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.     

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.     

How subunits cooperate in cAMP-induced activation of homotetrameric HCN2 channels

Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are tetrameric membrane proteins that generate electrical rhythmicity in specialized neurons and cardiomyocytes. The channels are primarily activated by voltage but are receptors as well, binding the intracellular ligand cyclic AMP. The molecular mechanism of channel activation is still unknown. Here we analyze the complex activation mechanism of homotetrameric HCN2 channels by confocal patch-clamp fluorometry and kinetically quantify all ligand binding steps and closed-open isomerizations of the intermediate states. For the binding affinity of the second, third and fourth ligand, our results suggest pronounced cooperativity in the sequence positive, negative and positive, respectively. This complex interaction of the subunits leads to a preferential stabilization of states with zero, two or four ligands and suggests a dimeric organization of the activation process: within the dimers the cooperativity is positive, whereas it is negative between the dimers.     

Dissociation of Muscimol, SR 95531, and Strychnine from GABAA and Glycine Receptors, Respectively, Suggests Similar Cooperative Interactions

Binding to gamma-aminobutyric acid-A (GABAA) receptors was studied in synaptosomal membranes of rat brain. Dissociation of [3H]muscimol and the GABAA antagonist [3H]2-(3-carboxypropyl)-3-amino-6-p-methoxyphenylpyridazinium bromide ([3H]SR 95531) binding elicited by 100-fold dilution was accelerated by excess of GABA or SR 95531. Control dissociation might be retarded by rebinding. The contribution of a rapid first phase of dissociation of the agonist [3H]muscimol was preferentially enhanced by SR 95531. In contrast, the dissociation of [3H]SR 95531 binding was preferentially accelerated by GABA. These opposite preferential accelerations can be explained by negative heterotropic cooperativity and a reversed affinity relationship of agonists and antagonists to GABAA binding sites with different affinities. Modification of the membranes by p-diazobenzenesulfonic acid (DSA) selectively decreased the accelerating effect of GABA on the dissociation of [3H]SR 95531 binding. [3H]Strychnine binding was studied in a membrane preparation of rat spinal cord. The dissociation of the antagonist [3H]strychnine elicited by dilution was preferentially accelerated by glycine. Again, pretreatment with DSA decreased selectively this negative heterotropic (i.e., allosteric) interaction. Chemical modification by DSA might be attributed to tyrosine residues responsible for similar allosteric interactions for the GABA- and glycine-gated chloride channels.     

Ligand Depletion in vivo Modulates the Dynamic Range and Cooperativity of Signal Transduction

Biological signal transduction commonly involves cooperative interactions in the binding of ligands to their receptors. In many cases, ligand concentrations in vivo are close to the value of the dissociation constant of their receptors, resulting in the phenomenon of ligand depletion. Using examples based on rotational bias of bacterial flagellar motors and calcium binding to mammalian calmodulin, we show that ligand depletion diminishes cooperativity and broadens the dynamic range of sensitivity to the signaling ligand. As a result, the same signal transducer responds to different ranges of signal with various degrees of cooperativity according to its effective cellular concentration. Hence, results from in vitro dose-response analyses cannot be applied directly to understand signaling in vivo. Moreover, the receptor concentration is revealed to be a key element in controlling signal transduction and we propose that its modulation constitutes a new way of controlling sensitivity to signals. In addition, through an analysis of the allosteric enzyme aspartate transcarbamylase, we demonstrate that the classical Hill coefficient is not appropriate for characterizing the change in conformational state upon ligand binding to an oligomeric protein (equivalent to a dose-response curve), because it ignores the cooperativity of the conformational change for the corresponding equivalent monomers, which are generally characterized by a Hill coefficient . Therefore, we propose a new index of cooperativity based on the comparison of the properties of oligomers and their equivalent monomers.     

