Consequences of the non-specific binding of a protein to a linear polymer: reconciliation of stoichiometric and equilibrium titration data for the thrombin-heparin interaction

Theoretical aspects of the thermodynamic characterization of cooperative protein interactions with non-specific segments of a linear polymer lattice have been re-examined. This reconsideration has not only provided an alternative derivation of recursive expressions for the stoichiometry of random ligand binding prior to elimination of the parking problem but also extended that treatment to include binding with overlap of additional lattice units. The major obstacle to thermodynamic characterization of non-specific protein-polymer interactions is determination of the lattice capacity for ligand, which in turn defines the length of the polymer segment to which the protein binds. Although these parameters are most readily obtained from studies under conditions that ensure essentially stoichiometric interaction, the endpoint of such a titration is likely to reflect the irreversible rather than the equilibrium binding capacity of the lattice for ligand. Consideration of published results for spectrofluorometric titrations of the thrombin-heparin system under stoichiometric conditions in such terms has permitted their reconciliation with results of a later publication on the interaction under equilibrium conditions.     

A historical perspective of the biophysics of the thrombin–heparin system: an example of nonspecific binding and the consequent parking problem in action

Difficulties are encountered in the thermodynamic characterization of interactions between a protein ligand and a linear acceptor, such as a polynucleotide or a polysaccharide, because of the involvement of more than one unit of the polymer chain in each attachment of a protein molecule. Complications arise from the fact that random attachment of ligand to the polymer chain, each unit of which is a potential binding site, initially leads to suboptimal location of protein molecules along the polymer chain—a situation that has to be rectified before the attainment of thermodynamic equilibrium can be realized. Kinetic as well as thermodynamic consequences of such nonspecific binding, termed the parking problem, therefore need to be considered in any quantitative characterization of the interaction between a large ligand and a linear polymer acceptor chain. Results for the thrombin–heparin interaction have been used to illustrate a thermodynamic characterization of nonspecific binding that takes into account these consequences of the parking problem.     

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.     

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. I. Homologous and heterologous binding to one or two classes of sites

We have developed a versatile computer program for optimization of ligand binding experiments (e.g., radioreceptor assay system for hormones, drugs, etc.). This optimization algorithm is based on an overall measure of precision of the parameter estimates (D-optimality). The program DESIGN uses an exact mathematical model of the equilibrium ligand binding system with up to two ligands binding to any number of classes of binding sites. The program produces a minimal list of the optimal ligand concentrations for use in the binding experiment. This potentially reduces the time and cost necessary to perform a binding experiment. The program allows comparison of any proposed experimental design with the D-optimal design or with assay protocols in current use. The level of nonspecific binding is regarded as an unknown parameter of the system, along with the affinity constant (Kd) and binding capacity (Bmax). Selected parameters can be fixed at constant values and thereby excluded from the optimization algorithm. Emphasis may be placed on improving the precision of a single parameter or on improving the precision of all the parameters simultaneously. We present optimal designs for several of the more commonly used assay protocols (saturation binding with a single labeled ligand, competition or displacement curve, one or two classes of binding sites), and evaluate the robustness of these designs to changes in parameter values of the underlying models. We also derive the theoretical D-optimal design for the saturation binding experiment with a homogeneous receptor class.     

Analytic binding isotherms describing competitive interactions of a protein ligand with specific and nonspecific sites on the same DNA oligomer

