly in the forward than in the backward direction of the catalytic step. These conditions imply blocking of some reaction steps and again degenerescence of the corresponding rate equation. The most frequent types of quaternary structure and subunit interactions, namely loose coupling between subunits, and tight coupling associated with conservation of at least one symmetry axis, have probably emerged as molecular organizations, which precisely allow both functional efficiency and simplicity to occur. Indeed these situations probably represent the term of two different evolutionary trends. Therefore enzymes that have not reached this state usually exhibit more complex kinetic behaviour. Wavy curves, “bumps” and turning points may be considered as manifestations of the ancestral character of an enzyme.     

Stability of steady states in nucleic acid poly (A-T) synthesis and the stirred flow reactor.

The template directed synthesis of poly[d(A-T)] from the nucleoside triphosphates in the presence of DNA polymerase I is carried out continuously in a stirred flow reactor for the first time. The initial objective is to test the kinetic stability of the established steady states at various flow rates. Graphical analysis predicts instable steady states for certain high flow rates. As a consequence of instabilities multiple steady states and steady-state hysteresis may occur. Steady-state hysteresis has now been found experimentally. For a different enzyme fraction of low exonuclease activity we found the steady-state absorbance at 260 nm to be almost invariant with flow rate at high enzyme concentrations even if the flow rate was increased by a large factor. We call this phenomenon kinetic buffering. Relaxation of a large flow perturbation approaches the steady state in a sigmoidal fashion. Concentration oscillations at 260 nm occurred in one experiment using an enzyme fraction of low exonuclease activity after perturbing the steady state by monomer (dATP). Advantages of the stirred flow reactor method over serial transfer are discussed.     

Kinetic properties of pyruvate kinase hybrids formed with native type L and inactivated type M subunits.

Bovine type M pyruvate kinase, which normally has hyperbolic kinetics with its substrates, was inactivated by treatment with trinitrobenzenesulfonic acid. The inactivation probably occurs through trinitrophenylation of the epsilon-amino group of a lysine residue in or near the ADP binding site. Although 90 to 95% of the enzymatic activity is lost by this treatment, the molecular weight and sedimentation coefficient of the trinitrophenylated enzyme are quite similar to values obtained with the native enzyme. The inactivated, trinitrophenylated type M pyruvate kinase was hybridized in vitro with the native bovine type L enzyme, which has sigmoidal kinetics with phosphoenolpyruvate but can be activated by fructose 1,6-diphosphate to give hyperbolic kinetics. Four enzymatically active species were produced, designated L4, L3M, L2M2, and LM3, according to their subunit composition. L4 and L3M have sigmoidal kinetics with phosphoenolpyruvate and are activated by fructose diphosphate. Little or no sigmoidicity was seen for L2M2, although this species is activated to a moderate degree by fructose diphosphate. LM3 appears to have hyperbolic kinetics and is activated only slightly by fructose diphosphate. The kinetic results obtained with hybrids containing trinitrophenylated type M subunits are quite similar to the results previously reported by Dyson and Cardenas ((1973) J. Biol. Chem. 248, 8482-8488) using native type M and type L subunits, indicating that the properties of a type L subunit are profoundly affected by the nature of the other subunits present in the tetramer. In fact, type L and type M subunits in a given hybrid seem to have similar kinetic responses toward phosphoenolpyruvate and fructose diphosphate.     

Kinetic model of the gating system of the sodium channel in a Ranvier node membrane

A kinetic model of the sodium channel gating system consisting of four subunits with three states--closed (X), open (Y) and inactivated (Z)--is proposed. For the channel to conduct, all the four subunits must be in the open state. The transitions between states X and Y are independent, while those between states X and Z are coupled, so that for the particle considered transition of one of two neighbouring particles into state Z increases the activation energy of the step by kT. The model fits rather well to the experimental data.     

An aspartate transcarbamylase lacking catalytic subunit interactions. Study of conformational changes by ultraviolet absorbance and circular dichroism spectroscopy.

