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.     

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.     

Determination of the volume changes induced by ligand binding to heat shock protein 90 using high-pressure denaturation

The volume changes accompanying ligand binding to proteins are thermodynamically important and could be used in the design of compounds with specific binding properties. Measuring the volumetric properties could yield as much information as the enthalpic properties of binding. Pressure-based methods are significantly more laborious than temperature methods and are underused. Here we present a pressure shift assay (PressureFluor, analogous to the ThermoFluor thermal shift assay) that uses high pressure to denature proteins. The PressureFluor method was used to study the ligand binding thermodynamics of heat shock protein 90 (Hsp90). Ligands stabilize the protein against pressure denaturation, similar to the stabilization against temperature denaturation. The equations that relate the ligand dosing, protein concentration, and binding constant with the volumes and compressibilities of unfolding and binding are presented.     

Study of ligand-receptor binding using SPME: investigation of receptor, free, and total ligand concentrations

The theoretical background and practical approaches for studying ligand-receptor (protein) binding by solid phase microextraction (SPME) are investigated, along with methods for simultaneous calculation of receptor, free, and total ligand concentrations. With the introduction of new extraction phases (restricted access materials, molecularly imprinted polymers, and immobilized antibodies), SPME allows better separation of small molecules of ligand from larger molecules of receptor, and improved accuracy. This sample preparation method based on nonexhaustive extraction is well suited as a general method to study and quantify systems involving multiple equilibriums, with significant advantages over currently used methods. SPME was used previously for the determination of protein binding constants, but only with conventional extraction phases and in simple cases, with a 1:1 combination ratio between the ligand and the receptor or when negligible depletion conditions were met. The new theoretical approach presented in this study allows the quantification of any binding equilibrium, regardless of the extent of depletion. Restricted-access particles are used as extraction phase, and if the amount of receptor is limited, selected regions of the binding curve may be obtained using a single sample, with a volume as low as 10 muL. The equations developed here are simple and independent of the analytical method used for the quantification of the amount of ligand. Three different practical approaches are presented: the method of multiple standard solutions, the method of successive extractions from the same sample and the method of successive additions to the same sample. The usefulness of this novel approach is demonstrated by using it to determine the binding parameters of some selected drugs to human serum albumin. These parameters are subsequently used to calculate albumin, free drug, and total drug concentrations from unknown mixtures. The results are in good agreement with previously published data. Quantification of the amount of ligand extracted by SPME is done by liquid chromatography coupled with tandem mass spectrometry.     

The exponential model for a regulatory enzyme: Its extension to describe the binding of two ligands

The exponential model for a regulatory enzyme (Ainsworth, 1977a) is extended to deal explicitly with the presence in solution of a second ligand. This is achieved by introducing exponential interaction coefficients which respectively describe how the affinity of the free and bound forms of the protein for the ligand depend on its fractional saturation by the second ligand. The basic equations, so derived, are applied to binding experiments where the ligands bind independently or competitively and to rate experiments where the ligands represent two substrates or one substrate and a modifier which may be either competitive or non-competitive in type. The conditions required to display linkage between the binding of the two ligands are established and it is also shown that rate data may display a maximum as one ligand concentration is varied at a fixed concentration of the other. The equations that are derived are tested by application to experimental data and the conditions that have to be met to justify such an application are discussed.     

Determination of lectin-sugar binding constants by microequilibrium dialysis coupled with high performance liquid chromatography

We used high performance liquid chromatography to determine the concentrations of free ligands after equilibrium dialysis to examine lectin-sugar interactions. The binding of p-nitrophenyl 1-thio-alpha-mannoside, p-nitrophenyl N-acetyl-1-thio-beta-glucosaminide, and the pyridylamino derivative of Man6GlcNAc2 to concanavalin A and Triticum vulgaris lectin was examined. The binding constant, Ka, and the concentration of total binding sites, [L]t, were calculated from the trace amounts of sugars and lectins using the equation, [S]/[LS] = 1/Ka[L]t + [S]/[L]t, where [S] is the concentration of free ligand and [LS] the concentration of bound ligand.     

Cytochrome P-450-dependent 14 alpha-demethylation of lanosterol in Candida albicans.

