Kinetics of allosteric conformational transition of a macromolecule prior to ligand binding

Two fundamentally different mechanisms of ligand binding are commonly encountered in biological kinetics. One mechanism is a sequential multistep reaction in which the bimolecular binding step is followed by first-order steps. The other mechanism includes the conformational transition of the macromolecule, before the ligand binding, followed by the ligand binding process to one of the conformational states. In stopped-flow kinetic studies, the reaction mechanism is established by examining the behavior of relaxation times and amplitudes as a function of the reactant concentrations. A major diagnostic tool for detecting the presence of a conformational equilibrium of the macromolecule, before the ligand binding, is the decreasing value of one of the reciprocal relaxation times with the increasing [ligand]. The sequential mechanism cannot generate this behavior for any of the relaxation times. Such dependence is intuitively understood on the basis of approximate expressions for the relaxation times that can be comprehensively derived, using the characteristic equation of the coefficient matrix and polynomial theory. Generally, however, the used approximations may not be fulfilled. On the other hand, the two kinetic mechanisms can always be distinguished, using the approach based on the combined application of pseudo-first-order conditions, with respect to the ligand and the macromolecule. The two experimental conditions differ profoundly in the extent of the effect of the ligand on the protein conformational equilibrium. In a large excess of the ligand, the conformational equilibrium of the macromolecule, before the ligand binding, is strongly affected by the binding process. However, in a large excess of the macromolecule, ligand binding does not perturb the internal equilibrium of the macromolecule. As a result, the normal mode, affected by the conformational transition, is absent in the observed relaxation process. In the case of a sequential mechanism, the number of relaxation times is not altered by different pseudo-first-order conditions. Thus, the approach provides a strong diagnostic criterion for detecting the presence of the conformational transition of the macromolecule and establishing the correct mechanism. Application of this approach is illustrated for the binding of 3'-O-(N-methylantraniloyl)-5'-diphosphate to the E. coli DnaC protein.     

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.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

Contributions to the binding free energy of ligands to avidin and streptavidin

The free energy of binding of a ligand to a macromolecule is here formally decomposed into the (effective) energy of interaction, reorganization energy of the ligand and the macromolecule, conformational entropy change of the ligand and the macromolecule, and translational and rotational entropy loss of the ligand. Molecular dynamics simulations with implicit solvation are used to evaluate these contributions in the binding of biotin, biotin analogs, and two peptides to avidin and streptavidin. We find that the largest contribution opposing binding is the protein reorganization energy, which is calculated to be from 10 to 30 kcal/mol for the ligands considered here. The ligand reorganization energy is also significant for flexible ligands. The translational/rotational entropy is 4.5-6 kcal/mol at 1 M standard state and room temperature. The calculated binding free energies are in the correct range, but the large statistical uncertainty in the protein reorganization energy precludes precise predictions. For some complexes, the simulations show multiple binding modes, different from the one observed in the crystal structure. This finding is probably due to deficiencies in the force field but may also reflect considerable ligand flexibility.     

The effect of ligand heterogeneity on the Scatchard plot. Particular relevance to lipoprotein binding analysis

Computer simulations of equilibrium binding studies of a mixture of two labeled ligands binding competitively to a single class of identical and independent sites (receptors) were performed to investigate how ligand heterogeneity affects the observed data in such studies. The simulated data are presented in Scatchard plots. Ligand heterogeneity was generally found to be indistinguishable from the case of a homogeneous ligand when usual experimental conditions applied (that is, Scatchard plots of the data were straight lines). Some factors that increased the probability of recognizing heterogeneity in the system were identified, however. These are 1) a large difference between the dissociation constants of the two ligands, 2) a high concentration of receptors relative to the dissociation constant of the higher-affinity ligand, 3) a high concentration of the lower-affinity ligand relative to that of the higher-affinity ligand, 4) a high specific activity of the lower-affinity ligand relative to that of the higher-affinity ligand, and 5) lack of experimental error. When ligand heterogeneity (under certain conditions) did cause curvilinearity in the Scatchard plot, the curve formed was always concave-downwards. Thus, ligand heterogeneity may occasionally mimic positive cooperativity, but never mimics negative cooperativity or multiple classes of binding sites. Implications of these findings for equilibrium binding studies involving lipoproteins (which are generally isolated as heterogeneous mixtures of particles) are discussed in detail. These findings are also relevant to equilibrium binding studies using ligands which are mixtures of stereoisomers or which contain chemical or radiochemical impurities.     

