Analysis of the effects of chloride and 2,3-diphosphoglycerate on the cooperative binding of oxygen to hemoglobin.

Analysis of experimental equilibrium constants for the oxygenation of hemoglobin leads to a plausible mechanism for the effect of pH and of chloride ions on cooperativity in hemoglobin. According to this mechanism, the structural changes responsible for cooperativity in chloride- and 2,3-diphosphoglycerate-free hemoglobin are affected only slightly by changes in pH, and the effect of chloride can be accounted for by sequential binding and release of chloride ions during oxygenation.     

Global conformational changes in allosteric proteins. A study of Escherichia coli cAMP receptor protein and muscle pyruvate kinase.

One of the basic features in allosteric regulation involves long range transduction of information. Based on crystallographic data on protein systems that are regulated by allosteric mechanisms, a global conformational change has always been observed. It is, therefore, important and useful to correlate the cooperativity of global structural change with the mode of binding of the regulatory ligand. Two systems were chosen for study, namely Escherichia coli cAMP receptor protein and muscle pyruvate kinase, which show negative and positive cooperativity in the binding of allosteric ligands, respectively. Quantitative titration of the global structural change, monitored by a high precision analytical gel chromatography technique, was conducted as a function of allosteric effector concentration. The results obtained for cAMP receptor protein show that the protein undergoes contraction upon binding of cAMP. The decreases in Stokes radius associated with complex formation are 0.1 +/- 0.1 and 0.7 +/- 0.1 A when one and two cAMP-binding sites are filled, respectively. The results for the pyruvate kinase system show a concerted structural change that quantitatively match the predicted behavior based on equilibrium constants derived from the analysis of steady state kinetic data by a two-state model. Hence, for these two systems, these results show that negative and positive cooperativity are correlated with sequential and concerted modes of structural change, respectively.     

Effects of ligand size on pH and organic phosphate-dependent affinity changes in carp hemoglobin as measured by isonitrile binding

The equilibria of the binding of methyl and ethyl isonitrile to carp hemoglobin have been measured at three pH values in the presence and absence of inositol hexaphosphate. The binding of methyl isonitrile is characterized by a higher overall dissociation constant, C1/2, and a higher Hill coefficient, n, than that of the ethyl derivative. The former is consistent with the greater hydrophobicity of ethyl isonitrile, and the latter is probably due to a greater intrinsic difference or heterogeneity in the binding affinities of the alpha- and beta-chains for the larger ligand. Changes in log C1/2 which result from alterations in pH or addition of organic phosphate are the same for both ligands within experimental error. This result is not consistent with affinity changes being the result of steric interactions between the protein and the ligand. At pH 6 in the presence of inositol hexaphosphate, equilibrium parameters estimated from overall rates of ligand binding and dissociation are in good agreement with direct equilibrium measurements. This is consistent with the protein being in a low-affinity, T-like state even when saturated with ligand under these conditions, resulting in a loss of cooperativity in ligand binding. At high pH, ligand binding remains cooperative, as evidenced by n values greater than unity, a general lack of agreement between measured equilibrium parameters and those estimated from overall kinetic constants, and differences in the kinetics of ligand binding as observed by rapid-mixing and flash photolysis techniques. Thus, the deoxygenated state of carp hemoglobin at high pH does not appear to be a good model of a deoxygenated R quaternary structural state.     

Chemical synthesis of [32P]pyrophosphate with high specific activity

Graphical methods have traditionally been the principal means for estimation of parameters (e.g., affinity constants, cooperativity parameters, and concentrations of receptor sites) in enzymology and ligand-binding problems. The present report provides a review of these methods as well as new results, as applied to three coordinate systems popularly used in ligand-binding studies: $\text{B}\text{F}$ vs [Bound]. $\text{B}\text{F}$ vs [Free], and $\text{B}\text{F}$ vs [Total]. We consider two extremely general models, the statistical mechanical model and the Adair model for equilibrium ligand binding. We also consider a very specialized case of receptor interaction wherein the equilibrium constannt of dissociation is linearly related to receptor occupancy. We collect previously described equations and derive new ones, to enable the user to estimate the parameters of the models in terms of relatively easily measurable graphical characteristics. We have evaluated the performance of these methods in representative cases using Monte Carlo studies. The results indicate the kind of precision and accuracy which can be obtained with typical experimental designs. Depending upon the magnitude of experimental error, the graphical methods can provide dependable values for the binding parameters. However, in general, the results obtained by the graphical methods should be regarded as reasonable initial estimates for further refinement by weighted nonlinear least-squares curve fitting.     

