The reversible cross-linking of receptors by ligands: theory for the prediction of binding responses.

The general concept of receptor aggregation through the action of a cross-linking ligand is considered, three models being examined in detail. In two, ligand self-interaction leads to the formation of receptor cross-links whereas, in the third, receptor cross-links are formed through a single ligand bridge. Binding equations in closed form are formulated for each case and are shown to predict both concave and convex Scatchard plots in binding studies conducted with such systems. The significant point which emerges is that while each of the systems gives rise to very different types of binding responses, the form of the binding response is always strongly dependent on the total concentration of receptor in the system.

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.

The self-association of zinc-free bovine insulin. A single model based on interactions in the crystal that describes the association pattern in solution at pH 2, 7 and 10.

Sedimentation equilibrium studies are used to establish that a new pattern for the self-association of zinc-free insulin in solution is applicable over a wide range of conditions of pH, ionic strength and temperature. In this pattern, which is based on information from the existing literature on the X-ray crystal structure of insulin, the insulin monomer is viewed as having two distinct faces both capable of self-interaction. Sedimentation equilibrium experiments were analysed using expressions formulated for this association pattern that describe the dependence of weight average molecular weight and monomer concentration on total protein concentration. It has thereby been possible to obtain values for the two association constants which govern the system for each set of conditions studied, due allowance having been made for composition dependent non-ideality effects. Furthermore, by relating the pH, temperature and ionic strength dependence of the association constants with properties of various amino acid residues on the surface of the insulin monomer, it has also been possible to assign tentatively each constant to a particular reaction domain.

The binding of a ligand to an acceptor undergoing indefinite self-association.

Explicit expressions are derived which describe the binding of a univalent ligand to equivalent and independent sites on each state of an acceptor undergoing indefinite self-association that is governed by an isodesmic equilibrium constant KI. From considerations of systems in which the same site-binding constant kA applies to all acceptor-ligand interactions, the general forms of binding curves and Scatchard plots are deduced for situations in which binding sites are either created or lost at each monomer-monomer interface. Greater generality is then introduced into the model by allowing ligand interactions with polymeric acceptor states to be governed by a site-binding constant kp that differs in magnitude from that for monomeric acceptor kA. Finally, experimental results with the glutamate dehydrogenase-GTP and lysozyme-saccharide systems are used to illustrate ways in which the present quantitative expressions may be applied to the characterization of inteactions between a ligand and an indefinitely self-associating acceptor.

Effect of thermodynamic nonideality in kinetic studies: evidence for reversible unfolding of urease during urea hydrolysis.

A combination of enzyme kinetic studies and active enzyme gel chromatography on Sepharose CL-6B was used to explore conformational changes of the enzyme urease as it catalyzes the hydrolysis of urea in 0.7 M phosphate buffer, pH 7.0, at 20 degrees C. It is shown that elucidation of this system is only possible by studying the effects of inert space-filling macromolecules (ovalbumin and bovine serum albumin) on enzymatic behavior. The resulting increases in reaction velocity are interpreted in terms of composition-dependent activity coefficients assessed on a statistical mechanical basis of excluded volume. The results are first considered in terms of two extreme models; one involving a volume change on the isomerization of the enzyme-substrate complex to its activated state, and the other an isomeric expansion of the enzyme-substrate complex to an inactive form. Although both extreme models provide satisfactory descriptions of the kinetic results, they lead to unrealistic values for the radii of the various states of the enzyme-substrate complex. It is concluded, therefore, that the two isomeric transitions act conjointly, a result in conformity with the previously postulated conformational change associated with formation of the activated enzyme-substrate complex [L. W. Nichol, M. J. Sculley, L. D. Ward, and D. J. Winzor (1983) Arch. Biochem. Biophys. 222, 574-581], and also with the well-established action of the substrate, urea, as an unfolding agent of proteins.

A macromolecular shape function based on sedimentation velocity parameters.

A volume-independent shape function, experimentally determinable from sedimentation velocity experiments, was formulated explicitly in terms of the axial ratio of a macromolecule considered as an ellipsoid of revolution. Use of this function offers a simple first approach to the elucidation of macromolecular geometry as illustrated by calculations for ovalbumin, bovine serum albumin, and myosin.

Thermodynamic nonideality as a probe of macromolecular isomerizations: application to the acid expansion of bovine serum albumin.

