A danger of low copy numbers for inferring incorrect cooperativity degree

Background  

A dose-response curve depicts the fraction of bound proteins as a function of unbound ligands. Dose-response curves are used to measure the cooperativity degree of a ligand binding process. Frequently, the Hill function is used to fit the experimental data. The Hill function is parameterized by the value of the dissociation constant and the Hill coefficient, which describes the cooperativity degree. The use of Hill's model and the Hill function has been heavily criticised in this context, predominantly the assumption that all ligands bind at once, which resulted in further refinements of the model. In this work, the validity of the Hill function has been studied from an entirely different point of view. In the limit of low copy numbers the dynamics of the system becomes noisy. The goal was to asses the validity of the Hill function in this limit, and to see in what ways the effects of the fluctuations change the form of the dose-response curves.     

Cooperation effects in binding of large ligands to DNA. II. Contact interactions between adsorbed ligands

Cooperative effects arising upon binding of biologically active ligands to DNA are considered. Equations are derived which enable one to describe the binding of two different ligands to DNA. We also consider the case when ligand can form two type of DNA complexes. The cooperative binding of the ligand in the vicinity of saturation level of binding can be described with a good accuracy by equation derived for the non-cooperative adsorption of the same ligand with some effective binding constant Keff. It is shown that cooperative effects arising upon binding of proteins and other ligands to DNA can be divided into two groups depending on the symmetry of interactions between the bound ligand molecules. In particular, if such interactions favor the formation of dimeric ligand species on the DNA, Keff approximately a1/2, where a is the ligand-ligand interaction constant. If cooperative interactions favor the formation of aggregates of unrestricted size, then Keff approximately aL+Y, where L is the size of the binding site for the ligand on DNA.     

Analysis of oxygen binding by hemoglobin on the basis of mean intrinsic thermodynamic quantities

The binding data for oxygenation of human hemoglobin, Hb, at various temperatures and in the absence and presence of 2,3-diphosphoglycerate, DPG, and inositol hexakis phosphate, IHP, were analyzed for extraction of mean intrinsic Gibbs free energy, DeltaGo, enthalpy, DeltaHo, and entropy, DeltaSo, of binding at various partial oxygen pressures. This method of analysis considers all the protein species present such as dimer and tetramer forms which were not considered by Imai et al. (Imai K et al., 1970, Biochim Biophys Acta 200: 189-196), in their analysis which was based on Adair equation. In this regard, the values of Hill equation parameters were estimated with high precision at all points of the binding curve and used for calculation of DeltaGo, DeltaHo and DeltaSo were also calculated by analysis of DeltaGo values at various temperatures using van't Hoff equation. The results represent the enthalpic nature of the cooperativity in Hb oxygenation and the compensation effect of intrinsic entropy. The interpretation of results also to be, into account the decrease of the binding affinity of sites for oxygen in the presence of DPG and IHP without any considerable changes in the site-site interaction (extent of cooperativity). In other words, the interactions between bound ligands, organic phosphates and oxygen, are more due to a decreasing binding affinity and not to the reduction of the cooperative interaction between sites. The results also document the more heterotropic effect of IHP compared to DPG.     

The Eps15 homology (EH) domain

The Eps15 homology (EH) domain was originally identified as a motif present in three copies at the NH2-termini of Eps15 and of the related molecule Eps15R. Both of these molecules are substrates for the tyrosine kinase activity of the epidermal growth factor receptor and hence the name 'Eps15 homology' or EH domain [Wong et al. (1994) Oncogene 9, 1591-1597; Wong et al. (1995) Proc. Natl. Acad. Sci. USA 92, 9530-9534; Fazioli et al. (1993) Mol. Cell. Biol. 13, 5814-5828] was derived. The motif was subsequently found in several proteins from yeast to nematode, thus establishing its evolutionary conservation. Initial studies with filter-binding assays and phage-displayed libraries demonstrated its protein:protein interaction abilities and identified specific ligands. Subsequently, structural analyses established the molecular bases of recognition between EH domains and cognate peptides. To date, several EH-containing and EH-binding proteins have been identified, which establish in the cell a network of protein:protein interactions, defined as the EH network. This network coordinates cellular functions connected with endocytosis, actin remodeling and intracellular transduction of signals.     

Cooperativity: over the Hill

Cooperativity, the ability of ligand binding at one site on a macromolecule to influence ligand binding at a different site on the same macromolecule, is a fascinating biological property that is often poorly explained in textbooks. The Hill coefficient is commonly used in biophysical studies of cooperative systems although it is not a quantitative measure of cooperativity. The free energy of interaction between binding sites (ΔΔG) is a more stringent definition of cooperativity and provides a direct quantitative measure of how the binding of ligand at one site affects the ligand affinity of another site.     