Energetics of cooperative protein-DNA interactions: comparison between quantitative deoxyribonuclease footprint titration and filter binding

Using the binding of cI repressor protein to the lambda right and left operators as a model system, we have analyzed the two common experimental techniques for studying the interactions of genome regulatory proteins with multiple, specific sites on DNA. These are the quantitative DNase footprint titration technique [Brenowitz, M., Senear, D. F., Shea, M. A., & Ackers, G. K. (1986) Methods Enzymol. 130, 132-181] and the nitrocellulose filter binding assay [Riggs, A., Suzuki, H., & Bourgeois, S. (1970) J. Mol. Biol. 48, 67-83]. The footprint titration technique provides binding curves that separately represent the fractional saturation for each site. In principle, such data contain the information necessary to determine the thermodynamic constants for local site binding and cooperativity. We show that in practice, this is not possible for all values of the constants in multisite systems, such as the lambda operators. We show how these constants can nevertheless be uniquely determined by using additional binding data from a small number of mutant operators in which the number of binding sites has been reduced. The filter binding technique does not distinguish binding to the individual sites and yields only macroscopic binding parameters which are composite averages of the various local site and cooperativity constants. Moreover, the resolution of even macroscopic constants from filter binding data for multisite systems requires ad hoc assumptions as to a relationship between the number of ligands bound and the filter retention of the complex. Our results indicate that no such relationship exists. Hence, the technique does not permit determination of thermodynamically valid interaction constants (even macroscopic) in multisite systems.     

Nonlinear effects in macromolecular assembly and dosage sensitivity

Haploinsufficiency refers to dominant abnormal phenotypes resulting from the absence of substantial activity from one allele at a normally diploid locus. Haploinsufficiency may also result from an altered stoichiometry in a macromolecular complex. Higher-than-diploid levels of a gene product can also induce abnormalities that may even resemble the haploinsufficient phenotype. Here, I explore possible non-linearities in the assembly of multimeric molecules from the perspective of dose effects. I propose that for any oligomer assembly reaction, there may be a set of conditions (initial subunit concentrations and equilibrium constants) such that changing the input concentration of one component (0.5 x or 1.5x) will lead to a minimum and non-proportional change of the final oligomer concentration. This buffer effect is a general property of multimeric systems in equilibrium and can be, in principle, exploited by selection to diminish dosage sensitivity. Other effects involving cooperativity or sequential assembly may also play a role in palliating the effect of changes in input amounts of monomers.     

Cooperative binding of oligonucleotides to adjacent sites of single-stranded DNA: sequence composition dependence at the junction

The quantitative parameters of cooperative binding of deoxyribooligonucleotides to adjacent sites by double helix formation have been determined as a function of sequence composition at the junction. The base stacks 5'-Py/p-Py-3', 5'-Pu/p-Py-3' and 5'-Pu/p-Pu-3' (p is phosphate group, Py and Pu are pyrimidine and purine nucleoside, respectively) including mismatches on the 3'-side of the junction were studied using complementary addressed modification titration (CAMT) at 25 degrees C and pH 7.5, 0.16 M NaCl, 0.02 M Na2HPO4, 0.1 mM EDTA. The equilibrium binding constants of alkylating derivatives of 8-mer oligonucleotides (reagents) with 22-mer oligonucleotides (targets) were determined using the dependence of the target limit modification extents on the concentrations of the reagents. The parameters of cooperativity were calculated as the ratio of binding constants of reagents in the presence and the absence of a second 8-mer oligonucleotides (effectors) occupying the adjacent site on the 22-mer targets. For the stacks 5'-Py/p-Py-3' the parameters of cooperativity were around unity both for matched and mismatched nucleotides at the junction indicating the absence of cooperativity. The parameters of cooperativity for the stacks 5'-Pu/p-Pu-3' were higher than for the stacks 5'-Pu/p-Py-3' in perfect and non-perfect duplexes. Discrimination of mismatches was higher in nicked than in normal duplexes.     

