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.     

Thermodynamics of information transfer between subunits in oligomeric enzymes and kinetic cooperativity. 1. Thermodynamics of subunit interactions, partition functions and enzyme reaction rate

The strength of quaternary constraints between two subunits of a polymeric enzyme depends upon the number of neighboring subunits and upon whether these subunits are liganded or not. These quaternary constraints between two subunits of a complex polymeric enzyme may be expressed, however, in terms of quaternary constraints that exist within ideal dimers. The influence of quaternary constraints on the reaction rate of a complex polymeric enzyme may thus be expressed in terms of the intersubunit strain that exists within dimers. This conclusion, that was far from evident, appears to be the consequence of the postulates of structural kinetics, and derive as well from usual thermodynamic principles. The structural steady-state equations may be expressed in terms of partition and sub-partition functions. As applied to structural kinetic models, a partition function expresses how, during the steady state, the energy of a population of enzyme molecules is distributed over n states. Similarly a sub-partition function describes how, during the steady state, the energy of these enzyme molecules is partitioned among only n-k of these states. Although the concept of partition function was initially formulated for equilibrium processes, it may be extended without any loss of generality to non-equilibrium processes. Moreover it is reminiscent of the concept of binding polynomial presented some years ago by Wyman for the equilibrium binding of a ligand to a protein. With this formalism derived from statistical mechanics, a structural rate equation may be derived from the ratio of a sub-partition function of degree n-1 and of a partition function of degree n. Again these properties are the consequence of the postulates of structural kinetics associated with simple ideas derived from statistical thermodynamics.     

Dimers generated from tetrameric phosphorylating glyceraldehyde-3-phosphate dehydrogenase from Bacillus stearothermophilus are inactive but exhibit cooperativity in NAD binding

Tetrameric phosphorylating glyceraldehyde-3-phosphate dehydrogenase (GAPDH) from Bacillus stearothermophilus has been described as a "dimer of dimers" with three nonequivalent interfaces, P-axis (between subunits O and P and between subunits Q and R), Q-axis (between subunits O and Q and between subunits P and R), and R-axis interface (between subunits O and R and between subunits P and Q). O-P dimers, the most stable and the easiest to generate, have been created by selective disruption of hydrogen bonds across the R- and Q-axis interfaces by site-directed mutagenesis. Asp-186 and Ser-48, and Glu-276 and Tyr-46, which are hydrogen bond partners across the R- and Q-axis interfaces, respectively, have been replaced with glycine residues. All mutated residues are highly conserved among GAPDHs from different species and are located in loops. Both double mutants D186G/E276G and Y46G/S48G were dimeric, while all single mutants remained tetrameric. As previously described [Clermont, S., Corbier, C., Mely, Y., Gerard, D., Wonacott, A., and Branlant, G. (1993) Biochemistry 32, 10178-10184], NAD binding to wild type GAPDH (wtGAPDH) was interpreted according to the induced-fit model and exhibited negative cooperativity. However, NAD binding to wtGAPDH can be adequately described in terms of two independent dimers with two interacting binding sites in each dimer. Single mutants D186G, E276G, and Y46G exhibited behavior in NAD binding similar to that of the wild type, while both dimeric mutants D186G/E276G and Y46G/S48G exhibited positive cooperativity in binding the coenzyme NAD. The fact that O-P dimer mutants retained cooperative behavior shows that (1) the P-axis interface is important in transmitting the information induced upon NAD binding inside the O-P dimer from one subunit to the other and (2) the S-loop of the R-axis-related subunit is not directly involved in cooperative binding of NAD in the O-P dimer. In both O-P dimer mutants, the absorption band of the binary enzyme-NAD complex had a highly decreased intensity compared to that of the wild type and, in addition, totally disappeared in the presence of G3P or 1,3-dPG. However, no enzymatic activity was detected, indicating that the formed ternary enzyme-NAD-G3P or -1, 3-dPG complex was not catalytically efficient. In the O-P dimers, the interaction with the S-loop of the R-axis-related subunit is disrupted, and therefore, the S-loop should be less structured. This resulted in increased accessibility of the active site to the solvent, particularly for the adenosine-binding site of NAD. Thus, together, this is likely to explain both the lowered affinity of the dimeric enzyme for NAD and the absence of activity.     

