Thermodynamic models of binding ligands to nucleic acids

Models of adsorption were considered, which describe the binding of biologically active ligands on DNA templates. The binding is described most comprehensively and in greatest detail by the distribution function, which determines the probability of detecting the preset number of adsorbed ligands on the template. In the case of noncooperative binding, this function corresponds to the Gaussian distribution and is characterized by two quantities: the mean value of the occupation of the template by ligands and the dispersion of occupation. The accuracy of the occupation of the template by ligands is inversely proportional to dispersion. As the length of the template and the number of reaction sites covered by one ligand upon binding increase, the accuracy of the occupation of the template by ligands increases. An important characteristic of binding is the degree of coverage of the template by ligands. This characteristic represents the portion of template reaction sites covered by all ligands adsorbed on the template. If polycations are bound to nucleic acid molecules, the coverage of the template determines the transition of nucleic acids to a compact state. The degree of template coverage for extended ligands depends only slightly on the binding constant in a wide range of concentrations of a free ligand in solution. Different adsorption models are considered from the unified point of view. The classification of cooperative interactions for a wide class of systems is given, from situations when several ligands are bound on nucleic acid templates to a situation when templates change by the action of ligands and begin to interact with each other.     

A general method of analysis of ligand-macromolecule equilibria using a spectroscopic signal from the ligand to monitor binding. Application to Escherichia coli single-strand binding protein-nucleic acid interactions

We describe a general method for the analysis of ligand-macromolecule binding equilibria for cases in which the interaction is monitored by a change in a signal originating from the ligand. This method allows the absolute determination of the average degree of ligand binding per macromolecule without any assumptions concerning the number of modes or states for ligand binding or the relationship between the fractional signal change and the fraction of bound ligand. Although this method is generally applicable to any type of signal, we discuss the details of the method as it applies to the analysis of binding data monitored by a change in fluorescence of a ligand upon binding to a nucleic acid. We apply the analysis to the equilibrium binding of Escherichia coli single-strand binding (SSB) protein to single-stranded nucleic acids, which is monitored by the quenching of the intrinsic tryptophan fluorescence of the SSB protein. With this method, one can quantitatively determine the relationship between the fractional signal change of the ligand and the fraction of bound ligand, LB/LT, and rigorously test whether the signal change is directly proportional to LB/LT. For E. coli SSB protein binding to single-stranded nucleic acids in its (SSB)65 binding mode [Lohman, T. M., & Overman, L. B. (1985) J. Biol. Chem. 260, 3594; Chrysogelos, S., & Griffith, J. (1982) Proc. Natl. Acad. Sci. U.S.A. 79, 5803], we show that the fractional quenching of the SSB fluorescence is equal to the fraction of bound SSB.     

A rapid assay for affinity and kinetics of molecular interactions with nucleic acids

The Differential Radial Capillary Action of Ligand Assay (DRaCALA) allows detection of protein interactions with low-molecular weight ligands based on separation of the protein-ligand complex by differential capillary action. Here, we present an application of DRaCALA to the study of nucleic acid-protein interactions using the Escherichia coli cyclic AMP receptor protein (CRP). CRP bound in DRaCALA specifically to (32)P-labeled oligonucleotides containing the consensus CRP binding site, but not to oligonucleotides with point mutations known to abrogate binding. Affinity and kinetic studies using DRaCALA yielded a dissociation constant and dissociation rate similar to previously reported values. Because DRaCALA is not subject to ligand size restrictions, whole plasmids with a single CRP-binding site were used as probes, yielding similar results. DNA can also function as an easily labeled carrier molecule for a conjugated ligand. Sequestration of biotinylated nucleic acids by streptavidin allowed nucleic acids to take the place of the protein as the immobile binding partner. Therefore, any molecular interactions involving nucleic acids can be tested. We demonstrate this principle utilizing a bacterial riboswitch that binds cyclic-di-guanosine monophosphate. DRaCALA is a flexible and complementary approach to other biochemical methods for rapid and accurate measurements of affinity and kinetics at near-equilibrium conditions.     