Ionization-linked cooperative interactions in the active site of horse liver alcohol dehydrogenase

Affinity labeling of horse liver alcohol dehydrogenase with iodoacetate in the presence of the activator imidazole has been studied from pH 6.1 to 10.5. The pH profiles for the dissociation constants of iodoacetate from the free enzyme and the enzyme-imidazole complex and of imidazole from the free enzyme and the binary enzyme-iodoacetate complex were determined. The variation with pH of the dissociation constants of iodoacetate (KI) and imidazole (KL) have in common a pKa of 8.6 assigned to the zinc-water ionization, and a pKa near 10. Lysine modification by ethyl acetimidate results in a higher affinity of iodoacetate to the enzyme at high pH as the pKa values of the lysine residues are increased. The binding of iodoacetate and imidazole at each enzyme subunit shows negative cooperativity at pH less than 9, with an interaction constant of 4.8 at pH 6.1. Positive cooperativity is observed at pH greater than 9, with an interaction constant of 0.5 at pH 10.5. The pH-dependent change in cooperativity results from the removal of the zinc-water ionization when imidazole becomes coordinated to the catalytic zinc ion. When iodoacetate binds at the anion binding site, a large perturbation of the zinc-water ionization is observed. Unlike imidazole, the binding of 1,10-orthophenanthroline and iodoacetate shows positive cooperativity at both pH 8.2 and 10.0 with an interaction constant as low as 0.06 at pH 10.0.     

Beta-adrenergic receptors: evidence for negative cooperativity.

The specific binding of [³H] (?)alprenolol to sites in frog erythrocyte membranes provides a tool for directly assessing ligand binding to adenylatecyclase coupled β-adrenergic receptors. Hill Plots of such binding data yield slopes (n_H=“Hill Coefficients”) less than 1.0, suggesting that negatively cooperative interactions among the β-adrenergic receptors may occur. The existence of such negative cooperativity was confirmed by a direct kinetic method. The dissociation of receptor bound [³H] (?)alprenolol was studied under two conditions: 1) with dilution of the ligand-receptor complex sufficient to prevent rebinding of the dissociated tracer and 2) with this same dilution in the presence of excess unlabeled (?)alprenolol. If the sites are independent, the dissociation rates must be the same in both cases. However, the presence of (?)alprenolol increases the rate of [³H] (?)alprenolol dissociation, indicating that negatively cooperative interactions among the β-adrenergic receptor binding sites do occur.     

Formyl peptide chemotaxis receptors on the rat neutrophil: experimental evidence for negative cooperativity

To examine the existence of negative cooperativity among formyl peptide chemotaxis receptors, steady-state binding of f Met-Leu-[3H]Phe to viable rat neutrophils and their purified plasma membranes was measured and the data were subjected to statistical analysis and to computer curve fitting using the NONLIN computer program. Curvilinear, concave upward Scatchard plots were obtained. NONLIN and statistical analysis of the binding data indicated that a two-saturable-sites model was preferable to a one-saturable-site model and statistically valid by the F-test (P less than .010). In addition, Hill coefficients of 0.80 +/- 0.02 were obtained. Kinetic dissociation experiments using purified plasma membranes showed evidence of site-site interactions of the destabilizing type (negative cooperativity). Thus, unlabeled f Met-Leu-Phe accelerated the dissociation of f Met-Leu-[3H]Phe under conditions where no rebinding of radioligand occurred. The rate of dissociation of f Met-Leu-[3H]Phe from the plasma membranes was dependent on the fold excess of unlabeled f Met-Leu-Phe used in the dilution medium; at the highest concentration tested (10,000-fold excess), the dissociation rate was more than double the dissociation rate seen with dilution alone. In addition, occupancy-dependent affinity was ascertained directly by studying the effect of increasing fractional receptor saturation with labeled ligand on the dissociation rate of the receptor-bound labeled ligand. These data showed that the f Met-Leu-[3H]Phe dissociation rate was dependent on the degree of binding site occupancy over the entire biologically relevant range of formyl peptide concentrations. Furthermore, monitoring of the time course of dissociation of the receptor/f Met-Leu-[3H]Phe receptor/f Met-Leu-[3H]Phe complex as a function of receptor occupancy revealed that receptor affinity for f Met-Leu-Phe remained occupancy-dependent during the entire time of dissociation examined (up to 10 min). Finally, the average affinity profile of the equilibrium binding data demonstrated a 60% decrease in receptor affinity in changing from the high affinity to the low affinity conformation.     

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.     