Resolvability of free energy changes for oxygen binding and subunit association by human hemoglobin.

Probability distributions of the free energy changes for oxygen binding, subunit association, and quaternary enhancement by human hemoglobin were obtained from Monte Carlo simulations performed on two independent sets of variable protein concentration equilibrium oxygen-binding data. Uncertainties in unliganded and fully liganded dimer to tetramer association free energy changes (0 delta G'2 and 4 delta G'2) were accounted for in the simulations. Distributions of the dimer to tetramer association free energy changes for forming singly and triply liganded tetramers (1 delta G'2 and 3 delta G'2) are well defined and quite symmetric, whereas that for forming doubly liganded tetramers (2 delta G'2) is poorly defined and highly asymmetric. The distribution of the dimer stepwise oxygen-binding free-energy change (delta g'2i) is well defined and quite symmetric as are those of the tetramer stepwise oxygen-binding free-energy changes for binding the first and last oxygens to tetramers (delta g'41 and delta g'44). Distributions of the intermediate tetramer stepwise oxygen-binding free-energy changes (delta g'42 and delta g'43) are poorly defined and highly asymmetric, but are compensatory in that their sum (delta g'4[2 + 3]) is again well defined and nearly symmetric. Distributions of the free energy changes corresponding to the tetramer product Adair oxygen binding constants (delta G'4i) are well defined and quite symmetric for i = 1, 3, 4 but not for i = 2. The distribution of delta g'44 - delta g'2i (the quaternary enhancement free energy change) is relatively narrow, nearly symmetric, and confined to the negative free-energy domain. This suggests that the quaternary enhancement free energy change (a) may be resolved with good confidence from this data and (b) is finite and negative under the conditions of these experiments. Our results also suggest two different four-state combinatorial switch models that provide accurate characterization of hemoglobin's functional behavior.     

Identification of a basic hybrid glutathione S-transferase from human liver. Glutathione S-transferase delta is composed of two distinct subunits (B1 and B2).

The purification of a hybrid glutathione S-transferase (B1 B2) from human liver is described. This enzyme has an isoelectric point of 8.75 and the B1 and B2 subunits are distinguishable immunologically and are ionically distinct. Hybridization experiments demonstrated that B1 B1 and B2 B2 could be resolved by CM-cellulose chromatography and have pI values of 8.9 and 8.4 respectively. Transferase B1 B2, and the two homodimers from which it is formed, are electrophoretically and immunochemically distinct from the neutral enzyme (transferase mu) and two acidic enzymes (transferases rho and lambda). Sodium dodecyl sulphate/polyacrylamide-gel electrophoresis demonstrated that B1 and B2 both have an Mr of 26 000, whereas, in contrast, transferase mu comprises subunits of Mr 27 000 and transferases rho and lambda both comprise subunits of Mr 24 500. Antisera raised against B1 or B2 monomers did not cross-react with the neutral or acidic glutathione S-transferases. The identity of transferase B1 B2 with glutathione S-transferase delta prepared by the method of Kamisaka, Habig, Ketley, Arias & Jakoby [(1975) Eur. J. Biochem. 60, 153-161] has been demonstrated, as well as its relationship to other previously described transferases.     

Single-site modifications of half-ligated hemoglobin reveal autonomous dimer cooperativity within a quaternary T tetramer