Many studies of specific protein-nucleic acid binding use short oligonucleotides or restriction fragments, in part to minimize the potential for nonspecific binding of the protein. However, when the specificity ratio is low, multiple nonspecifically bound proteins may occupy the region of DNA corresponding to one specific site; this situation was encountered in our recent calorimetric study of binding of integration host factor (IHF) protein to its specific 34-bp H' DNA site. Here, beginning from the analytical McGhee and von Hippel infinite-lattice nonspecific binding isotherm, we derive a novel analytic isotherm for nonspecific binding of a ligand to a finite lattice. This isotherm is an excellent approximation to the exact factorial-based Epstein finite lattice isotherm even for short lattices and therefore is of great practical significance for analysis of experimental data and for analytic theory. Using this isotherm, we develop an analytic treatment of the competition between specific and nonspecific binding of a large ligand to the same finite lattice (i.e., DNA oligomer) containing one specific and multiple overlapping nonspecific binding sites. Analysis of calorimetric data for IHF-H' DNA binding using this treatment yields enthalpies and binding constants for both specific and nonspecific binding and the nonspecific site size. This novel analysis demonstrates the potential contribution of nonspecific binding to the observed thermodynamics of specific binding, even with very short DNA oligomers, and the need for reverse (constant protein) titrations or titrations with nonspecific DNA to resolve specific and nonspecific contributions. The competition treatment is useful in analyzing low-specificity systems, including those where specificity is weakened by mutations or the absence of specificity factors.     

Effects of ligand multivalency in binding studies: a general counterpart of the Scatchard analysis

A general counterpart of the Scatchard analysis has been developed which takes into account the valence of the ligand. Its use is first demonstrated by application to binding data obtained by exclusion chromatography of mixtures of Dextran T2000 and concanavalin A (a bivalent ligand) on a column of porous glass beads (Glyceryl-CPG 170) equilibrated at 5 degrees C with phosphate-chloride buffer (pH 5.5), I 0.5. A recycling partition equilibrium study with Sephadex G-100 as gel phase then provides a quantitative evaluation of the interaction between haemoglobin and a monoclonal mouse antihaemoglobin antibody preparation in 0.1 M phosphate (pH 7.0) in order to emphasize the ability of the present analysis to consider collectively binding results obtained with a range of acceptor concentrations. Finally, the use of the generalized Scatchard analysis to assess acceptor site homogeneity is illustrated by reappraisal of results for the binding of glyceraldehyde-3-phosphate dehydrogenase to erythrocyte membranes.     

Effects of ligand multivalency in binding studies: a general counterpart of the Scatchard analysis

A general counterpart of the Scatchard analysis has been developed which takes into account the valence of the ligand. Its use is first demonstrated by application to binding data obtained by exclusion chromatography of mixtures of Dextran T2000 and concanavalin A (a bivalent ligand) on a column of porous glass beads (Glyceryl-CPG 170) equilibrated at 5°C with phosphate-chloride buffer (pH 5.5), I 0.5. A recycling partition equilibrium study with Sephadex G-100 as gel phase then provides a quantitative evaluation of the interaction between haemoglobin and a monoclonal mouse antihaemoglobin antibody preparation in 0.1 M phosphate (pH 7.0) in order to emphasize the ability of the present analysis to consider collectively binding results obtained with a range of acceptor concentrations. Finally, the use of the generalized Scatchard analysis to assess acceptor site homogeneity is illustrated by reappraisal of results for the binding of glyceraldehyde-3-phosphate dehydrogenase to erythrocyte membranes.     

Quantitative evaluation of solution equilibrium binding interactions by affinity partitioning: application to specific and nonspecific protein-heparin interactions

A variation of the quantitative affinity chromatography (QAC) method of Winzor, Chaiken, and co-workers for the analysis of protein-ligand interactions has been developed and used to characterize sequence-specific and nonspecific protein-heparin interactions relevant to blood coagulation. The method allows quantitation of the binding of two components, A and B, from the competitive effect of one component, B, on the partitioning of the other component, A, between an immobilized acceptor phase and solution phase at equilibrium. Under the conditions employed, the differences in total A concentrations yielding an equivalent degree of saturation of the immobilized acceptor in the absence and presence of B defines the concentration of A bound to B in solution, thereby enabling conventional Scatchard or nonlinear least-squares analysis of the A-B equilibrium interaction. Like the QAC method, quantitation of the competitor interaction does not depend on the nature of the affinity matrix interaction, which need only be described empirically. The additional advantage of the difference method is that only the total rather than the free competitor ligand concentration need be known. The method requires that the partitioning component A be univalent, but allows for multivalency in the competitor, B, and can in principle be used to study binding interactions involving nonidentical, interacting, or nonspecific overlapping sites. Both the binding constant and the stoichiometry for the specific antithrombin-heparin interaction as well as the apparent binding constant for the nonspecific thrombin-heparin interaction at low thrombin binding densities obtained using this technique were in excellent agreement with values determined using spectroscopic probes.     