The potential use of thermodynamic nonideality as an index of the coexistence of two isomeric protein states in equilibrium is explored in relation to the effect of inert space-filling macromolecular solutes on the gel chromatographic behavior of the system. Frontal gel chromatography, on Sephadex G-100, of bovine serum albumin at pH 3.2 in the presence and absence of a moderately high (15 g/liter) concentration of either Dextran T70 or Dextran T10 is then employed to establish that the progressive increase in the Stokes radius of albumin as the pH is lowered from 5 to 2 should not be viewed as a pH-dependent isomerization equilibrium between native and acid-expanded states. In addition, calculations based on parameters for the aspartate transcarbamoylase system point to the possible use of the present methodology to distinguish between preexistence and ligand induction of an isomerization equilibrium as the source of a sigmoidal effect in allosteric systems.

Indefinite self-association of a solute in linear and branched arrays.

Theory is formulated using reacted-site probability functions to relate the concentration of monomer to that of total solute for a multivalent monomer which undergoes indefinite self-association to form an equilibrium array of linear chains and branched networks governed by a single site-binding constant. In turn, this intrinsic constant is related to the stoichiometric equilibrium constants describing successive additions of monomer; and the characterization of the composition of the mixture at different total concentrations is discussed together with the onset of gelation, which occurs when each polymer (excluding the infinite network) attains a maximum concentration. Analogous expressions defining solution composition are presented for indefinitely self-associating systems involving non-identical sites when interactions occur in a head-to-tail fashion between dissimilar sites. Finally, a bivalent monomer is considered with head-to-head and tail-to-tail interactions forming an indefinite array of polymers with alternating bond types. It is shown that the latter description is quantitatively consistent with results obtained previously on the indefinitely self-associating zinc-free insulin system. The postulated self-association pattern involving two site-binding constants of magnitudes 5.75 X 10(4) M-1 and 0.85 X 10(4) M-1 is preferred to earlier suggested models on the basis of information available from X-ray crystallographic studies on insulin.

The influence of poly(ethylene glycol) 6000 on the properties of skeletal-muscle actin.

Poly(ethylene glycol) 6000 affected many of the properties of skeletal-muscle actin. It accelerated the rate and increased the extent of actin polymerization as measured by light-scattering and sedimentation studies respectively. Moreover, intrinsic-fluorescence measurements showed that addition of poly(ethylene glycol) 6000 decreased the rate of EDTA-induced denaturation of actin monomer and increased the temperature at which irreversible conformational changes occur in actin monomer. These effects occurred without any apparent direct binding interaction and are postulated to be a consequence of the effect of excluded volume on the thermodynamic activity of actin. A relationship based on spherical geometry was formulated which described the co-volume increment that occurs upon addition of a monomer to a long linear polymer in the presence of a space-filling macromolecule. The application of this relationship to the poly(ethylene glycol) 6000-actin system was not without assumption, but it permitted quantitative estimation of the co-volume increment which proved to be of the sign and magnitude required to explain the increased extent of actin polymerization found experimentally in the presence of various concentrations of poly(ethylene glycol) 6000. It is suggested that, in vivo, excluded volume may play a role in actin-filament formation and in the maintenance of the native G-actin structure.

Effects of thermodynamic nonideality in ligand binding studies.

Effects of thermodynamic nonideality are considered in relation to the quantitative characterization of the interaction between a small ligand. S, and a macromolecular acceptor. A, by two types of experimental procedure. The first involves determination of the concentration of ligand in dialysis equilibrium with the acceptor/ligand mixture, and the second, measurement of the concentration of unbound ligand in the reaction mixture by ultrafiltration or the rate of dialysis method. For each situation explicit expressions are formulated for the appropriate binding function with allowance for composition-dependent nonideality effects expressed in terms of molar volume, charge-charge interaction and covolume contributions. The magnitudes of these effects are explored with the aid of experimental studies on the binding of tryptophan and of methyl orange to bovine serum albumin. It is concluded for experiments conducted utilizing either equilibrium dialysis or frontal gel chromatography that, provided a correction is made for any Donnan redistribution of ligand, theoretically predicted acceptor-concentration dependence is likely to be negligible and that use of the conventional binding equation written for an ideal system is appropriate to the analysis of the results. Use of ultrafiltration or the rate of dialysis method requires examination of the assumption that the activity coefficient ratio y(A)y(s)/y(AS) for the reaction mixture approximates unity; but again reassurance is provided that nonideality manifested as a dependence of the binding function on acceptor concentration is unlikely to be significant.

Effects of thermodynamic nonideality in kinetic studies.