Competition dialysis: a method for the study of structural selective nucleic acid binding

Competition dialysis is a powerful new tool for the discovery of ligands that bind to nucleic acids with structural- or sequence-selectivity. The method is based on firm thermodynamic principles and is simple to implement. In the competition dialysis experiment, an array of nucleic acid structures and sequences is dialyzed against a common test ligand solution. After equilibration, the amount of ligand bound to each structure or sequence is determined by absorbance or fluorescence measurements. Since all structures and sequences are in equilibrium with the same free ligand concentration, the amount bound is directly proportional to the ligand binding affinity. Competition dialysis thus provides a direct and quantitative measure of selectivity, and unambiguously identifies which of the samples within the array are preferred by a particular ligand. We describe here the third generation implementation of the method, in which competition dialysis was adapted for use in a 96-well plate format. In this format, we have been able to greatly expand the array of nucleic acid structures studied, and now can routinely study the interactions of a ligand of interest with 46 different structures and sequences.     

Differences between apo and three holo forms of the intestinal fatty acid binding protein seen by molecular dynamics computer calculations

It is commonly believed that binding affinity can be estimated by consideration of local changes of ligand and protein. This paper discusses a set of molecular dynamics simulations of intestinal fatty acid binding protein addressing the protein's response to presence or absence of different ligands. A 5-ns simulation was performed of the protein without a ligand, and three simulations (one 5-ns and two 2-ns) were performed with different fatty acids bound. The results indicate that, although the basic protein structure is unchanged by the presence of the ligand, other properties are significantly affected by ligand binding. For example, zero-time covariance patterns between protein, bound waters, and ligand vary between the different simulations. Moreover, the interaction energies between ligand and specific residues indicate that different ligands are stabilized in different ways. In sum, the results suggest that binding thermodynamics within this system will need to be calculated not from a subset of nearby protein:ligand interactions, but will depend on a knowledge of the motions coupling together water, protein, and ligand.     

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.     

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

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

Kinetics of nonspecific binding reactions of proteins with DNA flexible coils: site-based and molecule-based association reactions

Domain effects on the pseudo-first-order kinetics of the reversible and irreversible association of proteins or other ligands with nucleic acids containing multiple binding sites are treated using the classical reaction-diffusion equation applied to a spherical cell model of the nucleic acid solution and a diffuse-sphere model for the nucleic acid chain molecule. Both uniform and Gaussian distributions of chain segments are analyzed. In general, the details of the segment distribution do not have a major effect on the kinetics of association. Domain effects are best examined experimentally by determining the effect of the molecular weight of the nucleic acid on the kinetics of the association reaction. A theoretical framework is presented that permits such data to be analyzed simply. Kinetic studies over a wide range of nucleic acid molecular weights are required in order to separate the contributions of diffusion and reaction to the observed kinetics, and to determine the contributions of site-based and molecule-based elements to the rate constants.     

Water counting: quantitating the hydration level of paramagnetic metal ions bound to nucleotides and nucleic acids

Binding of divalent metal ions plays a key role in the structure and function of ribozymes and other RNAs. In turn, the energetics and kinetics of the specific binding process are dominated by the balance between the cost of dehydrating the aqueous ion and the energy gained from inner-sphere interactions with the macromolecule. In this work, we introduce the use of the pulsed EPR technique of 2H Electron Spin-Echo Envelope Modulation (ESEEM) to determine the hydration level of Mn2+ ions bound to nucleotides and nucleic acids. Mn2+ is an excellent structural and functional mimic for Mg2+, the most common divalent ion of physiological interest. Comparison of data in D2O and H2O, with aqueous Mn2+ as a reference standard, allows a robust and precise determination of the number of bound water molecules, and therefore the number of RNA-derived ligands. Examples of applications to the mononucleotide models MnGMP and MnATP, as well as to the paradigmatic RNA system tRNAPhe, are shown.     