The Binding of Mercury by the Yeast Cell in Relation to Changes in Permeability

Yeast cells exposed to mercuric chloride suffer irreversible damage to the membrane, resulting in a loss of potassium and cellular anions to the medium. The maximal loss of K⁺, but not the time course of K⁺ loss is related to the mercury concentration, the relationship following a normal curve on a graph of log-concentration versus effect. It is concluded that the response is all or none for individual cells, and that with increasing concentrations of metal, the threshold is exceeded in an increasing proportion of the cells. Parallel studies of the binding of mercury by the cells indicate two distinct phases, only one of which is associated with the physiological response. The binding process is relatively slow but reaches an equilibrium state. Desorption is markedly dependent on temperature. No simple stoichiometric relationship exists between the binding of mercury and the physiological response (K⁺ loss).     

Preferential ligand binding to multi-state acceptor systems: the unexplored paradox of acceptor self-association that is ligand-mediated but detrimental to ligand binding

Consideration is given to the interactions of ligand with self-associating acceptor systems for which preferential ligand binding is an ambiguous term, in that the acceptor species with greater affinity for ligand possesses relatively fewer binding sites. A paradoxical situation wherein ligand-mediated self-association is seemingly detrimental to ligand binding is shown to be the predicted outcome for a transient range of ligand concentrations. This outcome reflects the existence of a critical point in the dependence of the extent of acceptor self-association upon ligand concentration that coincides with a cross-over point of ligand-binding curves for different, fixed total concentrations of acceptor. By classical differentiation methods the conditions for the existence of these critical points are established not only for two-state acceptor systems but also for three-state acceptor systems in which the ligand-binding form of monomer also undergoes reversible isomerization to an inactive state. Similar procedures are used to comment upon the forms of binding curves for the three-state acceptor systems, the Scatchard representations of which may exhibit as many as three critical points (two maxima and a minimum). This delineation of quantitative expressions for critical points and other distinctive features associated with the conflicting interplay of ligand-binding and self-association behaviour should provide a more definitive means of characterizing systems with one acceptor state the preferred binding form on affinity grounds but with the other the preferred state from the viewpoint of binding-site numbers.     

A new graphic method for determining the rate constant for affinity of a ligand for its receptor]

A new method of determination of the equilibrium constant for a ligand binding to acceptor and evaluation of the number of binding sites on the acceptor molecules (or cells) is suggested. The method is simpler, more convenient, and more precise than Klotz's or Scatchard's method.     

Molecular size of opiate (enkephalin) receptors in neuroblastoma-glioma hybrid cells as determined by radiation inactivation analysis

Opiate receptor binding decayed exponentially in mouse neuroblastoma-rat glioma (NG108-15) hybrid cell preparations following exposure to increasing doses of ionizing radiation (0.2 to 7.0 Mrads; 2.0 Mrads/min). Target size analysis revealed that [3H][D-Ala2, D-Leu5]enkephalin (agonist) and [3H]naloxone (antagonist) bound specifically to a component with an apparent molecular size of 200,000 +/- 20,000. Lyophilization of cells for the irradiation procedure did not significantly alter receptor affinity or binding capacity for these ligands. Furthermore, the loss of opiate receptor binding in irradiated cell samples could not be attributed to reduced receptor affinity since increasing concentrations of radiolabeled ligand failed to reverse the inhibition; nonspecific binding decreased only slightly under identical experimental conditions. The value of determining molecular size by radiation inactivation analysis was confirmed by showing that apparent target sizes for two representative lysosomal enzymes (beta-galactosidase and alpha-mannosidase) were consistent with results obtained previously using conventional methods. Thus, the data suggest that the ligand binding component of delta-opiate (enkephalin) receptors in NG108-15 cells has a minimum functional size of approximately 200,000.     