Analysis of receptor-ligand binding characteristics can be greatly hampered by the presence of non-specific binding, defined as low-affinity binding to non-receptor domains which is not saturable within the range of ligand concentrations used. Conventional binding analyses, e.g. according to the methods described by Scatchard or Klotz, relate the amount of specific receptor-ligand binding to the concentration of free ligand, and therefore require assumptions on the amount of non-specific binding. In this paper a method is described for determining the parameters of specific receptor-ligand interaction which does not require any assumption or separate determination of the amount of non-specific binding. If the concentration of labelled free ligand is constant, a plot of Fu/(B0*-B*) versus Fu yields a linear relationship, in the case of a single receptor class, in which Fu is the concentration of unlabelled free ligand, B0* is the total amount of labelled bound ligand in the absence of unlabelled ligand and B* is the total amount of labelled bound ligand in the presence of an unlabelled ligand concentration Fu; all of these data are readily obtained from binding studies. This linear relationship holds irrespective of the amount of non-specific binding, and the values for receptor density, ligand dissociation constant and a constant for non-specific binding can be readily obtained from it. If the concentration of labelled free ligand is not a constant for all data points, data are first converted according to a straightforward normalization procedure to permit the use of this relationship. The presence of multiple receptor classes with dissociation constants in the range of the ligand concentrations used results in a negative deviation from this linearity, and therefore the presence of multiple receptor classes can be discriminated unequivocally from non-specific binding. Both theoretical and practical advantages of the present method are described. The method, which will be referred to as the linear subtraction method, is illustrated using the binding of tumour promoters and polypeptide growth factors to their specific cellular receptors.     

Adsorption of cadmium ion and gallium ion to immobilized metallothionein fusion protein

A fusion protein made from maltose binding protein (pmal) and human metallothionein (MT) was expressed using E. coli. The purified recombinant protein (pmal-MT) was immobilized on Chitopearl resin, and characteristics of pmal-MT for metal binding were evaluated. As expected from the tertiary structure of metallothionein, the pmal-MT ligand adsorbed 12.1 cadmium molecules per one molecule of the ligand at pH 5.2. The pmal-MT ligand also bound 26.6 gallium molecules per one molecule of the ligand at pH 6.5. Neither cadmium ion nor gallium ion bound to a control protein bovine serum albumin (BSA). Adsorption isotherms for both ions were correlated by Langmuir-type equations. Two types of binding sites have been elucidated on the basis of HSAB (hard and soft acid and base) theory. It was suggested that gallium ion specifically binds to amino acid residues containing oxygen and nitrogen atoms, while cadmium ion binds to specific binding sites formed by multiple cysteine residues. The pmal-MT ligand bound these metals in the concentration range of 0.2-1.0 mM, and the bound metal ions could be eluted under relatively mild conditions (pH 2.0). The pmal-MT Chitopearl resin was stable and could be used repeatedly without loss of binding activity. Thus, this new ligand would be useful for recovery of toxic heavy metals and/or valuable metal ions from various aqueous solutions.     

The reversible cross-linking of receptors by ligands: theory for the prediction of binding responses

The general concept of receptor aggregation through the action of a cross-linking ligand is considered, three models being examined in detail. In two, ligand self-interaction leads to the formation of receptor cross-links whereas, in the third, receptor cross-links are formed through a single ligand bridge. Binding equations in closed form are formulated for each case and are shown to predict both concave and convex Scatchard plots in binding studies conducted with such systems. The significant point which emerges is that while each of the systems gives rise to very different types of binding responses, the form of the binding response is always strongly dependent on the total concentration of receptor in the system.     

Grand canonical Monte Carlo molecular and thermodynamic predictions of ion effects on binding of an oligocation (L8+) to the center of DNA oligomers.

Grand canonical Monte Carlo (GCMC) simulations are reported for aqueous solutions containing excess univalent salt (activities a +/- = 1.76-12.3 mM) and one of the following species: an octacationic rod-like ligand, L8+; a B-DNA oligomer with N phosphate charges (8 < or = N < or = 100); or a complex resulting from the binding of L8+ at the center of an N-mer (24 < or = N < or = 250). Simplified models of these multiply charged species are used in the GCMC simulations to predict the fundamental coulombic contributions to the following experimentally relevant properties: 1) the axial distance over which ligand binding affects local counterion concentrations at the surface of the N-mer; 2) the dependence on N of GCMC preferential interaction coefficients, gamma 32MC identical to delta C3/delta C2l a +/-, T, where C3 and C2 are, respectively, the molar concentrations of salt and the multiply charged species (ligand, N-mer or complex); and 3) the dependence on N of SaKobs identical to d in Kobs/d in a +/- = delta (magnitude of ZJ + 2 gamma 32J), where Kobs is the equilibrium concentration quotient for the binding of L8+ to the center of an N-mer and delta denotes the stoichiometric combination of terms, each of which pertains to a reactant or product J having magnitude of ZJ charges. The participation of electrolyte ions in the ligand binding interaction is quantified by the magnitude of SaKobs, which reflects the net (stoichiometrically weighted) difference in the extent of thermodynamic binding of salt ions to the products and reactants. Results obtained here from GCMC simulations yield a picture of the salient molecular consequences of binding a cationic ligand, as well as thermodynamic predictions whose applicability can be tested experimentally. Formation of the central complex is predicted to cause a dramatic reduction in the surface counterion (e.g., Na+) concentration over a region including but extending well beyond the location of the ligand binding site. For binding a cationic ligand, SaKobs is predicted to be negative, indicating net electrolyte ion release in the binding process. At small enough N, -SaKobs is predicted to decrease strongly toward zero with decreasing N. At intermediate N, -SaKobs appears to exceed its limiting value as N-->infinity.     