The effect of denaturants on protein thermal stability analyzed through a theoretical model considering multiple binding sites

A novel mathematical development applied to protein ligand binding thermodynamics is proposed, which allows the simulation, and therefore the analysis of the effects of multiple and independent binding sites to the Native and/or Unfolded protein conformations, with different binding constant values. Protein stability is affected when it binds to a small number of high affinity ligands or to a high number of low affinity ligands. Differential scanning calorimetry (DSC) measures released or absorbed energy of thermally induced structural transitions of biomolecules. This paper presents the general theoretical development for the analysis of thermograms of proteins obtained for n-ligands bound to the native protein and m-ligands bound to their unfolded form. In particular, the effect of ligands with low affinity and with a high number of binding sites (n and/or m > 50) is analyzed. If the interaction with the native form of the protein is the one that predominates, they are considered stabilizers and if the binding with the unfolded species predominates, it is expected a destabilizing effect. The formalism presented here can be adapted to fitting routines in order to simultaneously obtain the unfolding energy and ligand binding energy of the protein. The effect of guanidinium chloride on bovine serum albumin thermal stability, was successfully analyzed with the model considering low number of middle affinity binding sites to the native state and a high number of weak binding sites to the unfolded state.     

Kinetics of protein-nucleic acid interactions: use of salt effects to probe mechanisms of interaction

The kinetics of protein-nucleic acid interactions are discussed with particular emphasis on the effects of salt concentration and valence on the observed rate constants. A general review is given of the use of experimentally determined salt dependences of observed kinetic parameters as a tool to probe the mechanism of interaction. Quantitative analysis of these salt dependences, through the application of polyelectrolyte theory, can be used to distinguish reactions which occur in a single step from those reactions which involve distinct intermediates. For those rate constants which display a large salt dependence, in either the association or dissociation reaction, this is due to the high concentration of counterions (e.g., Na+) in the vicinity of the nucleic acid which are subsequently released (or bound in the case of dissociation) at some point before the rate limiting step of the reaction. A general discussion of other features which affect protein-nucleic acid kinetics, such as nucleic acid length and the ratio of nonspecific to specific DNA binding sites (in the case of sequence specific binding proteins), is also given. The available data on the nucleic acid binding kinetics of small ligands (ions, dyes, oligopeptides), nonspecific binding proteins (T4 gene 32 protein, fd gene 5 and Escherichia coli SSB), and sequence specific binding proteins (lac repressor, RNA polymerase, Eco RI restriction endonuclease) are discussed with emphasis on the interpretation of the experimentally determined salt dependences.     

Model for the irreversible dissociation kinetics of cooperatively bound protein–nucleic acid complexes

We present a quantitative model for the irreversible dissociation kinetics of cooperatively bound nonspecific protein–nucleic acid complexes. The model assumes that the major pathway of dissociation is via singly contiguously bound protein that “peels” off the ends of clusters of bound protein. It should therefore be most applicable for proteins that bind nucleic acids with high cooperativity (w > 10³). Furthermore, the model assumes that no redistribution of bound protein occurs during the time course of the dissociation. Solutions to the rate equations are presented for the entire time course of the dissociation. Under initial conditions such that the nucleic acid is less than fully saturated with protein, a single-exponential decay is predicted (if w is large). However, when the nucleic acid lattice is initially fully saturated, zero-order kinetics, corresponding to a constant rate of protein dissociation, is predicted. The experimental observation of zero-order dissociation kinetics in a cooperative protein–nucleic acid system is a good qualitative indicator for the dissociation mechanism discussed here. A discussion of the analysis of experimental data that enables one to extract molecular rate constants is presented. Furthermore, comparisons are made between the nonredistributing model presented here and Epstein's model [Epstein, I. R. (1979) Biopolymers 18 , 2037–2050] in which protein can translocate infinitely quickly while bound to the nucleic acid, and hence protein clusters redistribute during dissociation and maintain an equilibrium distribution on the nucleic acid at all times.