Individual-site binding data and the energetics of protein–DNA interactions

Individual-site isotherms for the binding of bacteriophage λ repressor to the left and right λ operators have been determined [D. F. Senear, M. Brenowitz, M. A. Shea, and G. K. Ackers (1986) Biochemistry, Vol. 25, pp. 7344–7354.] using the DNAse protection technique [ footprinting; D. J. Galas and A. Schmitz (1978) Nucleic Acids Research, Vol. 5, pp. 3157–3170]. These extensive data have been interpreted with a quantitative model that emphasized cooperative interactions between adjacently bound ligands [occupied ? occupied interactions; G. K. Ackers, A. D. Johnson, and M. A. Shea (1982) Proceedings of the National Academy of Science, USA, Vol. 79, pp. 1129–1133]. Overlooked in this model are the effects of cooperative interactions between a site containing a bound ligand and its neighboring unoccupied site (occupied ? unoccupied interactions). This paper reinterprets the existing data with a model that considers occupied ? unoccupied as well as occupied ? occupied interactions. The results yield parameters that differ substantially from those already reported. A discussion on the advisability of ignoring occupied ? unoccupied interactions is included. © 1993 John Wiley & Sons, Inc.     

Interactions of Escherichia coli primary replicative helicase DnaB protein with nucleotide cofactors.

Interactions between the Escherichia coli primary replicative helicase DnaB protein and nucleotide cofactors have been studied using several fluorescent nucleotide analogs and unmodified nucleotides. The thermodynamically rigorous fluorescent titration technique has been used to obtain true binding isotherms, independently of the assumptions of any relationships between the observed quenching of protein fluorescence and the degree of nucleotide binding. Fluorescence titrations using several MANT derivatives of nucleoside diphosphates (MANT-ADP, 3',2'-O-(N-methylantraniloyl)adenosine-5'-diphosphate; MANT-GDP, 3',2'-O(N-methylantraniloyl)guanosine-5'-diphosphate; MANT-CDP, 3',2'-O-(N-methylantraniloyl)cytidine-5'-diphosphate; MANT-UDP, 3',2'-O-(N-methylantraniloyl)uridine-5'-diphosphate) have shown that the DnaB helicase has a preference for purine nucleotides. Binding of all modified nucleotides is characterized by similar negative cooperativity, indicating that negative cooperative interactions are base-independent. Thermodynamic parameters for the interactions of the unmodified nucleotides (ADP, GDP, CDP, and UDP) and inorganic phosphate (P(i)) have been obtained by using the competition titration approach. To analyze multiple ligand binding to a finite circular lattice, for a general case in which each lattice binding site can exist in different multiple states, we developed a matrix method approach to derive analytical expressions for the partition function and the average degree of binding for such cases. Application of the theory to competition titrations has allowed us to extract the intrinsic binding constants and cooperativity parameters for all unmodified ligands. This is the first quantitative estimate of affinities and the mechanisms of binding of different unmodified nucleotides and inorganic phosphate for a hexameric helicase. The intrinsic affinities of all of the studied ATP analogs are lower than the intrinsic affinities of the corresponding ADP analogs. The implications of these results for the mechanism of helicase action are discussed.     

Model analysis of surfactant--polymer interaction as cooperative ligand binding to linear lattice

An improved model of the cooperative binding of monomeric ligands to a linear lattice is proposed for the analysis of surfactant association on the polymer. The interaction between bound ligands across an unoccupied site as well as the steric hindrance effect in consecutive bindings is taken into account here. Typical results of the model calculations are represented, and several least squares fittings of the binding isotherms of the ionic surfactant-polyelectrolyte systems are attempted. The characteristic binding behavior in those systems is interpretable by the feasible model of the interactions between surfactant molecules. The advantages and limitations of the analysis using this model also are discussed.     

A steady state model for analyzing the cellular binding, internalization and degradation of polypeptide ligands

We demonstrate that the interaction of polypeptide ligands with cells under physiological conditions can be described by a set of steady state equations. These equations include four new rate constants: V_r, the rate of insertion of receptors into the cell membrane; K_e, the endocytotic rate constant of occupied receptors; K_t, the turnover rate constant of unoccupied receptors; and K_h, the rate constant of hydrolysis of internalized ligand. Several simple procedures are described for determining these constants. In experiments in which epidermal growth factor and human fibroblasts were used, the cell-ligand interactions followed the predictions of the steady state model. The utility of the steady state equations is demonstrated by establishing the kinetic basis of the commonly observed “down regulation” phenomenon and by quantitating the effect of methylamine on the endocytotic and degradation rates of epidermal growth factor. We also show that the slope of a “Scatchard plot” of steady state binding data is a complex constant including terms for the endocytotic rate of both occupied and unoccupied receptors. The X-intercept of such a plot is a function of the insertion rate of new receptors, the internalization rate of occupied receptors and the degradation rate of the internalized ligand. The steady state equations allow one to predict changes in cellular ligand binding resulting from alterations in the four rate constants. They also provide a foundation for computer simulations of ligand-cell interactions, which closely correspond to experimental data. These approaches should facilitate studies on the control of cellular activities by these polypeptide ligands.     