The patterns of energetic response elicited by single-site hemoglobin mutations and chemical mocdifications have been determined in order to probe the dimer–dimer interface of the half-ligated tetramer (species[21]) that was previously shown to behave as allosterically distinct from both the unligated and fully ligated molecules¹. In this study the free energies of quaternary assembly(dimers to tetramers) were determined for aseries of 24 tetrameric species in which one dimeric half-molecule is ligated while the adjacent αβ dimer is unligated and contains a single amino acid modification. Assembly energies have also been determined for tetramers bearing the same amino acid modifications but where the hemesites were completely vacant and additionally where they were fully occupied. A total of 72 molecular species were thus characterized. It was found that mutationally induced perturbations to the free energy of quaternary assembly were identical for the half-ligated tetramers and the unligated tetramers over the entire spatial distrubution of altered sites, but exhibited a radically different pattern from that of the fully ligated molecules. These results indicate that the dimer–dimer interface of the half-ligated tetramer(species[21]) has the same quaternary sturcture as that of the unligated molecule, i.e, “quaternary T.” This quaternary structure assignment of species [21] strongly supports the operation of a Symmetry Rule which translates changes in hemesite ligation into six T → R quaternary switchpoints². Analysis of the observed Symmetry Rule behaviour in relation to the measured distribution of cooperative free energies for the partially ligated species reveals significant cooperativity between α and β subunits of the dimeric half-tetramer within quaternary T. The mutational results indicate that these interactions are not “paid for” by breaking or making noncovalent bonds at the dimer–dimer interface (α¹β²). They arise from structural and energetic changes that are “internal” to the ligated dimer even though its association with the unligated dimer is required for the cooperativity to occur. Free energy of “tertiary constraint” is thus generated by the first binding step and is propagated to the second hemesite while the dimer–dimer interface α¹β²serves as a constraint. The “sequential” cooperativity that occurs within the half-molecule is thus preconditioned by the constraint of a quaternary T interface; release of this constraint by dissociation produces only noncooperative dimers. When the constraint is released functionally by T to R dimer rearrangement (at each switch-point specified by the a Symmetry Rule) the alterations of interfacial bonds then dominate the energetics of cooperativity. © 1993 Wiley-Liss, Inc.     

Yeast glyceraldehyde-3-phosphate dehydrogenase. Evidence that subunit cooperativity in catalysis can be controlled by the formation of a complex with phosphoglycerate kinase

Sepharose-bound tetrameric, dimeric and monomeric forms of yeast glyceraldehyde-3-phosphate dehydrogenase were prepared, as well as immobilized hybrid species containing (by selective oxidation of an active center cysteine residue with H2O2) one inactivated subunit per tetramer or dimer. The catalytic properties of these enzyme forms were compared in the forward reaction (glyceraldehyde-3-phosphate oxidation) and reverse reaction (1,3-bisphosphoglycerate reductive dephosphorylation) under steady-state conditions. In the reaction of glyceraldehyde-3-phosphate oxidation, immobilized monomeric and tetrameric forms exhibited similar specific activities. The hybrid-modified dimer contributed on half of the total activity of a native dimer. The tetramer containing one modified subunit possessed 75% of the activity of an unmodified tetramer. In the reaction of 1,3-bisphosphoglycerate reductive dephosphorylation, the specific activity of the monomeric enzyme species was nearly twice as high as that of the tetramer, suggesting that only one-half of the active centers of the oligomer were acting simultaneously. Subunit cooperativity in catalysis persisted in an isolated dimeric species. The specific activity of a monomer associated with a peroxide-inactivated monomer in a dimer was equal to that of an isolated monomeric species and twice as high as that of a native immobilized dimer. The specific activity of subunits associated with a peroxide-inactivated subunit in a tetramer did not differ from that of a native immobilized tetramer; this indicates that interdimeric interactions are involved in catalytic subunit cooperativity. A complex was formed between the immobilized glyceraldehyde-3-phosphate dehydrogenase and soluble phosphoglycerate kinase. Three monomers of phosphoglycerate kinase were bound per tetramer of the dehydrogenase and one per dimer. Evidence is presented that if the reductive dephosphorylation of 1,3-bisphosphoglycerate proceeds in the phosphoglycerate kinase - glyceraldehyde-3-phosphate dehydrogenase complex, all active sites of the latter enzyme act independently, i.e. subunit cooperativity is abolished.     

Dihydroorotase from Escherichia coli: loop movement and cooperativity between subunits

Escherichia coli dihydroorotase has been crystallized in the presence of the product, L-dihydroorotate (L-DHO), and the structure refined at 1.9A resolution. The structure confirms that previously reported (PDB entry 1J79), crystallized in the presence of the substrate N-carbamyl-D,L-aspartate (D, L-CA-asp), which had a dimer in the asymmetric unit, with one subunit having the substrate, L-CA-asp bound at the active site and the other having L-DHO. Importantly, no explanation for the unusual structure was given. Our results now show that a loop comprised of residues 105-115 has different conformations in the two subunits. In the case of the L-CA-asp-bound subunit, this loop reaches in toward the active site and makes hydrogen-bonding contact with the bound substrate molecule. For the L-DHO-bound subunit, the loop faces in the opposite direction and forms part of the surface of the protein. Analysis of the kinetics for conversion of L-DHO to L-CA-asp at low concentrations of L-DHO shows positive cooperativity with a Hill coefficient n=1.57(+/-0.13). Communication between subunits in the dimer may occur via cooperative conformational changes of the side-chains of a tripeptide from each subunit: Arg256-His257-Arg258, near the subunit interface.     

