Negative co-operativity in clustered receptors as a possible basis for membrane action

A model for the interaction of a membrane receptor with a stimulating ligand is presented. It is assumed that (a) the receptor macromolecules are embedded in the membrane as a close packed two-dimensional cluster and (b) strong negative co-operative interaction occurs among the receptor molecules. The model explains the existence of (a) strong membrane stimulation by fractional ligand occupancy of the receptor; (b) the absence of positively co-operative binding curves for ligand to membrane receptors and (c) it provides a molecular explanation for the existence of “spare receptor”.     

Free energy coupling within macromolecules. The chemical work of ligand binding at the individual sites in co-operative systems

Individual-site binding curves such as those obtainable from techniques of DNase footprinting or nuclear magnetic resonance spectroscopy can be used to monitor structurally localized events within biopolymers. This paper discusses thermodynamic aspects of individual-site ligand binding for co-operative systems where the binding of ligand at a local site is coupled to binding of the same ligand species at other sites within the macromolecule. Individual-site binding isotherms have the following properties. (1) They provide a direct indication of the role played by the particular site in the overall binding reaction. (2) They can be used to determine the energetic contribution of loading the site regardless of the complexity of the system. (3) They can be used to resolve microscopic equilibrium constants and co-operativity constants in cases where the classical isotherm is incapable of such resolution. The microscopic constants bear a complex relation to the chemical work of loading each individual site. For a system with two interacting sites we derive analytical relationships between the individual-site loading energies and the microscopic constants. These relationships prescribe, for any values of the microscopic constants, how the co-operative energy is partitioned between events at the two sites. At fixed ligand activity the binding free energy can be estimated directly from an individual-site isotherm. This quantity, which is also a composite of the microscopic constants, provides a useful measure of site--site interaction. Several examples and applications are discussed for these properties of individual-site binding reactions.     

Interaction of polyamines with fragments and whole molecules of yeast phenylalanine-specific transfer RNA

Binding of the polyamines spermidine (∼-+3) and spermine (∼-+4) to yeast tRNA^phe has been investigated by equilibrium dialysis under the same conditions used to study Mn²⁺-tRNA^phe interactions (Schreier & Schimmel, 1974). The polyamines bind to tRNA^phe in a co-operative and a non-co-operative phase, which is analogous to the behavior found with Mn²⁺. In the co-operative phase, the empirical index of co-operativity is somewhat greater for the polyamines, however. Binding constants for both the co-operative and non-co-operative phases are similar for Mn²⁺ and spermidine, and are strongest for spermine. Estimates of the total number of ligand binding sites indicate that these numbers are inversely proportional to the charge on the ligand for all three ligands. The interaction of polyamines with four large fragments of tRNA^phe shows no evidence for co-operativity. These results, together with recent kinetic studies, collectively suggest that polyamine binding to the co-operative sites is associated with tertiary structure formation and that polyamine and divalent metal ion interactions with tRNA occur by phenomenologically similar mechanisms, in spite of their structural diversity.     

Comparison between the kinetics of heterogeneous and sequentially co-operative binding systems

The kinetics of ligand binding to a dimer displaying anticooperative interactions is analysed and compared with the kinetics of binding to two classes of independent sites. Both systems are characterized by a bi-exponential kinetics. However, the relation between the coefficients of these exponentials and the concentration of ligand is linear in case of sites heterogeneity and hyperbolic (parabolic in some cases) for a co-operative dimer. The pre-exponential factors are always negative in case of sites heterogeneity and their modulus increases monotonically as a hyperbolic function of the ligand concentration. In cases of anticooperative interaction, one of the pre-exponential factors can be positive and the modulus can change biphasically as a function of the concentration of ligand. The detailed study of binding kinetics at different ligand concentrations provides a potential tool to discriminate between binding sites heterogeneity and negative co-operativity.     

The binding of an indefinitely associating ligand to acceptor: consideration of monovalent ligand species binding to a multivalent acceptor

Currently available binding theory is extended to incorporate the concept of indefinite self-association of the ligand. Binding equations are formulated in closed form for the case of the binding to a multivalent acceptor of a ligand capable of isodesmically indefinitely self-associating in a "head-to-tail" mode such that each ligand state bears one site capable of interacting with the acceptor. It is shown both mathematically and by way of numerical example that this system will give rise exclusively to binding curves convex to the r-axis in Scatchard format. Thus, the system provides another example of a binding mechanism capable of generating an apparent negatively co-operative binding response.     