A modified form of aspartate transcarbamylase is synthesized by Escherichia coli in the presence of 2-thiouracil which does not exhibit homotropic cooperative interactions between active sites yet retains heterotropic cooperative interactions due to nucleotide binding. The conformational changes induced in the modified enzyme by the binding of different ligands (substrates, substrate analogs, a transition state analog, and nucleotide effectors) were studied using ultraviolet absorbance and circular dichroism difference spectroscopy. Comparison of the results for the modified enzyme and its isolated subunits to those for the native enzyme and its isolated subunits showed that the conformational changes detected by these methods are qualitatively similar in the two enzymes. Comparison of the absorbance difference spectra due to the binding of a transition substrate analog to the intact native or modified enzymes to the corresponding results for the isolated subunits suggested that ligand binding causes an increased exposure to solvent of certain tyrosyl and phenylalanyl residues in the intact enzymes but not in the isolated subunits. This result is consistent with a diminution of subunit contacts due to substrate binding in the course of homotropic interactions in the native enzyme. Such conformational changes, though perhaps necessary for homotropic cooperativity, are not sufficient to cause homotropic cooperativity since the modified enzyme gave identical perturbations. Interactions of the transition state analog, N-(phosphonacetyl)-L-aspartate, with the modified enzyme were studied. Enzyme kinetic data obtained at low aspartate concentrations showed that this transition state analog does not stimulate activity, but rather exhibits the inhibition predicted for the total absence of homotropic cooperative interactions in the modified enzyme. Spectrophotometric titrations of the number of catalytic sites with the transition state analog showed that the modified enzyme and its isolated subunits possess, respectively, four and two high affinity sites for the inhibitor instead of six and three observed in the case of the normal enzyme and its isolated catalytic subunits. These results are correlated with the lower specific enzymatic activities of the modified enzyme and its catalytic subunits compared to the normal corresponding enzymatic species.     

Effects of conformational selectivity and of overlapping kinetically influential ionizations on the characteristics of pH-dependent enzyme kinetics. Implications of free-enzyme pKa variability in reactions of papain for its catalytic mechanism.

The effects of selection by a small molecule, when binding to a protein, of a particular conformation from an equilibrium stereopopulation on the characteristics of the pH-dependence of reaction with a reactivity probe or substrate were determined by analysis of an appropriate kinetic model. For reaction in one protonic state containing an equilibrium mixture of two conformational isomers, the pH-second-order rate constant (k) profile is of conventional sigmoidal form. The apparent pKa value is a composite of the pKa values of the two conformational states. The value of pKapp. for a given enzyme under given experimental conditions will always be the same (provided that the site-specificity assumed in the model is maintained) irrespective of whether only one conformation reacts or both react, with the same or with different rate constants. The experimentally determined pH-independent rate constant (kapp.) is an average of the reactivities of the two conformational states weighted in favour of the predominant form. The presence of an additional but unreactive conformational state also affects the value of kapp. The possibility that overlapping acid dissociations that affect the reactivity of the enzyme might provide pH-k profiles often indistinguishable in practice from simple sigmoidal dissociation curves and subject to variability in apparent pKa values was evaluated by a simulation study. If two reactive protonic states of the enzyme respond differently to changes in the structure of the substrate or site-specific reactivity probe, differences in apparent pKa values of up to approx. 1 unit can be exhibited without deviation from sigmoidal behaviour being reliably observed. Differences in apparent pKa values observed in some site-specific reactions of papain and their possible consequences for its catalytic mechanism are discussed.     

Molecular mechanisms of rotational catalysis in the F(0)F(1) ATP synthase

Rotation of the F(0)F(1) ATP synthase gamma subunit drives each of the three catalytic sites through their reaction pathways. The enzyme completes three cycles and synthesizes or hydrolyzes three ATP for each 360 degrees rotation of the gamma subunit. Mutagenesis studies have yielded considerable information on the roles of interactions between the rotor gamma subunit and the catalytic beta subunits. Amino acid substitutions, such as replacement of the conserved gammaMet-23 by Lys, cause altered interactions between gamma and beta subunits that have dramatic effects on the transition state of the steady state ATP synthesis and hydrolysis reactions. The mutations also perturb transmission of specific conformational information between subunits which is important for efficient conversion of energy between rotation and catalysis, and render the coupling between catalysis and transport inefficient. Amino acid replacements in the transport domain also affect the steady state catalytic transition state indicating that rotation is involved in coupling to transport.     

Thermodynamics of the first transition in writhe of a small circular DNA by Monte Carlo simulation

Monte Carlo simulations are employed to investigate the thermodynamics of the first transition in writhe of a circular model filament corresponding to a 468 base-pair DNA. Parameters employed in these simulations are the torsional rigidity, C = 2.0 × 10⁻¹⁹ dyne cm², and persistence length, P = 500 Å. Intersubunit interactions are modeled by a screened Coulomb potential. For a straight line of subunits this accurately approximates the nonlinear Poisson-Boltzmann potential of a cylinder with the linear charge density of DNA. Curves of relative free energy vs writhe at fixed linking difference (Δ1) exhibit two minima, one corresponding to slightly writhed circles and one to slightly underwrithed figure-8's, whenever Δ1 lies in the transition region. The free energies of the two minima are equal when Δ1_c = 1.35, which defines the midpoint of the transition. At this midpoint, the free energy barrier between the two minima is found to be ΔG_bar = (0.20) k_BT at 298 K. Curves of mean potential energy vs writhe at fixed linking difference similarly exhibit two minima for Δ1 values in the transition region, and the two minimum mean potential energies are equal when Δ1 = 1.50. At the midpoint writhe, Δ1_c = 1.35, the difference in mean potential energy between the minimum free energy figure-8 and circle states is (1.3) k_BT, and the difference in their entropies is 1.3 k_B. Thus, the entropy of the minimum free energy figure-8 state significantly exceeds that of the circle at the midpoint of the transition. The first transition in writhe is found to occur over a rather broad range of Δ1 values from 0.85 to 1.85. The twist energy parameter (E_T), which governs the overall free energy of supercoiling, undergoes a sigmoidal decrease, while the translational diffusion coefficient undergoes a sigmoidal increase, over this same range. The static structure factor exhibits an increase, which reflects a decrease in radius of gyration associated with the circle to figure-8 transition. © 1996 John Wiley & Sons, Inc.     

