Interactions of lens proteins. Self-association and mixed-association studies of bovine alpha-crystallin and gamma-crystallin

Concentrated solutions of calf alpha-crystallin (up to 45 g/l) and gamma-crystallin (up to 67 g/l) were subjected to frontal exclusion chromatography at pH 7.3, ionic strength 0.17 and 20 degrees C. The experimental concentration dependence of the weight-average partition coefficient was compared with theoretical expressions, which include considerations of thermodynamic non-ideality effects, for the concentration dependence of a single solute and of a solute undergoing reversible self-association. Two types of association pattern were examined, discrete dimerization and indefinite self-association. The partition chromatography results are consistent with an indefinite self-association of gamma-crystallin, governed by an isodesmic association constant of 6.7 X 10(-3) l/g. alpha-Crystallin appears to self-associate either very weakly, with a maximal association constant of 0.9 X 10(-3) l/g, or not at all; the distinction depends on the assessment of the non-ideality coefficients. The consequences of excluded volume effects on these self-association equilibria at high total protein concentration are discussed. Mixtures of alpha-crystallin and gamma-crystallin were analyzed by frontal exclusion chromatography (up to 14 g/l) and sedimentation velocity (up to 115 g/l): no interaction was observed.     

Comparison of Methods for Characterizing Nonideal Solute Self-Association by Sedimentation Equilibrium

We have examined in detail analytical solutions of expressions for sedimentation equilibrium in the analytical ultracentrifuge to describe self-association under nonideal conditions. We find that those containing the radial dependence of total solute concentration that incorporate the Adams-Fujita assumption for composition-dependence of activity coefficients reveal potential shortcomings for characterizing such systems. Similar deficiencies are shown in the use of the NONLIN software incorporating the same assumption about the interrelationship between activity coefficients for monomer and polymer species. These difficulties can be overcome by iterative analyses incorporating expressions for the composition-dependence of activity coefficients predicted by excluded volume considerations. A recommendation is therefore made for the replacement of current software packages by programs that incorporate rigorous statistical-mechanical allowance for thermodynamic nonideality in sedimentation equilibrium distributions reflecting solute self-association.     

Self-association mode of a flavoenzyme D-amino acid oxidase from hog kidney. I. Analysis of apparent weight-average molecular weight data for the apoenzyme in terms of models

The self-association of D-amino acid oxidase apoenzyme in 0.1 M sodium pyrophosphate, pH 8.3, at 25 degrees C was studied by low-angle laser light scattering. The concentration (c) dependence of the apparent weight-average molecular weight (Mwapp) was determined over a wide concentration range of 0.04 to 6.1 mg/ml. The extrapolated Mwapp value, to zero enzyme concentration, corresponded to the Mr value of the monomer. The self-association mode of the apoenzyme was systematically explored with nonlinear least-squares analysis of the Mwapp versus c data. The simplest model that fitted the data well was a model of isodesmic indefinite self-association of the monomer with the isodesmic association constant of 0.467 +/- 0.034 liter/g. The monomer-dimer model proposed previously, but only in a low enzyme concentration range of less than 0.9 mg/ml at 5-20 degrees C (Henn, S. W., and Ackers, G. K. (1969) Biochemistry 8, 3829-3838), did not fit the Mwapp versus c data either in the limited low concentration range or in the whole concentration range examined at 25 degrees C. To test the validity of the chosen model, the observed sedimentation boundary profiles were compared with the idealized boundary profiles calculated for the better-fit models. The profile calculated with the model of the isodesmic indefinite self-association mechanism was qualitatively consistent with the observed ones. The utility of the nonlinear least-squares procedure for analyzing self-associating systems was demonstrated.     

