Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.     

Energetics of cooperative protein-DNA interactions: comparison between quantitative deoxyribonuclease footprint titration and filter binding

Using the binding of cI repressor protein to the lambda right and left operators as a model system, we have analyzed the two common experimental techniques for studying the interactions of genome regulatory proteins with multiple, specific sites on DNA. These are the quantitative DNase footprint titration technique [Brenowitz, M., Senear, D. F., Shea, M. A., & Ackers, G. K. (1986) Methods Enzymol. 130, 132-181] and the nitrocellulose filter binding assay [Riggs, A., Suzuki, H., & Bourgeois, S. (1970) J. Mol. Biol. 48, 67-83]. The footprint titration technique provides binding curves that separately represent the fractional saturation for each site. In principle, such data contain the information necessary to determine the thermodynamic constants for local site binding and cooperativity. We show that in practice, this is not possible for all values of the constants in multisite systems, such as the lambda operators. We show how these constants can nevertheless be uniquely determined by using additional binding data from a small number of mutant operators in which the number of binding sites has been reduced. The filter binding technique does not distinguish binding to the individual sites and yields only macroscopic binding parameters which are composite averages of the various local site and cooperativity constants. Moreover, the resolution of even macroscopic constants from filter binding data for multisite systems requires ad hoc assumptions as to a relationship between the number of ligands bound and the filter retention of the complex. Our results indicate that no such relationship exists. Hence, the technique does not permit determination of thermodynamically valid interaction constants (even macroscopic) in multisite systems.     

Affinity characterization-mass spectrometry methodology for quantitative analyses of small molecule protein binding in solution

Affinity characterization by mass spectrometry (AC–MS) is a novel LC–MS methodology for quantitative determination of small molecule ligand binding to macromolecules. Its most distinguishing feature is the direct determination of all three concentration terms of the equilibrium binding equation, i.e., (M), (L), and (ML), which denote the macromolecule, ligand, and the corresponding complex, respectively. Although it is possible to obtain the dissociation constant from a single mixing experiment, saturation analyses are still valuable for assessing the overall binding phenomenon based on an established formalism. In addition to providing the prerequisite dissociation constant and binding stoichiometry, the technique also provides valuable information about the actual solubility of both macromolecule and ligand upon dilution and mixing in binding buffers. The dissociation constants and binding mode for interactions of DNA primase and thymidylate synthetase (TS) with high and low affinity small molecule ligands were obtained using the AC–MS method. The data were consistent with the expected affinity of TS for these ligands based on dissociation constants determined by alternative thermal-denaturation techniques: TdF or TdCD, and also consistent enzyme inhibition constants reported in the literature. The validity of AC–MS was likewise extended to a larger set of soluble protein–ligand systems. It was established as a valuable resource for counter screen and structure–activity relationship studies in drug discovery, especially when other classical techniques could only provide ambiguous results.     

A Hierarchical Approach to Cooperativity in Macromolecular and Self-Assembling Binding Systems

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc. In this paper, we propose a novel approach for the analysis of the binding properties of complex macromolecular and self-assembling systems. To quantify the binding behaviour, we use the global association quotient defined as K _c = [occupied sites]/([free sites] L), L being the free ligand concentration. K _c can be easily related to other measures of cooperativity (such as the Hill number or the Scatchard plot) and to the free energies involved in the binding processes at each ligand concentration. In a previous work, it was shown that K_c could be decomposed as an average of equilibrium constants in two ways: intrinsic constants for Adair binding systems and elementary constants for the general case. In this study, we show that these two decompositions are particular cases of a more general expression, where the average is over partial association quotients, associated with subsystems from which the system is composed. We also show that if the system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic level and ends at the higher, aggregation level, the global association quotient can be decomposed following the hierarchical levels of macromolecular organisation. In this process, the partial association quotients of one level are expressed, in a recursive way, as a function of the partial quotients of the level that is immediately below, until the microscopic level is reached. As a result, the binding properties of very complex macromolecular systems can be analysed in detail, making the mechanistic explanation of their behaviour transparent. In addition, our approach provides a model-independent interpretation of the intrinsic equilibrium constants in terms of the elementary ones.     

