An equilibrium study of the cooperative binding of adenosine cyclic 3',5'-monophosphate and guanosine cyclic 3',5'-monophosphate to the adenosine cyclic 3',5'-monophosphate receptor protein from Escherichia coli

The binding of adenosine cyclic 3',5'-monophosphate (cAMP) and guanosine cyclic 3',5'-monophosphate (cGMP) to the adenosine cyclic 3',5'-monophosphate receptor protein (CRP) from Escherichia coli was investigated by equilibrium dialysis at pH 8.0 and 20 degrees C at different ionic strengths (0.05--0.60 M). Both cAMP and cGMP bind to CRP with a negative cooperativity that is progressively changed to positive as the ionic strength is increased. The binding data were analyzed with an interactive model for two identical sites and site/site interactions with the interaction free energy--RT ln alpha, and the intrinsic binding constant K and cooperativity parameter alpha were computed. Double-label experiments showed that cGMP is strictly competitive with cAMP, and its binding parameters K and alpha are not very different from that for cAMP. Since two binding sites exist for each of the cyclic nucleotides in dimeric CRP and no change in the quaternary structure of the protein is observed on binding the ligands, it is proposed that the cooperativity originates in ligand/ligand interactions. When bound to double-stranded deoxyribonucleic acid (dsDNA), CRP binds cAMP more efficiently, and the cooperativity is positive even in conditions of low ionic strength where it is negative for the free protein. By contrast, cGMP binding properties remained unperturbed in dsDNA-bound CRP. Neither the intrinsic binding constant K nor the cooperativity parameter alpha was found to be very sensitive to changes of pH between 6.0 and 8.0 at 0.2 M ionic strength and 20 degrees C. For these conditions, the intrinsic free energy and entropy of binding of cAMP are delta H degree = -1.7 kcal . mol-1 and delta S degree = 15.6 eu, respectively.     

Analysis of cooperativity and ion effects in the interaction of quinacrine with DNA

The interaction of quinacrine with calf thymus DNA was monitored at several different ionic strengths using spectrophotometric and equilibrium dialysis techniques. The binding results can be explained, assuming each base pair is a potential binding site, using a model containing two negative cooperative effects: (1) ligand exclusion at binding sites adjacent to a filled binding site and (2) ligand–ligand negative cooperativity at adjacent filled binding sites. The logarithm of the observed equilibrium constant (K_obs) determined by this model varies linearily with log[Na⁺], as predicted by the ion condensation theory for polyelectrolytes. When the log K_obs plot is correlated for sodium release by DNA in the intercalation conformational change, the predicted number of ion pairs between the ligand and DNA is approximately two, as expected for the quinacrine dication. Even though K_obs depends strongly on ionic strength, the ligand negative cooperativity parameter ω was found to be indpendent of ionic strength within experimental error. This finding is also in agreement with the ion condensation theory, which predicts a relatively constant amount of condensed counterion on the DNA double helix over this ionic strength range. Drugs would, therefore, experience a relatively constant ionic environment when complexed to DNA even though the ionic conditions of the solvent could change considerably.     

The "regulatory" sulfhydryl group of Penicillium chrysogenum ATP sulfurylase. Cooperative ligand binding after SH modification; chemical and thermodynamic properties

