The model of Monod, Wyman, and Changeux generates two sets of parameters when applied to oxygen binding in hemoglobin.

The model of Monod, Wyman and Changeux is applied to binding phenomena where the Mass Law and its expansion are employed. In this communication the model of Monod, Wyman and Changeux (MWC) is applied to analyze the oxygen binding reaction in hemoglobin. The symmetrical structure of the MWC model with its three parameters is such that two sets of these parameters, rather than one, fit experimental data for the binding of oxygen to hemoglobin.

The Nernst equation applied to oxidation-reduction reactions in myoglobin and hemoglobin. Evaluation of the parameters.

Analyses of the binding of oxygen to monomers such as myoglobin employ the Mass Action equation. The Mass Action equation, as such, is not directly applicable for the analysis of the binding of oxygen to oligomers such as hemoglobin. When the binding of oxygen to hemoglobin is analyzed, models incorporating extensions of mass action are employed.

pH effects on the binding of oxygen to non-vertebrate monomeric hemoglobins. A linked function model.

Monomeric invertabrate hemoglobins with high oxygen affinity usually contain a tyrosine in the distal region of the heme. This feature has stimulated investigations revealing that one of the properties resulting from the presence of the distal tyrosines is a decreased off rate on the binding of oxygen, thus developing the high affinity. Despite that fact that the pK value of the tyrosine group differs significantly from the groups it replaces little attention has been paid to the pH dependence of the binding of oxygen to the high affinity hemoglobins.

Structure of deoxyhemoglobin: ionizable groups and polyethylene glycol.

X-ray studies on deoxy-hemoglobin have been reported on crystals grown under conditions of high (about 2.5 M) and low salt (about 0.1 M).

The legacies of Langmuir, Ising, and Pauling: ligand binding and the helix-coil transition.

Multiple, independent sites or domains behave, on chemical change, in a manner predicted by Langmuir. Distortions of this behavior have been attributed to interactions between the domains, which vary with the progress of the changes occurring at the sites or domains. The two main models for nearest neighbor interactions perturbing the Langmuir prediction for independent domains are those of Ising and Pauling.

From glycine to glutamic acid: analysis of the proton-binding isotherm of glutamic acid.

The process of the analysis of the protonation of glycine is extended to the three-site molecule of glutamic acid with its amino and two carboxyl groups. Detailed data on the binding of protons to glutamic acid are available not only for protonation of the three groups simultaneously but also for derivatives in which the alpha and beta carboxyl groups are esterified. These data plus data on the protonation of glutaric acid provide the necessary information for a complete description of the protonation process with a limited number of reasonable assumptions.

Analysis of the binding of ligands to large numbers of sites: the binding of tryptophan to the 11 sites of the trp RNA-binding attenuation protein.

Analysis of the cooperative binding of ligands may provide insight into the underlying mechanisms of biological control. Binding of L-tryptophan at each juncture in the ring of 11 subunits of the trp RNA-binding attenuation protein exhibits cooperativity. To analyze binding of this kind we have developed both the matrix and combinatorial procedures for binding to large numbers of sites.

The multiple origins of cooperativity in binding to multi-site lattices.

Binding events involving the reversible association of ligands with polymeric lattices of binding sites are common in biology and frequently exhibit significant cooperativity in binding. Positive and negative cooperativity in binding may be detected by characteristic changes in binding curves for multiple binding, compared to the binding expected for simple, independent binding events that are based on combinatorial considerations only. Cooperativity arises from ligand-dependent interactions distinct from binding per se.

Energetics of protein-DNA interactions: an exact calculation for binding of ligands to a lattice of overlapping sites.

Exact equations are developed for analyzing the binding of ligands to a linear lattice of overlapping sites in which occupied-unoccupied as well as occupied-occupied interactions are included for the analysis of the binding isotherms. We demonstrate that positive cooperativity on the binding of ligands to multiple sites may derive from either occupied-unoccupied or occupied-occupied interactions. When the binding of proteins to linear polynucleotides and DNA has exhibited positive cooperativity protein-protein (occupied-occupied), interactions have heretofore been invoked as the sole energetic source in determining the cooperative effect.

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

Individual-site isotherms for the binding of bacteriophage lambda repressor to the left and right lambda operators have been determined [D. F. Senear, M.

Linked functions and the analysis of individual-site binding data.

Linked ligand functions for analyzing experimental data evaluated to yield macroscopic apparent binding constants were well developed by Adair and by Wyman. In this paper, expressions for the linked function (derivative) delta ln(K)/delta ln(c) are applied to both macroscopic association constants and individual-site association constants derived from individual-site binding data. A detailed treatment of a simple interacting system is presented.

Analysis of individual-site binding data.