Comprehensive investigation of the non-covalent binding of MRI contrast agents with human serum albumin

Three techniques, electrospray mass spectrometry, ultrafiltration, and proton relaxometry, are compared in the context of the quantitative analysis of non-covalent binding between human serum albumin (HSA) and MRI contrast agents. The study of the affinity by proton relaxometry reveals the association constant and the number of interaction sites assuming that all sites are identical and independent. Ultrafiltration was adapted for the study of paramagnetic complexes. This technique confirmed the results obtained by relaxometry. Electrospray mass spectrometry, an original method able to study non-covalent binding because of its soft ionization process that allows for the survival of weak binding, provides qualitative and quantitative results. Electrospray mass spectrometry confirmed the affinity measured by proton relaxometry and ultrafiltration. This technique requires very small amounts of products and directly gives the stoichiometry of the association, information not easily obtained by classic techniques. Nevertheless, proton relaxometry remains a useful and mandatory technique for determining the enhancement of the relaxation subsequent to the binding although it demands large amounts of compounds. It is to be pointed out that even if the three techniques lead to a similar ranking of the affinity of the contrast agents for HSA, the absolute values of the association constants disagree as a result of the difference in the experimental conditions (presence of salt, native protein or desalted one, approximations in the fitting of the data, liquid or gas phases).     

Isothermal titration calorimetry and surface plasmon resonance analysis using the dynamic approach

Biophysical techniques such as isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) are routinely used to ascertain the global binding mechanisms of protein-protein or protein-ligand interaction. Recently, Dumas etal, have explicitly modelled the instrument response of the ligand dilution and analysed the ITC thermogram to obtain kinetic rate constants. Adopting a similar approach, we have integrated the dynamic instrument response with the binding mechanism to simulate the ITC profiles of equivalent and independent binding sites, equivalent and sequential binding sites and aggregating systems. The results were benchmarked against the standard commercial software Origin-ITC. Further, the experimental ITC chromatograms of 2′-CMP + RNASE and BH3I-1 + hBCL_XL interactions were analysed and shown to be comparable with that of the conventional analysis. Dynamic approach was applied to simulate the SPR profiles of a two-state model, and could reproduce the experimental profile accurately.     

Cooperativity in Binding Processes: New Insights from Phenomenological Modeling

Cooperative binding is one of the most interesting and not fully understood phenomena involved in control and regulation of biological processes. Here we analyze the simplest phenomenological model that can account for cooperativity (i.e. ligand binding to a macromolecule with two binding sites) by generating equilibrium binding isotherms from deterministically simulated binding time courses. We show that the Hill coefficients determined for cooperative binding, provide a good measure of the Gibbs free energy of interaction among binding sites, and that their values are independent of the free energy of association for empty sites. We also conclude that although negative cooperativity and different classes of binding sites cannot be distinguished at equilibrium, they can be kinetically differentiated. This feature highlights the usefulness of pre-equilibrium time-resolved strategies to explore binding models as a key complement of equilibrium experiments. Furthermore, our analysis shows that under conditions of strong negative cooperativity, the existence of some binding sites can be overlooked, and experiments at very high ligand concentrations can be a valuable tool to unmask such sites.     

Macromolecule-ligand binding studied by the Hummel and Dreyer method: current state of the methodology

The use of the Hummel and Dreyer method to measure binding parameters of ligand-macromolecule associations is reviewed. The possibility to determine the number of binding sites and their association constants, even in the case of low affinity, and to control the free ligand concentration as an independent variable are the main advantages of the method. The conditions of the validity are rapid equilibrium kinetics, independence between ligand binding and macromolecule association, and identical retention rates between free and bound macromolecules. Initially developed on soft gels, the method has been applied to high-performance chromatography and capillary zone electrophoresis. Technical progress such as increase in resolution, detection sensitivity, and automation have improved its utilization. The binding parameters given by the Hummel and Dreyer method are in general similar to those obtained by other techniques, in comparable experimental conditions (equilibrium dialysis, ultrafiltration, frontal elution, vacancy peak method, vacancy affinity capillary electrophoresis, retention analysis, affinity chromatography and affinity capillary electrophoresis, physical methods). The choice between these methods is directed by material availability and practical constraints. Separation by new types of chromatographic columns or by capillary zone electrophoresis would enable the study of the simultaneous binding of different drugs on the same macromolecule and their competition.     