Structural stability of beta-lactoglobulin in the presence of kosmotropic salts. A kinetic and thermodynamic study

The thiol group of beta-lactoglobulin reacted very sluggishly with dithio-bis-nitro-benzoic acid as compared to that of glutathione at pH 6.85. The pKapp value of the thiol group of the protein was 9.35. In the presence of 3 M urea, the thiol group reacted completely with dithio-bis-nitrobenzoic acid at pH 6.85. Heating (from 50 degrees to 80 degrees) increased the exposure of the thiol by dissociating the dimer unit. From the pseudo-first order rate constants of heat-exposure of thiol, thermodynamic activation parameters, delta G++, delta H++, and delta S++, for the heat-dissociation of beta-lactoglobulin dimer were estimated to be 23,290 cal/mol, 31,160 cal/mol, and 22.9 e.u. (at 70 degrees), respectively. Addition of kosmotropic salts, chloride, tartrate, sulfate, phosphate, and citrate (0.2 M) decreased the heat-induced exposure of the thiol group (at 70 degrees), probably by decreasing the dissociation of the dimer at pH 6.85. The relative change in free energy of activation for the dissociation of the dimer, delta(delta G++dimer), in the presence of the salts was positive, suggesting that these additives increase the stability of the dimer against heat. These salts also increased the conformational stability of beta-lactoglobulin as revealed by an increase in -delta(delta G0conf) values in their presence. Both delta(delta G++dimer) and -delta(delta G0conf) values followed the order, chloride less than tartrate less than sulfate less than phosphate less than citrate. These salts seem to manifest their structure-stabilizing effect by increasing both inter- and intramolecular hydrophobic interactions via changes in structure of water.     

Description of the molecular mechanism of cooperativity in human hemoglobin cannot be limited to a first-order free energy coupling concept

Studies of the linkage between ligand binding and subunit assembly of oligomeric proteins have extensively used the concept of free energy coupling. The "order" of these free energy couplings was introduced [Weber, G. (1984) Proc. Natl. Acad. Sci. U.S.A. 81, 7098-7102] as the number of subunits that must be liganded to alter specific intersubunit interactions. This concept dictates that the ligation of fewer subunits has no effect, but once the order number of subunits becomes ligated, the specific intersubunit interaction energy between those particular subunits is completely eliminated. Weber's report claims that the free energy coupling between oxygen binding and the dimer-tetramer subunit assembly in stripped human hemoglobin A is "first order". This conclusion is based on the analysis of a set of previously published equilibrium constants [Mills, F. C., Johnson, M. L., & Ackers, G. K. (1976) Biochemistry 15, 5350-5362]. I subsequently reported that the original experimental data, from which the equilibrium constants were derived, are consistent with both the first-order and "second-order" free energy coupling concepts [Johnson, M. L. (1986) Biochemistry 25, 791-797]. I also demonstrated that more precise recent experimental data [Chu, A. H., Turner, B. W., & Ackers, G. K. (1984) Biochemistry, 23, 604-617] are consistent with both the first-order and second-order free energy coupling concepts. A recent article [Weber, G. (1987) Biochemistry 26, 331-332] disagrees that the oxygen-binding data for human hemoglobin A are consistent with a second-order model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamic and kinetic analysis of sensitivity amplification in biological signal transduction

Based on a thermodynamic analysis of the kinetic model for the protein phosphorylation-dephosphorylation cycle, we study the ATP (or GTP) energy utilization of this ubiquitous biological signal transduction process. It is shown that the free energy from hydrolysis inside cells, DeltaG (phosphorylation potential), controls the amplification and sensitivity of the switch-like cellular module; the response coefficient of the sensitivity amplification approaches the optimal 1 and the Hill coefficient increases with increasing DeltaG. We discover that zero-order ultrasensitivity is mathematically equivalent to allosteric cooperativity. Furthermore, we show that the high amplification in ultrasensitivity is mechanistically related to the proofreading kinetics for protein biosynthesis. Both utilize multiple kinetic cycles in time to gain temporal cooperativity, in contrast to allosteric cooperativity that utilizes multiple subunits in a protein.     