Experimental evidence is presented for concentration dependence of the pseudo-first-order rate constant describing the rate of inversion of sucrose by 2 M HCl; and also of the increase in maximal velocity for the catalytic reduction of pyruvate by lactate dehydrogenase that results from addition of the inert macromolecular solutes bovine serum albumin, ovalbumin, and Dextran T70. These somewhat unusual and seemingly diverse observations are examined in terms of a theory formulated on the basis of two equilibrium reactions, the first describing complex formation between two reactants, and the second isomerization of that complex to an activated state prior to product formation. This formulation permits consideration of activity coefficient ratios relevant to the equilibria and the expression of these ratios as power series in total solution composition. Quantitative assessment of the experimental results is made possible in these terms by estimating the magnitudes of the constant coefficients of the virial expansions as excluded volumes. It is concluded that the result observed in the sucrose inversion study finds rational explanation in thermodynamic nonideality factors governing the overall equilibrium between the reactants and the activated complex of sucrose and hydronium ion. For the enzyme-catalyzed reaction the same general equation applies but particular attention is given to the simplified form that is relevant to high substrate concentrations, where, in the absence of inert compounds, the conventional maximal velocity is approached. In this region an increase in velocity observed upon addition of an inert macromolecular component may be considered explicitly in terms of excluded volume effects related to a shape change in the isomerization between enzyme-substrate complex and its activated state.

Interpretation of the kinetics of consecutive enzyme-catalysed reactions: studies on the arginase-ornithine carbamoyltransferase system.

A method that permits the use of measurements on the concentration of the intermediate in a coupled enzymic assay in determining the presence or absence of an interaction between the enzymes is presented. The method is shown to be closely analogous to a previously formulated procedure involving the determination of the rate of production of the final product of such a sequence and is shown to be applicable regardless of the complexity of the operative kinetic mechanisms, provided it may be assumed that all enzyme-substrate complexes are in the steady-state. Kinetic results obtained with the arginase-ornithine carbamoyltransferase couple, in which the intermediate ornithine is monitored, are examined in these terms to conclude that no heterogeneous association is operative between the enzymes.

Exclusion chromatography of concentrated hemoglobin solutions. Comparison of the self-association behavior of the oxy and deoxy forms of the alpha 2 beta 2 species.

Theory pertaining to the interpretation of partition chromatography results obtained with self-associating protein systems studied at high total concentrations is extended to permit consideration of situations in which both monomeric and dimeric states partition. This development, which includes considerations of thermodynamic nonideality effects, permits a quantitative correlation of human oxyhemoglobin results reported previously and obtained in this work employing a different stationary matrix of controlled-pore glass beads. The two sets of results, obtained at pH 7.3 and 20 degree C, indicate that the alpha 2 beta 2 species of oxyhemoglobin self-associates. Two types of association pattern, discrete dimerization and an indefinite self-association, are examined. This is done for a realistic range of values for the radius, r. of the effective hard sphere appropriate to the calculation of the covolume of the alpha 2 beta 2 species in the assessment of the thermodynamic nonideality contribution. Assessed values of the isodesmic association constant range from 66 +/- 23 M-1 (r - 2.84 nm) to 154 +/- 26 M-1 (r = 3.13 nm). This mode of indefinite association is marginally favored over dimerization when the larger value of r is considered, the two patterns becoming virtually indistinguishable for the lower value of r. Partition chromatography results are also presented for human deoxyhemoglobin up to a total concentration of 225 g/l, and are analyzed in a similar fashion to show that the indefinite self-association pattern is favored, governed by an isodesmic constant in the range 91 +/- 9 M-1 (r = 2.84 nm) to 223 +/- 84 M-1 (r = 3.13 nm). Comparison of the constants assessed for the oxy and deoxy systems permits discussion of the concept that oxygen binds preferentially to the alpha 2 beta 2 species of deoxyhemoglobin in comparison with its polymers.

Multivalency of the partitioning species in quantitative affinity chromatography. Evaluation of the site-binding constant for the aldolase-phosphate interaction from studies with cellulose phosphate as the affinity matrix.

Theory is presented which describes the competitive interaction of a multivalent solute with a univalent ligand and an affinity matrix. The formulation accounts for cross-linking interactions of the multivalent solute, and of its complexes with ligand, with matrix interaction sites in terms of two site-binding constants pertaining respectively to ligand-solute and solute-matrix interactions. Explicit expression are derived which permit evaluation of these constants from experimental results obtained in partition equilibrium experiments or in frontal affinity chromatography studies. These relations are explored in partition equilibrium experiments conducted with cellulose phosphate as the matrix, aldolase as the solute, and phosphate as the ligand. At pH 7.4, I = 0.15, a value of 350 +/- 60 M-1 was obtained for the aldolase-phosphate site-binding constant, in close agreement with the corresponding value deduced from competitive inhibition studies. It is concluded that the present approach is particularly suited to the elucidation of weak interactions, which cannot be reliably studied by conventional means.