Heme reactivity of hemoglobins. Azide and fluoride binding equilibria of free and mercuriated ferri-gamma chains.

The free gamma chains, isolated from human foetal hemoglobin, are stable when oxidized and thus suitable for ligand binding and subunit equilibrium studies. The metaquo-ferri chains, with cysteine-F9 in the free state II ag gamma SH) possess several properties which are different from those of their p-mercuribenzoate derivative (III aq gammaSHgR); these are: stronger binding of a high-field ligand (N3- minus), altered spin equilibrium and an altered subunit equilibrium. A quantitative assessment of the free energy changes associated with all individual steps involved in changing the metaquo chains to their azide derivatives has been made. The results show that the higher apparent reactivity of III ag gammaSH (compared to IIIaq gammaSHgR) for the azide ion is not solely due to compensatory effects arising from differences of subunit dissociation or of spin equilibrium: other process(es) occurring in the ligand binding site have to be considered.     

Effects of ligand size on pH and organic phosphate-dependent affinity changes in carp hemoglobin as measured by isonitrile binding

The equilibria of the binding of methyl and ethyl isonitrile to carp hemoglobin have been measured at three pH values in the presence and absence of inositol hexaphosphate. The binding of methyl isonitrile is characterized by a higher overall dissociation constant, C1/2, and a higher Hill coefficient, n, than that of the ethyl derivative. The former is consistent with the greater hydrophobicity of ethyl isonitrile, and the latter is probably due to a greater intrinsic difference or heterogeneity in the binding affinities of the alpha- and beta-chains for the larger ligand. Changes in log C1/2 which result from alterations in pH or addition of organic phosphate are the same for both ligands within experimental error. This result is not consistent with affinity changes being the result of steric interactions between the protein and the ligand. At pH 6 in the presence of inositol hexaphosphate, equilibrium parameters estimated from overall rates of ligand binding and dissociation are in good agreement with direct equilibrium measurements. This is consistent with the protein being in a low-affinity, T-like state even when saturated with ligand under these conditions, resulting in a loss of cooperativity in ligand binding. At high pH, ligand binding remains cooperative, as evidenced by n values greater than unity, a general lack of agreement between measured equilibrium parameters and those estimated from overall kinetic constants, and differences in the kinetics of ligand binding as observed by rapid-mixing and flash photolysis techniques. Thus, the deoxygenated state of carp hemoglobin at high pH does not appear to be a good model of a deoxygenated R quaternary structural state.     

Selected-fit versus induced-fit protein binding: kinetic differences and mutational analysis

The binding of a ligand molecule to a protein is often accompanied by conformational changes of the protein. A central question is whether the ligand induces the conformational change (induced-fit), or rather selects and stabilizes a complementary conformation from a pre-existing equilibrium of ground and excited states of the protein (selected-fit). We consider here the binding kinetics in a simple four-state model of ligand-protein binding. In this model, the protein has two conformations, which can both bind the ligand. The first conformation is the ground state of the protein when the ligand is off, and the second conformation is the ground state when the ligand is bound. The induced-fit mechanism corresponds to ligand binding in the unbound ground state, and the selected-fit mechanism to ligand binding in the excited state. We find a simple, characteristic difference between the on- and off-rates in the two mechanisms if the conformational relaxation into the ground states is fast. In the case of selected-fit binding, the on-rate depends on the conformational equilibrium constant, whereas the off-rate is independent. In the case of induced-fit binding, in contrast, the off-rate depends on the conformational equilibrium, while the on-rate is independent. Whether a protein binds a ligand via selected-fit or induced-fit thus may be revealed by mutations far from the protein's binding pocket, or other "perturbations" that only affect the conformational equilibrium. In the case of selected-fit, such mutations will only change the on-rate, and in the case of induced-fit, only the off-rate.     

On the link between conformational changes,ligand binding and heat capacity

BackgroundConformational changes coupled to ligand binding constitute the structural and energetics basis underlying cooperativity, allostery and, in general, protein regulation. These conformational rearrangements are associated with heat capacity changes. ITC is a unique technique for studying binding interactions because of the simultaneous determination of the binding affinity and enthalpy, and for providing the best estimates of binding heat capacity changes.Scope of reviewStill controversial issues in ligand binding are the discrimination between the “conformational selection model” and the “induced fit model”, and whether or not conformational changes lead to temperature dependent apparent binding heat capacities. The assessment of conformational changes associated with ligand binding by ITC is discussed. In addition, the “conformational selection” and “induced fit” models are reconciled, and discussed within the context of intrinsically (partially) unstructured proteins.Major conclusionsConformational equilibrium is a major contribution to binding heat capacity changes. A simple model may explain both conformational selection and induced fit scenarios. A temperature-independent binding heat capacity does not necessarily indicate absence of conformational changes upon ligand binding. ITC provides information on the energetics of conformational changes associated with ligand binding (and other possible additional coupled equilibria).General significancePreferential ligand binding to certain protein states leads to an equilibrium shift that is reflected in the coupling between ligand binding and additional equilibria. This represents the structural/energetic basis of the widespread dependence of ligand binding parameters on temperature, as well as pH, ionic strength and the concentration of other chemical species. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Binding of specific ligand by linearly associating enzyme system