On the cooperative binding of large ligands to a one-dimensional homogeneous lattice: the generalized three-state lattice model

We present the general secular equation for three-state lattice models for the cooperative binding of large ligands to a one-dimensional lattice. In addition, a closed-form expression for the isotherm is also obtained, that can be used with all values of the cooperativity parameter omega(0 less than omega less than infinity) thus eliminating the need for multiple equations.     

An equilibrium binding study of the interaction of fructose 6-phosphate and fructose 1,6-bisphosphate with rabbit muscle phosphofructokinase.

Equilibrium binding studies of the interaction of rabbit muscle phosphofructokinase with fructose 6-phosphate and fructose 1,6-bisphosphate have been carried out at 5 degrees in the presence of 1-10 mM potassium phosphate (pH 7.0 and 8.0), 5 mM citrate (pH 7.0), or 0.22 mm adenylyl imidodiphosphate (pH 7.0 and 8.0). The binding isotherms for both fructose 6-phosphate and fructose 1,6-bisphosphate exhibit negative cooperativity at pH 7.0 and 8.0 in the presence of 1-10 mM potassium phosphate at protein concentrations where the enzyme exists as a mixture of dimers and tetramers (pH 7.0) or as tetramers (pH 8.0) and at pH 7.0 in the presence of 5 mM citrate where the enzyme exists primarily as dimers. The enzyme binds 1 mol of either fructose phosphate/mol of enzyme monomer (molecular weight 80,000). When enzyme aggregation states smaller than the tetramer are present, the saturation of the enzyme with either ligand is paralleled by polymerization of the enzyme to tetramer, by an increase in enzymatic activity and by a quenching of the protein fluorescence. At protein concentrations where aggregates higher than the tetramer predominate, the fructose 1,6-bisphosphate binding isotherms are hyperbolic. These results can be quantitatively analyzed in terms of a model in which the dimer is associated with extreme negative cooperativity in binding the ligands, the tetramer is associated with less negative cooperativity, and aggregates larger than the tetramer are associated with little or no cooperativity in the binding process. Phosphate is a competitive inhibitor of the fructose phosphate sites at both pH 7.0 and 8.0, while citrate inhibits binding in a complex, noncompetitive manner. In the presence of the ATP analog adenylyl imidodiphosphate, the enzyme-fructose 6-phosphate binding isotherm is sigmoidal at pH 7.0, but hyperbolic at pH 8.0. The characteristic sigmoidal initial velocity-fructose 6-phosphate isotherms for phosphofructokinase at pH 7.0, therefore, are due to an heterotropic interaction between ATP and fructose 6-phosphate binding sites which alters the homotropic interactions between fructose 6-phosphate binding sites. Thus the homotropic interactions between fructose 6-phosphate binding sites can give rise to positive, negative, or no cooperativity depending upon the pH, the aggregation state of the protein, and the metabolic effectors present. The available data suggest the regulation of phosphofructokinase involves a complex interplay between protein polymerization and homotropic and heterotropic interactions between ligand binding sites.     

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.     

An equilibrium study of the cooperative binding of adenosine cyclic 3',5'-monophosphate and guanosine cyclic 3',5'-monophosphate to the adenosine cyclic 3',5'-monophosphate receptor protein from Escherichia coli