Folding energetics of ligand binding proteins. I. Theoretical model

Heat capacity curves as obtained from differential scanning calorimetry are an outstanding source for molecular information on protein folding and ligand-binding energetics. However, deconvolution of C(p) data of proteins in the presence of ligands can be compromised by indeterminacies concerning the correct choice of the statistical thermodynamic ensemble. By convent, the assumption of constant free ligand concentration has been used to derive formulae for the enthalpy. Unless the ligand occurs at large excess, this assumption is incorrect. Still the relevant ensemble is the grand canonical ensemble. We derive formulae for both constraints, constancy of total or free ligand concentration and illustrate the equations by application to the typical equilibrium Nx <=> N + x <=> D + x. It is demonstrated that as long as the thermodynamic properties of the ligand can be completely corrected for by performing a reference measurement, the grand canonical approach provides the proper and mathematically significantly simpler choice. We demonstrate on the two cases of sequential or independent ligand-binding the fact, that similar binding mechanisms result in different and distinguishable heat capacity equations. Finally, we propose adequate strategies for DSC experiments as well as for obtaining first estimates of the characteristic thermodynamic parameters, which can be used as starting values in a global fit of DSC data.     

A model for the salt effect on adsorption equilibrium of basic protein to dye-ligand affinity adsorbent

A model describing the salt effect on adsorption equilibrium of a basic protein, lysozyme, to Cibacron Blue 3GA-modified Sepharose CL-6B (CB-Sepharose) has been developed. In this model, it is assumed that the presence of salt causes a fraction of dye-ligand molecules to lodge to the surface of the agarose gel, resulting from the induced strong hydrophobic interaction between dye ligand and agarose matrix. The salt effect on the lodging of dye-ligand is expressed by the equilibrium between salt and dye-ligand. For the interactions between protein and vacant binding sites, stoichiometric equations based either on cation exchanges or on hydrophobic interactions are proposed since the CB dye can be regarded as a cation exchanger contributed by the sulfonate groups on it. Combining with the basic concept of steric mass-action theory for ion exchange, which considers both the multipoint nature and the macromolecular steric shielding of protein adsorption, an explicit isotherm for protein adsorption equilibrium on the dye-ligand adsorbent is formulated, involving salt concentration as a variable. Analysis of the model parameters has yielded better understanding of the mechanism of salt effects on adsorption of the basic protein. Moreover, the model predictions are in good agreement with the experimental data over a wide range of salt and ligand concentrations, indicating the predictive nature of the model.     

A novel spectroscopic titration method for determining the dissociation constant and stoichiometry of protein-ligand complex.

We offer a new titration protocol for determining the dissociation constant and binding stoichiometry of protein-ligand complex, detectable by spectroscopic methods. This approach neither is limited to the range of protein or ligand concentrations employed during titration experiment nor relies on precise determinations of the titration "endpoint," i.e., the maximal signal changes upon saturation of protein by ligand (or vice versa). In this procedure, a fixed concentration of protein (or ligand) is titrated by increasing volumes of a stock ligand (or protein) solution, and the changes in the spectroscopic signal are recorded after each addition of the titrant. The signal for interaction between protein and ligand first increases, reaches a maximum value, and then starts decreasing due to dilution effect. The volume of the titrant required to achieve the maximum signal changes is utilized to calculate the dissociation constant and the binding stoichiometry of the protein-ligand complex according to the theoretical relationships developed herein. This procedure has been tested for the interaction of avidin with a chromophoric biotin analogue, 2-(4'-hydroxyazobenzene)benzoic acid by following the absorption signal of their interaction at 500 nm. The widespread applicability of this procedure to protein-ligand complexes detected by other spectroscopic techniques and its advantages over conventional methods are discussed.     