The binding of specific ligand by linearly associating enzyme system M in equilibrium to M2 in equilibrium to M3 in equilibrium... has been discussed. It is assumed that ligand is bound in the region of the contact of monomers and free monomer retains the subsites for specific ligand binding. The character of the dependences of the amount of bound ligand on enzyme and ligand concentrations and the influence of specific ligand on the distribution between oligomeric enzyme forms have been analysed. The high concentrations of specific ligand provoke the dissociation of enzyme oligomers because of occupation of both subsites in monomeric form. The situation is discussed when a specific ligand is the substrate which is converted to the product in an intact binding site located in the region of the contact of monomers. The inhibitory effect of high substrate concentrations has been interpreted, taking into account the blocking of the association of inactive monomers into active oligomers.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

Further consideration of systematic errors present in protein-ligand interactions

Relatively minor systematic errors present during measurements of protein-ligand interaction can lead to large inaccuracies in the calculated values of the equilibrium dissociation constant and the total concentration of the binding protein. These errors, which include binding of the ligand to low affinity material and underestimation of bound ligand, cause the calculation of the concentration of free ligand at equilibrium to be overestimated. We report herein a model of ligandprotein binding which incorporates these errors into the mathematical formulation of the equilibrium binding equation. The effect of these errors on the Scatchard plot is presented.     

Interpretation of Scatchard plots for aggregating receptor systems.

Aggregation of cell surface receptors, with each other or with other membrane proteins, occurs in a variety of experimental systems. The list of systems where receptor aggregation appears to be important in understanding ligand binding and cellular responses is growing rapidly. In this paper we explore the interpretation of equilibrium binding data for aggregating receptor systems. The Scatchard plot is a widely used tool for analyzing equilibrium binding data. The shape of the Scatchard plot is often interpreted in terms of multiple noninteracting receptor populations. Such an analysis does not provide a framework for investigating the role of receptor aggregation and will be misleading if there is a relation between receptor aggregation and ligand binding. We present a general model for the equilibrium binding of a ligand with any number of aggregating receptor populations and derive theoretical expressions for observable Scatchard plot features. These can be used to test particular models and estimate model parameters. We develop particular models and apply the general results in the cases of six aggregating receptor systems where ligand binding and receptor aggregation are related: cross-linking of monovalent cell surface proteins by monoclonal antibodies, cross-linking of cell surface antibodies by bivalent ligand, antibody-induced co-cross-linking of cell surface antibodies and Fc gamma receptors, ligand-enhanced aggregation of identical epidermal growth factor receptors, aggregation of heterologous receptors for interleukin 2 to form a high-affinity receptor, and association of receptors, including those for interleukins 5 and 6, with nonbinding accessory proteins that influence receptor affinity or effector function.     

Direct measurement of equilibrium constants for high-affinity hemoglobins

The biological functions of heme proteins are linked to their rate and affinity constants for ligand binding. Kinetic experiments are commonly used to measure equilibrium constants for traditional hemoglobins comprised of pentacoordinate ligand binding sites and simple bimolecular reaction schemes. However, kinetic methods do not always yield reliable equilibrium constants with more complex hemoglobins for which reaction mechanisms are not clearly understood. Furthermore, even where reaction mechanisms are clearly understood, it is very difficult to directly measure equilibrium constants for oxygen and carbon monoxide binding to high-affinity (K(D) < 1 micro M) hemoglobins. This work presents a method for direct measurement of equilibrium constants for high-affinity hemoglobins that utilizes a competition for ligands between the "target" protein and an array of "scavenger" hemoglobins with known affinities. This method is described for oxygen and carbon monoxide binding to two hexacoordinate hemoglobins: rice nonsymbiotic hemoglobin and Synechocystis hemoglobin. Our results demonstrate that although these proteins have different mechanisms for ligand binding, their affinities for oxygen and carbon monoxide are similar. Their large affinity constants for oxygen, 285 and approximately 100 micro M(-1) respectively, indicate that they are not capable of facilitating oxygen transport.     

