Protein symmetry and the co-operative ligand-binding behaviour predicted by allosteric Koshland models

It is shown that the nearest-neighbour interaction two-conformation allosteric models of Koshland, Nemethy & Filmer (1966) predict binding curves with a centre of symmetry when the protein is also symmetrical and induced-fit is assumed. When nonexclusive binding to both conformations is assumed, the models predict that the family of homotropic binding curves obtained by varying the heterotropic ligand has a centre of symmetry. It is argued that the symmetry or asymmetry of binding curves is the main experimentally verifiable prediction of allosteric models insofar as they are models of interaction between protein subunits.Symmetry in a binding curve greatly simplifies the analysis of cooperative behaviour. The co-operative features possible with a symmetric binding curve for a four-site protein are analysed. The sign of co-operativity may either be uniform or change twice as saturation increases; the conditions for the various possibilities are given. For example, in terms of the intrinsic binding constants per site A^∥₁, A2, etc. the necessary and sufficient condition for positive macroscopic co-operativity over the whole symmetric binding curve is A^∥₁≤ A2, A ^∥₁ ≤ A3 which should be contrasted with the obvious A^∥₁ ≤ Al, AZ ≤A^∥₃ (positive microscopic co-operativity) which is only a sufficient but not a necessary condition. A symmetric curve may have one or three, but no more, extrema of the “Hill coefficient” h. For three extrema a change of sign of microscopic (but not necessarily macroscopic) co-operativity is necessary but not sufficient. In the case where there are off-centre maxima of h, then h < 2 everywhere on the curve.The Koshland models predict qualitative and quantitative restrictions on the forms of binding curves additional to that of symmetry. In tetrameric induced fit models, negative co-operativity in the mid-region of the curve and positive co-operativity in the outside regions is possible, but not the opposite, and three extrema of h are possible with uniform positive but not with uniform negative co-operativity.Thus by recognising the importance of symmetry it has been possible to describe and categorise all the co-operativity behaviour possible with the most plausible Koshland tetrameric models. Several experimental examples of probable non-exclusive binding to proteins and enzymes are discussed, and it is shown how the symmetry point of view illuminates their interpretation.     

Studies on erythrocruorin. IV. Circular dichroism of earthworm erythrocruorin.

Circular dichroism spectra of Lumbricus erythrocruorin in the absence and in the presence of heme ligands have been analyzed under a variety of experimental conditions in view of the peculiarities in ligand binding displayed by this high molecular weight heme protein (M_r = 3 × 10⁶).The undisaociated molecule exists in a “metastable” form with high cooperativity in oxygen binding, which can be converted into a stable form with low co-operativity either by changes in pH or temperature; circular dichroism spectra of oxyerythrocruorin in the Soret region give direct evidence of a local alteration in the heme environment under the conditions which affect co-operativity in oxygen binding of the undissociated molecule. Similar, although more pronounced changes in the same spectral region are observed in the dissociated molecule of M_r = 270,000, which displays low co-operativity in oxygen binding.Deoxygenation is accompanied by an inversion in the double Soret-Cotton effect, which indicates a substantial rearrangement in the heme environment upon removal of the ligand.The double peak in the Soret region found in all erythrocruorin derivatives can be taken as an indication of a distinctive distribution of the aromatic side-chains interacting with the heme chromophore.     

Interactions of bacteriophage T4-coded gene 32 protein with nucleic acids: I. Characterization of the binding interactions

