Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

An application of CIFAP for predicting the binding affinity of Chk1 inhibitors derived from 2‐aminothiazole‐4‐carboxamide

Investigation of protein‐ligand interactions obtained from experiments has a crucial part in the design of newly discovered and effective drugs. Analyzing the data extracted from known interactions could help scientists to predict the binding affinities of promising ligands before conducting experiments. The objective of this study is to advance the CIFAP (compressed images for affinity prediction) method, which is relevant to a protein‐ligand model, identifying 2D electrostatic potential images by separating the binding site of protein‐ligand complexes and using the images for predicting the computational affinity information represented by pIC₅₀ values. The CIFAP method has 2 phases, namely, data modeling and prediction. In data modeling phase, the separated 3D structure of the binding pocket with the ligand inside is fitted into an electrostatic potential grid box, which is then compressed through 3 orthogonal directions into three 2D images for each protein‐ligand complex. Sequential floating forward selection technique is performed for acquiring prediction patterns from the images. In the prediction phase, support vector regression (SVR) and partial least squares regression are used for testing the quality of the CIFAP method for predicting the binding affinity of 45 CHK1 inhibitors derived from 2‐aminothiazole‐4‐carboxamide. The results show that the CIFAP method using both support vector regression and partial least squares regression is very effective for predicting the binding affinities of CHK1‐ligand complexes with low‐error values and high correlation. As a future work, the results could be improved by working on the pose of the ligands inside the grid.     

Analyzing a kinetic titration series using affinity biosensors

The classical method of measuring binding constants with affinity-based biosensors involves testing several analyte concentrations over the same ligand surface and regenerating the surface between binding cycles. Here we describe an alternative approach to collecting kinetic binding data, which we call "kinetic titration." This method involves sequentially injecting an analyte concentration series without any regeneration steps. Through a combination of simulation and experimentation, we show that this method can be as robust as the classical method of analysis. In addition, kinetic titrations can be more efficient than the conventional data collection method and allow us to fully characterize analyte binding to ligand surfaces that are difficult to regenerate.     

A Method for Removing Effects of Nonspecific Binding on the Distribution of Binding Stoichiometries: Application to Mass Spectroscopy Data

There is often an interest in knowing, for a given ligand concentration, how many protein molecules have one, two, three, etc. ligands bound in a specific manner. This is a question that cannot be addressed using conventional ensemble techniques. Here, a mathematical method is presented for separating specific from nonspecific binding in nonensemble studies. The method provides a way to determine the distribution of specific binding stoichiometries at any ligand concentration when using nonensemble (e.g., single-molecule) methods. The applicability of the method is demonstrated for ADP binding to creatine kinase using mass spectroscopy data. A major advantage of our method, which can be applied to any protein-ligand system, is that no previous information regarding the mechanism of ligand interaction is required.     

Isothermal titration calorimetry to determine association constants for high-affinity ligands

An important goal in drug development is to engineer inhibitors and ligands that have high binding affinities for their target molecules. In optimizing these interactions, the precise determination of the binding affinity becomes progressively difficult once it approaches and surpasses the nanomolar level. Isothermal titration calorimetry (ITC) can be used to determine the complete binding thermodynamics of a ligand down to the picomolar range by using an experimental mode called displacement titration. In a displacement titration, the association constant of a high-affinity ligand that cannot be measured directly is artificially lowered to a measurable level by premixing the protein with a weaker competitive ligand. To perform this protocol, two titrations must be carried out: a direct titration of the weak ligand to the target macromolecule and a displacement titration of the high-affinity ligand to the weak ligand-target macromolecule complex. This protocol takes approximately 5 h.     

Isoparametric analysis of binding and partitioning processes

An isoparametric method is described for the analysis of titration data pertaining to the binding of a ligand to an acceptor, or to the partition of a molecule between lipid and aqueous compartments. Where spectroscopic titrations are employed, the analysis does not require a priori choice of an association model, nor assumptions concerning a linear relationship between the spectroscopic signal and the amount of bound or partitioned ligand. The method has wide applicability and is illustrated with reference to (a) ligand-acceptor associations monitored by perturbation of the absorption or fluorescence signal of ligand or acceptor, and (b) cross-linking interactions such as those encountered in antigen-antibody precipitin reactions.     