Cooperative binding of oxygen to hemoglobin: analysis of accurate equilibrium binding data

Accurate equilibrium binding data for the oxygenation of hemoglobin are used (a) to show that various models for cooperativity are inconsistent with the best available experimental data, (b) to determine the equilibrium constants for binding of 2,3-diphosphoglycerate to hemoglobin molecules in intermediate stages of oxygenation, and (c) to deduce a mechanism for allosteric effects in hemoglobin which is consistent with the best available experimental data. The total free energy of cooperativity is defined and discussed.     

Analysis of hemoglobin oxygenation from combined equilibrium and kinetic data. Is quaternary enhancement necessary?

An experimental approach based on four independent techniques, in which kinetic and equilibrium measurements of subunit assembly reactions are combined with concentration-dependent oxygen-binding curves, has previously been used to resolve parameters of the linkage system for human hemoglobin over a wide range of conditions [(G.K. Ackers and H.R. Halvorson, Proc. Natl. Acad. Sci. U.S.A. 71 (1974) 4312; F.C. Mills et al., Biochemistry 15 (1976) 1093; M.L. Johnson et al., Biochemistry 15 (1976) 5363). Throughout this extensive body of results it has been found that the affinity for binding oxygen to tetramers at the fourth step exceeds the mean affinity of dissociated dimers. The existence of this "quaternary enhancement" effect has recently been questioned by Gibson and Edelstein (J. Biol. Chem. 262 (1987) 516) and by Philo and Lary (J. Biol. Chem. 265 (1990) 139) on the basis of kinetically derived oxygen-binding constants that do not exhibit quaternary enhancement. These authors have also suggested that quaternary enhancement might not be necessary to explain the oxygen-binding data mentioned above. In this study, we have explored the effect of constraining the numerical analysis of oxygen-binding data against the new kinetically derived binding constants. It is found that the sets of linkage constants which are compatible with both the oxygen-binding data and the new kinetically derived dimer binding constant require both quaternary enhancement and substantial dimer cooperativity. Increasing the dimer cooperativity to compensate completely for quaternary enhancement requires both dimeric and tetrameric binding constants that disagree with the kinetically derived values. Thus, the quaternary enhancement effect cannot be eliminated by readjustment of the remaining constants of the linkage system. Possible sources of the discrepancy between the kinetically derived binding constants and the otherwise self-consistent data from the other four techniques are discussed.     

A Hierarchical Approach to Cooperativity in Macromolecular and Self-Assembling Binding Systems

The study of complex macromolecular binding systems reveals that a high number of states and processes are involved in their mechanism of action, as has become more apparent with the sophistication of the experimental techniques used. The resulting information is often difficult to interpret because of the complexity of the scheme (large size and profuse interactions, including cooperative and self-assembling interactions) and the lack of transparency that this complexity introduces into the interpretation of the indexes traditionally used to describe the binding properties. In particular, cooperative behaviour can be attributed to very different causes, such as direct chemical modification of the binding sites, conformational changes in the whole structure of the macromolecule, aggregation processes between different subunits, etc. In this paper, we propose a novel approach for the analysis of the binding properties of complex macromolecular and self-assembling systems. To quantify the binding behaviour, we use the global association quotient defined as K _c = [occupied sites]/([free sites] L), L being the free ligand concentration. K _c can be easily related to other measures of cooperativity (such as the Hill number or the Scatchard plot) and to the free energies involved in the binding processes at each ligand concentration. In a previous work, it was shown that K_c could be decomposed as an average of equilibrium constants in two ways: intrinsic constants for Adair binding systems and elementary constants for the general case. In this study, we show that these two decompositions are particular cases of a more general expression, where the average is over partial association quotients, associated with subsystems from which the system is composed. We also show that if the system is split into different subsystems according to a binding hierarchy that starts from the lower, microscopic level and ends at the higher, aggregation level, the global association quotient can be decomposed following the hierarchical levels of macromolecular organisation. In this process, the partial association quotients of one level are expressed, in a recursive way, as a function of the partial quotients of the level that is immediately below, until the microscopic level is reached. As a result, the binding properties of very complex macromolecular systems can be analysed in detail, making the mechanistic explanation of their behaviour transparent. In addition, our approach provides a model-independent interpretation of the intrinsic equilibrium constants in terms of the elementary ones.     

