Lawrence W. Nichol

The molecular weight and stability of concanavalin A

Abstract The stability of concanavalin A is investigated in a wide range of environments by optical rotation, sedimentation and turbidity measurements. In the range of pH 4.5–5.6 ( I = 0.1), a single species of molecular weight 53 000 exists in solution. Below pH 4.5 this molecular weight is maintained, but a time-dependent change in protein conformation occurs. Above pH 5.6 the protein dimerizes, the extent of the reaction increasing with increasing pH. At pH 7 and above ( I = 0.1), the dimerization is accompanied by a time-dependent development of turbidity, which is essentially eliminated at pH 7 by either an increase of ionic strength (to values equal to or greater than 0.3) or by the addition of glucose. Nevertheless, even at I = 0.3 (pH 7) comparable proportions of monomer and dimer coexist as a non-equilibrium mixture. The results are discussed in relation to previous conflicting reports on the molecular weight of the protein and in terms of environments suitable for carbohydrate binding studies.

The indefinite self-association of lysozyme: consideration of composition-dependent activity coefficients

An improved iterative method for computing association constants from sedimentation equilibrium results obtained with self-interacting protein systems is presented which accounts for the composition-dependence of the activity coefficients of all oligomeric species. The method is based on the calculation of viral coefficients from covolume and charge considerations, the statistical mechanical basis of which is discussed in relation to the DLVO theory. The method is applied to results obtained with lysozyme in diethylbarbiturate buffer of pH 8.0 and ionic strength 0.15 at 15 degrees C. It is shown that these results, encompassing a range of total solute concentration up to 19.7 g/liter are consistent with self-association patterns comprising either a monomer--dimer--trimer system or an isodesmic indefinite self-association of the monomer, the latter being favored. A firmer distinction between these possibilities is sought on the basis of the dependence of the weight-average partition coefficient, determined by frontal gel chromatography, on total solute concentration (up to 56.6/liter). This analysis accounts for the composition-dependence of the ratio of the activity coefficients of partitioning monomer in mobile and stationary phases. It is concluded that all results are consistent with an indefinite self-association of lysozyme governed by a single association constant of 4.61 x 10(2) liter/mole.

The direct analysis of sedimentation equilibrium results obtained with polymerizing systems

Theory is presented in relation to sedimentation equilibrium results obtained with polymerizing systems, which permits evaluation of the activity of the monomer as a function of total weight concentration. In contrast to established methods, the suggested procedure does not involve the solution of simultaneous equations which are sums of exponentials or the determination of weight-average molecular weights. A major advantage of the method is that it avoids errors inherent in differentiation and integration steps. An extrapolation to infinite filution is involved, but this is to a defined limit and is uncomplicated by the existence of critical points in the relevant plot. The method is capable of detecting possible volume changes inherent on polymer formation, of treating systems where activity coefficients of solute species are functions of total concentration and of describing the system in terms of relevant equilibrium constants. These points and comparisons with existing methods of analysis are illustrated with numerical examples and with results obtained with lysozyme at pH 6.7. The lysozyme results are interpretable in terms of either a non-ideal monomer-dimer system or a monomer-dimer-trimer system.

Effect of inert polymers on protein self-association

In [l] polyethylene glycol (PEG) was reported to stimulate the self-association of the pyruvate dehydrogenase complex isolated from Azotobacter vinelandii. They state that the exact reasons for this phenomenon are not clear at present. It is our purpose to point out that this effect has a thermodynamic explanation in terms of the excluded volume interaction between the protein and the polymer. While we restrict our discussion to the consideration of protein self-association reactions, we refer to the detailed work in [2] on the effect of inert polymers on enzyme activity. The observation [2] that dextran promotes the inhibition of trypsin by serum albumin was interpreted in a manner consistent with the argument presented here. The biological significance of various aspects of polymer interactions has been reviewed in [3].

Polymerization Pattern of Insulin at pH 7.0

Sedimentation equilibrium results, obtained with bovine zinc-free insulin (with and without a component of proinsulin) at pH 7.0, I o.2, 25 degrees C, and up to a total concentration of 0.8 g/l., are shown to be consistent with three different polymerization patterns, all involving an isodesmic indefinite self-association of specified oligomeric species. The analysis procedure, based on closed solutions formed by summing infinite series, yields for each pattern a set of equilibrium constants, It is shown that a distinction between the possible patterns can be made by analyzing sedimentation equilibrium results obtained in a higher total concentration range (up to 4 g/1.) with insulin freed of zinc and proinsulin, account being taken of the composition dependence of activity coefficients. The favored pattern, which differs from that previously reported in the literature, involves the dimerization of monomeric insulin (mol wt 5734), governed by a dimerization constant of 11 X 10(4) M-1 and the isodesmic indefinite self-association of the dimer, described by an association constant of 1.7 X 10(4) M-1. This polymerization pattern is also shown to be consistent with the reaction boundary observed in sedimentation velocity experiments.

Effects of concentration-dependence in gel filtration.

Abstract The elution volumes of ovalbumin, trypsin and bovine serum albumin from a column of Sephadex G-100 have been shown to be functions of concentration; no such dependence is observed with Dextran-500. Asymmetry in the elution profile of ovalbumin has been shown to result from the concentration-dependence of migration rate. A second consequence of this type of velocity variation in transport experiments, viz. , the overestimation by frontal analysis of the amount of slower-moving species at the expense of faster-migrating solute has also been demonstrated for three synthetic mixtures. It has been found experimentally that, with reciprocals of elution volumes substituted for velocities, the equation proposed by Johnston and Ogston adequately corrects for this effect in gel-filtration.