A kinetic model of the interaction of stable GTP analogs with a system of opioid receptors

The effect of a stable GTP analog, GppNp, on the agonist binding to rat brain opioid receptors was studied. It was shown that the nucleotide used at low concentrations activates, and at high concentrations inhibits the ligand interaction with the mu-, delta- and kappa-receptors. The inhibiting effect of GppNp on the formation of the morphine and D-Ala2, D-Leu5-enkephalin complexes with high affinity opioid receptor binding sites is due to the decrease of the ligand affinity for the corresponding sites. A kinetic model of the GppNp effect on high affinity binding sites stipulating that in the course of nucleotide binding the GTP-binding protein dissociates and that the N-protein alpha-subunits thereby formed are liberated into the surrounding solution, was proposed. It was demonstrated that GppNp can modulate the properties of opioid receptors in the absence of the ligand in a system and the inhibiting effect of GppNp depends on the concentration of membrane preparation.     

A dynamic dialysis method for studying protein-ligand binding using chromatographic theory

A new dynamic dialysis method has been developed for studying protein-ligand binding phenomena. The method depends on analysis of the elution pattern of ligand in a single dialyzing process where the ligand concentration in the sample compartment changes greatly with time. The dialyzer is composed of a long, narrow chamber (the sample compartment) between two sheets of semipermeable membrane and two outside chambers (the sink compartment) connected as a single path. Eluting buffer flows in the sink compartment to exchange the ligand with the solution in the sample compartment. Therefore, the ligand concentration gradient in the sink compartment is in the longitudinal direction. The mathematical expressions to analyze the experimental data were derived from a modified theory of chromatography. Examination of the binding of sulfanilamide to bovine serum albumin using this method shows that these equations are valid for use in studying protein-ligand binding.     

Relative ligand binding to small or large aggregates measured by scanning correlation spectroscopy.

Cell surface receptors transduce signals, required to produce cellular activity, that may be mediated by ligand-induced receptor aggregation. Several receptor systems exhibit both low and high ligand affinities and some models of receptor activation associate receptor clusters with high or low ligand binding affinity. In the present work succinyl concanavalin A, which binds with both high and low affinity to receptors, was studied on 3T3 Swiss mouse fibroblasts, where preaggregation of receptors has been postulated. Scanning fluorescence correlation spectroscopy measurements were used to determine the relationship between the degree of ligand binding and the state of receptor aggregation. Correlation analysis of fluorescence fluctuations across the cell surface reveal that the variance of the fluctuations (quantitated by g[0]) increased when the ligand concentration was varied from 0.33 to 67 mg/L. The g(0) values reached a plateau at concentrations greater than approximately 10 mg/L. These data are incompatible with homogeneous receptor distributions or equal affinity receptor binding but are compatible with a partly aggregated receptor system with high affinity binding to small aggregates, and low affinity binding to large aggregates. Computer simulated scanning fluorescence correlation spectroscopy experiments confirm that background fluorescence from the cell does not account for the experimentally observed effects.     

In vitro plasma protein binding and aqueous aggregation behavior of astaxanthin dilysinate tetrahydrochloride

The tetrahydrochloride salt of astaxanthin di-L-lysinate (lys(2)AST) is a highly water-dispersible astaxanthin-amino acid conjugate, with an aqueous dispersibility of > or = 181.6 mg/mL. The statistical mixture of stereoisomers has been well characterized as an aqueous-phase superoxide anion scavenger, effective at micromolar (microM) concentrations. In the current study, the aqueous aggregation behavior and in vitro plasma protein binding [with fatty-acid-free human serum albumin (HSA) and alpha(1)-acid glycoprotein (AGP)] were investigated with a suite of techniques, including circular dichroism (CD) and UV-vis spectroscopy, ultrafiltration, competitive ligand displacement, and fluorescence quenching. Induced CD bands obtained in Ringer buffer solution of HSA demonstrated high affinity monomeric binding of the compound at low ligand per protein (L/P) ratios (in aqueous solution alone the carotenoid molecules formed card-pack aggregates). The binding constant ( approximately 10(6)M(-1)) and the binding stoichiometry (approximately 0.2 per albumin molecule) were calculated from CD titration data. CD displacement and ultrafiltration experiments performed with marker ligands of HSA indicated that the ligand binding occurred at a site distinct from the main drug binding sites of HSA (i.e., Sites I and II). At intermediate L/P ratios, both monomeric and aggregated ("chirally complexed") binding occurred simultaneously at distinct sites of the protein. At high L/P ratios, chiral complexation predominantly occurred on the asymmetric protein template. The tentative location of the chirally-complexed aggregation on the HSA template was identified as the large interdomain cleft of HSA, where carotenoid derivatives have been found to bind previously. Only weak binding to AGP was observed. These results suggest that parenteral use of this highly potent, water-dispersible astaxanthin-amino acid conjugate will result in plasma protein association, and plasma protein binding at sites unlikely to displace fatty acids and drugs bound at well-characterized binding sites on the albumin molecule.