Kinetics of ligand binding and quaternary conformational change in the homodimeric hemoglobin from Scapharca inaequivalvis

The kinetics of the reaction with oxygen and carbon monoxide of the homodimeric hemoglobin from the bivalve mollusc Scapharca inaequivalvis has been extensively investigated by flash and dye-laser photolysis, temperature jump relaxation, and stopped flow methods. The results indicate that cooperativity in ligand binding, already observed for oxygen at equilibrium, finds its kinetic counterpart in a large decrease of the oxygen dissociation velocity in the second step of the binding reaction. In the case of carbon monoxide, cooperativity is clearly evident in the increase of the combination velocity constant as the reaction proceeds. Therefore, the ligand-binding kinetics of this dimeric hemoglobin shows the characteristic features of the corresponding reactions of tetrameric hemoglobins. Analysis of the data in terms of the allosteric model proposed by Monod et al. (Monod, J., Wyman, J., and Changeux, J. P. (1965) J. Mol. Biol. 12, 88-118) has shown that the values of the allosteric parameters cannot be fixed uniquely for a dimeric hemoglobin. The rapid changes in absorbance observed at the isosbestic points of unliganded and liganded hemoglobin following laser photolysis provided a value of 7 X 10(4) S-1 at 20 degrees C for the rate of the ligand-free quarternary conformational change, postulated on the basis of cooperative ligand binding. Comparison of the rapid absorbance changes observed during ligand rebinding in this hemoglobin with those observed in tuna hemoglobin indicate that, at full photolysis, binding to the T state is followed by further binding and conversion to the liganded R state; at partial photolysis, population of the liganded T state occurs immediately and is followed by a decay to the liganded R state upon further ligand binding. These new results, in conjunction with previous equilibrium data on the same system, show unequivocally that the presence of two different types of chain is not an absolute prerequisite for cooperativity in hemoglobins, contrary to currently accepted ideas.     

Steady-state parameters of an enzyme from n.m.r. spin transfer with thermal variation.

N.m.r. spin-exchange analysis of enzymic reactions at chemical equilibrium is akin to radioactive-tracer-exchange analysis; unidirectional flux rates are obtained for the overall reaction. These data, by themselves, are not sufficient to define the values of all the individual rate constants or steady-state parameters. However, it is shown that, by measuring the dependence of the exchange rate constants on solute concentration and temperature, the individual rate constants, and hence the steady-state parameters, can be obtained for a simple enzyme system.     

Characterization of a new four-chain coiled-coil: influence of chain length on stability.

Limited information is available on inherent stabilities of four-chain-coils. We have developed a model system to study this folding motif using synthetic peptides derived from sequences contained in the tetramerization domain of Lac repressor. These peptides are tetrameric as judged by both gel filtration and sedimentation equilibrium and the tetramers are fully helical as determined by CD. The four-chain coiled-coils are well folded as judged by the cooperativity of thermal unfolding and by the extent of dispersion in aliphatic chemical shifts seen in NMR spectra. In addition, we measured the chain length dependence of this four-chain coiled-coil. To this end, we developed a general procedure for nonlinear curve fitting of denaturation data in oligomeric systems. The dissociation constants for bundles that contain alpha-helical chains 21, 28, and 35 amino acids in length are 3.1 x 10(-12), 6.7 x 10(-23), and 1.0 x 10(-38) M3, respectively. This corresponds to tetramer stabilities (in terms of the peptide monomer concentration) of 180 microM, 51 nM, and 280 fM, respectively. Finally, we discuss the rules governing coiled-coil formation in light of the work presented here.     