Evidence that the thyroid-stimulating hormone (TSH) receptor transmembrane domain influences kinetics of TSH binding to the receptor ectodomain

Thyroid-stimulating hormone (TSH)-induced reduction in ligand binding affinity (negative cooperativity) requires TSH receptor (TSHR) homodimerization, the latter involving primarily the transmembrane domain (TMD) but with the extracellular domain (ECD) also contributing to this association. To test the role of the TMD in negative cooperativity, we studied the TSHR ECD tethered to the cell surface by a glycosylphosphatidylinositol (GPI) anchor that multimerizes despite the absence of the TMD. Using the infinite ligand dilution approach, we confirmed that TSH increased the rate of dissociation (k(off)) of prebound (125)I-TSH from CHO cells expressing the TSH holoreceptor. Such negative cooperativity did not occur with TSHR ECD-GPI-expressing cells. However, even in the absence of added TSH, (125)I-TSH dissociated much more rapidly from the TSHR ECD-GPI than from the TSH holoreceptor. This phenomenon, suggesting a lower TSH affinity for the former, was surprising because both the TSHR ECD and TSH holoreceptor contain the entire TSH-binding site, and the TSH binding affinities for both receptor forms should, theoretically, be identical. In ligand competition studies, we observed that the TSH binding affinity for the TSHR ECD-GPI was significantly lower than that for the TSH holoreceptor. Further evidence for a difference in ligand binding kinetics for the TSH holoreceptor and TSHR ECD-GPI was obtained upon comparison of the TSH K(d) values for these two receptor forms at 4 °C versus room temperature. Our data provide the first evidence that the wild-type TSHR TMD influences ligand binding affinity for the ECD, possibly by altering the conformation of the closely associated hinge region that contributes to the TSH-binding site.     

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.     

GABA, depressants and chloride ions affect the rate of dissociation of 35S-t-butylbicyclophosphorothionate binding

The dissociation of 35S-TBPS was studied from binding sites of rat cerebral cortex. Monophasic dissociation plots became polyphasic and accelerated in the presence of micromolar concentrations of GABA suggesting the involvement of low (or super-low) affinity GABA receptors. The presence of the depressants etazolate, R(-)MPPB and ethanol resulted in similarly accelerated dissociation patterns. In contrast, the convulsants S(+)MPPB and pentamethylenetetrazol did not significantly affect the dissociation of TBPS. Dissociation initiated by dilution was not affected either by an excess of picrotoxin or by varying the equilibrium occupancy of the TBPS sites. These findings rule out the possibility of a kinetic cooperativity for the binding of convulsants. The removal of chloride ions also enhanced the rate of TBPS dissociation. Kinetic heterogeneity of the TBPS binding sites can be interpreted with allosteric interactions mediated by various sites at the GABA receptor complex coupled to different states of the chloride ionophore.     

An equilibrium binding study of the interaction of fructose 6-phosphate and fructose 1,6-bisphosphate with rabbit muscle phosphofructokinase.

Equilibrium binding studies of the interaction of rabbit muscle phosphofructokinase with fructose 6-phosphate and fructose 1,6-bisphosphate have been carried out at 5 degrees in the presence of 1-10 mM potassium phosphate (pH 7.0 and 8.0), 5 mM citrate (pH 7.0), or 0.22 mm adenylyl imidodiphosphate (pH 7.0 and 8.0). The binding isotherms for both fructose 6-phosphate and fructose 1,6-bisphosphate exhibit negative cooperativity at pH 7.0 and 8.0 in the presence of 1-10 mM potassium phosphate at protein concentrations where the enzyme exists as a mixture of dimers and tetramers (pH 7.0) or as tetramers (pH 8.0) and at pH 7.0 in the presence of 5 mM citrate where the enzyme exists primarily as dimers. The enzyme binds 1 mol of either fructose phosphate/mol of enzyme monomer (molecular weight 80,000). When enzyme aggregation states smaller than the tetramer are present, the saturation of the enzyme with either ligand is paralleled by polymerization of the enzyme to tetramer, by an increase in enzymatic activity and by a quenching of the protein fluorescence. At protein concentrations where aggregates higher than the tetramer predominate, the fructose 1,6-bisphosphate binding isotherms are hyperbolic. These results can be quantitatively analyzed in terms of a model in which the dimer is associated with extreme negative cooperativity in binding the ligands, the tetramer is associated with less negative cooperativity, and aggregates larger than the tetramer are associated with little or no cooperativity in the binding process. Phosphate is a competitive inhibitor of the fructose phosphate sites at both pH 7.0 and 8.0, while citrate inhibits binding in a complex, noncompetitive manner. In the presence of the ATP analog adenylyl imidodiphosphate, the enzyme-fructose 6-phosphate binding isotherm is sigmoidal at pH 7.0, but hyperbolic at pH 8.0. The characteristic sigmoidal initial velocity-fructose 6-phosphate isotherms for phosphofructokinase at pH 7.0, therefore, are due to an heterotropic interaction between ATP and fructose 6-phosphate binding sites which alters the homotropic interactions between fructose 6-phosphate binding sites. Thus the homotropic interactions between fructose 6-phosphate binding sites can give rise to positive, negative, or no cooperativity depending upon the pH, the aggregation state of the protein, and the metabolic effectors present. The available data suggest the regulation of phosphofructokinase involves a complex interplay between protein polymerization and homotropic and heterotropic interactions between ligand binding sites.     