A method of computing drug distribution in plasma using stepwise association constants: clofibrate acid as an illustrative example.

A program is described to compute the distribution of ligand among various complexes of ligand and protein using stepwise association constants. The key input data consists of stepwise association constants and the concentration of macromolecule and various concentrations of ligand. The key output data consists of the concentration of free drug and protein and the concentration of the various complexes.     

Online optimization of surface plasmon resonance-based biosensor experiments for improved throughput and confidence

The emergence of surface plasmon resonance-based optical biosensors has facilitated the identification of kinetic parameters for various macromolecular interactions. Normally, these parameters are determined from experiments with arbitrarily chosen periods of macromolecule and buffer injections, and varying macromolecule concentrations. Since the choice of these variables is arbitrary, such experiments may not provide the required confidence in identified kinetic parameters expressed in terms of standard errors. In this work, an iterative optimization approach is used to determine the above-mentioned variables so as to reduce the experimentation time, while treating the required standard errors as constraints. It is shown using multiple experimental and simulated data that the desired confidence can be reached with much shorter experiments than those generally performed by biosensor users.     

Adsorption of ligands on macromolecules in the fluctuating medium

In the present work fluctuations of number of ligands adsorbed on macromolecule are investigated. We have taken into account the adsorption and desorption of ligands under the circumstance of some adsorption centers fluctuations affected by medium fluctuation. The correlation function and spectral density of number of ligands adsorbed on macromolecule are calculated. The properties of these fluctuations which allow identifying a noisemaker are determined. It has been shown, thatfas andsluggis adsorption can be distinguished by properties of dispersion and spectral density. It has been also shown, that comparison of experimental and theoretical correlation functions (or spectral densities) allows to calculate constants of ligand - adsorption center binding and unbinding.     

Genome-scale phylogeny and the detection of systematic biases

Phylogenetic inference from sequences can be misled by both sampling (stochastic) error and systematic error (nonhistorical signals where reality differs from our simplified models). A recent study of eight yeast species using 106 concatenated genes from complete genomes showed that even small internal edges of a tree received 100% bootstrap support. This effective negation of stochastic error from large data sets is important, but longer sequences exacerbate the potential for biases (systematic error) to be positively misleading. Indeed, when we analyzed the same data set using minimum evolution optimality criteria, an alternative tree received 100% bootstrap support. We identified a compositional bias as responsible for this inconsistency and showed that it is reduced effectively by coding the nucleotides as purines and pyrimidines (RY-coding), reinforcing the original tree. Thus, a comprehensive exploration of potential systematic biases is still required, even though genome-scale data sets greatly reduce sampling error.     

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.     

The Interaction of DMSO with Model Membranes. II. Direct Evidence of DMSO Binding to Membranes: An NMR Study

Abstract

Modern techniques in nuclear magnetic resonance (NMR) allow investigators to probe molecular interactions with greater sensitivity and speed than ever before. Exploiting the nuclear Overhauser effect (NOE), the intermolecular interactions between dimethylsulfoxide (DMSO) and lipid vesicles were investigated. The DMSO methyl proton signal varies with experimental mixing time suggesting the system behaves in a manner similar to that of a ligand weakly binding to a macromolecule.     

Properties of trout hemoglobin covalently bound to a solid matrix.

