Analysis of individual-site binding data.

Individual-site isotherms add experimental data which may allow for a more detailed definition of the parameters in a system with interacting binding sites. Individual-site isotherms accomplish the following: (A) In general, they define little more than the total or combined isotherm except to reveal the existence of different sites. (B) Under the limiting conditions of symmetrical interactions in two site systems they define: (1) the ratio of the unperturbed or intrinsic binding constants rather than their actual values, (2) the unperturbed shape of the total isotherm, that is, the shape of the total isotherm if there were no ligand dependent interactions between the sites, and (3) the perturbation of the shape of the total isotherm derived from interactions between the sites. (C) They do not define the nature of the interactions; that is, they do not resolve the free energies of the interactions between the sites. (D) When some assumptions about the nature of the interactions are made they may aid in defining some free energies of interaction between the sites.     

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.     

Cooperative equilibrium curves generated by ordered ligand binding to multi-site molecules

The sigmoid shape of equilibrium curves in normal axes and Hill coefficients higher than unity, are indexes of cooperativity or homotropic allostery where the affinity for the ligand increases as saturation progresses. The mathematical transformation of the Adair scheme of equilibria in the Hill plot, reveals that sigmoid binding curves can also be generated by ordered ligand binding to a receptor with multiple binding sites of identical microscopic association constants. This mechanism only based on the law of mass action, could participate to some extent to certain cooperative effects observed in non-biological systems and perhaps in the physiological binding of oxygen to heme proteins.     

Co-operative binding interactions in affinity chromatography: Theoretical considerations

A theoretical relationship has been developed to allow the effect of free ligand concentration on the capacity of an affinity Chromatography matrix to be determined where the protein adsorbed shows co-operative binding. Computer simulations using literature values for association constants show that under optimal conditions resin capacity can be increased significantly in the presence of a small but finite concentration of free ligand. The model also allows prediction of the soluble ligand concentration required for biospecific elution. The results obtained suggest the possibility of a new elution technique, "reverse biospecific elution," that reduces the amount of free ligand required to effect elution.     

Use of binding site neighbor-effect parameters to evaluate the interactions between adjacent ligands on a linear lattice. Effects on ligand-lattice association.

A method using binding site "neighbor-effect" parameters (NEPs) is introduced to evaluate the effects of interaction between adjacent ligands on their binding to an infinite linear lattice. Binding site overlap is also taken into account. This enables the conditional probability approach of McGhee & von Hippel to be extended to more complex situations. The general equation for the isotherm is v/LF = SFKF, where v is the ratio of bound ligands to lattice residues, LF is the free ligand concentration, SF is the fraction of binding sites that are free, and KF is the average association constant of a free site. Solutions are derived for three cases: symmetric ligands, and asymmetric ligands on isotropic or anisotropic lattices. For symmetric ligands there is one NEP, E, which is the ratio of the average binding affinity of a free site if the status of the lattice residue neighboring one end of the site is unspecified (left to chance) to the affinity when this residue is free (holding the other neighbor constant). Thus KF is KE2, where K is the affinity of an isolated site. If a site is n residues long, SF is f ffn-1, where f = 1 - nv is the fraction of residues that are free and ff is the conditional probability that a free residue is bordered on a given side by another free residue. The expression for ff is 1/(1 + x/E), where x is v/f, E is (1 - x + [(1 - x)2 + 4x omega]1/2)/2, and omega is the co-operativity parameter. The binding of asymmetric ligands to an isotropic lattice is described by two NEPs; the last case involves four NEPs and a bound ligand orientation parameter. For each case, the expected length distribution of clusters of bound ligands can be calculated as a function of v. When Scatchard plots with the same intercepts and initial slope are compared, it is found that ligand asymmetry lowers the isotherm (relative to the corresponding symmetric ligand isotherm), whereas lattice anisotrophy raises it.     

The binding capacity is a probability density function.

The binding capacity of a system, or equivalently, the fluctuations of the number of ligands bound around the average value defined by the binding isotherm, can be regarded as a probability density function for the chemical potential of the ligand. The first moment of this density function is the mean ligand activity as defined by Wyman and gives the average free energy (in kT units) of binding per site. The second moment is directly related to the cooperativity of the system. These and higher moments can be obtained from numerical integration of experimental data in a direct way. An analytical expression for the moment generating function shows that the N independent coefficients of the partition function of a system containing N sites are uniquely defined by the first N moments of the binding capacity.     

Theoretical analysis of the footprinting experiment

In the footprinting experiment, an end-radiolabeled DNA restriction fragment is subjected to digest by an endonuclease in the presence and absence of a ligand which alters the endonuclease cleavage rate at sites of ligand-DNA contact. The location of these sites, and the strength of the ligand binding, are then deduced from the measured concentrations of the different oligonucleotides produced by the digest. We analyze the experiment in terms of coupled kinetic equations which take into account the cutting rates of endonuclease for sites with ligand present and absent, and the rates of binding and dissociation of the ligand to a site. As long as the ligand concentration remains essentially constant (which occurs, for example, if digest is terminated early enough to assure that all fragments result from single cuts by the endonuclease), the oligonucleotide concentrations reflect only the ligand binding equilibrium constant (ratio of rate constants) and the cutting rates in the presence and absence of ligand. We also show how the measured oligonucleotide concentrations (from, e.g. an autoradiogram) can be used to deduce the ligand equilibrium binding constants for the various sites on the polymer.     