A novel spectroscopic titration method for determining the dissociation constant and stoichiometry of protein-ligand complex.

We offer a new titration protocol for determining the dissociation constant and binding stoichiometry of protein-ligand complex, detectable by spectroscopic methods. This approach neither is limited to the range of protein or ligand concentrations employed during titration experiment nor relies on precise determinations of the titration "endpoint," i.e., the maximal signal changes upon saturation of protein by ligand (or vice versa). In this procedure, a fixed concentration of protein (or ligand) is titrated by increasing volumes of a stock ligand (or protein) solution, and the changes in the spectroscopic signal are recorded after each addition of the titrant. The signal for interaction between protein and ligand first increases, reaches a maximum value, and then starts decreasing due to dilution effect. The volume of the titrant required to achieve the maximum signal changes is utilized to calculate the dissociation constant and the binding stoichiometry of the protein-ligand complex according to the theoretical relationships developed herein. This procedure has been tested for the interaction of avidin with a chromophoric biotin analogue, 2-(4'-hydroxyazobenzene)benzoic acid by following the absorption signal of their interaction at 500 nm. The widespread applicability of this procedure to protein-ligand complexes detected by other spectroscopic techniques and its advantages over conventional methods are discussed.     

Consequences of ligand bivalency in interactions involving particulate receptors: equilibrium and kinetic studies with Sephadex-concanavalin A, butylagarose-phosphorylase b, and Fc receptor-IgG dimer interactions as model systems

Theoretical consideration is given to the interaction of a bivalent ligand with particulate receptor sites, not only from the viewpoint of quantitatively describing the binding behavior but also from that of the kinetics of ligand release upon infinite dilution of a receptor-ligand mixture. In the latter regard, a general expression is derived that describes the time dependence of the amount of ligand bound as a function of two rate constants for the stepwise dissociation of cross-linked ligand-receptor complex and a thermodynamic parameter expressing the initial ratio of singly linked to doubly linked ligand-receptor complexes. An experimental study of the interaction between Sephadex and concanavalin A is then used to illustrate application of this recommended theoretical approach for characterizing the binding behavior and dissociation kinetics of a bivalent ligand for a system in which all ligand-receptor interactions may be described by a single intrinsic association constant. Published results on the interaction of phosphorylase b with butylagarose are also shown to comply with this simplest model of the bivalent ligand hypothesis; but those for the interaction between immunoglobulin G (IgG) dimers and Fc receptors require modification of the model by incorporation of different intrinsic association constants for the successive binding of receptor sites to the bivalent ligand. These results emphasize the need to consider ligand bivalency as a potential phenomenon in studies of interactions between protein ligands and particulate receptors and illustrate procedures by which the effects of ligand bivalency may be identified and characterized.     

