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.     

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.     

EQUIL: Simulation and data analysis of binding reactions with arbitrary chemical models

We have developed an algorithm for simulation and analysis of arbitrary chemical systems in equilibrium, with emphasis on ligand binding reactions. The program EQUIL can treat reactions involving multiple ligands, multiple binding sites, ternary complex models, allosteric effectors, competitive and noncompetitive binding, conformational changes, cooperativity, and generally any scheme that can be represented as a set of chemical equations. EQUIL is based on a general thermodynamic model of chemical equilibria; it does not involve nonlinear transformation of experimental data, but it does require the user to define the model of interaction between ligands and receptors by writing down the appropriate chemical reactions. EQUIL contains features of particular importance to ligand binding experiments: variable binding capacities, nonspecific binding, and the ability to simultaneously analyze data from different types of experiments. Furthermore, the simulation feature of EQUIL allows the user to investigate the feasibility of experiments that could possibly distinguish between different reaction models. We illustrate the use of this program on personal computers to analyze and simulate simple and complicated interactions between ligands and receptors.     

Substrate-Modulated Thermal Fluctuations Affect Long-Range Allosteric Signaling in Protein Homodimers: Exemplified in CAP

The role of conformational dynamics in allosteric signaling of proteins is increasingly recognized as an important and subtle aspect of this ubiquitous phenomenon. Cooperative binding is commonly observed in proteins with twofold symmetry that bind two identical ligands. We construct a coarse-grained model of an allosteric coupled dimer and show how the signal can be propagated between the distant binding sites via change in slow global vibrational modes alone. We demonstrate that modulation on substrate binding of as few as 5-10 slow modes can give rise to cooperativity observed in biological systems and that the type of cooperativity is given by change of interaction between the two monomers upon ligand binding. To illustrate the application of the model, we apply it to a challenging test case: the catabolite activator protein (CAP). CAP displays negative cooperativity upon association with two identical ligands. The conformation of CAP is not affected by the binding, but its vibrational spectrum undergoes a strong modification. Intriguingly, the first binding enhances thermal fluctuations, yet the second quenches them. We show that this counterintuitive behavior is, in fact, necessary for an optimal anticooperative system, and captured within a well-defined region of the model's parameter space. From analyzing the experimental results, we conclude that fast local modes take an active part in the allostery of CAP, coupled to the more-global slow modes. By including them into the model, we elucidate the role of the modes on different timescales. We conclude that such dynamic control of allostery in homodimers may be a general phenomenon and that our model framework can be used for extended interpretation of thermodynamic parameters in other systems.     

Structural and thermodynamic aspects of cooperativity in the homodimeric hemoglobin from Scapharca inaequivalvis

The homodimeric cooperative hemoglobin from the mollusk Scapharca inaequivalvis displays an unusual subunit assembly with respect to vertebrate hemoglobins. The intersubunit contact region is formed by the two heme-carrying E and F helices, which bring the two hemes in contact with each other. At variance with tetrameric vertebrate hemoglobins, the ligand binding is not accompanied by a significant quaternary transition. The major ligand-linked changes are tertiary and are limited to the heme pocket and subunit interface. These unique structural features of HbI are not easily reconciled with the classical thermodynamic models used to describe cooperative ligand binding in vertebrate hemoglobins. The lack of distinct quaternary states and the absence of allosteric effectors suggested that cooperativity in HbI is entirely homotropic in origin. Thereafter, high resolution X-ray crystallographic data displayed the preferential binding of water molecules at the intersubunit interface in the unliganded protein with respect to the liganded one. These ordered water molecules were thus proposed to act as heterotropic effectors in HbI. The contribution of specific water binding to the observed cooperativity in HbI is discussed in the framework of the enthalpy-entropy compensation effect emerging from previous accurate equilibrium oxygen binding measurements.     

Unraveling Subunit Cooperativity in Homotetrameric HCN2 Channels

In a multimeric receptor protein, the binding of a ligand can modulate the binding of a succeeding ligand. This phenomenon, called cooperativity, is caused by the interaction of the receptor subunits. By using a complex Markovian model and a set of parameters determined previously, we analyzed how the successive binding of four ligands leads to a complex cooperative interaction of the subunits in homotetrameric HCN2 pacemaker channels. The individual steps in the model were characterized by Gibbs free energies for the equilibria and activation energies, specifying the affinity of the binding sites and the transition rates, respectively. Moreover, cooperative free energies were calculated for each binding step in both the closed and the open channel. We show that the cooperativity sequence positive-negative-positive determined for the binding affinity is generated by the combined effect of very different cooperativity sequences determined for the binding and unbinding rates, which are negative-negative-positive and no-negative-no, respectively. It is concluded that in the ligand-induced activation of HCN2 channels, the sequence of cooperativity based on the binding affinity is caused by two even qualitatively different sequences of cooperativity that are based on the rates of ligand binding and unbinding.     

