Binding isotherms and the interaction between proflavine and a DNA of high G · C content

Binding isotherms corresponding to several situations of ligand binding to a linear polymer are calculated, including cases of cooperativity or anticooperativity between the bound ligand states, multiple binding modes that are competitive or non competitive, and possible exclusion of an arbitrary number of adjacent sites upon occupancy of a site by a single ligand. The sequence generating function method of Lifson and Bradley is used, requiring the assumption that no end effects are involved. The case of strong binding of the dye proflavine to a DNA of high G. C content, that of M. lysodeikticus, is considered in detail, and a single model capable of reconciling the available kinetic and equilibrium data on this system, involving two competing binding modes, is discussed.     

Ligand-Induced Protein Mobility in Complexes of Carbonic Anhydrase II and Benzenesulfonamides with Oligoglycine Chains

This paper describes a biophysical investigation of residual mobility in complexes of bovine carbonic anhydrase II (BCA) and para-substituted benzenesulfonamide ligands with chains of 1–5 glycine subunits, and explains the previously observed increase in entropy of binding with chain length. The reported results represent the first experimental demonstration that BCA is not the rigid, static globulin that has been typically assumed, but experiences structural fluctuations upon binding ligands. NMR studies with ¹⁵N-labeled ligands demonstrated that the first glycine subunit of the chain binds without stabilization or destabilization by the more distal subunits, and suggested that the other glycine subunits of the chain behave similarly. These data suggest that a model based on ligand mobility in the complex cannot explain the thermodynamic data. Hydrogen/deuterium exchange studies provided a global estimate of protein mobility and revealed that the number of exchanged hydrogens of BCA was higher when the protein was bound to a ligand with five glycine subunits than when bound to a ligand with only one subunit, and suggested a trend of increasing number of exchanged hydrogens with increasing chain length of the BCA-bound ligand, across the series. These data support the idea that the glycine chain destabilizes the structure of BCA in a length-dependent manner, causing an increase in BCA mobility. This study highlights the need to consider ligand-induced mobility of even “static” proteins in studies of protein-ligand binding, including rational ligand design approaches.     

Affinity partitioning of vancomycin

The use of the Flanagan and Barondes model(14) describing affinity partitioning as an aid in designing separation systems is discussed. Experimental studies are described for affinity partitioning of vancomycin, a glycopeptide antibiotic, in a water-methoxypolyethylene glycol-dextran system using methoxypolyethylene glycol-dextran system using methoxypolyethylene glycol bound D-alanyl-Dalanyl-D-alanine or D-alanyl-D-alanine as the reversible affinity ligand. Even for this ideal case of 1:1 binding interaction, the model only qualitatively predicts the affinity effect when all model parameters are measured independently. The discrepancy between measured and predicted values can be attributed to a difference in exposed surface of the free antibiotic and ligand compared to that in the bound state.The effect of experimentally varying model parameters is also described. It was determined that a polymers-ligand which partitions more strongly to the top phase would provide the most significant enhancement to this affinity partitioning system. Such an improvement can be made by increasing the molecular weight of the hydrophobicity of the polymer-ligand. A process for vancomycin recovery from fermentation broth using D--alanyl-D-alanine sepharose as affinity ligand is described.     

A simple model for proteins with interacting domains. Applications to scanning calorimetry data

A simple thermodynamic model is formulated for the purpose of interpreting scanning calorimetry data on proteins that have interacting domains. Interactions are quantified by inclusion of an interface free energy, delta GAB, in the thermodynamics of unfolding for multidomain proteins. The assumption is made that delta GAB goes to zero with the unfolding of either domain involved in pairwise interaction, so the interaction term appears to stabilize only the domain with the lower TM. Application of the model to calorimetric data leads to an estimate of -25,000 cal/mol for interactions between the regulatory and catalytic subunits of native aspartate transcarbamoylase and to a value of 0 for delta GAB between the transmembrane and cytoplasmic domains of band 3 of the human erythrocyte membrane. Estimates of changes in delta GAB are also obtained for mutant forms of yeast phosphoglycerate kinase that have been altered in the hinge region between amino-terminal and carboxy-terminal domains. The model is also applied to ligand binding to proteins having domains that communicate through pairwise interaction. It is shown that whenever the delta GAB term is ligand-dependent, then attachment of the ligand to the binding domain will be partially controlled by the other (regulatory) domain. This situation can sometimes be recognized and quantified when calorimetric scans are carried out at varying ligand concentrations. According to the model, the binding of MgATP to the carboxy-terminal domain of phosphoglycerate kinase is strongly stabilized (ca. 20% of the unitary free energy of binding) by participation of the amino-terminal domain, which acts to increase the binding constant 25-fold.(ABSTRACT TRUNCATED AT 250 WORDS)     

