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 netropsin-DNA binding constants from footprinting data

A theory for deriving drug-DNA site binding constants from footprinting data is presented. Plots of oligonucleotide concentration, as a function of drug concentration, for various cutting positions on DNA are required. It is assumed that the rate of cleavage at each nucleotide position is proportional to the concentration of enzyme at that nucleotide and to the probability that the nucleotide is not blocked by drug. The probability of a nucleotide position not being blocked is calculated by assuming a conventional binding equilibrium for each binding site with exclusions for overlapping sites. The theory has been used to evaluate individual site binding constants for the antiviral agent netropsin toward a 139 base pair restriction fragment of pBR-322 DNA. Drug binding constants, evaluated from footprinting data in the presence of calf thymus DNA and poly(dGdC) as carrier and in the absence of carrier DNA, were determined by obtaining the best fit between calculated and experimental footprinting data. Although the strong sites on the fragment were all of the type (T.A)4, the value of the binding constant was strongly sequence dependent. Sites containing the dinucleotide sequence 5'-TA-3' were found to have significantly lower binding constants than those without this sequence, suggesting that an adenine-adenine clash produces a DNA structural alteration in the minor groove which discourages netropsin binding to DNA. The errors, scope, and limitations associated with the method are presented and discussed.     

Effects of ligand size on pH and organic phosphate-dependent affinity changes in carp hemoglobin as measured by isonitrile binding

The equilibria of the binding of methyl and ethyl isonitrile to carp hemoglobin have been measured at three pH values in the presence and absence of inositol hexaphosphate. The binding of methyl isonitrile is characterized by a higher overall dissociation constant, C1/2, and a higher Hill coefficient, n, than that of the ethyl derivative. The former is consistent with the greater hydrophobicity of ethyl isonitrile, and the latter is probably due to a greater intrinsic difference or heterogeneity in the binding affinities of the alpha- and beta-chains for the larger ligand. Changes in log C1/2 which result from alterations in pH or addition of organic phosphate are the same for both ligands within experimental error. This result is not consistent with affinity changes being the result of steric interactions between the protein and the ligand. At pH 6 in the presence of inositol hexaphosphate, equilibrium parameters estimated from overall rates of ligand binding and dissociation are in good agreement with direct equilibrium measurements. This is consistent with the protein being in a low-affinity, T-like state even when saturated with ligand under these conditions, resulting in a loss of cooperativity in ligand binding. At high pH, ligand binding remains cooperative, as evidenced by n values greater than unity, a general lack of agreement between measured equilibrium parameters and those estimated from overall kinetic constants, and differences in the kinetics of ligand binding as observed by rapid-mixing and flash photolysis techniques. Thus, the deoxygenated state of carp hemoglobin at high pH does not appear to be a good model of a deoxygenated R quaternary structural state.     

Modulation of glutamate-induced uncompetitive blocker binding to the NMDA receptor by temperature and by glycine

The effect of temperature on the binding of [3H]-N-[1-(2-thienyl)cyclohexyl]piperidine [( 3H]TCP) to the ion channel of the N-methyl-D-aspartate (NMDA) receptors was studied in washed rat brain-cortex membranes. Raising the temperature from 5 to 33 degrees C resulted in a significant increase in the association rates of [3H]TCP binding measured in the presence of 1 microM glutamate and 1 microM glycine, but was less effective in the absence of the added agonists. No such effects of temperature on the dissociation rates of [3H]TCP-receptor complexes were observed. In the absence of agonists, neither the association nor the dissociation binding components varied with temperature, suggesting a diffusion-controlled limitation of access of the ligand to its site within the nonactivated NMDA receptor. No evidence was found for a temperature-dependent change in the density of [3H]TCP binding sites or for heterogeneity of [3H]TCP binding sites associated with the NMDA receptor, even though when approaching equilibrium the binding kinetics in the presence of glutamate and glycine deviated from an ordinary bimolecular reaction scheme. The data were fitted instead to a two-exponent binding function, comprising the sum of a fast and a slow binding component. Their corresponding time constants exhibited an increase with temperature, and the increase of each one was correlated significantly with the corresponding decrease in the equilibrium binding constant; however, there was no temperature-related change in the relative proportions of the two components, with the fast binding component (alpha) accounting for 50-70% of the site population.(ABSTRACT TRUNCATED AT 250 WORDS)     

Study of strong to ultratight protein interactions using differential scanning calorimetry