Self-association mode of a flavoenzyme D-amino acid oxidase from hog kidney. II. Stoichiometry of holoenzyme association and energetics of subunit association

The self-association pattern of D-amino acid oxidase holoenzyme in 0.1 M sodium pyrophosphate, pH 8.3, at 25 degrees C was examined by the low-angle laser light-scattering method. As to the results of nonlinear least-squares analysis of the apparent weight-average molecular weight (Mwapp) versus protein concentration (c) data, the following three models fitted equally well the data over the concentration range of 0.03-11.4 mg/ml: 1) the model of isodesmic indefinite self-association of the monomer where the dimerization constant differs from the isodesmic association constant, 2) the model which involves the dimerization of the monomer and isodesmic indefinite self-association of the dimer, and 3) the model which involves the trimerization of the monomer and isodesmic indefinite self-association of the trimer. In a more limited concentration range (0.3-11.4 mg/ml), a model of isodesmic indefinite self-association of the stable dimer where the dimer does not dissociate into the monomers cannot be excluded from the above three models. Measurements with the concentration range lowered to 0.03 mg/ml enabled us to exclude unequivocally the model involving such a stable dimer and to extrapolate the Mwapp data to the Mr of the monomer at infinite dilution as in the case of the apoenzyme. The observed sedimentation boundary profiles were qualitatively consistent with the idealized boundary profiles calculated with the model which involves the dimerization of the monomer and isodesmic indefinite self-association of the dimer, so this model is the most probable of the models examined. These results provide the first evidence that the association mode of the holoenzyme is different from that of the apoenzyme, i.e. isodesmic indefinite self-association of the monomer (Tojo, H., Horiike, K., Shiga, K., Nishina, Y., Watari, H., and Yamano, T. (1985) J. Biol. Chem. 260, 12607-12614). The overall linkage scheme, between binding of coenzyme FAD and subunit association, was considered, and the overall free energy change in each process in the scheme was calculated. The total stabilization energies of the intersubunit interaction in the holoenzyme relative to the apoenzyme were found to be -2.2 kcal/mol at the dimerization step and -0.5 kcal/mol at the step of the addition of the dimer to any 2i-mer (i = 1,2, ...).     

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

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 $\text{g}\text{litre}$) 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 $\text{g}\text{litre}$) 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 $\text{litre}\text{g}$ found in this work is in reasonable agreement with previous findings.     

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.     

The self-association of human spectrin at high concentration.

The self-association of purified human spectrin has been studied at sedimentation equilibrium over a wide range of concentration (0-20 g/L) at 30 degrees C and pH 7.5. Coincidence of apparent weight average molecular weight and omega (r) plots as a function of total spectrin concentration indicated that equilibrium was attained and that no significant concentration of solute was incapable of participating in the self-association reaction. Under these conditions, no significant dissociation of the heterodimer to component polypeptide chains could be detected. The behavior of spectrin between 0 and 20 g/L can be described reasonably well by a cooperative isodesmic model, in which the protomer for association is the alpha beta heterodimer. With this model, the equilibrium constant for the heterodimer-tetramer step, K24, is 2 x 10(6) M-1, and K(iso), the equilibrium constant describing all other steps, is approximately 0.2 x 10(6) M-1. The returned value of the second virial coefficient for this model, 1.0 x 10(-7) L mol g-2, is consistent with the lower limit of values calculated for the heterodimer from the charge and Stokes radius of spectrin. On the other hand, the attenuated indefinite association model fails to describe the self-association of spectrin adequately over the range 0-20 g/L. Systematic decreases in the estimates of the second virial coefficient and the equilibrium constants for association beyond the tetramer suggest that the assumption of a single value of the second virial coefficient may not be appropriate for spectrin, and that non-ideality would best be taken into account by consideration of the detailed solution composition.     

Self-association of lysozyme. Thermochemical measurements: effect of chemical modification of Trp-62, Trp-108, and Glu-35.