Theoretical analysis of the footprinting experiment

In the footprinting experiment, an end-radiolabeled DNA restriction fragment is subjected to digest by an endonuclease in the presence and absence of a ligand which alters the endonuclease cleavage rate at sites of ligand-DNA contact. The location of these sites, and the strength of the ligand binding, are then deduced from the measured concentrations of the different oligonucleotides produced by the digest. We analyze the experiment in terms of coupled kinetic equations which take into account the cutting rates of endonuclease for sites with ligand present and absent, and the rates of binding and dissociation of the ligand to a site. As long as the ligand concentration remains essentially constant (which occurs, for example, if digest is terminated early enough to assure that all fragments result from single cuts by the endonuclease), the oligonucleotide concentrations reflect only the ligand binding equilibrium constant (ratio of rate constants) and the cutting rates in the presence and absence of ligand. We also show how the measured oligonucleotide concentrations (from, e.g. an autoradiogram) can be used to deduce the ligand equilibrium binding constants for the various sites on the polymer.     

Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3'-O-(N-methylantraniloyl)-5'-diphosphate to the E. coli DnaC protein.     

A method for binding parameters estimation of A1 adenosine receptor subtype: a practical approach

Working with pig brain striatum in which A1 and A2 adenosine receptor subtypes coexist, we describe an uncomplicated method for unequivocally obtaining the equilibrium parameters (KD and binding capacity) of A1 receptor without interference from ligand binding to A2 receptor. Also, the equilibrium parameter estimation method we propose avoids the experimental determination of nonspecific binding by the inclusion of the corresponding unknown parameter in the function. This not only saves time but also avoids the use of expensive radioligands in saturation experiments. The method is suitable for any system with two different receptor subtypes for the same physiological ligand, and good estimates of the equilibrium parameters corresponding to the subtype displaying the higher affinity for the ligand can be obtained.     

Theoretical Analysis of the Footprinting Experiment

Abstract

In the footprinting experiment, an end-radiolabeled DNA restriction fragment is subjected to digest by an endonuclease in the presence and absence of a ligand which alters the endonuclease cleavage rate at sites of ligand-DNA contact. The location of these sites, and the strength of the ligand binding, are then deduced from the measured concentrations of the different oligonucleotides produced by the digest. We analyze the experiment in terms of coupled kinetic equations which take into account the cutting rates of endonuclease for sites with ligand present and absent, and the rates of binding and dissociation of the ligand to a site. As long as the ligand concentration remains essentially constant (which occurs, for example, if digest is terminated early enough to assure that all fragments result from single cuts by the endonuclease), the oligonucleotide concentrations reflect only the ligand binding equilibrium constant (ratio of rate constants) and the cutting rates in the presence and absence of ligand. We also show how the measured oligonucleotide concentrations (from, e.g. an autoradiogram) can be used to deduce the ligand equilibrium binding constants for the various sites on the polymer.     

Equilibrium competition binding assay: inhibition mechanism from a single dose response

Inhibition of a receptor by a small-molecule compound in many cases is achieved via a competitive, uncompetitive or non-competitive mechanism. The receptor-inhibitor interaction is often probed through the displacement of a ligand in an equilibrium competition binding experiment. The previous solutions to receptor inhibition mechanisms were borrowed from steady-state enzyme inhibition mechanisms. The inhibition mechanism is determined by a visual inspection or a global fit of ligand dose response curves at a series of inhibitor concentrations. However these solutions only apply to situations when both the ligand and the inhibitor are not significantly depleted by the receptor. In most published equilibrium receptor binding studies, only the relative potency of the inhibitor is calculated. Ranking inhibitors tested under differing experimental conditions is often not possible. In the current paper, we offer exact mathematical solutions to uncompetitive and non-competitive inhibition, and demonstrate that in most cases both the inhibition mechanism and absolute potency of an inhibitor can be simultaneously determined from a single dose response of the inhibitor at a fixed concentration of the ligand. Therefore, an equilibrium competition assay provides a quick and facile method to determine the inhibition mechanism of a large number of inhibitors. The theory herein described is applicable to equilibrium competition binding experiments such as radioligand assays and fluorescence polarization assays.     