This paper reports the ligand binding properties of the major hemoglobin component from trout (Salmo irideus) covalently bound to a solid matrix (Sepharose or Sephadex). A comparison between the functional properties of this protein in solution and of the protein-matrix complex shows significant changes although the basic properties of the molecule are maintained on covalent binding to Sepharose (or Sephadex). Thus the Root effect, characteristic of Hb trout IV, is still present while the heme-heme interactions are, on the average, smaller in the matrix bound protein as compared to the soluble form. No differences in the O2 binding properties were observed when the protein was coupled to the resin, as the ligand bound or as the ligand free derivative. Although an unequivocal interpretation of the data is made difficult by the lack of information on the number and identity of the groups involved in the coupling, the main changes in the protein functional properties may be related to the chemical modifications "per se" more than to the immobilization imposed to the macromolecule by coupling to the matrix. Structural changes which mainly involve perturbation of the tertiary structure of the molecule may qualitatively rationalize the data.     

Distance-restrained docking of rifampicin and rifamycin SV to RNA polymerase using systematic FRET measurements: developing benchmarks of model quality and reliability

We are developing distance-restrained docking strategies for modeling macromolecular complexes that combine available high-resolution structures of the components and intercomponent distance restraints derived from systematic fluorescence resonance energy transfer (FRET) measurements. In this article, we consider the problem of docking small-molecule ligands within macromolecular complexes. Using simulated FRET data, we have generated a series of benchmarks that permit estimation of model accuracy based on the quantity and quality of FRET-derived distance restraints, including the number, random error, systematic error, distance distribution, and radial distribution of FRET-derived distance restraints. We find that expected model accuracy is 10 A or better for models based on: i), > or =20 restraints with up to 15% random error and no systematic error, or ii), > or =20 restraints with up to 15% random error, up to 10% systematic error, and a symmetric radial distribution of restraints. Model accuracies can be improved to 5 A or better by increasing the number of restraints to > or =40 and/or by optimizing the distance distribution of restraints. Using experimental FRET data, we have defined the positions of the binding sites within bacterial RNA polymerase of the small-molecule inhibitors rifampicin (Rif) and rifamycin SV (Rif SV). The inferred binding sites for Rif and Rif SV were located with accuracies of, respectively, 7 and 10 A relative to the crystallographically defined binding site for Rif. These accuracies agree with expectations from the benchmark simulations and suffice to indicate that the binding sites for Rif and Rif SV are located within the RNA polymerase active-center cleft, overlapping the binding site for the RNA-DNA hybrid.     

An easy-to-use tool for planning and modeling a calorimetric titration

Isothermal titration calorimetry (ITC) is widely employed to measure thermodynamic properties of binding interactions between two macromolecules or a macromolecule and a small ligand. No labeling of interacting species is required for ITC, but this advantage is offset by potentially material-consuming experimental optimization complicated by an indirect readout of an ITC titration. Here we present a simple, practical, and portable spreadsheet-based tool for planning and modeling an ITC titration experiment accompanied by basic guidelines.     

Relative spectral response as a function of sequential ligand binding

A unique method is presented for the determination of the critical number of ligands that must bind to a macromolecule to elicit a spectroscopic response. This method is based on analysis of ligand binding data. For example, four Ca2+ and two Mg2+ ions are necessary for mirroring the relative decrease in the intrinsic fluorescence of bovine prothrombin fragment 1. For application of the method, ligand loading and relative spectroscopic response data must be measured over a full range of concentrations.     

Cooperativity: over the Hill

Cooperativity, the ability of ligand binding at one site on a macromolecule to influence ligand binding at a different site on the same macromolecule, is a fascinating biological property that is often poorly explained in textbooks. The Hill coefficient is commonly used in biophysical studies of cooperative systems although it is not a quantitative measure of cooperativity. The free energy of interaction between binding sites (ΔΔG) is a more stringent definition of cooperativity and provides a direct quantitative measure of how the binding of ligand at one site affects the ligand affinity of another site.