Kinetics of large-ligand binding to one-dimensional lattices: theory of irreversible binding

Exact solutions are obtained for the time dependence of the extent of irreversible binding of ligands that cover more than one lattice site to a homogeneous one-dimensional lattice. The binding may be cooperative or noncooperative and the lattice either finite or infinite. Although the form of the solution is most convenient when the ligand concentration is buffered, exact numerical or approximate analytical solutions, including upper and lower bounds, can be derived for the case of variable ligand concentration as well. The physical reason behind the relative simplicity of the kinetics of irreversible as opposed to reversible binding in such systems is discussed.     

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.     

Scrambled isomers as key intermediates in the oxidative folding of ligand binding module 5 of the low density lipoprotein receptor

The ligand binding module five (LA5) of the low density lipoprotein receptor is a small, single-domain protein of 40 residues and three disulfide bonds with a calcium binding motif that is essential for its structure and function. Several mutations in LA5 have been reported to cause familial hypercholesterolemia by impairing a proper folding of the module. The current study reports the oxidative folding and reductive unfolding pathways of wild type and mutant LA5 modules through kinetic and structural analysis of the trapped intermediates. Wild type LA5 folding involves an initial phase of nonspecific packing where the sequential oxidation of its cysteines gives rise to complex equilibrated populations of intermediates. In the presence of calcium, the attainment of a coordination-competent conformation becomes the rate-limiting step of folding while binding of the ion funnels both thermodynamically and kinetically the folding reaction toward the native state. In the absence of calcium, a scrambled isomer (termed Xa) constitutes the global free energy minimum of the folding process. Xa and the native form are stable, inter-convertible species whose relative populations at equilibrium appear displaced in disease-linked mutants toward the scrambled form. Because stable scrambled isomers such as Xa avoid the exposition of reactive cysteines in misfolded modules, they might constitute a strategy to prevent wrong interactions with other domains during folding of the receptor. Comparison of the folding pathways of wild type and mutant LA5 provides the molecular basis to understand how LA modules fold into a functional conformation or upon mutation misfold and lead to disease.     

Statistical fluctuations in processes of gene expression regulation: consideration of the problem from point of view of statistical mechanics

The regulation of gene expression is a basic problem of biology. In some cases, the gene activity is regulated by specific binding of regulatory proteins to DNA. In terms of statistical mechanics, this binding is described as the process of adsorption of ligands on the one-dimensional lattice and has a probability nature. As a random physical process, the adsorption of regulatory proteins on DNA introduces a noise to the regulation of gene activity. We derived equations, which make it possible to estimate this noise in the case of the binding of the lac repressor to the operator and showed that these estimates correspond to experimental data. Many ligands are able to bind nonspecifically to DNA. Nonspecific binding is characterized by a lesser equilibrium constant but a greater number of binding sites on the DNA, as compared with specific binding. Relations are presented, which enable one to estimate the probability of the binding of a ligand on a specific site and on nonspecific sites on DNA. The competition between specific and nonspecific binding of regulatory proteins plays a great role in the regulation of gene activity. Similar to the one-dimensional "lattice gas" of particles, ligands adsorbed on DNA produce "one-dimensional" pressure on proteins located at the termini of free regions of DNA. This pressure, an analog of osmotic pressure, may be of importance in processes leading to changes in chromatin structure and activation of gene expression.     