A "release" protocol for isothermal titration calorimetry

Isothermal titration calorimetry (ITC) has become a standard method for investigating the binding of ligands to receptor molecules or the partitioning of solutes between water and lipid vesicles. Accordingly, solutes are mixed with membranes (or ligands with receptors), and the subsequent heats of incorporation (or binding) are measured. In this paper we derive a general formula for modeling ITC titration heats in both binding and partitioning systems that allows for the modeling of the classic incorporation or binding protocols, as well as of new protocols assessing the release of solute from previously solute-loaded vesicles (or the dissociation of ligand/receptor complexes) upon dilution. One major advantage of a simultaneous application of the incorporation/binding and release protocols is that it allows for the determination of whether a ligand is able to access the vesicle interior within the time scale of the ITC experiment. This information cannot be obtained from a classical partitioning experiment, but it must be known to determine the partition coefficient (or binding constant and stochiometry) and the transfer enthalpy. The approach is presented using the partitioning of the nonionic detergent C12EO7 to palmitoyloleoylphosphatidylcholine vesicles. The release protocol could also be advantageous in the case of receptors that are more stable in the ligand-saturated rather than the ligand-depleted state.     

Limitations in linearized analyses of binding equilibria: binding of TNP-ATP to the H<Subscript>4</Subscript>-H<Subscript>5</Subscript> loop of Na/K-ATPase

Binding of TNP-ATP [2',3'- O-(2,4,6-trinitrophenyl)adenosine 5'-triphosphate, a fluorescent analogue of ATP] to the K605 protein was studied. This is an isolated N-domain in the cytoplasmic loop of the Na/K-ATPase alpha-subunit, lying between membrane-spanning segments 4 and 5 (sequence L(354)-I(604)). A titration equation is derived that explicitly makes it possible to relate the fluorescence of TNP-ATP and K605 solutions to total probe concentration in the sample. Using this, it is possible to obtain the value of the dissociation constant from the titration experiment without resorting to the Scatchard plot, which is far from optimal from the statistical point of view. Using the new formula with non-linear regression analysis, a value of the dissociation constant K(D) for TNP-ATP binding to the K605 protein of 3.03 +/- 0.28 microM at 22 degrees C was obtained. A series of fits to simulated data with added noise demonstrated clearly the advantage of non-linear regression using the new formula over the commonly employed linear regression using the Scatchard plot. The procedure presented is generally applicable to binding assays using changes in the fluorescence of ligands on binding.     

Evaluation of linked protonation effects in protein binding reactions using isothermal titration calorimetry.

A theoretical development in the evaluation of proton linkage in protein binding reactions by isothermal titration calorimetry (ITC) is presented. For a system in which binding is linked to protonation of an ionizable group on a protein, we show that by performing experiments as a function of pH in buffers with varying ionization enthalpy, one can determine the pK(a)'s of the group responsible for the proton linkage in the free and the liganded states, the protonation enthalpy for this group in these states, as well as the intrinsic energetics for ligand binding (delta H(o), delta S(o), and delta C(p)). Determination of intrinsic energetics in this fashion allows for comparison with energetics calculated empirically from structural information. It is shown that in addition to variation of the ligand binding constant with pH, the observed binding enthalpy and heat capacity change can undergo extreme deviations from their intrinsic values, depending upon pH and buffer conditions.     

Reaction of canine plasminogen with 6-aminohexanoate: a thermodynamic study combining fluorescence, circular dichroism, and isothermal titration calorimetry