Co-operative binding interactions in affinity chromatography: Theoretical considerations

A theoretical relationship has been developed to allow the effect of free ligand concentration on the capacity of an affinity Chromatography matrix to be determined where the protein adsorbed shows co-operative binding. Computer simulations using literature values for association constants show that under optimal conditions resin capacity can be increased significantly in the presence of a small but finite concentration of free ligand. The model also allows prediction of the soluble ligand concentration required for biospecific elution. The results obtained suggest the possibility of a new elution technique, "reverse biospecific elution," that reduces the amount of free ligand required to effect elution.     

A mathematical model for dynamics of CD40 clustering

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand–receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.     

Nature of protamine-DNA complexes. A special type of ligand binding co-operativity

The mode of protamine binding to DNA double helices has been analyzed for the example of clupein Z from herring and DNA samples from bacteriophages lambda and PM2 by measurements of light-scattering intensities, ultracentrifugation and kinetics. The light-scattering intensity of DNA increases co-operatively at a threshold clupein concentration suggesting co-operative binding of clupein to double helices. These data are first analyzed in terms of a model with a transition at a threshold degree of binding. The parameters resulting from this analysis appear to be reasonable, but are shown to be in contrast with data on the absolute degree of clupein binding to DNA obtained by centrifugation experiments. An analysis of the kinetics associated with clupein binding to DNA by measurements of the time-dependence of light-scattering intensities in the time range of seconds demonstrates directly that clupein-induced intermolecular interactions of DNA molecules are essential. The rate constants of DNA association increase co-operatively at threshold clupein concentrations, which correspond to those observed in the equilibrium titrations. Above the threshold, the rate constants arrive at a level that is almost constant, but shows some decrease with increasing clupein concentrations. These results are described by a model with a monomer and a dimer state of DNA, which bind ligands with different affinities according to an excluded-site binding scheme. When the ligand binding constant is larger for the dimer than for the monomer state, as should be expected, binding of ligands drives the DNA from the monomer to the dimer state, even if the dimerization equilibrium in the absence of ligands is far in favor of the monomer. The transition from the monomer to the dimer state proves to be strongly co-operative. When the ligand concentration is increased to higher values, the dimers may be converted back to monomers due to an increased extent of ligand binding to the monomer state. The model is consistent with the available experimental data. The analysis of the data by the model indicates the existence of a reaction unit much below the DNA chain length, corresponding to about 80 nucleotide residues. The present model describes ligand driven intermolecular association; an analogous model is applicable to ligand driven intramolecular association. In summary, the co-operativity of clupein binding to DNA double helices is not due to nearest neighbor interactions, but results from thermodynamic coupling of clupein binding with clupein-induced DNA association.     

Theoretical aspects of DNA-protein interactions: co-operative and non-co-operative binding of large ligands to a one-dimensional homogeneous lattice

The interaction of proteins binding non-specifically to DNA, as well as the properties of many other interacting ligand-lattice systems important in molecular biology, requires a fundamentally different type of theoretical analysis than that provided by the classical Scatchard independent-binding-site treatment. Exact and relatively simple equations describing the binding of both non-interacting and interacting (co-operative) ligands to a homogeneous one-dimensional lattice are derived in terms of ligand site size, intrinsic binding constant and ligand-ligand co-operativity (equations (10) and (15) in the text). The mathematical approach is based on simple conditional probabilities, and reveals some largely unrecognized characteristics of such lattice binding systems. The results indicate that the binding of any non-interacting ligand covering more than one lattice residue results in non-linear (convex downward) Scatchard plots. The introduction of positive ligand-ligand co-operativity antagonizes this non-linearity, and eventually leads to plots of the opposite curvature. The maxima, limiting slopes, and intercepts of such plots can be used to estimate the required binding parameters. The method can be extended to systems involving heterogeneous ligands, and some types of heterogeneous lattices. Procedures for applying the method to a variety of interacting systems are presented, and a preliminary analysis is carried out for some selected sets of data from the literature.     