The binding of adenosine cyclic 3',5'-monophosphate (cAMP) and guanosine cyclic 3',5'-monophosphate (cGMP) to the adenosine cyclic 3',5'-monophosphate receptor protein (CRP) from Escherichia coli was investigated by equilibrium dialysis at pH 8.0 and 20 degrees C at different ionic strengths (0.05--0.60 M). Both cAMP and cGMP bind to CRP with a negative cooperativity that is progressively changed to positive as the ionic strength is increased. The binding data were analyzed with an interactive model for two identical sites and site/site interactions with the interaction free energy--RT ln alpha, and the intrinsic binding constant K and cooperativity parameter alpha were computed. Double-label experiments showed that cGMP is strictly competitive with cAMP, and its binding parameters K and alpha are not very different from that for cAMP. Since two binding sites exist for each of the cyclic nucleotides in dimeric CRP and no change in the quaternary structure of the protein is observed on binding the ligands, it is proposed that the cooperativity originates in ligand/ligand interactions. When bound to double-stranded deoxyribonucleic acid (dsDNA), CRP binds cAMP more efficiently, and the cooperativity is positive even in conditions of low ionic strength where it is negative for the free protein. By contrast, cGMP binding properties remained unperturbed in dsDNA-bound CRP. Neither the intrinsic binding constant K nor the cooperativity parameter alpha was found to be very sensitive to changes of pH between 6.0 and 8.0 at 0.2 M ionic strength and 20 degrees C. For these conditions, the intrinsic free energy and entropy of binding of cAMP are delta H degree = -1.7 kcal . mol-1 and delta S degree = 15.6 eu, respectively.     

Thermodynamic model of cooperativity in a dimeric protein: unique and independent parameters formulation.

A model of the cooperative interaction of ligand binding to a dimeric protein is presented based upon the unique and independent parameters (UIP) thermodynamic formulation (Gutheil and McKenna, Biophys. Chem. 45 (1992) 171-179). The analysis is developed from an initial model which includes coupled conformational and ligand binding equilibria. This completely general model is then restricted to focus on conformationally mediated cooperative interactions between the ligands and the expressions for the apparent ligand binding constant and the apparent ligand-ligand interaction constant are derived. The conditions under which there is no cooperative interaction between the ligands are found as roots to a polynomial equation. Consideration of the distribution of species among the various conformational states in this general model leads to a set of inequalities which can be represented as a two dimensional plot of boundaries. By superimposing a contour plot of the value of the apparent ligand-ligand interaction constant over the plot of boundaries a complete graphical representation of this system is achieved similar to a phase diagram. It is found that the parameter space homologous to Koshland-Nemethy-Filmer type of model is most consistent with both positive and negative cooperativity in this model. The maximal amount of positive and negative cooperativity are found to be simple functions of Kc, the equilibrium constant associated with the change of a subunit and ligand from the unligated to ligated conformation. It is shown that under certain limiting conditions the apparent allosteric interaction between ligands is equal to the conformational interaction between subunits. The methods presented are generally applicable to the theoretical analysis of thermodynamic interactions in complex systems.     

Competitive cooperative bindings of a small ligand to a linear polymer. II. Investigations on the mechanisms of proflavine binding to poly (A) and DNA.

Experimental binding isotherms relative to the interactions between proflavine and poly(A) or DNA are analyzed by comparison with theoretical models dealing with competitive cooperative bindings. In the case of poly(A), there are apparently no specific binding sites for the positive co-operative binding (complex I) leading to dye aggregation along the polyanionic chain. The second complex (complex II) seems to involve specific base-dye interactions, but it cannot be said whether this binding displays negative cooperativity or noncooperativity. None of the two simpler theoretical models agree quantitatively with all experimental data. A plausible interpretation can be given if it is assumed that (i) the electrostatic binding of one isolated bound dye molecule (nucleus of complex I) involves a definite interaction between a phosphate group and the positive charge of the dye; (ii) the structure of complex II is such that a dye–phosphate ionic interaction is maintained. In the case of DNA, our model of monoexclusive interactions fits the data more closely than does the model of biexclusive interactions. This gives experimental support for structural models in which the intercalated molecule interacts preferentially with one strand of the double helix and blocks only one phosphate for electrostatic binding. In order to propose a mechanism consistent with equilibrium and relaxation kinetic data, a modified reaction scheme is considered which takes account of the cooperativity effects in external binding and extends previous models.     

Binding of n-mers to one-dimensional lattices with longer than close-contact interactions

A general formalism is derived for the evaluation of binding isotherms of n-mers (ligands) to one-dimensional polymers in the presence of ligand-ligand interactions which extend over several binding sites with distance-dependent interaction energies (multi-parameter model). This is an extension of the usual n-mer binding theory developed by several investigators in which ligand-ligand interaction occurs only when two ligands are in close contact (one-parameter model). The difference in binding isotherms between a one-parameter model and a multi-parameter model is studied numerically using the present formalism.     