A note on Ca2+ binding to calmodulin

Binding of Ca2+ to calmodulin has been simulated on the basis of a model that assumes two classes, two sites in each class, of Ca2+ binding sites. With properly chosen values of binding constants for the two classes of sites, and with the assumption that certain degree of positive cooperativity exists between the two sites in each class, the overall binding isotherm can be generated so that it appears to be a single-transition, non-cooperative binding curve of four equivalent sites. Thus this model offers a resolution for some of the discrepancies among Ca2+ binding studies of calmodulin.     

Binding of lead ion to bovine serum albumin studied by ion selective electrode

The binding of Pb2+ to bovine serum albumin (BSA) at neutral pH was studied using lead ion selective electrode. The binding data was treated according to Scatchard Equation. The number of binding classes and the number of binding sites, intrinsic dissociation constants and stepwise binding constants for each class were determined. Two binding classes were found. Four binding sites in the first class and five binding sites in the second class were determined. Binding in the first class was stronger than in the second. Similar binding studies were carried out with heat treated BSA. It was found that not only the number of binding sites but also the strength of binding increases upon heat treatment.     

Sequestration electrochemistry: the interaction of chlorpromazine and human orosomucoid

A simple and rapid method is presented for determination of the association constants and stoichiometries describing ligand macromolecule interactions. Based on flow injection analysis and electrochemical detection by amperometry, the only requirements for direct measurements are that the ligand have redox properties and that these properties change upon binding to the macromolecule. Bound ligand may then be measured in the presence of free ligand. Detection limits are of the order of 2 pmol of ligand or less, a level that should provide access to previously unmeasurable systems. For the exemplary system, chlorpromazine and human orosomucoid, K0ass was determined as 0.39 X 10(6) M-1 with 0.76 chlorpromazine binding sites of this affinity per orosomucoid molecule.     

Fluorescence study of the ligand stereospecificity for binding to lumazine protein.

6,7-Dimethyllumazine derivatives, substituted at the 8-position with aldityls or monohydroxyalkyl groups, have been examined for their binding ability to lumazine apo-protein from two strains of Photobacterium phosphoreum using fluorescence dynamics techniques. On the protein the lumazine has a nearly monoexponential decay of fluorescence with lifetime 13.8 ns (20 degrees C). In free solution the lifetime is 9.6 ns. The concentration of free and bound lumazine in an equilibrium mixture can be recovered readily by analysis of the fluorescence decay. Only the aldityl derivatives D-xylityl and 3'-deoxy-D-ribityl, having stereoconfigurations at the 2' and 4' positions identical to the natural ligand, 8-(1'-D-ribityl), show comparable dissociation constants (0.3 microM, 20 degrees C, pH 7.0). D-Erythrityl and L-arabityl have dissociation constants of 1-2 microM. All other ligands show no interaction at all or have dissociation constants in the range 6-80 microM, which can still be determined semi-quantitatively using the fluorescence decay technique. In the case of these very weakly bound ligands, unambiguous detection of bound ligand can be shown by a long correlation time (23 ns, 2 degrees C) for the fluorescence anisotropy decay. Examination of the bound D-xylityl compound's fluorescence anisotropy decay at high time resolution (< 100 ps) shows rigid association, i.e. no mobility independent of the macromolecule. All bound ligands appear to be similarly positioned in the binding site. The influence of the stereoconfiguration at the 8-position found for lumazine protein parallels that previously observed for the enzyme riboflavin synthase, where the lumazines are substrates or inhibitors. This is consistent with the finding of significant sequence similarity between these proteins. The binding rigidity may have implications for the mechanism of the enzyme.     