Co-operativity and the methods of plotting binding and steady-state kinetic data.

The features that distinguish positive from negative co-operativity in double-reciprocal Eadie-Hofstee-Scatchard and Hanes plots, often incorrectly stated to be the sign of curvature or second derivatives, are explained. It is shown how to determine the 'Hill exponent' and interaciton free energies from curves in these plots, and in the simple plot of ligand binding or velocity against free ligand or substrate concentration. New types of plots, where the kind of co-operative behaviour is more obvious than in the traditional ones, are proposed.     

Co-operative ligand binding in a protein composed of subunits

The mechanism of the co-operative ligand binding in a protein composed of subunits is studied on a realistic assumption that the strain energy due to the ligand binding is stored in weak contacts between the subunits. In a pair of subunits, which is the minimum co-operative unit, two competitive mechanisms operate; the expansion or contraction of the weak contacts results in negative co-operativity, and positive co-operativity can be produced by the alternation of the contacts.Emphasizing the above role of the weak contacts, and taking into account the widespread interaction which correlates the alternation of the contacts in one interface of subunits with that in another interface, we construct a general partition function to describe the co-operative effects in proteins composed of more than two subunits. The partition function thus obtained includes those of the two allosteric models (Monod, Wyman & Changeux, 1965; Koshland, Nemethy & Filmer, 1966) in the two extreme cases of the strength of the widespread interaction.The partition function is applied to the analysis of the molecular mechanism of heme-heme interaction by the curve fitting to the experimental data for hemoglobin solution under various conditions. The comparison of the parameter values thus determined with the molecular structure leads us to one interpretation that the widespread interaction originates from contact connecting three subunits. This interpretation suggests that the strength of the widespread interaction can be changed by modification of an amino acid residue in the intermediate subunit, and that this interaction plays an essential role in the manifestation of the co-operativity. The reduced co-operativity in mutant hemoglobins can also be explained along these lines.     

A method for determining kinetic parameters at high enzyme concentrations.

A graphical method is described which allows determination of kinetic parameters when substrate, inhibitor or activator concentrations must be in the vicinity of the enzyme concentration and a significant fraction of ligand is bound. Velocity is measured at several ligand: enzyme ratios at two or more enzyme concentrations. Results are obtained in terms of free and bound ligand corresponding to particular velocities. The relationship between velocity and bound and free ligand may then be analysed by any desired plotting technique. Preknowledge of the reaction mechanism or experimental determination of Vmax. is not required. The relationship between ligand bound and enzyme activity need not be linear and the method is equally suitable for analysing co-operative as well as simple kinetics. Application of the method is demonstrated by analysis of the inhibition of fructose, 1,6-bisphosphatase by AMP.     

The interaction of substituted and rigidly linked diquinolines with DNA

Viscometric measurements with circular and sonicated rodlike DNA fragments were used to explore whether ring substituents or conformationally restricted linkers promote bifunctional intercalation amongst a series of binuclear 4-aminoquinolines bridged via their 4-amino group. We find that ligands comprising unsubstituted quinolines and piperazine or pyrazole linkages bisintercalate. Quinoline-substituted alkyl-linked dimers intercalate in either a mixed monofunctional-bifunctional mode or bind with only one of their chromophores intercalated depending on the nature of the substituents. Equilibrium dialysis measurements show that the binding affinity for calf thymus DNA of the compounds studied ranges from (1.2-12) . 10(4) M-1 in buffer of ionic strength 0.1. Both co-operative and antico-operative binding isotherms were obtained and there is evidence for a second binding mode for the piperazine-linked diquinoline at saturating binding levels. For this compound the high-affinity association constant decreases with increasing ionic strength, 3.4 cations being released per bound ligand molecule. Partition dialysis measurements with DNAs of differing base composition indicate that the compounds studied are either AT selective or sequence neutral depending on ligand structure. For example, the pyrazole linker imparts a marked specificity for binding to AT-rich DNA, whereas the piperazine linker does not. Kinetic measurements using the surfactant-sequestration method reveal that DNA-diquinoline complexes dissociate very rapidly by complex mechanisms with rate constants greater than 100 s-1 in buffer of ionic strength 0.1.     

