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. If we designate the initial site as (-) and the changed site as (+), then the Langmuir requirement for independence of sites yields a set of nearest neighbor interactions such that the (- -), (- +), (+ -), and (+ +) interactions are all identical. This identity is usually characterized as "no interactions." Ising, in dealing with electron pairs, invoked nearest neighbor interactions such that the interactions of the (- -) paris equaled those of the (+ +) pairs, but with the (- +) and (+ -) pairs differing from the reference (- -) pair. Pauling, on the other hand, postulated that only the (- -) and (+ -) pairs interacted differently. A dichotomy has arisen in the application of these two models, with some investigators ignoring or overlooking one of the models. We explore these models, alone and combined, with exact partition functions generated in reasonable computer times for hundreds of sites employing our combinatorial algorithm.

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. The assumptions lead to the conclusion that stabilization of the molecule of glutamic acid occurs on all steps of the protonation with the predominant stabilization occurring in the early steps of the reaction. An Appendix is included showing that the experimental data for both glycine and glutamic acid can be generated with hypothetical molecules. For glycine, identical experimental isotherms can result from protonation of two different nitrogen groups as well as two different negative groups. With glutamic acid three hypothetical molecules are capable of generating the identical experimental isotherms. They are (i) three nitrogen groups, (ii) three negative groups, and (iii) two nitrogen groups combined with one negative group. Interpretation of binding data requires explicit assumptions defining both the interactions and the nature of the binding sites.

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. A new, exact, and fast combinatorial procedure is presented. In this procedure the sites may be single or overlapping in a linear lattice or in the form of a ring. The dimensions of the ring of 11 binding sites for L-tryptophan on the trp RNA-binding attenuation protein are such as to prevent direct interactions between the L-tryptophan molecules. Reasonable and explicit assumptions on analyzing the binding data lead to the conclusion that binding of L-tryptophan raises the energy level of (destabilizes) the 11 membered structure.

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. Ligand-dependent nearest neighbor interactions may be of two types referred to as ligand-lattice (which can only occur if a bound ligand is unneighbored) and ligand-ligand (which can occur if two or more bound ligands are adjacent). The molecular mechanisms underlying these two sources of cooperativity are not the same. Identical cooperative binding curves may be produced by changes from unity in parameters representing either one or both of these interaction types. Positive cooperativity may equally result from destabilizing ligand-lattice interactions that disfavor initial, unneighbored binding, stabilizing ligand-ligand interactions that favor subsequent, neighbored binding, or both. The structural origins of these are different, and cooperativity may emerge from multiple structural interactions.

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. Models and equations developed previously for the analysis of these binding isotherms have included only the protein-protein interactions (usually characterized with the symbol omega). The exact equations of this paper are capable of analyzing binding data in a manner to evaluate the relative importance of both occupied-unoccupied and occupied-occupied interactions. Relations derived here are employed to analyze some existing data, and the resulting parameter values are compared to those developed with equations employing only the protein-protein (occupied-occupied) interactions. The resulting parameter values are qualitatively different. Values of the binding constants differ by about three orders of magnitude. When only protein-protein interactions are taken into account, the resulting free energy of interaction is negative, indicating attractive forces between bound protein molecules; when both occupied-unoccupied and occupied-occupied interactions are applied, the resulting free energies of interaction are positive, indicating destabilizing forces acting primarily on the polynucleotide lattice.

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. 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.

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. We demonstrate that data from individual-site isotherms can be interpreted only after explicit assumptions specifying the nature of the ligand-dependent interactions are made.

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. (C) They do not define the nature of the interactions; that is, they do not resolve the free energies of the interactions between the sites. (D) When some assumptions about the nature of the interactions are made they may aid in defining some free energies of interaction 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. Two conceptually distinct free energy differences may contribute to cooperativity in an aggregation reaction. One is the free energy difference in ligand binding between the monomer and the aggregate. The other is derived from ligand-dependent interactions between the sites of the aggregate. In this analysis an explicit distinction is made between the experimentally accessible constants and those derived from assumed models. Experimental measurements of an aggregation cycle in which all of the species in equilibrium are defined do not allow for an evaluation of the energies of interaction without some model (or assumption). In the analysis presented, an explicit assumption is employed relating the constant for binding of the ligand to the isolated monomer and the constant for the binding of the ligand to aggregate under conditions where there are no ligand-dependent interactions.

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. Martell & M. Calvin (1952) Chemistry of the Metal Chelate Compounds, Prentice-Hall, Englewood Cliffs, New Jersey]. Reactions are formulated in this paper to show that anions, chelating to positively charged clusters, are also capable of developing the cooperative binding of protons. Extension of these simple reactions to those where clusters of ionizable groups are shared between domains of macromolecules provides models for cooperative binding, which include the allosteric, Bohr, anion, and cation effects in proteins.

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 Monte Carlo method is developed as an accurate means of evaluating uncertainties in parameter values for nonlinear models. Examples are given for both actual and synthetic data.

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. Procedures are illustrated for deriving interaction parameters from binding data. The interaction parameters for about 25 representative compounds with two and three interacting ionizable groups are evaluated and tabulated.

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 8.0, buffer, and the other 0.01 M tris(hydroxymethyl)aminomethane, pH 8.0, and 3 M urea buffer, were employed. The purified protein has a native molecular weight of 114,000 as determined by sedimentation equilibrium analysis. Circular dichroism data showed that the protein has 28% helical structure, 29% beta-structure, and 15% beta-turns, and the rest is random coil. Addition of the purified protein to clathrin results in the polymerization of clathrin to homogeneous size baskets of sedimentation velocity 150 S. A scan of the Coomassie Blue stained electrophoresis gels of the polymerized baskets shows that, for every clathrin trimer, there is approximately one 100-kDa protein molecule.

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. The primary site of TSH binding on the HDL particle is likely to be located on its protein moieties, since other lipoprotein classes, which share similar lipids with HDL, do not bind TSH. 125I-labeled apolipoprotein A-I binds TSH in the solid-phase assay and titration of DNS-TSH with apolipoprotein A-I causes perturbations nearly identical to those observed with intact HDL. One HDL particle has at least 12 binding sites for TSH with an association constant, K = 10(7) M-1 whereas one apolipoprotein A-I molecule binds one or two TSH molecules with an association constant slightly lower than that for HDL (K = 10(6) M-1). The lipid moieties of HDL also appears to be perturbed by the interaction with TSH.

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 +/- 3.1. Seventy-one tripeptides occur only once with an expected value of 37.1 +/- 6.1. These results suggest that some peptides not found in certain species are reserved for use only in other species. The proposal is made that small peptides serve as species specific markers and function as signals in the recognition process for activation of the immune response.

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. The rate of polymerization is sensitive to all the variables investigated. The reaction is very slow at pH approximately 7 and becomes very rapid by pH approximately 6. The polymerization is readily reversed by increasing the pH slightly. The time dependence of the polymerization does not conform to either a first- or a second-order reaction but to a higher order. Increasing temperature increases the rate but decreases the extent of reaction. Increasing the salt concentration decreases the rate. The effects of several salts on the rate follow the Hofmeister ranking, with the exception of sulfate.