In this paper we examine molecular details of the interaction of bacteriophage T4-coded gene 32 protein with oligo- and polynucleotides. It is shown that the binding affinity (K_oligo) of oligonucleotides of length (l) from two to eight nucleotide residues for gene 32 protein is essentially independent of base composition or sugar type. This binding also shows little dependence on salt concentration and on oligonucleotide length; even the expected statistical length factor in K_oligo is not observed, suggesting that binding occurs at the end of the oligonucleotide lattice and that the oligonucleotide is not free to move across the binding site. Co-operative (contiguous) or isolated binding of gene 32 protein to polynucleotides is very different; here binding is highly salt dependent ($\text{? log Kω}\text{? log}\text{[NaCl]}\text{～- ?7}\text{)}$ and essentially stoichiometric at salt concentrations less than ~0.2 m (for poly(rA)). Binding becomes much weaker and the binding isotherms appear typically co-operative (sigmoid) in protein concentration at higher salt concentrations. We demonstrate, by fitting the co-operative binding isotherms to theoretical plots at various salt concentrations and also by measuring binding at very low protein binding density (ν), that the entire salt dependence of Kω is in the intrinsic binding constant (K); the co-operativity parameter (ω) is essentially independent of salt concentration. Furthermore, by determining titration curves in the presence of salts containing a series of different anions and cations, it is shown that the major part of the salt dependence of the gene 32 protein-polynucleotide interaction is due to anion (rather than to cation) displacement effects. Binding parameters of oligonucleotides of length sufficient to bind two or more gene 32 protein monomers show behavior intermediate between the oligonucleotide and the polynucleotide binding modes. These different binding modes probably reflect different conformations of the protein; the results are analyzed to produce a preliminary molecular model of the interactions of gene 32 protein with nucleic acids in its different binding modes.     

Nucleic acid binding properties of Escherichia coli ribosomal protein S1. II. Co-operativity and specificity of binding site II.

The following properties characterize the interaction of nucleic acid binding site II of Escherichia coli ribosomal protein S1 with oligo- and polyribonucleotides; all have been determined with site I complexed with oligo- or polydeoxyribonucleotides. (1) The intrinsic binding constant (K) of site II to single-stranded polyribonucleotides is fairly independent of base composition, though cytidinecontaining polymers bind with approximately threefold higher intrinsic affinities than do the comparable adenine-containing species. (2) Poly(rC) is bound to site II co-operatively; the co-operativity parameter (ω) ? 31. Poly(rA) shows no binding co-operativity. The site size (n) for both polyribonucleotides binding at site II is about ten nucleotide residues. (3) The K value for site II is ? 4 × 10⁵m^?1 for poly(rA), and ? 1 × 10⁶m^?1 for poly(rC), in 0.12 m-Na⁺. Unlike site I, the binding affinity of site II increases somewhat with increasing salt concentration, suggesting that phosphate—basic protein residue contacts are not involved. (4) Varying Mg^{2 +} concentration has no effect on K, and changes in the concentration of either Mg²⁺ or Na⁺ do not affect the magnitude of site II co-operativity. (5) Reaction of the exocyclic amino groups of poly (rC) with formaldehyde drastically reduces the affinity of site II for this polynucleotide, while the affinity of poly (rC) for site I is not altered by this treatment. (6) No major sequence specificity of K for site II is found with either homogeneous polynucleotides or the 3′ terminal dodecanucleotide of 16 S ribosomal RNA; we conclude that selectivity of S1 binding via site II depends largely on the presence or absence of base compositiondependent binding co-operativity.The binding properties of site II probably account for the ability of S1 to inhibit translation at high S1 to ribosome ratios (“factor i” activity). Possible mechanisms for the role of S1 protein as a part of the phage Qβ replicase complex and in protein synthesis are discussed in relation to the binding properties of site I and site II.     

Mixed and uniform co-operativity of ligand binding to multisite proteins: the co-operativity types allowed by the adair equation and conditions for them

It is proved for the first time that the macroscopic co-operativity of binding to a protein with q binding sites may change signs over a single binding curve any number of times from 0 to (q-2), but no more than (q-2). n changes of sign of macroscopic co-operativity requires as a necessary condition at least n changes of sign of microscopic co-operativity, but this necessary condition is not a sufficient one. The necessary and sufficient condition that decides whether there are two changes of sign in a four-site protein is obtained. There are no changes when K₁K₃(K₂-K₄)+K₁K₂(K₃-K₂)+K₂K₃(K₄-K₃) is positive, and two changes when it is negative, presuming the above mentioned necessary conditions to be satisfied. The K's of this formula are the “intrinsic” per-site Adair constants. As a result, the conditions for all six co-operativity types possible with a four-site protein are now known.     