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.     

Analysis of the dynamic equilibrium of histone oligomers in a solution. The nature of forces stabilizing the (H2A-H2B-H3-H4)2 octamer structure

Dynamic equilibrium analysis of the (H2A-H2B-H3-H4)2 histone octamer with lower oligomers was performed in 2 M NaCl. Calculated data on the relative content of histone oligomers upon changing protein concentration in solution are given. The red shift of lambda max for histone tyrosine fluorescence spectra is shown to be due to hydrogen bond formation by tyrosyl OH-groups. Analysis of free energy changes of histone oligomers upon association (delta G = -17,37 +/- 0,14 kcal/mole) as well as the effect of urea on histone octamer dissociation made it possible to conclude that virtually all tyrosyls in octamer form hydrogen bonds. Intermolecular hydrogen bonds formed by tyrosyls contribute substantially to octamer stabilization. The (H2A-H2B) dimer positive cooperativity in association with the (H3-H4)2 tetramer was found. This cooperativity is caused by interaction between association sites with a two order increase in an apparent constant of dimers with tetramer association. The histone octamer was determined to be of asymmetric structure due to unequivolency of the two binding sites for the (H2A-H2B) dimers.     

Application of the one- and two-dimensional Ising models to studies of cooperativity between ion channels.

The Ising model of statistical physics provides a framework for studying systems of protomers in which nearest neighbors interact with each other. In this article, the Ising model is applied to the study of cooperative phenomena between ligand-gated ion channels. Expressions for the mean open channel probability, rho o, and the variance, sigma 2, are derived from the grand partition function. In the one-dimensional Ising model, interactions between neighboring open channels give rise to a sigmoidal rho o versus concentration curve and a nonquadratic relationship between sigma 2 and rho o. Positive cooperativity increases the slope at the midpoint of the rho o versus concentration curve, shifts the apparent binding affinity to lower concentrations, and increases the variance for a given rho o. Negative cooperativity has the opposite effects. Strong negative cooperativity results in a bimodal sigma 2 versus rho o curve. The slope of the rho o versus concentration curve increases linearly with the number of binding sites on a protomer, but the sigma 2 versus rho o relationship is independent of the number of ligand binding sites. Thus, the sigma 2 versus rho o curve provides unambiguous information about channel interactions. In the two-dimensional Ising model, rho o and sigma 2 are calculated numerically from a series expansion of the grand partition function appropriate for weak interactions. Virtually all of the features exhibited by the one-dimensional model are qualitatively present in the two-dimensional model. These models are also applicable to voltage-gated ion channels.     

Mechanism of the stabilization of ribonuclease A by sorbitol: preferential hydration is greater for the denatured then for the native protein.

The effect of interactions of sorbitol with ribonuclease A (RNase A) and the resulting stabilization of structure was examined in parallel thermal unfolding and preferential binding studies with the application of multicomponent thermodynamic theory. The protein was stabilized by sorbitol both at pH 2.0 and pH 5.5 as the transition temperature, Tm, was increased. The enthalpy of the thermal denaturation had a small dependence on sorbitol concentration, which was reflected in the values of the standard free energy change of denaturation, delta delta G(o) = delta G(o) (sorbitol) - delta G(o)(water). Measurements of preferential interactions at 48 degrees C at pH 5.5, where protein is native, and pH 2.0 where it is denatured, showed that sorbitol is preferentially excluded from the denatured protein up to 40%, but becomes preferentially bound to native protein above 20% sorbitol. The chemical potential change on transferring the denatured RNase A from water to sorbitol solution is larger than that for the native protein, delta mu(2D) > delta mu(2N), which is consistent with the effect of sorbitol on the free energy change of denaturation. The conformity of these results to the thermodynamic expression of the effect of a co-solvent on denaturation, delta G(o)(W) + delta mu(D)(2)delta G(o)(S) + delta mu(2D), indicates that the stabilization of the protein by sorbitol can be fully accounted for by weak thermodynamic interactions at the protein surface that involve water reversible co-solvent exchange at thermodynamically non-neutral sites. The protein structure stabilizing action of sorbitol is driven by stronger exclusion from the unfolded protein than from the native structure.     