Heats of dilution and of saccharide binding for hen egg white lysozyme have been measured at 30 degrees, 0.1 ionic strength, and pH 7 over the range 3 to 95 mg of protein/ml. The concentration dependence of the apparent relative molar enthalpy of lysozyme derived from these results gives the thermodynamic parameters for the formation of an intermolecular contact in an indefinite (head-to-tail) self-association process as delta G 0 = -3.9 kcal/mol, delta H 0 = -6.4 kcal/mol, and delta S 0 = -8,3 e.u. Oxindolealanine-62-lysozyme does not undergo self-association reactions that can be detected calorimetrically. This derivative reacts with native lysozyme to form hybrid polymeric species with free energy and enthalpy of interaction similar to those for the polymers of native lysozyme. These results are consistent with the intermolecular contact in the self-assocaition of lysozyme being asymmetric (head-to-tail). The heat of dilution of the derivative of lysozyme in which Glu-35 is blocked as the ester with oxindolealanine-108 is like that observed for native lysozyme in acid solution and is independent of pH. The concentration difference spectrum that develops through self-association is of the shape expected for introduction of an indole chromophore into a charge-free region of the intermolecular contact. The foregoing results indicate that Glu-35 and Trp-62 are part of the contact, that perturbation of Trp-108 does not make a principle contribution to the concentration difference spectrum, and that no acid group other than Glu-35 is perturbed by self-association. There is a small change in the heat of (GlcNAc)3 binding over the range 0.005 to 0.034 M saccharide. These data give the value of -1 kcal/mol for the enthalpy change for formation of the 2:1 saccharide-enzyme complex (ES2) from ES and S.     

A thermodynamic model for the self-association of human spectrin

The self-association of human spectrin at 28.8 degrees C in 0.11 M salt (pH 7.5) has been studied by means of sedimentation equilibrium. Coincidence of omega function plots as a function of total spectrin concentration (0-2 g/L) indicated that equilibrium was achieved and that no significant concentration of solute was incapable of participating in the self-association reaction. On the basis of the root-mean-square deviation of the fits and the randomness of the residuals, the behavior can be described equally well, either by a cooperative isodesmic model, in which K12 approximately 2 x 10(6) M-1 and all other K approximately 10(6) M-1, or by an attenuated scheme in which K(i-1)i approximately (3.5 x 10(6)/i M-1. The returned values of the second virial coefficient, B, for both these models fall within the range calculated from the charge and Stokes radius of spectrin. A mechanism for spectrin self-association consistent with both schemes is proposed in which spectrin heterodimers undergo a reversible opening at the self-association interface. These open heterodimers then undergo indefinite self-association to form a series of open-chain oligomers in dynamic equilibrium with closed-loop oligomers.     

Determination of the parameters of self-association by direct fitting of the omega function

Nonlinear regression is used to fit the omega function vs. protein concentration curves (first described by B.K. Milthorpe, P.D. Jeffrey and L.W. Nichol, Biophys. Chem. 3 (1975) 169) obtained from sedimentation equilibrium experiments on self-associating macromolecules. Nonlinear regression allows the direct fit of these curves with discrete or indefinite self-association reaction models in order to obtain values for the equilibrium constants and second virial coefficient. The method is independent of the choice of reference concentration and avoids the original method of extrapolating an omega function curve to zero concentration and then using the extrapolated value to construct a monomer activity curve used for analysis. This extrapolation can become very difficult for mild to strong self-associations where incorrectly extrapolated values lead to systematic error in the monomer activity curves. The method is applied to results from a mild, indefinite self-association, exemplified by the self-association of human spectrin, and to computer-simulated data of weak, mild and strong, indefinite self-associations.     

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.     

Direct analysis of solute self-association by sedimentation equilibrium

An improved procedure is described for the characterization of solute self-association by sedimentation equilibrium. Whereas previous statistical-mechanical approaches to allowance for the effects of thermodynamic nonideality have entailed tedious iteration because of their specification of activity coefficients in terms of the equilibrium concentrations of all species, such reliance upon knowledge of the solution composition is avoided by the adaptation of an alternative statistical-mechanical formulation [T. L. Hill and Y. D. Chen (1973) Biopolymers, Vol. 12, pp. 1285–1312] in which thermodynamic nonideality is expressed in terms of total solute concentration. The development of an analysis in terms of a relationship with total solute concentration as the experimental variable allows this attribute of the Adams-Fujita approach to be retained without sacrifice of statistical-mechanical rigor. Its use is illustrated by application to Rayleigh interferometric records of sedimentation equilibrium distributions reflecting α-chymotrypsin dimerization and lysozyme self-association. © 1996 John Wiley & Sons, Inc.     