Benzodiazepine ligands can act as allosteric modulators of the Type 1 cholecystokinin receptor

The cholecystokinin (CCK₁) receptor is a G protein-coupled receptor important for nutrient homeostasis. The molecular basis of CCK-receptor binding has been debated, with one prominent model suggesting occupation of the same region of the intramembranous helical bundle as benzodiazepines. Here, we used a specific assay of allosteric ligand interaction to probe the mode of binding of devazepide, a prototypic benzodiazepine ligand. Devazepide elicited marked slowing of dissociation of pre-bound CCK, only possible through binding to a topographically distinct allosteric site. This effect was disrupted by chemical modification of a cysteine in the benzodiazepine-binding pocket. Application of an allosteric model to the equilibrium interaction between a series of benzodiazepine ligands and CCK yielded quantitative estimates of each modulator’s affinity for the allosteric site, as well as the degree of negative cooperativity for the interaction between occupied orthosteric and allosteric sites. The allosteric nature of benzodiazepine binding to the CCK₁ receptor provides new opportunities for small molecule drug development.     

Delineation of the allosteric mechanism of a cytidylyltransferase exhibiting negative cooperativity.

The dimeric enzyme CTP:glycerol-3-phosphate cytidylyltransferase (GCT) displays strong negative cooperativity between the first and second binding of its substrate, CTP. Using NMR to study the allosteric mechanism of this enzyme, we observe widespread chemical shift changes for the individual CTP binding steps. Mapping these changes onto the molecular structure allowed the formulation of a detailed model of allosteric conformational change. Upon the second step of ligand binding, NMR experiments indicate an extensive loss of conformational exchange broadening of the backbone resonances of GCT. This suggests that a fraction of the free energy of negative cooperativity is entropic in origin.     

Is there a toxicological advantage for non-hyperbolic kinetics in cytochrome P450 catalysis? Functional allostery from "distributive catalysis"

The cytochrome P450s (CYPs) are the major enzymatic detoxification and drug metabolism system. Recently, it has become clear that several CYP isoforms exhibit positive and negative homotropic cooperativity. However, the toxicological implications of allosteric kinetics have not been considered, nor understood. The allosteric kinetics are particularly enigmatic in several respects. In many cases, CYPs bioactivate substrates to more toxic products, thus making it difficult to rationalize a functional advantage for positive cooperativity. Also, CYPs exhibit cooperativity with many structurally diverse ligands, in marked contrast to the specificity observed with other allosteric systems. Here, kinetic simulations are used to compare the probabilistic time- and concentration-dependent integrated toxicity function during conversion of substrate to product for CYP models exhibiting Michaelis-Menten (non-cooperative) kinetics, positive cooperativity, or negative cooperativity. The results demonstrate that, at low substrate concentrations, the slower substrate turnover afforded by cooperative CYPs compared with Michaelis-Menten enzymes can be a significant toxicological advantage, when toxic thresholds exist. When present, the advantage results from enhanced "distribution" of toxin in two pools, substrate and product, for an extended period, thus minimizing the chance that either exceeds its toxic threshold. At intermediate concentrations, the allosteric kinetics can be a modest advantage or modest disadvantage, depending on the kinetic parameters. However, at high substrate concentrations associated with a high probability of toxicity, fast turnover is desirable, and this advantage is provided also by the cooperative enzymes. For the positive homotropic cooperativity, the allosteric kinetics minimize the probability of toxicity over the widest range of system parameters. Furthermore, this apparent functional cooperativity is achieved without specific molecular recognition that is the hallmark of "traditional" allostery.     

Lateral density of receptor arrays in the membrane plane influences sensitivity of the E. coli chemotaxis response

In chemotactic bacteria, transmembrane chemoreceptors, CheA and CheW form the core signalling complex of the chemotaxis sensory apparatus. These complexes are organized in extended arrays in the cytoplasmic membrane that allow bacteria to respond to changes in concentration of extracellular ligands via a cooperative, allosteric response that leads to substantial amplification of the signal induced by ligand binding. Here, we have combined cryo-electron tomographic studies of the 3D spatial architecture of chemoreceptor arrays in intact E. coli cells with computational modelling to develop a predictive model for the cooperativity and sensitivity of the chemotaxis response. The predictions were tested experimentally using fluorescence resonance energy transfer (FRET) microscopy. Our results demonstrate that changes in lateral packing densities of the partially ordered, spatially extended chemoreceptor arrays can modulate the bacterial chemotaxis response, and that information about the molecular organization of the arrays derived by cryo-electron tomography of intact cells can be translated into testable, predictive computational models of the chemotaxis response.     