Hysteretic properties of soluble F1 ATPase from Escherichia coli. II. Nucleotide effects on the slow changes of the enzyme kinetic behaviour.

In a previous paper from this laboratory it was shown that EC.F₁ ATPase exhibits a temperature dependent transition between two stable states, called L (low activity) and H (high activity). They differ three-fold in specific activity. I report here the effects of ADP and ATP on this transition. Both nucleotides were found to shift the equilibrium between the two states in the direction of the L state. Further, the velocity of conversion from one state to the other was accelerated by the presence of the nucleotides. It was shown that the two states of the enzyme exhibit different kinetic properties in that: (i) the L state gives a hyperbolic curve when specific activity is plotted against substrate concentration, and ADP produces an immediate competitive inhibition and (ii) the H state exhibits negative cooperativity when such a curve is plotted, and shows a delayed competitive inhibition by ADP. Furthermore, when enzyme in the H state is loaded with ATP its complex kinetic behavior disappears; ADP does not have this effect. The data are interpreted to mean that the H state depleted of ATP may act as an enzyme bearing two alternative catalytic sites.     

Generalized microscopic reversibility, kinetic co-operativity of enzymes and evolution.

Generalized microscopic reversibility implies that the apparent rate of any catalytic process in a complex mechanism is paralleled by substrate desorption in such a way that this ratio is held constant within the reaction mechanism [Whitehead (1976) Biochem. J. 159, 449--456]. The physical and evolutionary significances of this concept, for both polymeric and monomeric enzymes, are discussed. For polymeric enzymes, generalized microscopic reversibility of necessity occurs if, within the same reaction sequence, the substrate stabilizes one type of conformation of the active site only. Generalized microscopic reversibility suppresses the kinetic co-operativity of the slow transition model [Ainslie, Shill & Neet (1972) J. Biol. Chem. 247, 7088--7096]. This situation is obtained if the free-energy difference between the corresponding transition states of the two enzyme forms is held constant along the reaction co-ordinate. This situation implies that the 'extra costs' of energy (required to pass each energy barrier) that are not covered by the corresponding binding energies of the transition states vary in a similar way along the two reaction co-ordinates. The regulatory behaviour of monomeric enzymes is discussed in the light of the concept of 'catalytic perfection' proposed by Albery & Knowles [(1976) Biochemistry 15, 5631--5640]. These authors claim that an enzyme will be catalytically 'perfect' when its catalytic efficiency is maximum. If this situation occurs for a monomeric enzyme obeying either the slow transition or the mnemonical model, it can be shown that the kinetic co-operativity disappears. In other words, kinetic co-operativity of a monomeric enzyme is 'paid for' at the expense of catalytic efficiency, and the monomeric enzyme cannot be simultaneously co-operative and catalytically very efficient. This is precisely what has been found experimentally in a number of cases.     

Important subunit interactions in the chloroplast ATP synthase

General structural features of the chloroplast ATP synthase are summarized highlighting differences between the chloroplast enzyme and other ATP synthases. Much of the review is focused on the important interactions between the epsilon and gamma subunits of the chloroplast coupling factor 1 (CF(1)) which are involved in regulating the ATP hydrolytic activity of the enzyme and also in transferring energy from the membrane segment, chloroplast coupling factor 0 (CF(0)), to the catalytic sites on CF(1). A simple model is presented which summarizes properties of three known states of activation of the membrane-bound form of CF(1). The three states can be explained in terms of three different bound conformational states of the epsilon subunit. One of the three states, the fully active state, is only found in the membrane-bound form of CF(1). The lack of this state in the isolated form of CF(1), together with the confirmed presence of permanent asymmetry among the alpha, beta and gamma subunits of isolated CF(1), indicate that ATP hydrolysis by isolated CF(1) may involve only two of the three potential catalytic sites on the enzyme. Thus isolated CF(1) may be different from other F(1) enzymes in that it only operates on 'two cylinders' whereby the gamma subunit does not rotate through a full 360 degrees during the catalytic cycle. On the membrane in the presence of a light-induced proton gradient the enzyme assumes a conformation which may involve all three catalytic sites and a full 360 degrees rotation of gamma during catalysis.