ATP sulfurylase from Penicillium chrysogenum is a homohexamer that contains three free sulfhydryl groups/subunit, only one of which (designated SH-1) can be modified by disulfide, maleimide, and halide reagents under nondenaturing conditions. Modification of SH-1 has only a small effect on kcat but causes the [S]0.5 values for MgATP and SO4(2-) (or MoO4(2-) to increase by an order of magnitude. Additionally, the velocity curves become sigmoidal with a Hill coefficient (nH) of about 2 (Renosto, F., Martin, R. L., and Segel, I. H. (1987) J. Biol. Chem. 262, 16279-16288). Direct equilibrium binding measurements confirmed that [32P]MgATP binds to the SH-modified enzyme in a positively cooperative fashion (nH = 2.0) if a sulfate subsite ligand (e.g. FSO3-) is also present. [35S]Adenosine 5'-phosphosulfate (APS) binding to the SH-modified enzyme displayed positive cooperativity (nH = 1.9) in the absence of a PPi subsite ligand. The results indicate that positive cooperativity requires occupancy of the adenylyl and sulfate (but not the pyrophosphate) subsites. [35S]APS binding to the native enzyme displayed negative cooperativity (or binding to at least two classes of sites). Isotope trapping profiles for the single turnover of [35S]APS: (a) confirmed the equilibrium binding curves, (b) indicated that all six sites/hexamer are catalytically active, and (c) showed that APS does not dissociate at a significant rate from E.APS.PPi. The MgPPi concentration dependence of [35S]APS trapping was indicative of MgPPi binding to two classes of sites on both the native and SH-modified enzyme. Inactivation of the native or SH-modified enzyme by phenylglyoxal in the presence of saturating APS was biphasic. The semilog plots suggested that only half of the sites were highly protected. The cumulative data suggest a model in which pairs of sites or subunits can exist in three different states designated HH (both sites have a high APS affinity, as in the native free enzyme), LL (both sites have a low APS affinity as in the SH-modified enzyme), and LH (as in the APS-occupied native or SH-modified enzyme). Thus, the HH----LH transition displays negative cooperativity for APS binding while the LL----LH transition displays positive cooperativity. The relative reactivities of like-paired SH-reactive reagents were in the order: N-phenylmaleimide greater than N-ethylmaleimide; dithionitropyridine greater than dithionitrobenzoate; thiolyte-MQ greater than thiolyte-MB. The log kmod versus pH curve indicates that the pKa of SH-1 is greater than 9.(ABSTRACT TRUNCATED AT 400 WORDS)     

The binding of [3H]R-PIA to A1 adenosine receptors produces a conversion of the high- to the low-affinity state

Kinetic evidence for negative cooperativity on the binding of [3H]R-PIA to A1 adenosine receptors was obtained from dissociation experiments at different ligand concentrations and from the equilibrium isotherm. The dissociation curves indicate that there is an apparent ligand-induced transformation of high- to low-affinity states of the receptor. At concentrations of 18.2 nM R-PIA or higher there was only found the low-affinity state of the receptor. In view of these results equilibrium binding data were analyzed by the usual two-state model (assuming that there is an interconversion between them) and by the negative cooperativity model employing the Hill equation.     

The relationship between effector binding and inhibition of activity in D-3-phosphoglycerate dehydrogenase

The binding of L-serine to phosphoglycerate dehydrogenase from Escherichia coli displays elements of both positive and negative cooperativity. At pH 7.5, approximately 2 mol of serine are bound per mole of tetrameric enzyme. A substantial degree of positive cooperativity is seen for the binding of the second ligand, but the binding of the third and fourth ligand display substantial negative cooperativity. The data indicate a state of approximately 50% inhibition when only one serine is bound and approximately 80-90% inhibition when two serines are bound. This is consistent with the tethered domain hypothesis that has been presented previously. Comparison of the data derived directly from binding stoichiometry to the binding constants determined from the best fit to the Adair equation, produce a close agreement, and reinforce the general validity of the derived binding constants. The data also support the conclusion that the positive cooperativity between the binding to the first and second site involves binding sites at opposite interfaces over 110 A apart. Thus, an order of binding can be envisioned where the binding of the first ligand initiates a conformational transition that allows the second ligand to bind with much higher affinity at the opposite interface. This is followed by the third ligand, which binds with lesser affinity to one of the two already occupied interfaces, and in so doing, completes a global conformational transition that produces maximum inhibition of activity and an even lower affinity for the fourth ligand, excluding it completely. Thus, maximal inhibition is accomplished with less than maximal occupancy of effector sites through a mechanism that displays strong elements of both positive and negative cooperativity.     

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.     

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.     

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.     

Ligand-dependent aggregation and cooperativity: a critique

Ligand-dependent site-site (or subunit-subunit) interactions provide the basis for explaining cooperativity in chemical reactions. Even in the simplest possible nonaggregating system, interpretation of the interactions in terms of structural details requires an explicit assumption (or model) for the binding of the ligand to the sites when there are no interactions. This paper develops in detail the processes by which aggregation will yield ligand-dependent cooperativity. Two conceptually distinct free energy differences may contribute to cooperativity in an aggregation reaction. One is the free energy difference in ligand binding between the monomer and the aggregate. The other is derived from ligand-dependent interactions between the sites of the aggregate. In this analysis an explicit distinction is made between the experimentally accessible constants and those derived from assumed models. Experimental measurements of an aggregation cycle in which all of the species in equilibrium are defined do not allow for an evaluation of the energies of interaction without some model (or assumption). In the analysis presented, an explicit assumption is employed relating the constant for binding of the ligand to the isolated monomer and the constant for the binding of the ligand to aggregate under conditions where there are no ligand-dependent interactions.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