Cooperative binding of the bisubstrate analog N-(phosphonacetyl)-L-aspartate to aspartate transcarbamoylase and the heterotropic effects of ATP and CTP

Most investigations of the allosteric properties of the regulatory enzyme aspartate transcarbamoylase (ATCase) from Escherichia coli are based on the sigmoidal dependence of enzyme activity on substrate concentration and the effects of the inhibitor, CTP, and the activator, ATP, on the saturation curves. Interpretations of these effects in terms of molecular models are complicated by the inability to distinguish between changes in substrate binding and catalytic turnover accompanying the allosteric transition. In an effort to eliminate this ambiguity, the binding of the 3H-labeled bisubstrate analog N-(phosphonacetyl)-L-aspartate (PALA) to aspartate transcarbamoylase in the absence and presence of the allosteric effectors ATP and CTP has been measured directly by equilibrium dialysis at pH 7 in phosphate buffer. PALA binds with marked cooperativity to the holoenzyme with an average dissociation constant of 110 nM. ATP and CTP alter both the average affinity of ATCase for PALA and the degree of cooperativity in the binding process in a manner analogous to their effects on the kinetic properties of the enzyme; the average dissociation constant of PALA decreases to 65 nM in the presence of ATP and increases to 266 nM in the presence of CTP while the Hill coefficient, which is 1.95 in the absence of effectors, becomes 1.35 and 2.27 in the presence of ATP and CTP, respectively. The isolated catalytic subunit of ATCase, which lacks the cooperative kinetic properties of the holoenzyme, exhibits only a very slight degree of cooperativity in binding PALA. The dissociation constant of PALA from the catalytic subunit is 95 nM. Interpretation of these results in terms of a thermodynamic scheme linking PALA binding to the assembly of ATCase from catalytic and regulatory subunits demonstrates that saturation of the enzyme with PALA shifts the equilibrium between holoenzyme and subunits slightly toward dissociation. Ligation of the regulatory subunits by either of the allosteric effectors leads to a change in the effect of PALA on the association-dissociation equilibrium.     

Mathematical modeling suggests cooperative interactions between a disordered polyvalent ligand and a single receptor site

BACKGROUND: The CDK inhibitor Sic1 must be phosphorylated on at least six sites in order to allow its recognition by the SCF ubiquitin ligase subunit Cdc4. However, because Cdc4 appears to have only a single phospho-epitope binding site, the apparent cooperative dependence on the number of phosphorylation sites in Sic1 cannot be accounted for by traditional thermodynamic models of cooperativity. RESULTS: We develop a general kinetic model, which predicts an unexpected multiplicative increase in affinity as a function of ligand sites. This effect, termed allovalency, derives from a high local concentration of interaction sites moving independently of each other. Modeling of this interaction by a first exit time approach indicates that the probability of ligand rebinding increases exponentially with the number of sites. This type of interaction is relatively immune to loss of any one site and may be easily tuned to any given threshold by adjusting the properties of individual sites. CONCLUSIONS: The allovalency model suggests that a previously undescribed mechanism may underlie certain cooperative interactions. The widespread occurrence of flexible polyvalent ligands in biological systems suggests that this principle may be broadly applicable.     

Global conformational changes in allosteric proteins. A study of Escherichia coli cAMP receptor protein and muscle pyruvate kinase.

One of the basic features in allosteric regulation involves long range transduction of information. Based on crystallographic data on protein systems that are regulated by allosteric mechanisms, a global conformational change has always been observed. It is, therefore, important and useful to correlate the cooperativity of global structural change with the mode of binding of the regulatory ligand. Two systems were chosen for study, namely Escherichia coli cAMP receptor protein and muscle pyruvate kinase, which show negative and positive cooperativity in the binding of allosteric ligands, respectively. Quantitative titration of the global structural change, monitored by a high precision analytical gel chromatography technique, was conducted as a function of allosteric effector concentration. The results obtained for cAMP receptor protein show that the protein undergoes contraction upon binding of cAMP. The decreases in Stokes radius associated with complex formation are 0.1 +/- 0.1 and 0.7 +/- 0.1 A when one and two cAMP-binding sites are filled, respectively. The results for the pyruvate kinase system show a concerted structural change that quantitatively match the predicted behavior based on equilibrium constants derived from the analysis of steady state kinetic data by a two-state model. Hence, for these two systems, these results show that negative and positive cooperativity are correlated with sequential and concerted modes of structural change, respectively.     