Conditions for the various types of co-operativity allowed by the adair,equation and their relation with the algebraic character of binding polynomials

A convenient way to obtain for any number, n, of sites, the functions of the constants of the Adair equation that decide the type of co-operativity of ligand binding to a non-dissociating protein is given and is illustrated by the examples n = 4 and n = 5. These functions are invariants of the binding polynomial and various of its derivatives.Although there are some simple sufficient conditions (inequalities relating successive Adair constants) for some co-operativity types, the full necessary and sufficient conditions even for uniform positive and negative co-operativity depend on very complicated functions of the constants for n > 4.However there are alternative ways of writing binding polynomials known as canonical forms. Up to at least n = 5, and probably beyond, the conditions that are complicated in terms of Adair constants are very simple in terms of the constants of canonical forms. For instance any fourth-degree polynomial can be written in the form p(x - α)⁴ + q(x - β)⁴ + 6μ (x - α)²(x - β)² although in three different ways. For one of these ways, the sign of μ distinguishes between mixed and uniform co-operativity. For any kind of mixed co-operativity μ > 0, while μ < 0 corresponds to uniform co-operativity. Advantages of the use of canonical forms are briefly commented on.     

Roles of nucleotide substructures in the regulation of cystathionine β-synthase domain-containing pyrophosphatase

BackgroundRegulatory cystathionine β-synthase (CBS) domains are ubiquitous in proteins, yet their mechanism of regulation remains largely obscure. Inorganic pyrophosphatase which contains regulatory CBS domains as internal inhibitors (CBS-PPase) is activated by ATP and inhibited by AMP and ADP; nucleotide binding to CBS domains and substrate binding to catalytic domains demonstrate positive co-operativity.Methods: Here, we explore the ability of an AMP analogue (cAMP) and four compounds that mimic the constituent parts of the AMP molecule (adenine, adenosine, phosphate, and fructose-1-phosphate) to bind and alter the activity of CBS-PPase from the bacterium Desulfitobacterium hafniense.ResultsAdenine, adenosine and cAMP activated CBS-PPase several-fold whereas fructose-1-phosphate inhibited it. Adenine and adenosine binding to dimeric CBS-PPase exhibited high positive co-operativity and markedly increased substrate binding co-operativity. Phosphate bound to CBS-PPase competitively with respect to a fluorescent AMP analogue.ConclusionsProtein interactions with the adenine moiety of AMP induce partial release of the internal inhibition and determine nucleotide-binding co-operativity, whereas interactions with the phosphate group potentiate the internal inhibition and decrease active-site co-operativity. The ribose moiety appears to enhance the activation effect of adenine and suppress its contribution to both types of co-operativity.General significanceOur findings demonstrate for the first time that regulation of a CBS-protein (inhibition or activation) is determined by a balance of its interactions with different chemical groups of the nucleotide and can be reversed by their modification. Differential regulation by nucleotides is not uncommon among CBS-proteins, and our findings may thus have a wider significance.     

Co-operative response of chemically excitable membrane: I. Formulation: Unified theory of co-operativity

The lattice-model of Changeux, Thiery, Tung & Kittel (1966) was extended in order to examine the co-operative response of chemically excitable membrane and the exact mathematical correspondence to the Ising model was shown. In this model, two conformational states S and R with different affinities for the ligand are assumed to be accessible to each protomer, which is interacting with the nearest-neighbor protomers. The model is applicable to any kind of symmetrically interacting system consisting of oligomers and lattices and is an extension of previously proposed models of allosteric protein. It includes the model of Monod, Wyman, & Changeux (1965) and that of Koshland, Némethy & Filmer (1966) as the extreme cases of the oligomer. By assuming that a state-transition from S to R in a protomer is accompanied by a unit increase in conductance, the characteristics of dose-response curves of chemically excitable membrane are examined. The Hill's coefficient n_H of dose-response curve, the measure of the co-operativity, is shown to be proportional to the square of the mean fluctuation of the state function, the fraction of protomers in R state.     

A two-state tension-displacement model for hemoglobin-ligand binding

Based on the Perutz view of hemoglobin co-operativity and the methodology of statistical physics, a two-state (t → r) model for the co-operative response is presented. The motion of the iron atom with respect to the heme plane is assumed to be the important feature of the binding process, and results in an expression for hemoglobin saturation as an explicit function of the internal tension of the hemoglobin molecule. Closure of the equation is achieved with the assumption of linearity between the internal tension and the displacement of the iron atom above the heme plane. The result is a linear dependence of log_e [(ψ/(1?ψ)/(1/X_L)] on the fractional saturation, ψ, the slope and intercept being expressed in terms of physically realizable parameters characteristic of the hemoglobin-ligand reaction. Agreement with experimental data for hemoglobin-oxygen and hemoglobin-carbon monoxide is obtained using parameter values that are reasonable in terms of the interactions they represent.     