Negatively cooperative binding of high-density lipoprotein to the HDL receptor SR-BI

Scavenger receptor class B, type I (SR-BI), is a high-density lipoprotein (HDL) receptor, which also binds low-density lipoprotein (LDL), and mediates the cellular selective uptake of cholesteryl esters from lipoproteins. SR-BI also is a coreceptor for hepatitis C virus and a signaling receptor that regulates cell metabolism. Many investigators have reported that lipoproteins bind to SR-BI via a single class of independent (not interacting), high-affinity binding sites (one site model). We have reinvestigated the ligand concentration dependence of (125)I-HDL binding to SR-BI and SR-BI-mediated specific uptake of [(3)H]CE from [(3)H]CE-HDL using an expanded range of ligand concentrations (<1 μg of protein/mL, lower than previously reported). Scatchard and nonlinear least-squares model fitting analyses of the binding and uptake data were both inconsistent with a single class of independent binding sites binding univalent lipoprotein ligands. The data are best fit by models in which SR-BI has either two independent classes of binding sites or one class of sites exhibiting negative cooperativity due to either classic allostery or ensemble effects ("lattice model"). Similar results were observed for LDL. Application of the "infinite dilution" dissociation rate method established that the binding of (125)I-HDL to SR-BI at 4 °C exhibits negative cooperativity. The unexpected complexity of the interactions of lipoproteins with SR-BI should be taken into account when interpreting the results of experiments that explore the mechanism(s) by which SR-BI mediates ligand binding, lipid transport, and cell signaling.     

Hybrid tetramers reveal elements of cooperativity in Escherichia coli D-3-phosphoglycerate dehydrogenase

d-3-Phosphoglycerate dehydrogenase from Escherichia coli is a tetramer of identical subunits that is inhibited when l-serine binds at allosteric sites between subunits. Co-expression of two genes, the native gene containing a charge difference mutation and a gene containing a mutation that eliminates serine binding, produces hybrid tetramers that can be separated by ion exchange chromatography. Activity in the hybrid tetramer with only a single intact serine binding site is inhibited by approximately 58% with a Hill coefficient of 1. Thus, interaction at a single regulatory domain interface does not, in itself, lead to the positive cooperativity of inhibition manifest in the native enzyme. Tetramers with only two intact serine binding sites purify as a mixture that displays a maximum inhibition level that is less than that of native enzyme, suggesting the presence of a population of tetramers that are unable to be fully inhibited. Differential analysis of this mixture supports the conclusion that it contains two forms of the tetramer. One form contains two intact serine binding sites at the same interface and is not fully inhibitable. The second form is a fully inhibitable population that has one serine binding site at each interface. Overall, the hybrid tetramers show that the positive cooperativity observed for serine binding is mediated across the nucleotide binding domain interface, and the negative cooperativity is mediated across the regulatory domain interface. That is, they reveal a pattern in which the binding of serine at one interface leads to negative cooperativity of binding of a subsequent serine at the same interface and positive cooperativity of binding of a subsequent serine to the opposite interface. This trend is propagated to subsequent binding sites in the tetramer such that the negative cooperativity that is originally manifest at one interface is decreased by subsequent binding of ligand at the opposite interface.     

Carbohydrate binding properties of the stinging nettle (Urtica dioica) rhizome lectin

The interaction of the stinging nettle rhizome lectin (UDA) with carbohydrates was studied by using the techniques of quantitative precipitation, hapten inhibition, equilibrium dialysis, and uv difference spectroscopy. The Carbohydrate binding site of UDA was determined to be complementary to an N,N',N"-triacetylchitotriose unit and proposed to consist of three subsites, each of which has a slightly different binding specificity. UDA also has a hydrophobic interacting region adjacent to the carbohydrate binding site. Equilibrium dialysis and uv difference spectroscopy revealed that UDA has two carbohydrate binding sites per molecule consisting of a single polypeptide chain. These binding sites either have intrinsically different affinities for ligand molecules, or they may display negative cooperativity toward ligand binding.     