Competitive binding assays for high-affinity binders in the presence of endogenous ligands: application to biotin-binding proteins

Endogenous ligands complicate radioligand-binding assays of high-affinity binding proteins by obscuring binding sites or by diluting the labeled ligand. We have developed a mathematical model for such systems where radioligand and endogenous ligand are structurally identical. Data which relate radioligand binding at equilibrium as a function of sample volume can be plotted such that the concentrations of endogenous ligand and binder are graphically determined; however, a more precise determination may be done by nonlinear regression with the aid of a microcomputer. The method is demonstrated for the assay of biotin-binding proteins in the presence of a range of endogenous biotin concentrations below and above that required to saturate the binding sites.     

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.     

Conformational selection or induced fit? A critical appraisal of the kinetic mechanism

For almost five decades, two competing mechanisms of ligand recognition, conformational selection and induced fit, have dominated our interpretation of ligand binding in biological macromolecules. When binding-dissociation events are fast compared to conformational transitions, the rate of approach to equilibrium, k(obs), becomes diagnostic of conformational selection or induced fit based on whether it decreases or increases, respectively, with the ligand concentration, [L]. However, this simple conclusion based on the rapid equilibrium approximation is not valid in general. Here we show that conformational selection is associated with a rich repertoire of kinetic properties, with k(obs) decreasing or increasing with [L] depending on the relative magnitude of the rate of ligand dissociation, k(off), and the rate of conformational isomerization, k(r). We prove that, even for the simplest two-step mechanism of ligand binding, a decrease in k(obs) with [L] is unequivocal evidence of conformational selection, but an increase in k(obs) with [L] is not unequivocal evidence of induced fit. Ligand binding to glucokinase, thrombin, and its precursor prethrombin-2 are used as relevant examples. We conclude that conformational selection as a mechanism for a ligand binding to its target may be far more common than currently believed.     

Effects of thermodynamic nonideality in ligand binding studies

Effects of thermodynamic nonideality are considered in relation to the quantitative characterization of the interaction between a small ligand. S, and a macromolecular acceptor. A, by two types of experimental procedure. The first involves determination of the concentration of ligand in dialysis equilibrium with the acceptor/ligand mixture, and the second, measurement of the concentration of unbound ligand in the reaction mixture by ultrafiltration or the rate of dialysis method. For each situation explicit expressions are formulated for the appropriate binding function with allowance for composition-dependent nonideality effects expressed in terms of molar volume, charge-charge interaction and covolume contributions. The magnitudes of these effects are explored with the aid of experimental studies on the binding of tryptophan and of methyl orange to bovine serum albumin. It is concluded for experiments conducted utilizing either equilibrium dialysis or frontal gel chromatography that, provided a correction is made for any Donnan redistribution of ligand, theoretically predicted acceptor-concentration dependence is likely to be negligible and that use of the conventional binding equation written for an ideal system is appropriate to the analysis of the results. Use of ultrafiltration or the rate of dialysis method requires examination of the assumption that the activity coefficient ratio y(A)y(s)/y(AS) for the reaction mixture approximates unity; but again reassurance is provided that nonideality manifested as a dependence of the binding function on acceptor concentration is unlikely to be significant.     

Subunit iron spin heterogeneity in human aquomethemoglobin A

On the basis of a reaction scheme in which the ligand binding steps are preceded by fast iron spin transitions (Okonjo, K.O. (1980) Eur. J. Biochem. 105, 329-334; Iwuoha, E.I. and Okonjo, K.O. (1985) Biochim. Biophys. Acta 829, 327-334), the spin equilibrium constants of methemoglobin subunits are calculated from kinetic and equilibrium binding parameters with azide ion as ligand. The results demonstrate the existence of thermodynamic spin heterogeneity within the tetramer.     

Misuse of thermodynamics in the interpretation of isothermal titration calorimetry data for ligand binding to proteins

Isothermal titration calorimetry (ITC) has given a mass of data on the binding of small molecules to proteins and other biopolymers, with particular interest in drug binding to proteins chosen as therapeutic indicators. Interpretation of the enthalpy data usually follows an unsound protocol that uses thermodynamic relations in circumstances where they do not apply. Errors of interpretation include incomplete definitions of ligand binding and equilibrium constants and neglect of the non-ideality of the solutions under study, leading to unreliable estimates of standard free energies and entropies of binding. The mass of reported thermodynamic functions for ligand binding to proteins estimated from ITC enthalpies alone is consequently of uncertain thermodynamic significance and utility. ITC and related experiments to test the protocol assumptions are indicated. A thermodynamic procedure avoiding equilibrium constants or other reaction models and not requiring protein activities is given. The discussion draws attention to the fundamental but neglected relation between the thermodynamic activity and bioactivity of drugs and to the generally unknown thermodynamic status of ligand solutions, which for drugs relates directly to effective therapeutic dosimetry.