A study of the complex-formation of phenylalanyl-tRNA-synthetase from Escherichia coli using the tRNA-Phe method of small-angle x-ray scattering

The method of small-angle X-ray scattering was employed to analyse the equilibrium enzyme-substrate complexes in solution. A new approach of analysis of the experimental data was developed. This type of analysis provides the determination of dissociation constants and structural parameters of enzyme-substrate complexes. The radius of gyration (Rg) and dimensions of half-axis of the equivalent prolonged ellipsoid (a, b) of E. coliphenylalanyl-tRNA synthetase and its complexes with one or two tRNA(Phe) molecules have been determined. The values of these parameters speak in favour of structural rearrangements due to the interaction of the enzyme with tRNA(Phe). The thermodynamic characteristics of phenylalanyl-tRNA synthetase complexes with tRNA(Phe) testify to the negative cooperativity in binding of two tRNA molecules with the enzyme.     

Determination of binding constants for cooperative site-specific protein-DNA interactions using the gel mobility-shift assay

We have investigated the question of whether the gel mobility-shift assay can provide data that are useful to the demonstration of cooperativity in the site-specific binding of proteins to DNA. Three common patterns of protein-DNA interaction were considered: (i) the cooperative binding of a protein to two sites (illustrated by the Escherichia coli Gal repressor); (ii) the cooperative binding of a bidentate protein to two sites (illustrated by the E. coli Lac repressor); and (iii) the cooperative binding of a protein to three sites (illustrated by the lambda cI repressor). A simple, rigorous, and easily extendable statistical mechanical approach to the derivation of the binding equations for the different patterns is presented. Both simulated and experimental data for each case are analyzed. The mobility-shift assay provides estimates of the macroscopic binding constants for each step of ligation based on its separation of liganded species by the number of ligands bound. Resolution of the binding constants depends on the precision with which the equilibrium distribution of liganded species is determined over the entire range of titration of each of the sites. However, the evaluation of cooperativity from the macroscopic binding constants is meaningful only for data that are also accurate. Some criteria that are useful in evaluating accuracy are introduced and illustrated. Resolution of cooperative effects is robust only for the simplest case, in which there are two identical protein binding sites. In this case, cooperative effects of up to 1,000-fold are precisely determined. For heterogeneous sites, cooperative effects of greater than 1,000-fold are resolvable, but weak cooperativity is masked by the heterogeneity. For three-site systems, only averaged pair-wise cooperative effects are resolvable.     

The mechanism of self-assembly of the multi-enzyme complex tryptophan synthase from Escherichia coli.

The alpha subunit is bound with negative cooperativity to the holo beta 2 subunit of tryptophan synthase in phosphate buffer. Thus it is feasible to measure separately the rates of formation both of the stable alpha beta 2 subcomplex from beta 2, and of the mature alpha 2 beta 2 complex from alpha beta 2, using stopped-flow techniques. Addition of each alpha subunit proceeds in two steps; an initial alpha beta protomer is formed rapidly, which subsequently isomerizes slowly to the equilibrium state. The rates of dissociation of both the alpha beta 2 and alpha 2 beta 2 complexes were measured by trapping released alpha subunit with enzymically inactive reduced beta 2 subunit. The reversal of the slow isomerization both determines the rate of dissociation, and accounts for the high overall affinity of the beta protomer for the alpha subunit. The data fit to a sequential assembly mechanism consisting of seven protein species and yields values for most of the rate constants and all of the microscopic equilibrium constants. Negative cooperativity arises from a weaker initial binding of the second alpha subunit, as expressed by its larger off-constant, possibly due to steric hindrance. The kinetics of binding of L-serine and indolepropanol phosphate during the assembly process shows that the beta protomer is already partially activated in the initial alpha beta complex. Full activation is achieved in the slow isomerization reaction. In contrast, the alpha subunit gains high affinity for indolepropanol phosphate only in the isomerization reaction. These observations indicate that the isomerization involves synchronous conformation changes of both alpha and beta protomers.