Pharmacological characterization of INCB3344, a small molecule antagonist of human CCR2

The chemokine receptor 2 (CCR2) directs migration of monocytes and has been proposed to be a drug target for chronic inflammatory diseases. INCB3344 was first published as a small molecule nanomolar inhibitor of rodent CCR2. Here, we show that INCB3344 can also bind human CCR2 (hCCR2) with high affinity, having a dissociation constant (K_d) of approximately 5 nM. The binding of the compound to the receptor is rapid and reversible. INCB3344 potently inhibits hCCR2 binding of monocyte chemoattractant protein-1 (MCP-1) and MCP-1-induced signaling and function in hCCR2-expressing cells, including ERK phosphorylation and chemotaxis, and is competitive against MCP-1 in vitro. INCB3344 also blocks MCP-1 binding to monocytes in human whole blood, with potency consistent with in vitro studies. The whole blood binding assay described here can be used for monitoring pharmacodynamic activity of CCR2 antagonists in both preclinical models and in the clinic.     

Comparative thermodynamics of opioid receptor ligand interaction in the bovine adrenal medulla membranes—Evidence of opioid site heterogeneity

1. A marked dependence on temperature of agonist binding δ, μ and κ₁₋₃, opioid sites in the bovine adrenal medulla was observed, at the range of 0 to 37°C. These changes concern kinetic (k₁) and equilibrium constants (K_d), but not binding capacities (B_max).2. These dependences are different for each ligand and each opioid receptor, suggesting their molecular heterogeneity.3. The comparative thermodynamics indicates that the interaction of opioid agonists with their receptor is exergonic (ΔG° < 0) and entropy driven (ΔS° > 0).4. The comparison of Van't Hoff and Arrhenius plots indicates a discrete mechanism in the binding of each opioid receptor.     

Letter: Kinetic negative co-operativity in the allosteric model of Monod, Wyman and Changeux

The co-operativity of homotropic interactions between substrate molecules in oligomeric enzymes is analyzed in the frame of the concerted transition theory of Monod et al. (1965). A discussion of the Hill coefficient n_H allows determination of the conditions for negative co-operativity (n_H < 1). This phenonomenon, usually taken as indicative of a sequential mechanism (Koshland et al., 1966), can be accounted for by the concerted model when the enzyme represents a K-V or V system, i.e. when the two protomer conformational states postulated in the theory differ in their catalytic activity. However, only negative co-operativity for catalysis can be explained by the concerted model, not negative co-operativity of binding.     

Impact of hapten presentation on antibody binding at lipid membrane interfaces

We report the effects of ligand presentation on the binding of aqueous proteins to solid supported lipid bilayers. Specifically, we show that the equilibrium dissociation constant can be strongly affected by ligand lipophilicity and linker length/structure. The apparent equilibrium dissociation constants (K_D) were compared for two model systems, biotin/anti-biotin and 2,4-dinitrophenyl (DNP)/anti-DNP, in bulk solution and at model membrane surfaces. The binding constants in solution were obtained from fluorescence anisotropy measurements. The surface binding constants were determined by microfluidic techniques in conjunction with total internal reflection fluorescence microscopy. The results showed that the bulk solution equilibrium dissociation constants for anti-biotin and anti-DNP were almost identical, K_D(bulk) = 1.7 ± 0.2 nM vs. 2.9 ± 0.1 nM. By contrast, the dissociation constant for anti-biotin antibody was three orders of magnitude tighter than for anti-DNP at a lipid membrane interface, K_D = 3.6 ± 1.1 nM vs. 2.0 ± 0.2 μM. We postulate that the pronounced difference in surface binding constants for these two similar antibodies is due to differences in the ligands’ relative lipophilicity, i.e., the more hydrophobic DNP molecules had a stronger interaction with the lipid bilayers, rendering them less available to incoming anti-DNP antibodies compared with the biotin/anti-biotin system. However, when membrane-bound biotin ligands were well screened by a poly(ethylene glycol) (PEG) polymer brush, the K_D value for the anti-biotin antibody could also be weakened by three orders of magnitude, 2.4 ± 1.1 μM. On the other hand, the dissociation constant for anti-DNP antibodies at a lipid interface could be significantly enhanced when DNP haptens were tethered to the end of very long hydrophilic PEG lipopolymers (K_D = 21 ± 10 nM) rather than presented on short lipid-conjugated tethers. These results demonstrate that ligand presentation strongly influences protein interactions with membrane-bound ligands.     