Data from differential scanning calorimetry (DSC) may be used to estimate very large binding constants that cannot be conveniently measured by more conventional equilibrium techniques. Thermodynamic models have been formulated to describe interacting systems that involve either one thermal transition (protein-ligand) or two thermal transitions (protein-protein) and either 1:1 or higher binding stoichiometry. Methods are described for obtaining binding constants and heats of binding by two different methods: calculation or simulation fitting of data. Extensive DSC data on 2'CMP binding to RNase are presented and analyzed by the two methods. It is found that the methods agree when binding sites are completely saturated, but substantial errors arise in the calculation method when site saturation is incomplete and the transition of liganded molecules overlaps that of unliganded molecules. This arises primarily from an inability to determine TM (i.e., the temperature where concentrations of folded and unfolded protein are equal) under weak-binding conditions. Results from simulation show that the binding constants and heats of binding from the DSC method agree quantitatively with corresponding estimates obtained from equilibrium methods when extrapolated to the same temperature. It was also found from the DSC data that the binding constant decreases with increasing concentration of ligand, which might arise from nonideality effects associated with dimerization of 2'CMP. Simulations show that the DSC method is capable of estimating binding constants for ultratight interactions up to perhaps 10(40) M-1 or higher, while most equilibrium methods fail well below 10(10) M-1. DSC data from the literature on a number of interacting systems (trypsin-soybean trypsin inhibitor, trypsin-ovomucoid, trypsin-pancreatic trypsin inhibitor, chymotrypsin-subtilisin inhibitor, subtilisin BPN-subtilisin inhibitor, RNase S protein-RNase S peptide, avidin-biotin, ovotransferrin-Fe3+, superoxide dismutase-Zn2+, alkaline phosphatase-Zn2+, and assembly of regulatory and catalytic subunits of aspartate transcarbamoylase) were analyzed by simulation fitting or by calculation. Apparent single-site binding constants ranged from ca. 10(5) to 10(20) M-1, while the interaction constant for assembly of aspartate transcarbamoylase was estimated as 10(37) in molarity units. For most of these systems, the DSC interaction constants compared favorably with other literature estimates, for some it did not for reasons unknown, while for still others this represented the first estimate. Simulations show that for proteins having two binding sites for the same ligand within a single cooperative unit, ligand rearrangement will occur spontaneously during a DSC scan as the transition temperature of the unliganded protein is approached.(ABSTRACT TRUNCATED AT 400 WORDS)     

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.     

Kinetics of ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor. I. A computer simulation of the influence of mass transport.

The influence of mass transport on ligand binding to receptor immobilized in a polymer matrix, as detected with an evanescent wave biosensor, was investigated. A one-dimensional computer model for the mass transport of ligand between the bulk solution and the polymer gel and within the gel was employed, and the influence of the diffusion coefficient, the partition coefficient, the thickness of the matrix, and the distribution of immobilized receptor were studied for a variety of conditions. Under conditions that may apply to many published experimental studies, diffusion within the matrix was found to decrease the overall ligand transport significantly. For relatively slow reactions, small spatial gradients of free and bound ligand in the gel are found, whereas for relatively rapid reactions strong inhomogeneities of ligand within the gel occur before establishment of equilibrium. Several types of deviations from ideal pseudo-first-order binding progress curves are described that resemble those of published experimental data. Extremely transport limited reactions can in some cases be fitted with apparently ideal binding progress curves, although with apparent reaction rates that are much lower than the true reaction rates. Nevertheless, the ratio of the apparent rate constants can be semiquantitatively consistent with the true equilibrium constant. Apparently "cooperative" binding can result from high chemical on rates at high receptor saturation. Dissociation in the presence of transport limitation was found to be well described empirically by a single or a double exponential, with both apparent rate constants considerably lower than the intrinsic chemical rate constant. Transport limitations in the gel can introduce many generally unknown factors into the binding progress curve. The simulations suggest that unexpected deviations from ideal binding progress curves may be due to highly transport influenced binding kinetics. The use of a thinner polymer matrix could significantly increase the range of detectable rate constants.     

Mathematical analysis of ligand-induced monomerization and dimerization in the monomer dimer equilibrium of proteins. Application to D-amino acid oxidase.