The role of subunit cooperativity on ryanodine receptor 2 calcium signaling

The ryanodine receptor type 2 (RyR2) is composed of four subunits that control calcium (Ca) release in cardiac cells. RyR2 serves primarily as a Ca sensor and can respond to rapid sub-millisecond pulses of Ca while remaining shut at resting concentrations. However, it is not known how the four subunits interact for the RyR2 to function as an effective Ca sensor. To address this question, and to understand the role of subunit cooperativity in Ca-mediated signal transduction, we have developed a computational model of the RyR2 composed of four interacting subunits. We first analyze the statistical properties of a single RyR2 tetramer, where each subunit can exist in a closed or open conformation. Our findings indicate that the number of subunits in the open state is a crucial parameter that dictates RyR2 kinetics. We find that three or four open subunits are required for the RyR2 to harness cooperative interactions to respond to sub-millisecond changes in Ca, while at the same time remaining shut at the resting Ca levels in the cardiac cell. If the required number of open subunits is lowered to one or two, the RyR2 cannot serve as a robust Ca sensor, as the large cooperativity required to stabilize the closed state prevents channel activation. Using this four-subunit model, we analyze the kinetics of Ca release from a RyR2 cluster. We show that the closure of a cluster of RyR2 channels is highly sensitive to the balance of cooperative interactions between closed and open subunits. Based on this result, we analyze how specific interactions between RyR2 subunits can induce persistent Ca leak from the sarcoplasmic reticulum (SR), which is believed to be arrhythmogenic. Thus, these results provide a framework to analyze how a pharmacologic or genetic modification of RyR2 subunit cooperativity can induce abnormal Ca cycling that can potentially lead to life-threatening arrhythmias.     

The thermodynamics of bovine and porcine insulin and proinsulin association determined by concentration difference spectroscopy

Difference spectroscopy was used to determine the equilibrium constants and thermodynamic parameters for the monomer-dimer association of bovine and porcine insulin and bovine proinsulin at pH 2.0 and 7.0. At pH 2 delta G degree 25, delta S degree, and delta H degree for dimerization of bovine insulin were found to be -6.6 kcal/mol, -18 cal/mol-deg, and -12 kcal/mol, respectively. Porcine insulin behaved similarly to bovine insulin in its dimerization properties in that delta G degree 25, delta S degree, and delta H degree were found to be -6.8 kcal/mol, -14 cal/mol-deg, and -11 kcal/mol, respectively. At pH 7 delta G degree 25, delta S degree, and delta H degree for dimerization of bovine insulin were found to be -7.2 kcal/mol, -16 cal/mol/deg, and -12 kcal/mol, respectively. At pH 7.0 delta G degree 25, delta S degree, and delta H degree for dimerization of porcine insulin were -6.7 kcal/mol, -11.6 cal/mol-deg, and -10 kcal/mol, respectively. The similarity in the thermodynamic parameters of both insulin species at the different pH's suggests that there are minimal structural changes at the monomer-monomer contact site over this pH range. The dimerization of both insulin species is under enthalpic control. This may suggest that the formation of the insulin dimer is not driven by hydrophobic bonding but, rather, is driven by the formation between subunits of four hydrogen bonds in an apolar environment. At pH 2 delta G degree 25, delta S degree, and delta H degree for dimerization of bovine proinsulin were found to be -5.3 kcal/mol, -26 cal/mol-deg, and -13 kcal/mol, respectively. At pH 7 delta G degree 25, delta S degree, and delta H degree for dimerization of proinsulin were -5.9 kcal/mol, -4.2 cal/mol-deg, and -7.2 kcal/mol, respectively. Although the presence of the C-peptide on proinsulin does not drastically affect the overall free energy change of dimer formation (as compared to insulin), the other thermodynamic parameters are rather drastically altered. This may be because of electrostatic interactions of groups on the C-peptide with groups on the B-chain which are near the subunit contact site in the insulin dimer.     