A quantitative plot for the determination of negatively co-operative ligand binding sites in proteins

The paper describes a method for determining the number of interacting ligand binding sites for co-operative proteins. The method is simple and is particularly applicable in the case of negatively co-operative ligand binding.     

The relationship between effector binding and inhibition of activity in D-3-phosphoglycerate dehydrogenase

The binding of L-serine to phosphoglycerate dehydrogenase from Escherichia coli displays elements of both positive and negative cooperativity. At pH 7.5, approximately 2 mol of serine are bound per mole of tetrameric enzyme. A substantial degree of positive cooperativity is seen for the binding of the second ligand, but the binding of the third and fourth ligand display substantial negative cooperativity. The data indicate a state of approximately 50% inhibition when only one serine is bound and approximately 80-90% inhibition when two serines are bound. This is consistent with the tethered domain hypothesis that has been presented previously. Comparison of the data derived directly from binding stoichiometry to the binding constants determined from the best fit to the Adair equation, produce a close agreement, and reinforce the general validity of the derived binding constants. The data also support the conclusion that the positive cooperativity between the binding to the first and second site involves binding sites at opposite interfaces over 110 A apart. Thus, an order of binding can be envisioned where the binding of the first ligand initiates a conformational transition that allows the second ligand to bind with much higher affinity at the opposite interface. This is followed by the third ligand, which binds with lesser affinity to one of the two already occupied interfaces, and in so doing, completes a global conformational transition that produces maximum inhibition of activity and an even lower affinity for the fourth ligand, excluding it completely. Thus, maximal inhibition is accomplished with less than maximal occupancy of effector sites through a mechanism that displays strong elements of both positive and negative cooperativity.     

Interaction of polyamines with fragments and whole molecules of yeast phenylalanine-specific transfer RNA

Binding of the polyamines spermidine (∼-+3) and spermine (∼-+4) to yeast tRNA^phe has been investigated by equilibrium dialysis under the same conditions used to study Mn²⁺-tRNA^phe interactions (Schreier & Schimmel, 1974). The polyamines bind to tRNA^phe in a co-operative and a non-co-operative phase, which is analogous to the behavior found with Mn²⁺. In the co-operative phase, the empirical index of co-operativity is somewhat greater for the polyamines, however. Binding constants for both the co-operative and non-co-operative phases are similar for Mn²⁺ and spermidine, and are strongest for spermine. Estimates of the total number of ligand binding sites indicate that these numbers are inversely proportional to the charge on the ligand for all three ligands. The interaction of polyamines with four large fragments of tRNA^phe shows no evidence for co-operativity. These results, together with recent kinetic studies, collectively suggest that polyamine binding to the co-operative sites is associated with tertiary structure formation and that polyamine and divalent metal ion interactions with tRNA occur by phenomenologically similar mechanisms, in spite of their structural diversity.     

Applications of isothermal titration calorimetry – the research and technical developments from 2011 to 2015

Isothermal titration calorimetry is a widely used biophysical technique for studying the formation or dissociation of molecular complexes. Over the last 5 years, much work has been published on the interpretation of isothermal titration calorimetry (ITC) data for single binding and multiple binding sites. As over 80% of ITC papers are on macromolecules of biological origin, this interpretation is challenging. Some researchers have attempted to link the thermodynamics constants to events at the molecular level. This review highlights work carried out using binding sites characterized using x‐ray crystallography techniques that allow speculation about individual bond formation and the displacement of individual water molecules during ligand binding and link these events to the thermodynamic constants for binding. The review also considers research conducted with synthetic binding partners where specific binding events like anion‐π and π‐π interactions were studied. The revival of assays that enable both thermodynamic and kinetic information to be collected from ITC data is highlighted. Lastly, published criticism of ITC research from a physical chemistry perspective is appraised and practical advice provided for researchers unfamiliar with thermodynamics and its interpretation. Copyright © 2016 John Wiley & Sons, Ltd.     

Theoretical Analysis of the Footprinting Experiment

Abstract

In the footprinting experiment, an end-radiolabeled DNA restriction fragment is subjected to digest by an endonuclease in the presence and absence of a ligand which alters the endonuclease cleavage rate at sites of ligand-DNA contact. The location of these sites, and the strength of the ligand binding, are then deduced from the measured concentrations of the different oligonucleotides produced by the digest. We analyze the experiment in terms of coupled kinetic equations which take into account the cutting rates of endonuclease for sites with ligand present and absent, and the rates of binding and dissociation of the ligand to a site. As long as the ligand concentration remains essentially constant (which occurs, for example, if digest is terminated early enough to assure that all fragments result from single cuts by the endonuclease), the oligonucleotide concentrations reflect only the ligand binding equilibrium constant (ratio of rate constants) and the cutting rates in the presence and absence of ligand. We also show how the measured oligonucleotide concentrations (from, e.g. an autoradiogram) can be used to deduce the ligand equilibrium binding constants for the various sites on the polymer.     