Mechanisms of ligand binding by monoclonal anti-fluorescyl antibodies

Binding of fluorescyl ligand by five IgG anti-fluorescyl hybridoma proteins (4-4-20, 6-10-6, 20-4-4, 20-19-=1, 20-20-3) was examined. Relative reduction in fluorescence of bound fluorescein, deuterium oxide (D2O)-induced enhancement of fluorescence, and the effects of pH on binding kinetics were measured for each clone. Individual hybridoma proteins (all of which bind fluorescein with relatively high affinity) exhibited significant differences in the relative contribution of various forces (hydrophobicity, hydrogen bonding, ionic interactions) to binding and hence, affinity. The extent of such variations in binding mechanisms among monoclonal antibodies binding the same hapten is indicative of the extreme functional diversity of active sites. In addition, ligand binding by clone 20-20-3 was examined in greater detail. ABsorption spectra of ligand bound by purified intact antibody, Fab fragments, and reassociated heavy and light chains indicated that protonation of the fluorescyl ligand by a residue within the active site contributed significantly to the binding free energy. Comparative dissociation rates of fluorescein and a structural analog, rhodamine 110, were used to quantitatively substantiate the contribution of this interaction. Association and dissociation rate studies with fluorescein and antibody indicated that: 1) the active site appeared to undergo a conformational change upon ligand binding, and 2) neither intact disulfides nor intersite cooperativity affected the dissociation rate of bound ligand. Observed mechanisms of ligand binding are discussed in terms of proposed mechanisms of antibody affinity maturation and diversity.     

Leukotriene B4 binding sites in guinea-pig alveolar macrophages

Leukotriene B4 binding sites were investigated in alveolar macrophages obtained from guinea-pigs by brochoalveolar lavage. Analysis of the binding data was compatible with a two-receptors model. Best-fit computer-assisted evaluation of the results yielded a KD = 0.33 +/- 0.18 nM with 618 +/- 138 binding sites/cell for the high-affinity receptor, and KD = 52.9 +/- 12.3 nM with 95,400 +/- 37,900 sites/cell for the low-affinity binding site. Study of the dissociation rate of labelled ligand induced by dilution only and by dilution plus excess unlabelled ligand showed no differences in the two situations. These data suggest that the finding of two receptors is not due to negative cooperativity. Since most studies failed to demonstrate two distinct LTB4-binding proteins, the present results reinforces the hypothesis of LTB4 receptors in guinea-pig alveolar macrophages being a single protein with interchangeable affinity states.     

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.     

THE SPECIFIC INTERACTION OF S-100 PROTEIN WITH SYNAPTOSOMAL PARTICULATE FRACTIONS. SITE-SITE INTERACTIONS AMONG S-100 BINDING SITES1

Abstract— The Scatchard plot of the specific binding of the brain-specific S-100 protein to synaptosomal particulate fractions (SYN) is curvilinear, concave upwards. This could indicate the existence either of multiple classes of sites with different but fixed affinities, or of site-site interactions of the type defined as negative cooperativity among a single class of sites. To discriminate between these possibilities, the dissociation test described by De Meyts et al. (1976) for demonstrating negative cooperativity among insulin binding sites of human lymphocytes or liver membranes, was applied to the interaction of S-100 with SYN. The results show that the dissociation of the ¹²⁵I-labelled S-100-site complex is faster due to an ‘infinite’(100-fold) dilution of the complex plus an excess of unlabelled S-100 than due to dilution only, the effect of unlabelled S-100 being specific and dose-dependent. ¹²⁵I-IabeIIed S-100 dissociation is time, temperature, and Ca^{2 +}-dependent. The effect of unlabelled S-100 is more evident at a low site occupancy than at a high one, suggesting that at high site occupancies ¹²⁵I-labelled S-100 binding sites could be already negatively cooperating. It can be reasonably excluded that the effect of unlabelled S-100 is due to inhibition of rebinding of the dissociated tracer. Na⁺ and K⁺ stimulate the dissociation even at physiological concentrations. At low pH ¹²⁵I-labelled S-100 dissociates very little, while at high pH dissociation is greatly stimulated. Finally, the protein denaturating reagent urea accelerates the dissociation even at concentrations as low as 1m. These data suggest that negative cooperativity occurs among S-100 binding sites, but do not exclude other possibilities. Together with previously reported findings, they further support the view that S-100 binds to highly specific sites in nervous membranes.