Removal of tropomyosin overlap modifies cooperative binding of myosin S-1 to reconstituted thin filaments of rabbit striated muscle

Cooperative binding of myosin S-1.ADP to regulated F-actin was previously reported and has been interpreted by a two-state model in which an important source of cooperativity is nearest neighbor interactions between the 7-actin.tropomyosin (TM).troponin units (functional units) (Hill, T.L., Eisenberg, E., and Greene, L. (1980) Proc. Natl. Acad. Sci. U.S.A. 77, 3186-3190). It has been postulated that the head-to-tail overlap between adjacent TM molecules is the structural basis of the nearest neighbor interactions. We tested the hypothesis by examining S-1.ADP binding to reconstituted regulated F-actin containing either intact TM or nonpolymerizable TM from which the COOH-terminal 11 residues were removed. In the absence of Ca2+, substitution of nonpolymerizable TM for TM reduced significantly the slope of the steeply rising phase of the sigmoidal S-1.ADP binding curve. Nevertheless, considerable residual cooperativity remained. Analysis of the data using the two-state model of Hill et al. suggests that removal of TM overlap abolishes nearest neighbor interactions, while the concerted change of the state of 7 actins in a functional unit can account for the residual cooperativity.     

Asymmetric distribution of cooperativity in the binding cascade of normal human hemoglobin. 2. Stepwise cooperative free energy

Stepwise cooperative free energies and intermediate Hill coefficients are used to assess the presence of noncooperative sequences in the database of binding free energies previously obtained for the eight partially ligated intermediates of human hemoglobin, encompassing a variety of hemesite analog substitutions. This analysis is prompted by the observed noncooperative binding of two ligands to hemoglobins that are partially substituted with Zn2+-heme, an analog of deoxy Fe2+-heme (Holt et al. (2005) Biochemistry 44, XXXXX). The results show that noncooperative binding sequences are observed in all hemesite analog studied to date. The noncooperative binding observed in (alpha2Znbeta2FeO2) and (alpha2FeO2beta2Zn) is therefore not a Zn-specific substitution artifact. One of several binding sequences from singly to triply ligated hemoglobin is also observed to occur with little or no positive cooperativity. These results demonstrate the variability possible among different ligation pathways in a highly cooperative multi-subunit system such as hemoglobin. As a direct consequence of this variability, differences among ligation pathways are not always detectable using cooperativity functions based on statistical distributions, such as the Hill coefficient n(H). The limitations of Hill coefficient analysis in evaluating cooperativity in intermediates of complex systems is contrasted with the utility of the stepwise binding parameters.     

Molecular cooperativity of drebrin(1-300) binding and structural remodeling of f-actin

Drebrin A, an actin-binding protein, is a key regulatory element in synaptic plasticity of neuronal dendrites. Understanding how drebrin binds and remodels F-actin is important for a functional analysis of their interactions. Conventionally, molecular models for protein-protein interactions use binding parameters derived from bulk solution measurements with limited spatial resolution, and the inherent assumption of homogeneous binding sites. In the case of actin filaments, their structural and dynamic states—as well as local changes in those states—may influence their binding parameters and interaction cooperativity. Here, we probed the structural remodeling of single actin filaments and the binding cooperativity of DrebrinA_1-300 –F–actin using AFM imaging. We show direct evidence of DrebrinA_1-300-induced cooperative changes in the helical structure of F-actin and observe the binding cooperativity of drebrin to F-actin with nanometer resolution. The data confirm at the in vitro molecular level that variations in the F-actin helical structure can be modulated by cooperative binding of actin-binding proteins.     

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.     

Protein-protein interactions in signaling cascades

The process of signal transduction is dependent on specific protein-protein interactions. In many cases these interactions are mediated by modular protein domains that confer specific binding activity to the proteins in which they are found. Rapid progress has been made in the biochemical characterization of binding interactions, the identification of binding partners, and determination of the three-dimensional structures of binding modules and their ligands. The resulting information establishes the logical framework for our current understanding of the signal transduction machinery. In this overview a variety of protein interaction modules are discussed, and issues relating to binding specificity and the significance of a particular interaction are considered.     

A new measure of cooperativity in protein-ligand binding

An allosteric binding system consisting of a single ligand and a nondissociating macromolecule having multiple binding sites can be represented by a binding polynomial. Various properties of the binding process can be obtained by analyzing the coefficients of the binding polynomial and such functions as the binding curve and the Hill plot. The Hill plot has an asymptote of unit slope at each end and the departure of the slope from unity at any point can be used to measure the effective interaction free energy at that point. Of particular interest in detecting and measuring cooperativity are extrema of the Hill slope and its value at the half-saturation point. If the binding polynomial is symmetric, then there is an extremum of the Hill slope at the half-saturation point. This value, the Hill coefficient, is a convenient measure of cooperativity. The purpose of this paper is to express the Hill coefficient for symmetric binding polynomials in terms of the roots of the polynomial and to give an interpretation of cooperativity in terms of the geometric pattern of the roots in the complex plane. This interpretation is then applied to the binding polynomials for the MWC (Monod-Wyman-Changeux) and KNF (Koshland-Nemethy-Filmer) models.     

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.     