An analytical approach to the measurement of equilibrium binding constants: application to EGF binding to EGF receptors in intact cells measured by flow cytometry

In ligand binding studies, ligand depletion often limits the accuracy of the results obtained. This problem is approached by employing the simple observation that as the concentration of receptor in the assay is reduced, ligand depletion is also reduced. Measuring apparent K(D)'s of a ligand at multiple concentrations of receptor with extrapolation to infinitely low receptor concentration takes ligand depletion into account and, depending on the binding model employed, yields a K(D) within the defined limits of accuracy. We apply this analysis to the binding of epidermal growth factor (EGF) to the EGF receptor expressed in intact 32D cells, using a homogeneous fluorescein-labeled preparation of EGF and measuring binding by flow cytometry. Binding isotherms were carried out at varying cell densities with each isotherm fit to the generally applied model with two independent binding sites. Examination of the variation in the K(D)'s versus cell density yields a high-affinity site that accounts for 18% of the sites and a lower affinity site that accounts for the remainder. However, further examination of these data suggests that while consistent with each individual isotherm, the simple model of two independent binding sites that is generally applied to EGF binding to the EGF receptor is inconsistent with the changes in the apparent K(D)'s seen across varying cell densities.     

Comparison between the kinetics of heterogeneous and sequentially co-operative binding systems

The kinetics of ligand binding to a dimer displaying anticooperative interactions is analysed and compared with the kinetics of binding to two classes of independent sites. Both systems are characterized by a bi-exponential kinetics. However, the relation between the coefficients of these exponentials and the concentration of ligand is linear in case of sites heterogeneity and hyperbolic (parabolic in some cases) for a co-operative dimer. The pre-exponential factors are always negative in case of sites heterogeneity and their modulus increases monotonically as a hyperbolic function of the ligand concentration. In cases of anticooperative interaction, one of the pre-exponential factors can be positive and the modulus can change biphasically as a function of the concentration of ligand. The detailed study of binding kinetics at different ligand concentrations provides a potential tool to discriminate between binding sites heterogeneity and negative co-operativity.     

The binding of copper ions to copper-free bovine superoxide dismutase. Copper distribution in protein samples recombined with less than stoicheiometric copper ion/protein ratios.

Samples of superoxide dismutase containing less than stoicheiometric amounts of Cu2+ were obtained by either partial re-addition of Cu2+ to the Cu2+-free protein or partial removal of Cu2+ by controlled CN-treatment. In these samples the distribution of the metal between the two identical sites on the two subunits was studied by quantitative gel electrophoresis and found to be statistical only in the process of copper removal by CN-. In the other case the distribution fits a model of co-operative interaction between the two sites, where the sites are equivalent for the binding of the first Cu2+ ion, but the occupation of the first site lowers the activation energy of the binding of the second Cu2+ ion. This indicates that binding of Cu2+ ion at its site on one subunit brings about conformational changes that facilitate Cu2+ binding on the other subunit. These results may relate to possible intersubunit interactions during the catalytic activity.     

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.     

Designing cyclopentapeptide inhibitor as potential antiviral drug for dengue virus ns5 methyltransferase

NS5 methyltransferase (Mtase) has a crucial role in the replication of dengue virus. There are two active sites on NS5 Mtase i.e., SAM and RNA-cap binding sites. Inhibition of the NS5 Mtase activity is expected to prevent the propagation of dengue virus. This study was conducted to design cyclic peptide ligands as enzyme inhibitors of dengue virus NS5 Mtase through computational approach. Cyclopentapeptides were designed as ligand of SAM binding site as much as 1635 and 736 cyclopentpeptides were designed as ligand of RNA-cap binding site. Interaction between ligand and NS5 Mtase has been conducted on the Docking simulation. The result shows that cyclopentapeptide CTWYC was the best peptide candidate on SAM binding site, with estimated free binding energy -30.72 kca/mol. Cyclopentapeptide CYEFC was the best peptide on RNA-cap binding site with estimated free binding energy -22.89 kcal/mol. Both peptides did not have tendency toward toxicity properties. So it is expected that both CTWYC and CYEFC ligands could be used as a potential antiviral drug candidates, which can inhibit the SAM and RNA-cap binding sites of dengue virus NS5 Mtase.     

A theoretical approach to the binding of amphipathic molecules to globular proteins.

1. A theory based on a multiple equilibrium model with stoicheiometric binding constants has been formulated. It is applicable to the interaction of amphipathic molecules with charged macromolecules. 2. The theory has been applied to the binding of sodium n-dodecyl sulphate to ribonuclease A, beta-lactoglobulin and bovine serum albumin. 3. Over the ranges of surfactant concentration where binding is non-co-operative and co-operative, the experimental data can be satisfactorily fitted with energy and co-operatively parameters which are of comparable magnitude for the three globular proteins. 4. The results imply that the energy of interaction of sodium n-dodecyl sulphate with the proteins is equivalent to the formation of approximately four CH2 hydrophobic bonds.