The linkage between the four-step binding of oxygen and the binding of heterotropic anionic ligands in hemoglobin

The linkage between the four-step binding of oxygen and the binding of heterotropic anionic ligands in hemoglobin was investigated by accurately measuring and analyzing the oxygen equilibrium curves of human adult hemoglobin in the presence and absence of various concentrations of one or two of the following materials: chloride (Cl-), 2,3-diphosphoglycerate (DPG), and inositol hexaphosphate (IHP). Each equilibrium curve was analyzed according to the Adair equation to evaluate the four-step oxygen equilibrium constants (Adair constants) and the median oxygen pressure. The binding constants of the anions for the molecular species of hemoglobin carrying j oxygen molecules, Hb(O2)j(j=0,1,...,4), were evaluated from the dependences of the Adair constants and the median oxygen pressure on the anion concentration by introducing a model which takes the competitive binding of Cl- and DPG or IHP into account. Assumptions made in the model are: (a) the hemoglobin molecule has two oxygen-linked binding sites for Cl- which are equivalent and independent and (b) no Cl- can be bound to hemoglobin to which DPG or IHP is already bound and vice versa. Thus, we could obtain values for the intrinsic binding constants of Cl- and DPG, i.e., the constants in the absence of other competitive anions. For IHP, only the binding constants and apparent binding constants for Hb and Hb(O2)2 were obtained. Values of the Cl- binding constants and apparent binding constants for DPG and IHP, i.e., the binding constants in the presence of Cl- for Hb and Hb(O2)4, were in reasonable agreement with literature values. From the binding constants we calculated anion binding curves for Hb(O2)j(J=0,1,...,4), the number of anions bound to Hb(O2)J, And the relationship between fractional anion saturation of hemoglobin and fractional oxygen saturation. The numbers of released anions are not uniform with respect to oxygenation step. This non-uniformity is the reason for the changes in the shape of the oxygen equilibrium curve with anion concentration changes and for the non-uniform dependences of the Adair constants on anion concentration, and also results in non-linear relations between anion saturation and oxygen saturation. The anion binding constants and various binding properties of the anions derived from those constants are consistent with those observed by other investigators using different techniques, indicating that the present model describes the oxygen-linked competitive anion binding well.     

Calorimetric analysis of aspartate transcarbamylase from Escherichia coli: binding of cytosine 5'-triphosphate and adenosine 5'-triphosphate.

The binding of CTP and ATP to aspartate transcarbamylase at pH 7.8 and 8.5 at 25 degrees has been investigated by equilibrium dialysis and flow microcalorimetry. The binding isotherms for CTP at both pH 7.8 and 8.5 and ATP AT PH 8.5 can be fit by a model which assumes three tight, three moderately tight, and six weak binding sites. The binding isotherms for ATP at pH 7.8 are best fit by a model which assumes six tight and six weaker sites. Both finite differenceH binding and finite differenceS binding are negative for both nucleotides at both pH values, so that the binding is enthalpy driven. For both nucleotides, finite differenceH is the same for the first two classes of binding sites, implying that the difference in the dissociation constants of these two classes of sites is the result of entropic effects. Direct pH measurements and calorimetric measurements in two buffers with very different heats of ionization (Tris and Hepes) indicate that the binding of both nucleotides is accompanied by the binding of protons. In the pH range 6.7-8.4, the number of moles of protons bound per mole of nucleotide increases as the pH decreases.     

Kinetics of phloretin binding to phosphatidylcholine vesicle membranes

The submillisecond kinetics for phloretin binding to unilamellar phosphatidylcholine (PC) vesicles was investigated using the temperature-jump technique. Spectrophotometric studies of the equilibrium binding performed at 328 nm demonstrated that phloretin binds to a single set of independent, equivalent sites on the vesicle with a dissociation constant of 8.0 microM and a lipid/site ratio of 4.0. The temperature of the phloretin-vesicle solution was jumped by 4 degrees C within 4 microseconds producing a monoexponential, concentration-dependent relaxation process with time constants in the 30--200-microseconds time range. An analysis of the concentration dependence of relaxation time constants at pH 7.30 and 24 degrees C yielded a binding rate constant of 2.7 X 10(8) M-1 s-1 and an unbinding constant of 2,900 s-1; approximately 66 percent of total binding sites are exposed at the outer vesicle surface. The value of the binding rate constant and three additional observations suggest that the binding kinetics are diffusion limited. The phloretin analogue, naringenin, which has a diffusion coefficient similar to phloretin yet a dissociation constant equal to 24 microM, bound to PC vesicle with the same rate constant as phloretin did. In addition, the phloretin-PC system was studied in buffers made one to six times more viscous than water by addition of sucrose or glycerol to the differ. The equilibrium affinity for phloretin binding to PC vesicles is independent of viscosity, yet the binding rate constant decreases with the expected dependence (kappa binding alpha 1/viscosity) for diffusion-limited processes. Thus, the binding rate constant is not altered by differences in binding affinity, yet depends upon the diffusion coefficient in buffer. Finally, studies of the pH dependence of the binding rate constant showed a dependence (kappa binding alpha [1 + 10pH-pK]) consistent with the diffusion-limited binding of a weak acid.     