Effects of heterogeneity and cooperativity on the forms of binding curves for multivalent ligands

An exploratory investigation is made of the binding behavior that is likely to be encountered with multivalent ligands under circumstances where a single intrinsic binding constant does not suffice to describe all acceptor-ligand interactions. Numerical simulations of theoretical binding behavior have established that current criteria for recognizing heterogeneity and cooperativity of acceptor sites on the basis of the deviation of the binding curve from rectangular hyperbolic form for univalent ligands also apply to the interpretation of the corresponding binding curves for multivalent ligands. However, for systems in which the source of the departure from equivalence and independence of binding sites resides in the ligand, these criteria are reversed. On the basis of these observations a case is then made for attributing results of an experimental binding study of the interaction between pyruvate kinase and muscle myofibrils to positive cooperativity of enzyme sites rather than to heterogeneity or negative cooperativity of the myofibrillar sites.     

Effects of excluded surface area and adsorbate clustering on surface adsorption of proteins I. Equilibrium models

Statistical-thermodynamic models for the equilibrium adsorption of proteins onto homogeneous, locally planar surfaces are presented. An extension of earlier work [R.C. Chatelier, A.P. Minton, Biophys. J. 71 (1996) 2367], the models presented here allow for the formation of a broadly heterogeneous population of adsorbate clusters in addition to excluded volume interactions between all adsorbate species. Calculations are carried out for three simple models for the structure of adsorbate, illustrating similarities and differences in the equilibrium properties of maximally compact clusters, minimally compact clusters and isomerizing clusters. Depending upon the strength of attractive interactions between adsorbate molecules, the resulting equilibrium isotherms may exhibit negative cooperativity, positive cooperativity, essentially no apparent cooperativity, or a mixture of positive cooperativity at low surface density and negative cooperativity at high surface density of adsorbate. The condition of apparent lack of cooperativity, which might naively be interpreted as evidence of a lack of interaction between adsorbate molecules, actually conceals a balance between attractive and repulsive interactions and extensive clustering of adsorbate.     

The Escherichia coli F1F0 ATP synthase displays biphasic synthesis kinetics

The F1F0 proton-translocating ATPase/synthase is the primary generator of ATP in most organisms growing aerobically. Kinetic assays of ATP synthesis have been conducted using enzymes from mitochondria and chloroplasts. However, limited data on ATP synthesis by the model Escherichia coli enzyme are available, mostly because of the lack of an efficient and reproducible assay. We have developed an optimized assay and have collected synthase kinetic data over a substrate concentration range of 2 orders of magnitude for both ADP and Pi from the synthase enzyme of E. coli. Negative and positive cooperativity of substrate binding and positive catalytic cooperativity were all observed. ATP synthesis displayed biphasic kinetics for ADP indicating that 1) the enzyme is capable of catalyzing efficient ATP synthesis when only two of three catalytic sites are occupied by ADP; and 2) occupation of the third site further activates the rate of catalysis.     

The dependence of flux,sensitivity and response of the flux on the concentrations of substrate and modifiers for cooperative enzymes

The sensitivity (change of flux per unit change in the concentration of substrate) and response (change of flux per unit change in the concentration of modifier) are studied for a two-site Adair model in which cooperativity arises from both binding and catalytic interactions. For positive cooperativity, the sensitivity is weakly dependent on the Hill coefficient for the binding case, but can increase without limit for the catalytic case. Negatively cooperative enzymes (binding only) give very large sensitivities compared with positively or non-interacting systems, but the sensitivity rapidly decreases as the saturation increases above 25%. Modifiers greatly enhance the sensitivity; large changes in flux can be obtained for small changes in the concentrations of substrates and modifiers. In general, increasing the degree of kinetic cooperativity decreases the degree of binding cooperativity; selective pressure to maximize the sensitivity and response of allosteric enzymes may act to optimize cooperativity of binding modifiers and kinetic cooperativity of substrate turnover. The initial velocity equations including modifiers can be extended to bi-substrate, cooperative kinetics. The kinetics of methanol dehydrogenase are discussed.     

Kinetic mechanism of ligand binding in human ileal bile acid binding protein as determined by stopped-flow fluorescence analysis

Cooperative ligand binding to human ileal bile acid binding protein (I-BABP) was studied using the stopped-flow fluorescence technique. The kinetic data obtained for wild-type protein are in agreement with a four-step mechanism where after a fast conformational change on the millisecond time scale, the ligands bind in a sequential manner, followed by another, slow conformational change on the time scale of seconds. This last step is more pronounced in the case of glycocholate (GCA), the bile salt that binds with high positive cooperativity and is absent in mutant I-BABP proteins that lack positive cooperativity in their bile salt binding. These results suggest that positive cooperativity in human I-BABP is related to a slow conformational change of the protein, which occurs after the second binding step. Analogous to that in the intestinal fatty acid binding protein (I-FABP), we hypothesize that ligand binding in I-BABP is linked to a disorder-order transition between an open and a closed form of the protein.