The thermodynamics of the binding of 6-aminohexanoate (6-AH) to dog glu-plasminogen has been studied. Fluorescence titrations revealed four binding sites. Three yielded positive fluorescence changes on ligand binding; one yielded a negative fluorescence change. The fluorescence data gave no indication of cooperative interactions. Binding was studied using circular dichroism (CD). Near 295 nm there were small changes associated with binding ligand. These were magnified at 235 nm, a wavelength that is mainly associated with tryptophan bands. The dissociation constants obtained from the fluorescence were applied to the CD data and fit quite well. Below 220 nm, there were no significant differences between samples with or without 6-AH and, therefore, no substantial change in the secondary structure of the protein. Isothermal titration calorimetry was used in combination with the binding constants from fluorescence to study the enthalpy and entropy contributions to 6-AH binding. The enthalpies of association for the four sites are all negative. Their absolute values are small for the tight sites and large for the weakest. -TDeltaS is negative for the tight sites and positive for the weakest. The binding of 6-AH to plasminogen is entropically driven for the two tightest sites and enthalpically driven for the weakest site. The binding of 6-AH to lys-plasminogen has been studied and differs slightly from binding to glu-plasminogen. Most importantly, the binding of 6-AH for the weak site goes from enthalpy- to entropy-driven as is found with the other sites.     

Interactions in affinity partition studied using fluorescence spectroscopy.

Fluorescence titration has been used to determine the binding constant and number of binding sites for the textile triazine dye Procion Yellow HE-3G to lactate dehydrogenase from rabbit muscle (E.C. 1.1.1.27). Triazine dye was either free in solution or attached to one of the polymer carriers, polyethylene glycol or dextran. Titrations were performed in solutions of buffer, dextran, and polyethylene glycol. Aqueous two-phase systems composed of polyethylene glycol and dextran were prepared and the binding constant and number of binding sites for ligand polyethylene glycol-Procion Yellow to lactate dehydrogenase were determined in both upper and lower phases of these systems. Affinity partition of lactate dehydrogenase in a PEG-dextran system was also performed using PEG-Procion Yellow as ligand, and partition coefficients of lactate dehydrogenase showed good agreement with theoretical partition coefficients calculated from the binding constant and number of binding sites obtained from fluorescence titration. The advantage of using fluorescence titration to determine affinity of a polymer ligand for a protein is that measurement of binding strength can be made in the actual environment encountered by protein-ligand complex during the purification process.     

Combination of isothermal titration calorimetry and time-resolved luminescence for high affinity antibody-ligand interaction thermodynamics and kinetics

For experiments using synthetic ligands as probes for biological experiments, it is useful to determine the specificity and affinity of the ligands for their receptors. As ligands with higher affinities are developed (K(A)>10(8)M(-1); K(D)<10(-8)M), a new challenge arises: to measure these values accurately. Isothermal titration calorimetry measures heat produced or consumed during ligand binding, and also provides the equilibrium binding constant. However, as normally practiced, its range is limited. Displacement titration, where a competing weaker ligand is used to lower the apparent affinity of the stronger ligand, can be used to determine the binding affinity as well as the complete thermodynamic data for ligand-antibody complexes with very high affinity. These equilibrium data have been combined with kinetic measurements to yield the rate constants as well. We describe this methodology, using as an example antibody 2D12.5, which captures yttrium S-2-(4-aminobenzyl)-1, 4, 7, 10-tetraazacyclododecanetetraacetate.     

Ligand-induced self-association of human chorionic gonadotropin. Positive cooperativity in the binding of 8-anilino-1-naphthalenesulfonate.

Human chorionic gonadotropin (hCG) self-associates to form higher molecular weight species in the presence of the fluorescence probe 8-anilino-1-naphthalenesulfonate (ANS). Sedimentation equilibrium and fluorescence titration data have been analyzed in terms of a monomer-dimer-tetramer model in which the various oligomers have different affinities and/or capacities for the ligand. The results indicate that the ligand affinities are in the order tetramer greater than dimer greater than monomer whereas the numbers of ligand binding sites per mole of hCH are in the reverse order. Consequently, addition of ANS first shifts the equilibrium from monomer to tetramer and gives rise to positive cooperativity in the titration curves. At sufficiently high ANS concentration (approximately 0.5 mM), the equilibrium shifts back to the dimer because of its greater binding capacity. This is manifested by a second phase in the titration curve and a decrease in the polarization of ANS fluorescence. The results are discussed in terms of the general problem of ligand controlled protein association and are contrasted to results reported to the previous paper for the homolgous protein, human luteinizing hormone.     