The critical micelle condition revisited.

Several simple alternatives have been examined as a possible basis for micellar size distributions which are internally consistent with the experimentally required concept of a threshold concentration, the critical micelle condition. Among these are the two-state system, monomer in equilibrium with a single high polymer, indefinite self-association, and continuous self-association with an arbitrary upper limit beyond which all further association is absolutely prohibited. Of these, only the last is a possible choice, although lacking experimental support. This report considers in deeper detail a thermodynamic model for micelle distributions, the so-called shell model of the present author, which is in basic agreement with an earlier statistic-mechanical study [Hoeve CA & Benson GC (1957), Colloid Polym Sci, 252, 56] in predicting the possibility of broad distributions of micellar species. A self-consistent distribution model which predicts a critical micelle condition must also predict a location with respect to degree of polymerization having a minimum concentration. Thus, the molar distribution function for the shell model satisfies this requirement, whereas the equivalent concentration distribution function fails to do so, as would the statistical models for multiple ligand binding. Moreover, the position of this minimum is predicted to change with concentration.     

Interactions of lysozyme in concentrated electrolyte solutions from dynamic light-scattering measurements

The diffusion of hen egg-white lysozyme has been studied by dynamic light scattering in aqueous solutions of ammonium sulfate as a function of protein concentration to 30 g/liter. Experiments were conducted under the following conditions: pH 4-7 and ionic strength 0.05-5.0 M. Diffusivity data for ionic strengths up to 0.5 M were interpreted in the context of a two-body interaction model for monomers. From this analysis, two potential-of-mean-force parameters, the effective monomer charge, and the Hamaker constant were obtained. At higher ionic strength, the data were analyzed using a model that describes the diffusion coefficient of a polydisperse system of interacting protein aggregates in terms of an isodesmic, indefinite aggregation equilibrium constant. Data analysis incorporated multicomponent virial and hydrodynamic effects. The resulting equilibrium constants indicate that lysozyme does not aggregate significantly as ionic strength increases, even at salt concentrations near the point of salting-out precipitation.     

Analysis of protein self-association by combined calorimetric and molecular sieve studies: application to beta-lactoglobulin A

The application of isothermal calorimetry to the study of self-association reactions between identical protein subunits has been explored to assess the types of information obtainable from heat of dilution curves (i.e., the molar heat of dilution as a function of total solute concentration). Relationships between the heat of dilution, subunit association constants, and enthalpies of formation for the various association complexes in a self-associating system have been formulated. A method is described for constructing heat of dilution curves from sequential step-wise dilution experiments in a batch-type calorimeter. The relationship between calorimetric and van't Hoff enthalpies is formulated for systems undergoing self-association reactions. Comparison between the two is shown by numerical simulation to provide a very sensitive test for the presence of intermediate species.Calorimetric measurements were made on the self-association of β?lactoglobulin-A at 5.0 °C, pH 4.65, in 0.1 m NaCl and in 0.1 m acetate. Heat of dilution curves constructed from these data were used to estimate the equilibrium constant and enthalpy of formation, assuming a monomer-tetramer association process. Values of 31 ± 4 kcal/mole tetramer for the enthalpy and 1.3 ± 1.0 × 10¹¹ liter³/mole³ for the constant of tetramerization were determined from the calorimetric measurements in NaCl. The corresponding values for calorimetric measurements in acetate were 33 ± 4 kcal/mole and 1.6 ± 1.0 × 10¹¹ liter³/mole³.The calorimetric results were compared with thermodynamic information obtained from association data between 5 and 25 °C in 0.1 m acetate using molecular sieve chromatography. Within experimental error, the molecular sieve data at 5 °C could be fit to a monomer-tetramer association reaction with a monomer molecular weight of 36,000. From these studies a van't Hoff enthalpy of 38 ± 4 kcal/mole tetramer and an equilibrium constant of 4.6 ± 1.0 × 10¹¹ liter³ mole³ at 5 °C were obtained. Comparison between calorimetric and van't Hoff enthalpies indicates that the self-association of β-lactoglobulin-A under these conditions can be adequately described by a monomer-tetramer reaction. The results suggest that, a small fraction (e.g., 5–10%) of species having intermediate states of aggregation may be present, but preclude the presence of large fractions of intermediate species having appreciable enthalpies of association.     