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.     

DNA bis-intercalation: Theoretical calculation of binding curves

A statistical mechanical calculation of the binding properties of DNA bis-intercalators is presented, based on the sequence-generating function method of Lifson. The effects of binding by intercalation of one or both chromophores of a bifunctional intercalating agent are examined. The secular equation for a general model that includes the effects of neighbor (nearest and non-nearest) exclusion and/or cooperativity in the binding of both singly and doubly intercalated ligands is derived. Numerical results for binding curves are presented for a more restricted model in which each type of bound ligand rigorously excludes its nearest neighbor and the total number of sites covered by a doubly intercalated ligand is variable. At low values of free ligand concentration bis-intercalation dominates the binding process, while at high value of free ligand concentration, intercalation of only one chromophore per ligand becomes significant due to the unavailability of contiguous free sites required for bis-intercalation. Also, depending on the binding parameters, the free energy of the system can be lowered by a loss of doubly intercalated ligands in favor of singly intercalated ones. Corresponding to this transition in binding mode, the average number of sites occupied by a bound ligand decreases from that characteristic of bis-intercalation to that characteristic of mono-intercalation as free ligand concentration increases. An analysis of Scatchard plots describing bis-intercalation is presented.     

Cooperativity: over the Hill

Cooperativity, the ability of ligand binding at one site on a macromolecule to influence ligand binding at a different site on the same macromolecule, is a fascinating biological property that is often poorly explained in textbooks. The Hill coefficient is commonly used in biophysical studies of cooperative systems although it is not a quantitative measure of cooperativity. The free energy of interaction between binding sites (ΔΔG) is a more stringent definition of cooperativity and provides a direct quantitative measure of how the binding of ligand at one site affects the ligand affinity of another site.     

Quantitative measurements of the cooperativity in an EF-hand protein with sequential calcium binding.

Positive cooperativity, defined as an enhancement of the ligand affinity at one site as a consequence of binding the same type of ligand at another site, is a free energy coupling between binding sites. It can be present both in systems with sites having identical ligand affinities and in systems where the binding sites have different affinities. When the sites have widely different affinities such that they are filled with ligand in a sequential manner, it is often difficult to quantify or even detect the positive cooperativity, if it occurs. This study presents verification and quantitative measurements of the free energy coupling between the two calcium binding sites in a mutant form of calbindin D9k. Wild-type calbindin D9k binds two calcium ions with similar affinities and positive cooperativity--the free energy coupling, delta delta G, is around -8 kJ.mol-1 (Linse S, et al., 1991, Biochemistry 30: 154-162). The mutant, with the substitution Asn 56-->Ala, binds calcium in a sequential manner. In the present work we have taken advantage of the variations among different metal ions in terms of their preferences for the two binding sites in calbindin D9k. Combined studies of the binding of Ca2+, Cd2+, and La3+ have allowed us to conclude that in this mutant delta delta G < -6.4 kJ.mol-1, and that Cd2+ and La3+ also bind to this protein with positive cooperativity. The results justify the use of the (Ca2+)1 state of the Asn 56-->Ala mutant, as well as the (Cd2+)1 state of the wild type, as models for the half-saturated states along the two pathways of cooperative Ca2+ binding in calbindin D9k.     

Lack of negative cooperativity among binding sites for prostaglandin F2alpha in bovine corpus luteum cell membranes.

The Scatchard analysis of equilibrium prostaglandin (PG) F₂α binding revealed that the binding was heterogeneous. The Hill plot of the same data had a slope of 0.68. This suggested that the heterogeneous nature of [³H] PGF₂α binding was either due to the presence of negative cooperativity or to the presence of two groups of independent binding sites. The kinetic experiments revealed that the presence of excess unlabeled PGF₂α in a diluting medium had no effect on dissociation rates at 25 fold dilution and it even retarded dissociation at higher dilutions. Furthermore, the observations that the low affinity PGF₂α binding sites can exist in the absence of high affinity binding sites and high affinity binding sites can be selectively abolished by treatment with N-ethylmaleimide suggest that negative cooperativity was not responsible for heterogeneous [³H] PGF₂α binding.