Functional properties of the hemoglobin from the South American snake Mastigodryas bifossatus

The hemolysate of Mastigodryas bifossatus shows two major hemoglobins with very close isoelectric points, and four different globin chains. The stripped hemolysate exhibits a low alkaline Bohr effect (Δlog P₅₀/ΔpH = −0.30 between pH7 and 8) and a decrease of the co-operativity from 2.3 to unity when the pH increases from 6.15 to 8.5. In the presence of ATP, large changes in the oxygen affinity and co-operativity are observed. The Bohr effect rises to −0.46 and the n₅₀ values stay at around 3 in the pH range 6–9. An increase in temperature induces a large decrease in the oxygen affinity for the stripped hemolysate. In the pH range between 7.5 and 8.5, the values of AH in kcal/M are around 10 fold larger for the stripped protein than for the protein in the presence of ATP. Measurements of rapid kinetics of oxygen dissociation and carbon monoxide binding reflect the ATP sensitivity observed in equilibrium experiments.     

Contributions of water transfer energy to protein‐ligand association and dissociation barriers: Watermap analysis of a series of p38α MAP kinase inhibitors

In our previous work, we proposed that desolvation and resolvation of the binding sites of proteins can serve as the slowest steps during ligand association and dissociation, respectively, and tested this hypothesis on two protein‐ligand systems with known binding kinetics behavior. In the present work, we test this hypothesis on another kinetically‐determined protein‐ligand system—that of p38α and eight Type II BIRB 796 inhibitor analogs. The k_on values among the inhibitor analogs are narrowly distributed (10⁴ ≤ k_on ≤ 10⁵ M^?1 s^?1), suggesting a common rate‐determining step, whereas the k_off values are widely distributed (10^?1 ≤ k_off ≤ 10^?6 s^?1), suggesting a spectrum of rate‐determining steps. We calculated the solvation properties of the DFG‐out protein conformation using an explicit solvent molecular dynamics simulation and thermodynamic analysis method implemented in WaterMap to predict the enthalpic and entropic costs of water transfer to and from bulk solvent incurred upon association and dissociation of each inhibitor. The results suggest that the rate‐determining step for association consists of the transfer of a common set of enthalpically favorable solvating water molecules from the binding site to bulk solvent. The rate‐determining step for inhibitor dissociation consists of the transfer of water from bulk solvent to specific binding site positions that are unfavorably solvated in the apo protein, and evacuated during ligand association. Different sets of unfavorable solvation are evacuated by each ligand, and the observed dissociation barriers are qualitatively consistent with the calculated solvation free energies of those sets.     

First structural evidence for the mode of diffusion of aromatic ligands and ligand-induced closure of the hydrophobic channel in heme peroxidases

The mode of binding of aromatic ligands in the substrate binding site on the distal heme side in heme peroxidases is well understood. However, the mode of diffusion through the extended hydrophobic channel and the regulatory role of the channel are not yet clear. To provide answers to these questions, the crystal structure of the complex of lactoperoxidase and 3-amino-1,2,4-triazole (amitrole) has been determined, which revealed the presence of two ligand molecules, one in the substrate binding site and the second in the hydrophobic channel. The binding of ligand in the channel induced a remarkable conformational change in the side chain of Phe254, which flips from its original distant position to interact with the trapped ligand in the hydrophobic channel. As a result, the channel is completely blocked so that no ligand can diffuse through it to the substrate binding site. Another amitrole molecule is bound to lactoperoxidase in the substrate binding site by replacing three water molecules, including the crucial iron-bound water molecule, W1. In this arrangement, the amino nitrogen atom of amitrole occupies the position of W1 and interacts directly with ferric iron. As a consequence, it prevents the binding of H₂O₂ to heme iron. Thus, the interactions of amitrole with lactoperoxidase obstruct both the passage of ligands through the hydrophobic channel as well as the binding of H₂O₂. This explains the amitrole toxicity. From binding studies, the dissociation constant (K _d) for amitrole with lactoperoxidase was found to be approximately 5.5 × 10⁻⁷ M, indicating high affinity.