We have mathematically analyzed ligand-induced monomerization and dimerization in a protein monomer-dimer equilibrium system, in which the monomer has one and the dimer two binding sites. These dimer sites have the same binding constants for the first ligand but may cooperatively interact when one of them is occupied by a ligand molecule. In this system, the apparent dimerization constant and the apparent molecular weight are functions of free ligand concentration, and depend on the intrinsic binding constants of the ligand molecule to the monomer and the dimer. The behavior of these functions is classified into 17 cases according to the values of the three intrinsic binding constants, and some calculated examples are shown graphically for selected parameters. The theory was also applied to D-amino acid oxidase [EC 1.4.3.3], a flavoprotein, and the pH dependence of the apparent dimerization constant and the apparent molecular weight in the presence of ligand, p-aminobenzoate, were studied theoretically using parameters obtained in our previous experiments (5).     

Competitive inhibition of specific steroid-protein binding: Practical use of relative competition ratios for the derivation of equilibrium inhibition constants

The relative competition ratio (RCR) is widely used to express the relative affinities of inhibitor(s) and agonist for a binding protein. The RCR is not a constant; it depends on the concentrations of binding sites and of radioactive hormone, and on the presence of nonsaturable binding component(s). According to the assay conditions used, equating the RCR value to the ratio Ka/Ki of the equilibrium association constants of agonist and inhibitor can lead to large errors. In the case of homogeneous non-interacting binding sites, simple correction factors permit one to calculate the ratio Ka/Ki from the measured RCR value. Calculations are given for the eventual contribution of nonsaturable binding components. Corrections can be unnecessary under well defined experimental conditions, where the bound fraction of hormone in absence of competitor is reduced by using a large dilution of binding protein and/or an increased concentration of radioactive hormone.     

Interaction of effecting ligands with lac repressor and repressor-operator complex.

The equilibrium association constants for the binding of a wide variety of effecting ligands of the lac repressor were measured by equilibrium dialysis. Also, detailed investigations of the apparent rate of dissociation of repressor-operator comples as a function of ligand concentration were carried out for several inducers and anti-inducers. The affinity of repressor-ligand comples for operator DNA was evaluated from the specific rate constants at saturating concentrations of effecting ligand. By fitting the experimental data depicting the functional dependence of the rate of dissociation upon ligand concentrations to calculated curves, assuming simple models of the induction mechanism, the equilibrium association constant for the binding of effecting ligand to repressor-operator comples was determined. Inducers reduce the affinity of lac repressor for operator DNA by a factor of approximately 1000 under standard conditions; the extent of destabilization depends on Mg2+ ion concentration. Anti-inducers increase the affinity of repressor for operator at most a factor of five. Only one neutral ligand, which binds to repressor without altering the stability of repressor-operator comples, was found. No homotropic or heterotropic interactions in the binding of effecting ligands either to repressor or to repressor-operator complex are evident.     

Determination of an antibody-antigen binding constant by enzyme immunoassay and a theory for analysis of competitive binding of two ligands to heterogeneous receptor

A method for determining antigen-antibody binding constants by using enzyme-labeled antigens has been developed. In the measurement, enzyme-labeled and unlabeled antigens (Ag* and Ag) were allowed to compete in binding to the antibody (Ab) under conditions where Ag* much less than Ab much less than Ag. The data were analyzed according to a new theory developed for the analysis of competitive binding of two ligands to a heterogeneous receptor. The theory indicates that the binding degree of a labeled ligand measured at various concentrations of the receptor can be used to prepare a standard curve relating the binding degree of the labeled ligand and the average of the concentrations of the free receptor components which are in binding equilibrium with another unlabeled ligand. For homogeneous receptors, the method gives usual binding constants for the unlabeled ligand, but for heterogeneous receptors, it gives a new type of average binding constant for the unlabeled ligand in which the contribution of each receptor component is amplified in proportion to its affinity against the labeled ligand. This average binding constant was named the "affinity-average binding constant." A rabbit anti-blasticidin S (BLS) antiserum analyzed by the present method using beta-galactosidase-labeled BLS as the labeled ligand was found to be fairly homogeneous with respect to the affinity and to have a binding constant of 1.48 +/- 0.24 (S.D.) X 10(8) M-1 for unlabeled BLS.     

Direct measurement of the weak interactions between a mouse Fc receptor (Fc gamma RII) and IgG1 in the absence and presence of hapten: a total internal reflection fluorescence microscopy study.