Binding of a gating modifier toxin induces intersubunit cooperativity early in the Shaker K channel's activation pathway

Potassium currents from voltage-gated Shaker K channels activate with a sigmoid rise. The degree of sigmoidicity in channel opening kinetics confirms that each subunit of the homotetrameric Shaker channel undergoes more than one conformational change before the channel opens. We have examined effects of two externally applied gating modifiers that reduce the sigmoidicity of channel opening. A toxin from gastropod mucus, 6-bromo-2-mercaptotryptamine (BrMT), and divalent zinc are both found to slow the same conformational changes early in Shaker's activation pathway. Sigmoidicity measurements suggest that zinc slows a conformational change independently in each channel subunit. Analysis of activation in BrMT reveals cooperativity among subunits during these same early steps. A lack of competition with either agitoxin or tetraethylammonium indicates that BrMT binds channel subunits outside of the external pore region in an allosterically cooperative fashion. Simulations including negatively cooperative BrMT binding account for its ability to induce gating cooperativity during activation. We conclude that cooperativity among K channel subunits can be greatly altered by experimental conditions.     

Spin equilibrium and quaternary structure change in hemoglobin A. Experiments on a quantitative probe of the stereochemical mechanism of hemoglobin cooperativity

The molecular mechanism of hemoglobin cooperativity was studied kinetically by flash photolysis on mixed-state hemoglobins which consist of three ferrous carboxy subunits and one hybrid ferric subunit including fluoromet, azidomet, cyanatomet, and thiocyanatomet. The effects of conformational transitions on the hybrid subunit were detected by kinetic absorption spectroscopy after the CO was fully photodissociated from the binding sites by a large pulse of light from a tunable dye laser. The hemoglobin conformational transition rate was observed to depend on its state of ligation. At 22 degrees C, pH 7, and 0.1 M phosphate, the deoxy R yields T conformational change rate is 4 x 10(4)s-1. The rate decreases to 1.4 x 10(4)s-1 for singly ligated hemoglobin. The R yields T conformation change alters the energy separation between high- and low-spin states for azidomet, cyanatomet, and thiocyanatomet subunits by about 700, 300, and 300 cal/mol, respectively. There are two possible implications of this result: (1) the iron atom spin state is not the only major factor in the determination of its position with respect to the heme plane or (2) the change with conformation of the protein force exerted by the proximal histidine on the iron atom (for an iron to heme-plane displacement of less than 0.3 A) is less than 50% of that expected from simple models in which this motion is responsible for cooperativity.     

Thermodynamics of active-site ligand binding to Escherichia coli glutamine synthetase

Active-site ligand interactions with dodecameric glutamine synthetase from Escherichia coli have been studied by calorimetry and fluorometry using the nonhydrolyzable ATP analogue 5'-adenylyl imidodiphosphate (AMP-PNP), L-glutamate, L-Met-(S)-sulfoximine, and the transition-state analogue L-Met-(S)-sulfoximine phosphate. Measurements were made with the unadenylylated enzyme at pH 7.1 in the presence of 100 mM KCl and 1.0 mM MnCl2, under which conditions the two catalytically essential metal ion sites per subunit are occupied and the stoichiometry of active-site ligand binding is equal to 1.0 equiv/subunit. Thermodynamic linkage functions indicate that there is strong synergism between the binding of AMP-PNP and L-Met-(S)-sulfoximine (delta delta G' = -6.4 kJ/mol). In contrast, there is a small antagonistic effect between the binding of AMP-PNP and L-glutamate (delta delta G' = +1.4 kJ/mol). Proton effects were negligible (less than or equal to 0.2 equiv of H+ release or uptake/mol) for the different binding reactions. The binding of AMP-PNP (or ATP) to the enzyme is entropically controlled at 303 K with delta H = +5.4 kJ/mol and delta S = +150 J/(K.mol). At 303 K, the binding of L-glutamate (delta H = -22.2 kJ/mol) or L-Met-(S)-sulfoximine [delta H = -45.6 kJ/mol with delta Cp approximately equal to -670 +/- 420 J/(K.mol)] to the AMP-PNP.Mn.enzyme complex is enthalpically controlled with opposing delta S values of -29 or -46 J/(K.mol), respectively. The overall enthalpy change is negative and the overall entropy change is positive for the simultaneous binding of AMP-PNP and L-glutamate or of AMP-PNP and L-Met-(S)-sulfoximine to the enzyme. For the binding of the transition-state analogue L-Met-(S)-sulfoximine phosphate (which inactivates the enzyme by blocking active sites), both enthalpic and entropic contributions also are favorable at 303 K [delta G' approximately equal to -109 and delta H = -54.8 kJ/mol of subunit and delta S approximately equal to +180 J/(K.mol)].