The effects of E7 and E11 mutations on the kinetics of ligand binding to R state human hemoglobin

Association and dissociation rate constants for O2, CO, and methyl isocyanide binding to native and distal pocket mutants of R state human hemoglobin were measured using ligand displacement and partial photolysis techniques. Individual rate constants for the alpha and beta subunits were resolved by comparisons between the kinetic behavior of the native and mutant proteins. His-E7 was replaced with Gly and Gln in both alpha and beta subunits and with Phe in beta subunits alone. In separate experiments Val-E11 was replaced with Ala, Leu, and Ile in each globin chain. The parameters describing ligand binding to R state alpha subunits are sensitive to the size and polarity of the amino acids at positions E7 and E11. The distal histidine in this subunit inhibits the bimolecular rate of binding of both O2 and CO, sterically hinders bound CO and methyl isocyanide, and stabilizes bound O2 by hydrogen bonding. The Val-E11 side chain in alpha chains also appears to be part of the kinetic barrier to O2 and CO binding since substitution with Ala causes approximately 10-fold increases in the association rate constants for the binding of these diatomic ligands. However, substitution of Val-E11 by Ile produces only small decreases in the rates of ligand binding to alpha subunits. For R state beta subunits, the bimolecular rates of O2 and CO binding are intrinsically large, approximately 2-5-fold greater than those for alpha subunits, and with the exception of Val-E11----Ile mutation, little affected by substitutions at either the E7 or E11 positions. For the beta Val-E11----Ile mutant the association rate and equilibrium constants for all three ligands decreased 10-50-fold. All of these results agree with Shaanan's conclusions that the distal pocket in liganded beta subunits is more open whereas in alpha subunits bound ligands are more sterically hindered by adjacent distal residues (Shaanan, B. (1983) J. Mol. Biol. 171, 31-59). In the case of O2 binding to alpha subunits, the unfavorable steric effects are compensated by the formation of a hydrogen bond between the nitrogen atom of His-E7 and bound dioxygen.     

Determination,a l'equilibre,des constantes d'association de ligands radioactifs ou non radioactifs par une methode non graphique

The present work deals with the determination of association constants at equilibrium by a non-graphical method in binding systems containing one specific receptor. Equations have been derived from that originally described by Lea (Biochim. Biophys. Acta, 322, 68–74), the terms of which are obtained from the data of simple displacement curves of a bound radioactive ligand by unlabelled competitors identical or different in nature. By knowing the function relating the variations of the bound ligand (B) to the affinity constant (K_i) and the quantity (M_i) of competitor for a given system, it is possible to calculate any of these parameters when the two others are measured. Thus, it becomes easy to compare the relative affinities of differents receptors for the same ligand or that of one receptor for various labelled or unlabelled ligands. Furthermore, theoretical displacement curves can be drawn and compared to experimental data, when only knowing the affinity constant of a specific binding system in given conditions. These modes of calculation have been tested in a study of interactions between various steroids and a fraction of human serum proteins precipitated by ammonium sulfate (30–45%) and containing the sex hormone-binding globulin. Association constants thus obtained agree well with those reported in the literature and determined by graphical procedures.     

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.     

Cooperative effects during the binding of large ligands with DNA. Non-contact interaction between adsorbed ligands

Equations are derived to describe the cooperative binding of large ligands to DNA. A mathematical approach is developed which enables one to give a simple probabilistic interpretation of binding equations and to solve them in the general case when long-range interactions are allowed between bound ligands. These interactions can be mediated by conformation changes induced in the DNA in the course of binding process and transformed over some distances beyond the DNA region immediately covered by a bound ligand molecule (allosteric effect of DNA). Interactions between ligand molecules can be formally described in terms of model potential characterizing pairwise interactions between bound ligands. A procedure is developed which allows one to determined the form of such potential from experimentally measured binding isotherms. It is based on a comparison of experimental binding isotherms with the appropriate curves calculated for the case of non-interacting ligands.     