Total internal reflection fluorescence microscopy (TIRFM) has been used to directly measure the weak dissociation constants of IgG with a mouse IgG receptor (moFc gamma RII) that has been purified and reconstituted into substrate-supported planar membranes. Dissociation constants were measured for three different mouse monoclonal anti-dinitrophenyl (DNP) IgG1 antibodies and for polyclonal mouse IgG, in the absence and presence of saturating amounts of hapten (DNP-glycine). The dissociation constant for polyclonal mouse IgG was 3 microM, which agrees well with previous results. The dissociation constants for the three monoclonal antibodies with moFc gamma RII ranged from 2 microM to 3 microM and were not statistically different, suggesting that changes in moFc gamma RII dissociation constants which may exist within the IgG1 subclass are less than the error of the TIRFM measurements (approximately 20%). The measured IgG1-moFc gamma RII dissociation constants were not different for individual monoclonal antibodies in the absence or presence of saturating concentrations of DNP-glycine, directly showing that possible allosteric changes which might occur upon hapten binding and affect the equilibrium characteristics of Fc receptor binding are small. This work demonstrates a new approach for quantitatively examining the effects of solution components on weak receptor-ligand interactions.     

Co-operativity and enzymatic activity in polymer-activated enzymes. A one-dimensional piggy-back binding model and its application to the DNA-dependent ATPase of DNA gyrase

The binding of a ligand to a one-dimensional lattice in the presence of a second ("rider") ligand, which binds only to the first ligand (piggy-back binding), is studied. A model derived from this study is used to analyze the effects of co-operativity on the reaction rates of enzymes activated by polymeric cofactors that provide multiple binding sites for the enzyme. It is found that in the presence of strong co-operativity, the steady-state reaction rates of polymer-activated enzymes can be very different from the Michaelis-Menten paradigm. By adjusting the co-operativity parameters and the binding constants of the ligands, the model can generate apparent auto-catalytic enhancement by substrates at low substrate concentrations and apparent substrate inhibition at high substrate concentrations. The model is shown to be able to explain the differences in the rates of ATP hydrolysis by DNA gyrase in the presence of long versus short DNA molecules and in the presence of long DNA molecules at different gyrase to DNA ratios.     

DESIGN: computerized optimization of experimental design for estimating Kd and Bmax in ligand binding experiments. I. Homologous and heterologous binding to one or two classes of sites

We have developed a versatile computer program for optimization of ligand binding experiments (e.g., radioreceptor assay system for hormones, drugs, etc.). This optimization algorithm is based on an overall measure of precision of the parameter estimates (D-optimality). The program DESIGN uses an exact mathematical model of the equilibrium ligand binding system with up to two ligands binding to any number of classes of binding sites. The program produces a minimal list of the optimal ligand concentrations for use in the binding experiment. This potentially reduces the time and cost necessary to perform a binding experiment. The program allows comparison of any proposed experimental design with the D-optimal design or with assay protocols in current use. The level of nonspecific binding is regarded as an unknown parameter of the system, along with the affinity constant (Kd) and binding capacity (Bmax). Selected parameters can be fixed at constant values and thereby excluded from the optimization algorithm. Emphasis may be placed on improving the precision of a single parameter or on improving the precision of all the parameters simultaneously. We present optimal designs for several of the more commonly used assay protocols (saturation binding with a single labeled ligand, competition or displacement curve, one or two classes of binding sites), and evaluate the robustness of these designs to changes in parameter values of the underlying models. We also derive the theoretical D-optimal design for the saturation binding experiment with a homogeneous receptor class.     

Nature of protamine-DNA complexes. A special type of ligand binding co-operativity