Control of kinetics by cooperative interactions

Cooperative effects in ligand binding and dissociation kinetics are much less investigated than steady state kinetics or equilibrium binding. Nevertheless, cooperativity in ligand binding leads necessarily to characteristic properties with respect to kinetic properties of the system. In case of positive cooperativity as found in oxygen binding proteins, a typical property is an autocatalytic ligand dissociation behavior leading to a time dependent, apparent ligand dissociation rate. To follow systematically the influence of the various potentially involved parameters on this characteristic property, simulations based on the simple MWC model were performed which should be relevant for all types of models based on the concept of an allosteric unit. In cases where the initial conformational distribution is very much dominated by the R-state, the intrinsic kinetic properties of the T-state are of minor influence for the observed ligand dissociation rate. Even for fast conformational transition rates, the R-state properties together with the size of the allosteric unit and the allosteric equilibrium constant define the shape of the curve. In such a case, a simplified model of the MWC-scheme (the irreversible n-chain model) is a good approximation of the full scheme. However, if in the starting conformational distribution some liganded T-molecules are present (a few percent is enough), the average off-rates can be significantly altered. Thus, the assignment of the initial rates to R-state properties has to be done with great care. However, if the R-state strongly dominates initially it is even possible to get an estimation of the lower limit for the number of interacting subunits from kinetic data: similar to the Hill-coefficient for equilibrium conditions, a measure for "kinetic cooperativity" can be derived by comparing initial and final ligand dissociation rates.     

Comparison of the effects of chemical and isotopic dilution on the dissociation of bound labeled ligands

The dissociation of a labeled ligand from a binding structure to which it is reversibly attached can be promoted either by dilution or by chase. The kinetics of the dissociation brought up by dilution can be modified or not by the presence of various concentrations of cold ligand, according to the molecular mechanism of interaction. Analog computer simulation leads to the following results: (i) no cooperativity, monomolecular dissociation: no modification; (ii) positive or negative cooperativity (sequential models): acceleration, no modification, or slowing down (according to the kinetic constants); (iii) positive cooperativity (concerted model): no modification; (iv) two-step interaction: no modification if both interaction steps take place in the same phase, otherwise acceleration; and, (v) bimolecular association and dissociation: acceleration. This methodology could be used in order to characterize the molecular properties of various binding structures in the field of drug and hormone receptors as well as in enzymology.     

Kinetics of ligand binding and quaternary conformational change in the homodimeric hemoglobin from Scapharca inaequivalvis

The kinetics of the reaction with oxygen and carbon monoxide of the homodimeric hemoglobin from the bivalve mollusc Scapharca inaequivalvis has been extensively investigated by flash and dye-laser photolysis, temperature jump relaxation, and stopped flow methods. The results indicate that cooperativity in ligand binding, already observed for oxygen at equilibrium, finds its kinetic counterpart in a large decrease of the oxygen dissociation velocity in the second step of the binding reaction. In the case of carbon monoxide, cooperativity is clearly evident in the increase of the combination velocity constant as the reaction proceeds. Therefore, the ligand-binding kinetics of this dimeric hemoglobin shows the characteristic features of the corresponding reactions of tetrameric hemoglobins. Analysis of the data in terms of the allosteric model proposed by Monod et al. (Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88-118) has shown that the values of the allosteric parameters cannot be fixed uniquely for a dimeric hemoglobin. The rapid changes in absorbance observed at the isosbestic points of unliganded and liganded hemoglobin following laser photolysis provided a value of 7 X 10(4) S-1 at 20 degrees C for the rate of the ligand-free quarternary conformational change, postulated on the basis of cooperative ligand binding. Comparison of the rapid absorbance changes observed during ligand rebinding in this hemoglobin with those observed in tuna hemoglobin indicate that, at full photolysis, binding to the T state is followed by further binding and conversion to the liganded R state; at partial photolysis, population of the liganded T state occurs immediately and is followed by a decay to the liganded R state upon further ligand binding. These new results, in conjunction with previous equilibrium data on the same system, show unequivocally that the presence of two different types of chain is not an absolute prerequisite for cooperativity in hemoglobins, contrary to currently accepted ideas.     

Structural requirements for cooperativity in ileal bile acid-binding proteins

Ileal bile acid-binding proteins (I-BABP), belonging to the family of intracellular lipid-binding proteins, control bile acid trafficking in enterocytes and participate in regulating the homeostasis of these cholesterol-derived metabolites. I-BABP orthologues share the same structural fold and are able to host up to two ligands in their large internal cavities. However variations in the primary sequences determine differences in binding properties such as the degree of binding cooperativity. To investigate the molecular requirements for cooperativity we adopted a gain-of-function approach, exploring the possibility to turn the noncooperative chicken I-BABP (cI-BABP) into a cooperative mutant protein. To this aim we first solved the solution structure of cI-BABP in complex with two molecules of the physiological ligand glycochenodeoxycholate. A comparative structural analysis with closely related members of the same protein family provided the basis to design a double mutant (H99Q/A101S cI-BABP) capable of establishing a cooperative binding mechanism. Molecular dynamics simulation studies of the wild type and mutant complexes and essential dynamics analysis of the trajectories supported the role of the identified amino acid residues as hot spot mediators of communication between binding sites. The emerging picture is consistent with a binding mechanism that can be described as an extended conformational selection model.