Analysis of receptor binding displacement curves by a nonhomologous ligand, on the basis of an equivalent competition principle

An exact method for the analysis of receptor-ligand binding data when labeled bound ligand is displaced by a nonhomologous ligand with a different dissociation constant is described. The present method, which is based on an equivalent competition principle for the homologous and the nonhomologous ligand, converts displacement curves into a linear form and is also applicable to situations in which free concentrations of ligand are significantly smaller than the added concentrations as a result of ligand binding. It is shown that the dissociation constant of the nonhomologous ligand is given directly by the concentration of this nonhomologous ligand added and the free concentration of unlabeled homologous ligand required to give the same level of displacement of labeled bound ligand. On the basis of these displacement characteristics, all binding parameters for receptor interaction of the nonhomologous ligand can be obtained and expressed, for example, in a Scatchard plot. The present method, which is referred to as the equivalent competition method, is also evaluated in this study with respect to the effects of nonspecific ligand binding and the presence of multiple receptor classes.     

The stabilization by a coenzyme analog of a conformational change induced by substrate in 6-phosphogluconate dehydrogenase.

The reaction of NADP⁺ with periodate yields a coenzyme analog that can be bound to the NADP⁺ binding site of 6-phosphogluconate dehydrogenase from Candida utilis. This coenzyme analog can be irreversibly bound to the enzyme by reduction with sodium borohydride. The binding of one molecule of inhibitor to only one of the two subunits of the enzyme causes the inactivation of this subunit but does not alter the catalytic activity of the other subunit. Thus the two subunits do not have apparent catalytic interactions. When the reaction between the enzyme and the coenzyme analog is carried out in the presence of the substrate, the covalent modification of only one subunit causes the inactivation of both subunits. In this case the two subunits show an extreme negative cooperativity. It is suggested that the binding of the substrate induces in the enzyme molecule a conformational change that is stabilized by the irreversible binding of the coenzyme analog.     

The exponential model for a regulatory enzyme: Its extension to describe the binding of two ligands

The exponential model for a regulatory enzyme (Ainsworth, 1977a) is extended to deal explicitly with the presence in solution of a second ligand. This is achieved by introducing exponential interaction coefficients which respectively describe how the affinity of the free and bound forms of the protein for the ligand depend on its fractional saturation by the second ligand. The basic equations, so derived, are applied to binding experiments where the ligands bind independently or competitively and to rate experiments where the ligands represent two substrates or one substrate and a modifier which may be either competitive or non-competitive in type. The conditions required to display linkage between the binding of the two ligands are established and it is also shown that rate data may display a maximum as one ligand concentration is varied at a fixed concentration of the other. The equations that are derived are tested by application to experimental data and the conditions that have to be met to justify such an application are discussed.     

Analysis of ligand binding curves in terms of species fractions

The ligand binding curve for a macromolecular system presents the average number or ligand molecules bound per macromolecule as a function of the chemical potential or the logarithm of the ligand concentration. We show that various observable properties of this curve, for example its asymptotes and derivatives, are expressible in terms of linear combinations of the mole fractions α_i of macromolecules binding i molecules of ligand. Whenever enough such properties of the binding curve are known, the linear equations in α_i can be solved to give the mole fractions of each of the various macromolecular species. An application of these results is that a Hill plot for hemoglobin-ligand equilibrium where the asymptotes approach unit slope can be made to yield the four Adair constants by a simple algebraic method. A second use is that a knowledge of the first and second derivatives of the binding curve at points along the curve can yield the species fractions as functions of the degree of saturation without direct knowledge of the ligand binding constants. These methods are illustrated by some numerical examples.     

Binding of ADP to beef-heart mitochondrial ATPase (F1)

1. ADP binding to beef-heart mitochondrial ATPase (F₁), in the absence of Mg²⁺, has been determined by separating the free ligand by ultrafiltration and determining it in the filtrate by a specially modified isotachophoretic procedure.2. Since during the binding experiments the ‘tightly’ bound ADP (but not the ATP) dissociates, it is necessary to take this into account in calculating the binding parameters.3. The binding data show that only one tight binding site (K_d about 0.5 μM) for ADP is present.4. It is not possible to calculate from the binding data alone the number of or the dissociation constants for the weak binding sites. It can be concluded, however, that the latter is not less than about 50 μM.     