The mode of protamine binding to DNA double helices has been analyzed for the example of clupein Z from herring and DNA samples from bacteriophages lambda and PM2 by measurements of light-scattering intensities, ultracentrifugation and kinetics. The light-scattering intensity of DNA increases co-operatively at a threshold clupein concentration suggesting co-operative binding of clupein to double helices. These data are first analyzed in terms of a model with a transition at a threshold degree of binding. The parameters resulting from this analysis appear to be reasonable, but are shown to be in contrast with data on the absolute degree of clupein binding to DNA obtained by centrifugation experiments. An analysis of the kinetics associated with clupein binding to DNA by measurements of the time-dependence of light-scattering intensities in the time range of seconds demonstrates directly that clupein-induced intermolecular interactions of DNA molecules are essential. The rate constants of DNA association increase co-operatively at threshold clupein concentrations, which correspond to those observed in the equilibrium titrations. Above the threshold, the rate constants arrive at a level that is almost constant, but shows some decrease with increasing clupein concentrations. These results are described by a model with a monomer and a dimer state of DNA, which bind ligands with different affinities according to an excluded-site binding scheme. When the ligand binding constant is larger for the dimer than for the monomer state, as should be expected, binding of ligands drives the DNA from the monomer to the dimer state, even if the dimerization equilibrium in the absence of ligands is far in favor of the monomer. The transition from the monomer to the dimer state proves to be strongly co-operative. When the ligand concentration is increased to higher values, the dimers may be converted back to monomers due to an increased extent of ligand binding to the monomer state. The model is consistent with the available experimental data. The analysis of the data by the model indicates the existence of a reaction unit much below the DNA chain length, corresponding to about 80 nucleotide residues. The present model describes ligand driven intermolecular association; an analogous model is applicable to ligand driven intramolecular association. In summary, the co-operativity of clupein binding to DNA double helices is not due to nearest neighbor interactions, but results from thermodynamic coupling of clupein binding with clupein-induced DNA association.     

Kinetics of [3H]muscimol binding to the GABAA receptor in bovine brain membranes

The binding of the GABA receptor agonist [3H]muscimol to membrane preparations from bovine cerebral cortex has been investigated in equilibrium and kinetic experiments. Equilibrium binding curves are biphasic and suggest that [3H]muscimol binds to both high-affinity (Kd approximately 10 nM) and low-affinity (Kd approximately 0.5 microM) sites. Binding to each class of sites is inhibited by GABA and by the specific GABAA receptor antagonist bicuculline. The kinetics of [3H]muscimol binding have been measured by using both manual filtration assays and an automated rapid filtration technique which permits the measurement of ligand dissociation on subsecond time scales. Association and dissociation curves are biphasic at all concentrations of [3H]muscimol studied, even under conditions of low receptor saturation when no significant occupancy of the low-affinity sites would be expected. These results cannot be simply explained by the presence of two populations of binding sites in the membrane preparations but suggest the existence of two forms of the monoliganded receptor. Dissociation constants for these two forms have been estimated to be 16 and 82 nM at 23 degrees C. At higher ligand concentrations, kinetic measurements have suggested that the binding of [3H]muscimol to low-affinity sites is accompanied by a slow conformational change of the receptor-ligand complex.     

Magnesium ion requirements for yeast enolase activity.

It has generally been concluded that two divalent cations are required for enolase activity, even though the enzyme is a homodimer that specifically binds four metal ions in the presence of substrate. This paper reports a reinvestigation of the stoichiometry of enolase activation. Specific ion electrode measurements of Mg2+ binding in the presence and absence of substrate are compared with stopped-flow measurements of the velocity of 2-phosphoglycerate dehydration. It is concluded that the enzyme is inactive when only two metal-binding sites are filled and that four sites must be populated with Mg2+ for full activity. An ordered binding mechanism is proposed that quantitatively predicts the activation of enolase by the four Mg2+ ions from their measured dissociation constants and the Michaelis constant for the dehydration reaction. To explain the loss of enzymatic activity at still higher metal concentrations, the binding of additional, inhibitory Mg2+ ions is postulated.     

Iodination significantly influences the binding of human transferrin to the transferrin receptor

The human transferrin receptor (TfR) and its ligand, the serum iron carrier transferrin, serve as a model system for endocytic receptors. Although the complete structure of the receptor's ectodomain and a partial structure of the ligand have been published, conflicting results still exist about the magnitude of equilibrium binding constants, possibly due to different labeling techniques. In the present study, we determined the equilibrium binding constant of purified human TfR and transferrin. The results were compared to those obtained with either iodinated TfR or transferrin. Using an enzyme-linked assay for receptor-ligand interactions based on the published direct calibration ELISA technique, we determined an equilibrium constant of Kd=0.22 nM for the binding of unmodified human Tf to surface-immobilized human TfR. In a reciprocal experiment using soluble receptor and surface-bound transferrin, a similar constant of Kd=0.23 nM was measured. In contrast, covalent labeling of either TfR or transferrin with 125I reduced the affinity 3-5-fold to Kd=0.66 nM and Kd=1.01 nM, respectively. The decrease in affinity upon iodination of transferrin is contrasted by an only 1.9-fold decrease in the association rate constant, suggesting that the iodination affects rather the dissociation than the association kinetics. These results indicate that precautions should be taken when interpreting equilibrium and rate constants determined with covalently labeled components.