Binding equations for interacting systems comprising multivalent acceptor and bivalent ligand: application to antigen-antibody systems.

Abstract Consideration is given to the reversible interaction of a bivalent ligand, B, with a multivalent acceptor, A (possessing f reactive sites) which leads to the formation of a series of complexes, AiBj, comprising networks of alternating acceptor and ligand molecules. A binding equation is derived on the basis of a site association constant, k, defined in terms of reacted site probability functions. This equation, which relates the binding function, r (the moles of ligand bound per mole of acceptor) to the concentration of unbound ligand, mb, is used to show that plots of r vs. 2kmB constructed with fixed but different values of k m A intersect at the point ( m B = 1 2k , r = f 2 ) where the extent of reaction and the concentrations of those complexes for which j i = f 2 attain maximal values. Corresponding Scatchard plots are shown by numerical example to be non-linear, their second derivative being positive for all r. It follows that such deviations from linearity cannot be taken alone as evidence for site heterogeneity in cross-linking systems. The binding equation obtained directly is shown to be identical with that obtained with f = 2 by summation procedures involving the general expression for concentrations of complexes, mAiBj, formulated in terms of appropriate statistical factors. In this way, previous findings on precipitation and gel formation in cross-linking systems are correlated with the present development of binding theory.

The study of multiple polymerization equilibria by glass bead exclusion chromatography with allowance for thermodynamic non-ideality effects.

Abstract Two related aspects are explored of the frontal exclusion chromatography of proteins employing controlled-pore glass beads as the stationary phase. First, it is shown theoretically that, despite the absence of osmotic shrinkage effects previously encountered with Sephadex matrices, the experimentally measurable partition coefficient of a single non-associating solute will be dependent on its concentration due to the differing ratios of activity coefficients in mobile and stationary phases at different total concentrations. The effect is demonstrated with results obtained using ovalbumin in phosphate buffer of pH 7.4, and is Shown to be consistent (up to a solute concentration of 5 g litre ) with theoretical prediction formulated in terms of a single virial coefficient. Secondly, it is shown for self-associating systems that it is possible to determine the monomer concentration as a function of total concentration, provided the stationary phase is selected to ensure exclusion of all oligomeric species except monomer: the relation derived for this purpose accounts for the concentrationdependence of the partition coefficient of monomer, again as a first approximation involving one virial coefficient. Such information on the monomer concentration permits elucidation of the polymerization characteristics of the system in terms of the types of species present and the relevant equilibrium constants. The feasibility of the method, its likely sources of error and the relative contribution of the non-ideality effect are investigated using bovine glutamate dehydrogenase (up to a total concentration of 5.4 g litre ) in phosphate buffer of pH 6.9. This system was selected since comparison was possible with results obtained by other methods, which have established the enzyme polymerization pattern as an isodesmic indefinite self-association. The isodesmic equilibrium constant of 1.5 ± 0.3 litre g found in this work is in reasonable agreement with previous findings.

The polymerization pattern of zinc(II)-insulin at pH 7.0

Sedimentation equilibrium experiments were conducted at pH 7.0 using solutions of bovine insulin containing 2 mol of zinc(II) ions per six base-mol of insulin. A detailed analysis of these results revealed the existence of a stable zinc-insulin hexamer together with linked polymerization reactions. Specifically these are a background polymerization of zinc-free insulin as previously described by Jeffrey et al. ((1976) Biochemistry 15, 4660--4665) and a slight tendency for the zinc-insulin hexamer to undergo indefinite self-association. Equilibrium constants governing these reactions are reported together with equations which permit calculation of the composition of the solution at any given total concentration. Comment is made on the possible biological significance of this linked polymerization pattern, and on the likely identity of the structure of the stable zinc-insulin hexamer with that previously reported from X-ray crystallographic studies.

Chromatographic evidence of the self-association of oxyhemoglobin in concentrated solutions: its biological implications

Expressions that take into account the effects of thermodynamic non-ideality, described in terms of a high-order virial expansion, are derived for the concentration-dependence of the weight-average partition coefficient in exclusion chromatography of a single solute and of a solute undergoing reversible self-association. Comparison of the concentration-dependences predicted by those expressions with results obtained for bovine and human oxyhemoglobins on CPG-10-120 porous glass beads in 0.156 I phosphate-chloride buffer, pH 7.3, shows that neither oxyhemoglobin conforms with the concept of it being a single alpha 2 beta 2 entity with Stokes radius of 3.13 nm, the experimental value. Previously published osmotic pressure and sedimentation equilibrium results are also shown to be inconsistent with this concept. On the other hand, both sets of exclusion chromatography results are consistent with the joint operation of thermodynamic non-ideality and reversible association of the alpha 2 beta 2 species. From the magnitude of the equilibrium constant, derived for either of two possible modes of association, it is calculated that only half of the oxyhemoglobin would be in the alpha 2 beta 2 states under conditions of oxygen saturation and a concentration of 320 g/liter, that pertaining in the red blood cell. The consequences of this association phenomenon are discussed in relation to the oxygen binding curves obtained by others in the presence and absence of 2,3-diphosphoglycerate (DPG). An explanation is provided of the observed dependence on hemoglobin concentration of oxygen-binding in the presence of DPG, and of the absence of such an effect in DPG-free solutions. It is concluded that the control of oxygen binding to hemoglobin in the physiological situation involves the joint operation of self-association and allosteric effects.