The effect of multiple binding modes on empirical modeling of ligand docking to proteins.

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.     

Kinetics of ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor. I. A computer simulation of the influence of mass transport.

The influence of mass transport on ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor, was investigated. A one-dimensional computer model for the mass transport of ligand between the bulk solution and the polymer gel and within the gel was employed, and the influence of the diffusion coefficient, the partition coefficient, the thickness of the matrix, and the distribution of immobilized receptor were studied for a variety of conditions. Under conditions that may apply to many published experimental studies, diffusion within the matrix was found to decrease the overall ligand transport significantly. For relatively slow reactions, small spatial gradients of free and bound ligand in the gel are found, whereas for relatively rapid reactions strong inhomogeneities of ligand within the gel occur before establishment of equilibrium. Several types of deviations from ideal pseudo-first-order binding progress curves are described that resemble those of published experimental data. Extremely transport limited reactions can in some cases be fitted with apparently ideal binding progress curves, although with apparent reaction rates that are much lower than the true reaction rates. Nevertheless, the ratio of the apparent rate constants can be semiquantitatively consistent with the true equilibrium constant. Apparently "cooperative" binding can result from high chemical on rates at high receptor saturation. Dissociation in the presence of transport limitation was found to be well described empirically by a single or a double exponential, with both apparent rate constants considerably lower than the intrinsic chemical rate constant. Transport limitations in the gel can introduce many generally unknown factors into the binding progress curve. The simulations suggest that unexpected deviations from ideal binding progress curves may be due to highly transport influenced binding kinetics. The use of a thinner polymer matrix could significantly increase the range of detectable rate constants.     

Functional consequences of ligand-linked dissociation in hemoglobin from the sea cucumber molpadia arenicola

It has been established that Molpadia hemoglobin tends to dissociate into subunits as oxygen is bound. The kinetics and equilibria of carbon monoxide and ehtylisocyanide binding reported here show a dependence on protein concentration that supports the conclusions that the aggregated hemoglobin has a lower ligand affinity than the dissociated subunits. This is true for the isolated D-chain as well as for the unfractionated hemolysate that contains four distinct polypeptide chains (A-D). This indicates that even homopolymers of Molpadia hemoglobin have lower ligand affinity than the dissociated subunits. At high protein concentration hemolysates of Molpadia hemoglobin show slight cooperativity. The time course of ligand binding to the deoxy D-chain also suggests cooperative interactions, The low affinity of the aggregated state may have a different molecular explanation than in human hemoglobin were tetramers of identical subunits (as in Hb H) show high oxygen affinity. The absence of tyrosine and histidine at the C-tremini of the Molpadia D-chains also suggests a different stabilization of the low affinity deoxy state. An additional functional difference between Molpadia hemoglobin and human hemoglobin is that organic phosphate do not alter the ligand affinity of the sea cucumber hemoglobin.     

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.     

ELISA-based assay for scatchard analysis of ligand-receptor interactions

A simple, nonradioactive method is presented that can be used for performing large numbers of binding assays of cell membrane receptors with their ligands. The method adopts the simple membrane preparation and biotin-based quantitation methods of the semi-intact cell endocytosis assays. After binding of the biotinylated ligand to its receptors on the semi-intact cell membranes, a rapid centrifugation step separates the membranes from unbound ligand. Bound ligand is subsequently released by detergent, captured by a specific antibody coated on the surface of microwells, and quantitated with peroxidase-conjugated streptavidin in a colorimetric assay. Using this assay, Scatchard analysis was performed on the data for the specific binding of iron-loaded transferrin to its receptors on mouse fibroblasts and yieldedK _d values similar to those obtained with other published methods. The assay is sensitive, rapid, and also convenient, because aliquots of semi-intact cells can be stored frozen. The perforated plasma membrane of the cells offers the additional possibility of screening factors that interact with the cytoplasmic domain of the receptors for their possible effects on the parameters of the extracellular ligand-receptor interaction.