Conjoined hemoglobins. Loss of cooperativity and protein-protein interactions

Hemoglobin cross-linked as a bis(isophthalamide) of the epsilon-amino groups of lysine 82 of each beta-subunit binds and releases oxygen with a Hill coefficient indicative of cooperative oxygen binding (typically approximately 2.0). However, connecting two such cross-linked tetramers with a relatively short covalent linkage produces cross-linked bis-tetramers that bind oxygen with Hill coefficients near unity. To separate the effect of the linkages from the effects of protein-protein interactions in the conjoined proteins, reagents (1 and 2) were used to produce bis-tetramers (A and B). These have a considerably greater distance between cross-linked tetramers than earlier examples. Yet, the bis-tetramers (A and B) bind oxygen with minimal cooperativity (n(50) = 1.4, 1.2). To assess the effect of the linkage itself, cross-linked tetramers (Cand D) were prepared from reactions with the same reagents. These bind oxygen with cooperativity similar to that of cross-linked tetramers without the extended chain (C, n(50) = 2.0; D, n(50) = 1.8). Other tetramers (E and F) with flexible, saturated hydrocarbon appendages were also prepared. These also showed cooperativity in oxygen binding (E, n(50) = 1.7; F, n(50) = 1.8) despite their high degree of hydrophobicity. Thus, the intertetrameric linkages themselves do not induce the loss of cooperativity, leading to the conclusion that solution effects of the tetramers upon one another are the source of the decline in cooperativity: protein-protein interactions are most significant in disrupting the cooperativity of the bis-tetramers, regardless of the span or composition of the linker. This suggests that effects of oligomerization of hemoglobin within red cell substitutes should be considered in terms of such interactions.     

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.     

DNA-protein cooperative binding through variable-range elastic coupling

Cooperativity plays an important role in the action of proteins bound to DNA. A simple mechanism for cooperativity, in the form of a tension-mediated interaction between proteins bound to DNA at two different locations, is proposed. These proteins are not in direct physical contact. DNA segments intercalating bound proteins are modeled as a worm-like chain, which is free to deform in two dimensions. The tension-controlled protein-protein interaction is the consequence of two effects produced by the protein binding. The first is the introduction of a bend in the host DNA and the second is the modification of the bending modulus of the DNA in the immediate vicinity of the bound protein. The interaction between two bound proteins may be either attractive or repulsive, depending on their relative orientation on the DNA. Applied tension controls both the strength and the range of protein-protein interactions in this model. Properties of the cooperative interaction are discussed, along with experimental implications.     

Intramolecular cooperativity in a protein binding site assessed by combinatorial shotgun scanning mutagenesis

Combinatorial shotgun alanine-scanning was used to assess intramolecular cooperativity in the high affinity site (site 1) of human growth hormone (hGH) for binding to its receptor. A total of 19 side-chains were analyzed and statistically significant data were obtained for 145 of the 171 side-chain pairs. The analysis revealed that 90% of the side-chain pairs exhibited no statistically significant pair interactions, and the remaining 10% of side-chain pairs exhibited only small interactions corresponding to cooperative interaction energies with magnitudes less than 0.4 kcal/mol. The statistical predictions were tested by measuring affinities for purified mutant proteins and were found to be accurate for five of six side-chain pairs tested. The results reveal that hGH site 1 behaves in a highly additive manner and suggest that shotgun scanning should be useful for assessing cooperative effects in other protein-protein interactions.     

Non-additivity in protein-protein interactions

The energy of binding between proteins may be seen as the sum of the contributions of the individual amino acid residues. These contributions are additive when the binding energy, due to different amino acid residues, is independent of the interactions between amino acids in the same polypeptide chain. A measure of non-additivity is the coupling free energy. In this communication it is shown that: (1) the coupling free energy is the sum of intramolecular and intermolecular contributions; and (2), when additivity exists, experimentally determined values for the free energy of transfer of amino acids from water to the hydrophobic protein-protein interface are a very good approximation of their contribution to the energy of binding. Additivity cycles can be useful in determining the precise conditions where this approximation holds.     

Protein stabilization by specific binding of guanidinium to a functional arginine-binding surface on an SH3 domain

Guanidinium hydrochloride (GuHCl) at low concentrations significantly stabilizes the Fyn SH3 domain. In this work, we have demonstrated that this stabilizing effect is manifested through a dramatic (five- to sixfold) decrease in the unfolding rate of the domain with the folding rate being affected minimally. This behavior contrasts to the effect of NaCl, which stabilizes this domain by accelerating the folding rate. These data imply that the stabilizing effect of GuHCl is not predominantly ionic in nature. Through NMR studies, we have identified a specific binding site for guanidinium, and we have determined a dissociation constant of 90 mM for this interaction. The guanidinium-binding site overlaps with a functionally important arginine-binding pocket on the domain surface, and we have shown that GuHCl is a specific inhibitor of the peptide-binding activity of the domain. A different SH3 domain possessing a similar arginine-binding pocket is also thermodynamically stabilized by GuHCl. These data suggest that many proteins that normally interact with arginine-containing ligands may also be able to specifically interact with guanidinium. Thus, some caution should be used when using GuHCl as a denaturant in protein folding studies. Since arginine-mediated interactions are often important in the energetics of protein-protein interactions, our observations could be relevant for the design of small molecule inhibitors of protein-protein interactions.