Defining the secondary structural requirements of a cocaine-binding aptamer by a thermodynamic and mutation study

Isothermal titration calorimetry (ITC) was used to measure the binding affinity and thermodynamics of a cocaine-binding aptamer as a function of pH and NaCl concentration. Tightest binding was achieved at a pH value of 7.4 and under conditions of no added NaCl. These data indicate that ionic interactions occur in the ligand binding mechanism. ITC was also used to measure the binding thermodynamics of a variety of sequence variants of the cocaine-binding aptamer that analyzed which regions and nucleotides of the aptamer are important for maintaining high-affinity binding. Individually, each of the three stems can be shortened, resulting in a reduced binding affinity. If all three stems are shortened, no binding occurs. If all three of the stems in the aptamer are lengthened by five base pairs ligand affinity increases. Changes in nucleotide identity at the three-way junction all decrease the affinity of the aptamer to cocaine. The greatest decrease in affinity results from changes that disrupt the GA base pairs and the identity of T19.     

A universal thermodynamic approach to analyze biomolecular binding experiments

Binding processes of any kind can be characterized as an association of a given ligand with some binding factor. This includes macromolecules as well as supramolecular aggregates such as micelles or membranes. The underlying molecular binding mechanism may be more or less complicated due to various intermediate steps (involving for instance conformational changes, aggregation, cooperativity, etc.). A sensible discussion of possible binding models naturally calls for a model-independent access to basic thermodynamic properties. The present contribution will demonstrate how this can quite generally be accomplished by a pertinent processing of properly selected experimental data. The method requires a series of titration measurements comprising the use of variable amounts of both the ligand and the binding factor. It leads to a linear mass conservation plot (i.e. amount of the ligand vs. a matching amount of the binding factor) whose slope and ordinate intercept are equal to the binding ratio (i.e. bound ligand per binding factor) and the free ligand concentration, respectively. This establishes the specific binding isotherm. The approach also reveals latent structurally determined features of the applied physical measuring signal. A number of examples including specific binding, unspecific adsorption and insertion in two-dimensional molecular films will illustrate the methodology.     

The electronic state of heme in cytochrome oxidase II. Oxidation-reduction potential interactions and heme iron spin state behavior observed in reductive titrations.

Magnetic circular dichroism (MCD), electron paramagnetic resonance (EPR), and optical absorption spectroscopies have been used to monitor the concentrations of oxidized and reduced heme and copper during stoichiometric reductive titrations of purified beef heart cytochrome oxidase. The MCD data are deconvoluted to obtain the concentrations of reduced cytochromes a and a3 during the titrations; analysis of the EPR spectra provides complementary data on the concentrations of the EPR-detectable species. For the native enzyme in the absence of exogenous ligands, cytochromes a and a3 are reduced to approximately the same extent at all points in the titration. The reduction of the EPR-detectable copper, on the other hand, initially lags the reduction of the two cytochromes but in the final stages of the titration is completely reduced prior to either cytochrome a or a3. These non-Nernstian titration results are interpreted to indicate that the primary mode of heme-heme interaction in cytochrome oxidase involves shifts in oxidation-reduction potential for each of the two cytochromes such that a change in oxidation state for one of the hemes lowers the oxidation-reduction potential of the second heme by approximately 135 mV. In these titrations high spin species are detected which account for 0.25 spin/oxidase maximally. Evidence is presented to indicate that at least some of these signals can be attributed to cytochrome a3+ which has undergone a low-spin to high-spin state transition in the course of the titration. In the presence of carbon monoxide the oxidation-reduction properties of cytochromes a and a3 are markedly altered. The a32+. CO complex is fully formed prior to reduction of either cytochrome a3+ or the EPR-detectable copper. The g = 3 EPR signal attributed to cytochrome a3+ decreases as the MCD intensity of cytochrome a2+ increases; no significant high-spin intensity is observed at any intermediate stage of reduction. We interpret these Nernstian titration results to indicate that in the presence of ligands the oxidation-reduction potential of cytochrome a relative to cytochrome a3 is determined by the oxidation-reduction state of the stabilized cytochrome a3 ligand complex; if ligand binding occurs to reduced cytochrome a3 then cytochrome a titrates with a lower potential; cytochrome a titrates with a higher potential if oxidized cytochrome a3 is stabilized by ligand binding.