Thermodynamics and kinetics of co-operative protein-nucleic acid binding: II. Studies on the binding between protamine and calf thymus DNA

Unspecific binding of a protamine, namely fluorescein-labelled clupeine Z, to double-stranded calf thymus DNA was studied using fluorescence titration methods and chemical relaxation techniques. Both equilibrium and kinetic data have been analysed using general theoretical approaches discussed in the accompanying paper. The results agree well with the predictions made on the basis of a standard co-operative binding model.Basic parameters evaluated are the co-operative binding constant (K), the coefficient measuring co-operative interaction between nearest neighbours (q), the number of nucleotides occupied by one protamine molecule (n) and the rate constant of dissociation at the ends of bound ligand sequences (K_D). Values obtained at 20 °C, pH 7.5 and 0.4 m-NaCl were K = 5.8 × 10⁷m^?1, q = 1700, n = 20 and K_D = 0.29 s^?1. They have been found to be sensitive to the concentration of added salt (NaCl). This effect apparently reflects the essentially electrostatic nature of the binding process. The results can be satisfactorily described in terms of competitive binding of sodium ions.     

Protein fluorescence of nicotinamide nucleotide-dependent dehydrogenases

1. The decrease in the protein fluorescence (F) of Neurospora crassa glutamate dehydrogenase is linearly related to the increase in the fraction of the coenzyme sites occupied by NADPH (alpha) at pH6.35. Under these conditions NADPH causes this enzyme to dissociate to monomers. 2. There is a non-linear relationship of F to alpha for NADH binding to give the alcohol dehydrogenase-NADH-isobutyramide complex, the l-glycerol 3-phosphate dehydrogenase-NADH complex and the bovine glutamate dehydrogenase-NADH-glutamate complex. The non-linearity is accurately represented by F=[1-alpha(1-x)](n) where n is the number of NADH-binding sites per protein molecule. 3. The co-operative binding of GTP to bovine glutamate dehydrogenase in the presence of NADH gives a linear relationship between F and alpha. 4. The prediction from the equation F=[1-alpha(1-x)](n) that initial tangents to non-linear protein-fluorescence-quenching curves will intercept the fluorescence when alpha=1 at a value of total ligand concentration less than the sum of the concentration of binding sites in the solution plus the dissociation constant of ligand is quantitatively fulfilled. 5. Non-linear protein-fluorescence titrations may be used to obtain information about the distribution of ligand among the protein molecules in solution.     

Inhibition of co-operative enzymes by substrate-analogues: Possible implications for the physiological significance of negative co-operativity illustrated by phenylalanine metabolism in higher plants

The “Hill” equation for co-operative binding-systems has been extended to describe the effect of substrate-analogue on the binding of substrate to an oligomeric protein. It is demonstrated that the more negatively co-operative the binding-system, the more sensitive is the binding of substrate to inhibition by increases in the relative concentration of substrate-analogue. It is proposed that the physiological significance of negative co-operativity for enzymes may be complementary to the physiological significance of positive co-operativity. The effect of negative co-operativity is to make substrate binding more sensitive to inhibition by relative increases in the concentration of substrate-analogue (e.g. for many enzymes product of the reaction) at the expense of decreased sensitivity of substrate binding to relative changes in substrate concentration compared to a system with equivalent, independent substrate binding sites. In contrast, the effect of positive co-operativity is to make the enzyme more sensitive to relative changes in substrate concentration at the expense of decreased sensitivity to inhibition by relative increases in product concentration, compared to an enzyme without co-operative binding.     