A spectroscopic study of metal ion and ligand binding to β-lactamase II

β-Lactamase II has two metal-binding sites. The electronic spectra of Cd(II)- and Co(II)-substituted β-lactamase II have been investigated. It is suggested that a thiol ligand is involved in metal binding at the first site. The stoichiometric dissociation constants for Co(II) binding to β-lactamase II were estimated to be 0.13 and 2.66 mM (pH 6.0, 4°C, 1 M NaCl) by equilibrium dialysis. Competition between Zn(II) and Co(II) for the first metal binding site suggests a value of 0.7 μM (pH 6.0, 30°C, 1 M NaCl) for the dissociation constant o Zn(II).The electronic spectra of the Co(II) enzyme lead to the suggestion that the coordination geometries around the metal ions in the first and second sites are related to those of a distorted tetrahedron and octahedron, respectively.     

Binding modes of 6,7 di-substituted 4-anilinoquinoline-3-carbonitriles to EGFR

4-Anilino-3-cyanoquinolines were reported to have irreversible binding to epidermal growth factor receptor kinase (EGFRK) by forming a covalent linkage to C773. Our initial docking studies gave results inconsistent with the in vitro data and showed two different binding modes. To perceive the exact mode of binding of these ligands, two models of the ligand-EGFR complexes were considered: (1) reversible binding mode in which the ligand had hydrogen bond interactions at the binding site and (2) irreversible binding mode wherein the ligand's Michael acceptor side chain has proximity to the sulfhydryl group of C773 of EGFR, thereby enabling a covalent interaction. The irreversible binding mode correlated better than reversible binding mode with respect to in vitro data. However, our results indicate that both modes are being adopted by the ligands and could be utilized to design more potent EGFRK inhibitors.     

Interaction of lipophorin with the plasma membrane of locust flight muscles

Binding of high-density lipophorin (HDLp) to a plasma membrane preparation of locust flight muscle tissue was studied using a radiolabelled ligand binding assay and ligand blotting techniques. Analysis at 33 degrees C of the concentration-dependent total binding of tritium-labelled HDLp ([3H]HDLp) to the membrane preparation revealed the presence of a single specific binding site with an equilibrium dissociation constant of Kd = 9 (+/- 2) X 10(-7) M and a maximal binding capacity of 84 (+/- 10) ng X (micrograms protein)-1. Unlabelled HDLp as well as unlabelled low-density lipophorin (LDLp) competed with [3H]HDLp for binding to the identified binding site. In addition, ligand blotting demonstrated that both HDLp and LDLp bind specifically to a 30-kDa protein in the plasma membrane preparation, suggesting the involvement of this protein in the binding of lipophorins to the isolated membranes. A possible relationship between the identified binding of lipophorins and the observed co-purification of lipophorin lipase activity with the plasma membranes is discussed.     

Multiple binding of bilirubin to human serum albumin and cobinding with laurate

Numerical analysis of multiple binding of two ligands to one carrier has been accomplished, using the principle of several sets of acceptable binding constants, with bilirubin-laurate-albumin as an example. Binding of bilirubin to defatted human serum albumin was investigated by a spectroscopic method, based upon a difference of light absorption spectrum for free and bound bilirubin. The observations were supplemented with previous data from an independent technique, measurement of oxidation rates of free bilirubin with hydrogen peroxide and peroxidase. A continuous isotherm was obtained, showing binding of at least 4 mol bilirubin per mole albumin with the following stoichiometric binding constants, 1.11 X 10(8), 1.7 X 10(7), 8 X 10(5), and 4 X 10(4) M-1 at pH 8.2, ionic strength 0.15 M, 25 degrees C. The binding is anticooperative at all steps. A saturation level was not reached. Cobinding of bilirubin and laurate was studied, with up to 2 mol of each ligand per mole albumin, using the peroxidase method for determination of free equilibrium concentrations of bilirubin, and a dialysis rate technique for free laurate. The findings could be described in terms of a stoichiometric model. Heterotropic cooperativity was present among the first bilirubin and the first and second laurate molecules. More than two molecules of either ligand can be bound at the same time.