Properties of passive binding of calcium to endoplasmic reticulum from adipocytes.

Calcium binding to isolated adipocyte microsomes enriched in endoplasmic reticulum has been characterized. Binding was concentration-dependent, saturable, and totally dissociable. Steady state was reached within 20 min at all calcium concentrations tested. Three apparent classes of binding sites were identified in kinetic and steady state studies using calcium concentrations from 1 muM to 10 mM. The affinity constants (and maximum binding capacities) as determined by computer analysis for the three classes were 2.1 X 10(5) M-1 (0.28 nmol of calcium/mg of protein), 1.3 X 10(4) M-1 (1.1 nmol/mg), and 1.3 X 10(2) M-1 (35 nmol/mg). The dissociation rate constants for the high and intermediate affinity classes of sites were 1.6 X 10(-3) S-1, respectively, and the association rate constant for the high affinity sites was 8 X 10(2) M-1 S-1. The affinity constant calculated from the rate constants was 5.0 X 10(5) M-1 for the high affinity sites in agreement with the value obtained in studies at steady state. The three classes of binding sites were specific for calcium. Magnesium was a noncompetitive inhibitor of calcium binding to all three classes of sites with a Ki of 9 to 12 mM. Calcium binding at 1 muM calcium was 50% inhibited by 18 muM La3+, 600 muM Sr2+, or 2.7 mM Ba2+. These data represent the first analysis of passive calcium binding to endoplasmic reticulum from nonmuscular cells and the first report of corresponding rate constants for either endoplasmic or sarcoplasmic reticulum. The characteristics of the binding are consistent with the properties of calcium transport by endoplasmic reticulum of adipocytes. The characteristics and specificity of the calcium binding constitute further evidence that endoplasmic reticulum plays an important role in cellular calcium homeostasis.     

Investigation of the dark interaction between furocoumarins and DNA

The complexes between some furocoumarins and DNA have been studied using various physicochemical techniques. Flow-dichroism measurements data strongly support the intercalation of the planar furocoumarin molecules between two base pairs of duplex DNA. The equilibrium dialysis and spectrophotometric data show relatively low values of the association constants of the complexes and a small number of molecules able to intercalate in DNA, thus indicating that furocoumarins have a relatively low affinity for DNA in the complex formation. The biological and photobiological consequences connected with these results are discussed.The binding curves obtained using some polynucleotides and various DNA samples having different composition with regard to base pairs, have shown that the regions of the macromolecule having alternate sequences of purine and pyrimidine represent sites useful for intercalation. No preference has been observed for A-T or G-C.     

Graphical analyses on binding of ligands to a two-sited system. Theoretical treatments exemplified on yeast phosphoglycerate kinase

Equilibrium studies on ATP^4? and 3-P-glycerate binding to phosphoglycerate kinase (ATP:3-phospho-d-glycerate 1-phosphotransferase, EC 2.7.2.3) have been performed. The results show that the enzyme contains two binding sites for both ligands, as was earlier suggested to explain some of the kinetic results. As long as structural information is lacking analysis of binding data can be analyzed if assumptions are made whether the sites are equivalent or nonequivalent, and whether ligation of these sites is mutually dependent or not. To understand the experimental results explicit expressions were derived for the limiting slopes and intercepts of Klotz and Scatchard plots, respectively, in terms of the intrinsic affinity constants valid under the separate assumptions made. The algebraic expressions for the limiting slopes were analyzed in order to ascertain the relationship between the form of these graphical plots, the prevailing types of binding site, and the intrinsic affinity constants. The results show that in case the equivalence of the binding sites is questionable it is necessary to be careful when the type of interaction is being determined. In certain cases it might be difficult to distinguish between positive and negative interaction. Sites that appear to be equivalent and independent could equally well be nonequivalent and dependent.