Light-scattering studies of the alpha-ketoglutarate dehydrogenase complex from escherichia coli. I. Characterization of the self-association of the complex

The self-association of Escherichia coli alpha-ketoglutarate dehydrogenase complex (KGDC) purified by a column Chromatographic technique, was characterized by light-scattering photometry. The complex adopts a solution conformation somewhat larger than that observed in the electron microscope. The evidence suggests a nonideal indefinite self-association model for KGDC in KCl, phosphate buffer. The KGDC monomer has a molecular charge of about -3 x 10(2) at neutral pH. The self-association is promoted by increasing KCl concentrations, pH (in the range from 6.3 to 7.4) and temperature (from 20 to 30 degrees C). The effects of pH changes suggest a release of protons during the self-association and a minor 'preferential' interaction of phosphate ions. For the association of one monomer to the aggregate at neutral pH and 25 degrees C. DeltaG degrees = -7.8 kcal mol(-1). DeltaH degrees = 24 kcal mol(-1) and DeltaS degrees = 1.1 x 10(2) cal mol(-1) K(-1). These data indicate that hydrophobic interactions drive the association. Thermodynamically, the self-association of KGDC is a complex phenomenon and may serve to stabilize the enzyme complex in solution.     

Hidden self-association of proteins

Sedimentation equilibrium measurements were carried out on solutions of bovine serum albumin, aldolase, and ovalbumin in phosphate-buffered saline, pH 7.2, at 10 degrees C. The data obtained for each protein were analyzed to yield the dependence of apparent weight-average molecular weight upon protein concentration, over a concentration range of ca 1-200 g/L. Using the approximate theory of Chatelier and Minton [1987) Biopolymers 26, 507-524), models are formulated for the dependence of apparent weight-average molecular weight upon concentration in non-ideal solutions containing proteins which may self-associate according to a monomer/n-mer or a monomer/dimer/tetramer scheme. The concentration dependence data for serum albumin may be accounted for, assuming either no self-association or weak monomer/dimer association. The data for aldolase may be accounted for assuming either weak monomer/dimer or weak monomer/trimer association. The data for ovalbumin may be accounted for assuming either weak monomer/trimer or weak monomer/dimer/tetramer association. The associations do not approach saturation at the highest concentrations studied, and the standard-state free energy changes accompanying self-association amount to less than 4 kcal/mol of intermolecular contacts, suggesting that non-specific clustering of protein molecules at high concentration rather than the formation of specific complexes is being observed.     

Self-association of sodium cholate in isotonic saline solutions

The self-association of dialyzed solutions of sodium cholate in isotonic saline solutions has been studied by vapor pressure osmometry and sedimentation equilibrium. These studies were carried out at 25, 31 and 37 degrees C. In all experiments the self-association could be described as a two-equilibrium constant, indefinite self-association in which odd species beyond monomer were absent. The plots of M1/Mna or M1/Mwa vs. c were quite smooth with no sharp breaks; this suggested that there were no critical phenomena. The temperature dependence of the self-association was quite small. Our results are in accord with other studies on sodium cholate which indicate that the self-association involves several species, and that it is not a monomer-n-mer self-association.