Individual-site isotherms add experimental data which may allow for a more detailed definition of the parameters in a system with interacting binding sites. Individual-site isotherms accomplish the following: (A) In general, they define little more than the total or combined isotherm except to reveal the existence of different sites. (B) Under the limiting conditions of symmetrical interactions in two site systems they define: (1) the ratio of the unperturbed or intrinsic binding constants rather than their actual values, (2) the unperturbed shape of the total isotherm, that is, the shape of the total isotherm if there were no ligand dependent interactions between the sites, and (3) the perturbation of the shape of the total isotherm derived from interactions between the sites.

Ligand-dependent aggregation and cooperativity: a critique.

Ligand-dependent site-site (or subunit-subunit) interactions provide the basis for explaining cooperativity in chemical reactions. Even in the simplest possible nonaggregating system, interpretation of the interactions in terms of structural details requires an explicit assumption (or model) for the binding of the ligand to the sites when there are no interactions. This paper develops in detail the processes by which aggregation will yield ligand-dependent cooperativity.

Ionization of clusters. IV. Cooperativity and allosterism derived from shared clusters in macromolecules.

Clusters of ionizable groups are examined for conditions that develop cooperativity (1) on the binding of protons, and (2) on the binding of an associated ligand when the clusters are shared between domains or subunits in macromolecules. Cooperative binding isotherms for protons have long been observed (but not emphasized as cooperative binding) when studies have been done on clusters for the evaluation of metal ion complexation [A. E.

Evaluation of uncertainties for parameters in binding studies: the sum-of-squares profile and Monte Carlo estimation.

Methods for characterization and evaluation of uncertainties in the parameter values for binding experiments are presented. A sum-of-squares profile is defined and illustrated. Sum-of-squares profiles give a qualitative description of both the uncertainties and correlation of parameters.

The ionization of clusters. II. Pairwise isotropic interactions and individual site binding data.

Evaluation of the parameters describing the binding of protons to clusters of interacting sites requires some reasonable assumptions and procedures because it is impossible to observe an unperturbed site in its interacting environment. When the unperturbed sites are not identical, individual site binding data allow for the evaluation of the differences (or ratios) between the unperturbed (or intrinsic) binding constants but not their actual values (or the interaction energies). In this paper we extend our previous treatment of the ionization of clusters in order to generalize pairwise isotropic interactions and take into account the present availability of individual site binding data.

Ionization of clusters. III. Evaluation of interaction parameters from binding data.

Interactions between ionizable groups on the same molecule modulate the binding of protons to an extent where the binding constants may be shifted by orders of magnitude. The first two papers of this series discussed the family of carboxylic acids, pairwise isotropic interactions, and evaluation of single site binding data. This paper presents an extended group of hypothetical binding isotherms.

Purification and characterization of a molecular weight 100,000 coat protein from coated vesicles obtained from bovine brain.

A protein designated as a 100-kDa protein on the basis of sodium dodecyl sulfate gel electrophoresis was purified from coated vesicles obtained from bovine brain, with uncoated vesicles as starting material. Two gel filtration steps, one involving 0.5 M tris(hydroxymethyl)aminomethane, pH 8.

The uniqueness of protein sequences: molecular territoriality.

The number of tripeptides which do not occur and which occur only a small number of times in the existing data bank of protein sequences is much larger than that expected on the basis of random selection (from Monte Carlo analyses). Forty tripeptides are not found in the data bank of 289 500 amino acids while the value expected on the basis of random selection is 8.0 +/- 3.

Thyrotropin interaction with high-density lipoproteins.

Human high-density lipoproteins (HDL), but not other lipoprotein classes, bind bovine thyrotropin (TSH) with moderately high affinity. Binding of 125I-labeled HDL to TSH has been measured in a solid-phase assay; it is saturable and can be displaced by unlabeled HDL but not by other lipoproteins or bovine serum albumin. The interaction of HDL with TSH has been studied by fluorescence spectroscopy: HDL specifically modifies the fluorescence properties of the biologically active dansyl derivative (DNS, (5-dimethyl-aminonaphtalene-1-sulfonyl) chloride) of TSH (DNS-TSH) causing a 12 nm shift to lower wavelength of the emission maximum, a two-fold increase of the quantum yield and a significant increase of fluorescence polarization.

Polymerization of clathrin protomers into basket structures.

The effects of pH, ionic strength, temperature, and protein concentration on the rate of clathrin (8 S) polymerization to form coat (or basket) structures (approximately 300 S) have been measured by turbidity. The extent of polymerization has also been evaluated under the same experimental conditions by analytical centrifugation. The characteristic polygonal structure of the re-formed coat was confirmed by electron microscopy.