Effects of co-operative ligand binding on protein amide NH hydrogen exchange

Amide protection factors have been determined from NMR measurements of hydrogen/deuterium amide NH exchange rates measured on assigned signals from Lactobacillus casei apo-DHFR and its binary and ternary complexes with trimethoprim (TMP), folinic acid and coenzymes (NADPH/NADP(+)). The substantial sizes of the residue-specific DeltaH and TDeltaS values for the opening/closing events in NH exchange for most of the measurable residues in apo-DHFR indicate that sub-global or global rather than local exchange mechanisms are usually involved. The amide groups of residues in helices and sheets are those most protected in apo-DHFR and its complexes, and the protection factors are generally related to the tightness of ligand binding. The effects of ligand binding that lead to changes in amide protection are not localised to specific binding sites but are spread throughout the structure via a network of intramolecular interactions. Although the increase in protein stability in the DHFR.TMP.NADPH complex involves increased ordering in the protein structure (requiring TDeltaS energy) this is recovered, to a large extent, by the stronger binding (enthalpic DeltaH) interactions made possible by the reduced motion in the protein. The ligand-induced protection effects in the ternary complexes DHFR.TMP.NADPH (large positive binding co-operativity) and DHFR.folinic acid.NADPH (large negative binding co-operativity) mirror the co-operative effects seen in the ligand binding. For the DHFR.TMP.NADPH complex, the ligand-induced protection factors result in DeltaDeltaG(o) values for many residues being larger than the DeltaDeltaG(o) values in the corresponding binary complexes. In contrast, for DHFR.folinic acid.NADPH, the DeltaDeltaG(o) values are generally smaller than many of those in the corresponding binary complexes. The results indicate that changes in protein conformational flexibility on formation of the ligand complex play an important role in determining the co-operativity in the ligand binding.     

P22 repressor mutants deficient in co-operative binding and DNA loop formation.

We show here, both in vivo and in vitro, that P22 repressor binds co-operatively to operator sites separated by an integral number of turns of the DNA helix. We measure this co-operativity in vivo using an assay in which repression of a promoter requires co-operative binding of P22 repressors to two separated (non-adjacent) operator sites. We report the isolation of mutant repressors that have high affinity for single operator sites, but are defective in co-operative binding. Six different mutants, all bearing single amino acid changes in the carboxyl domain, have been isolated. We purified the two mutants most deficient in co-operative binding, and found that they bind non-co-operatively in vitro to adjacent as well as to non-adjacent pairs of operator sites.     

Salt-dependent changes in the DNA binding co-operativity of Escherichia coli single strand binding protein

The co-operative nature of the binding of the Escherichia coli single strand binding protein (SSB) to single-stranded nucleic acids has been examined over a range of salt concentrations (NaCl and MgCl2) to determine if different degrees of binding co-operativity are associated with the two SSB binding modes that have been identified recently. Quantitative estimates of the binding properties, including the co-operativity parameter, omega, of SSB to single-stranded DNA and RNA homopolynucleotides have been obtained from equilibrium binding isotherms, at high salt (greater than or equal to 0.2 M-NaCl), by monitoring the fluorescence quenching of the SSB upon binding. Under these high salt conditions, where only the high site size SSB binding mode exists (65 +/- 5 nucleotides per tetramer), we find only moderate co-operativity for SSB binding to both DNA and RNA, (omega = 50 +/- 10), independent of the concentration of salt. This value for omega is much lower than most previous estimates. At lower concentrations of NaCl, where the low site size SSB binding mode (33 +/- 3 nucleotides/tetramer) exists, but where SSB affinity for single-stranded DNA is too high to estimate co-operativity from classical binding isotherms, we have used an agarose gel electrophoresis technique to qualitatively examine SSB co-operativity with single-stranded (ss) M13 phage DNA. The apparent binding co-operativity increases dramatically below 0.20 M-NaCl, as judged by the extremely non-random distribution of SSB among the ssM13 DNA population at low SSB to DNA ratios. However, the highly co-operative complexes are not at equilibrium at low SSB/DNA binding densities, but are formed only transiently when SSB and ssDNA are directly mixed at low concentrations of NaCl. The conversions of these metastable, highly co-operative SSB-ssDNA complexes to their equilibrium, low co-operativity form is very slow at low concentrations of NaCl. At equilibrium, the SSB-ssDNA complexes seem to possess the same low degree of co-operativity (omega = 50 +/- 10) under all conditions tested. However, the highly co-operative mode of SSB binding, although metastable, may be important during non-equilibrium processes such as DNA replication. The possible relation between the two SSB binding modes, which differ in site size by a factor of two, and the high and low co-operativity complexes, which we report here, is discussed.