Graphical approach to non-ideal cases of self-associating protein systems

Self-association of diisopropylphosphoryl-alpha-chymotrypsin: the involvement of active site of the enzyme in its self-association behaviour

The self-association of diisopropylphosphoryl(DIP)-alpha-chymotrypsin is studied in order to find out whether the active site of the enzyme is involved in its self-association behaviour or not. Sedimentation coefficient as well as the weight-average (Archibald) molecular weight data are obtained as a function of concentration using an analytical ultracentrifugation technique. The analysis indicated that the experimental data fits the model of indefinite self-association. The comparison of the data with earlier data on alpha-chymotrypsin revealed that after the modification at the active site, the association constant for the self-association is reduced by about 47%, and the system deviated from ideality. Results showed further that Ser-195, at the active site, appears to be involved in the self-association behaviour of alpha-chymotrypsin; however, the participation of other groups at the active site is also implicated.

Average quantities accessible to the analysis of sedimentation equilibrium data for self-association systems

This paper shows that analysis of sedimentation equilibrium data, searching for average molecular weights, gives quantities which are dependent on the total protein concentration of the samples, while knowledge of the molecular weight of the monomeric subunits allows a more meaningful search for the concentrations of the individual polymeric components of the system. From these the various average molecular weights can be construed, and the various dissociation equilibrium constants evaluated. Also, in this paper considerations are proposed on the meaning of nonideality terms in associating systems and possible ways for estimating them. As an example the proposed procedures have been applied to measurements of sedimentation equilibrium in carbonmonoxyhemoglobin.

Analysis of various indefinite self-associations of the AK type

Although we and others have developed equations to analyze for some indefinite self-associations that might be encountered, it is felt in some cases that these models, known as the sequential, equal equilibrium constant (SEK) models, might overestimate the size of aggregates encountered at higher solute concentrations. Thus, Garland and Christian proposed two attenuated equilibrium constant (AK) models that might overcome this problem. Their methods were restricted to ideal solutions and to osmometric procedures. We have removed these restrictions, and we have developed equations for analyzing four AK models that might be encountered. Various tests to aid in distinguishing these models are presented. These procedures have been tested with two simulated examples of a Type III AK indefinite self-association.

A sedimentation equilibrium study of the temperature-dependent association of bovine beta-casein

The temperature-dependent association of beta-casein was studied by the sedimentation equilibrium method. The weight-average molecular weight of the protein was determined in 0.2 M sodium phosphate buffer (pH 6.7) at 20, 15, 10 and 2 degrees C, and was found to be dependent markedly on both temperature and protein concentration. The data were well fitted by a monomer-n-mer association scheme, and the values of n, the second viral coefficient, and the free energy change for the association (association constant) were evaluated. The results show that temperature not only shifts the equilibrium but alters the polymer size: the values of n are 49, 22, and 12 at 20, 15, and 10 degrees C, respectively; the free energy change per monomer becomes more negative with increasing temperature, indicating that the attraction between the monomers in a polymer is stronger at higher temperature. This effect of temperature is in contrast to that of ionic strength which affects mainly the equilibrium. The enthalpy change, entropy change, and heat capacity change for the association were also estimated and were indicative of the formation of a considerable amount of hydrophobic bonds upon association.

Graphical analysis of nonideal monomer N-mer, isodesmic, and type II indefinite self-associating systems by equilibrium ultracentrifugation

A graphical procedure is described by which one can obtain in principle the monomer molecular weight, stoichiometry, equilibrium constant, and second virial coefficient of nonideal monomer N-mer, isodesmic, and type II indefinite self-associating systems. In addition, a method is presented for obtaining both the equilibrium constant and the second virial coefficient from the maximum in a plot of apparent molecular weight vs. concentration if the monomer molecular weight and stoichiometry are known. The usefulness and limitations of the methods are discussed, as well as the quality and range of data required for determination of the relevant parameters. The techniques described are applicable to analysis of self-associating systems by osmotic pressure and light scattering, as well as equilibrium ultracentrifugation measurements.

Thermodynamic compensation process in interacting protein systems: definition of thermodynamic compensatory temperature, (Tc)

In our thermodynamic analysis of the non-linear Van't Hoff expression as applied to several self-associating systems -- specifically in the cases of bovine liver L-glutamate dehydrogenase (GDH), glucagon and S-carboxymethylated apo A-II protein from human high density lipoprotein -- we have examined the interrelationships of a number of thermodynamic temperatures as they affect the association process. We found the principal determinants of the linear thermodynamic compensation process to be delta S0(T)/delta C0p(T) = (delta T'C)/(Texp), where (delta T'C) = Texp). We have defined the unique compensatory temperature, (TC), for any interacting system, at which the contributions of enthalpy and entropy to the association process are balanced.

Analysis of various indefinite self-associations

Two methods have been developed for the analysis of four types of indefinite self-associations. Unlike previous treatments by others, the procedures can be applied to nonideal cases. The two methods were first tested with simulated data, and it was found that one could indeed distinguish between the four types of indefinite self-associations. For a more realistic test, sedimentation equilibrium experiments were performed on solutions of beta-lactoglobulin A at 16 degrees C in 0.15 ionic strength acetate buffer, pH 4.65. The self-association of the beta-lactoglobulin A was best described by either method as a sequential indefinite self-association having two equilibrium constants and one second virial coefficient.

Ultracentrifugal studies of human luteinizing hormone and its subunits: dependence on protein concentration and ionic strength

Purified human pituitary luteinizing hormone (hLH) and its alpha and beta subunits have been examined by physical methods. Freshly prepared hLH showed three closely adjacent bands on electrophoresis in polyacrylamide gels under alkaline conditions, but on standing even in the freeze-dried condition additional bands appeared. alpha and beta subunits gave bands which were quite different from the main hLH bands but comparable with the additional bands, as well as traces of hLH bands. hLH was investigated at three ionic strengths (0.1, 0.2, 0.5) at pH 5.9 +/- 0.1. Sedimentation velocity experiments demonstrated a complex system of association-dissociation which was further investigated by sedimentation equilibrium. Association occurred at the higher protein concentrations at each ionic strength, but to a significantly higher level at I = 0.5. Only at I = 0.1, pH 5.8, was there a clear indication over a range of protein concentration of the occurrence of a species of molecular weight 32 000 +/- 2000, in fair agreement only with the sum of the molecular weights of the alpha and beta subunits. At higher ionic strengths, there were indications of dissociation at low protein concentration (less than 0.10 g/100 mL) as well as association at higher values (greater than 0.20 g/100 mL). In view of the occurrence of molecular weights less than 28 000 at I = 0.2, HLH was treated in terms of a monomer of molecular weight 14 000, and some evidence was obtained for tetramer formation (4M = M4). At higher ionic strength this model does not apply and it is thought that indefinite association may be occurring to some extent also. The alpha subunit gave indications of association from its sedimentation coefficient vs. concentration plot, and sedimentation equilibrium (at pH 5.9 I = 0.1) demonstrated molecular weights increasing with increasing concentration. Evidence for tetramer formation also was obtained. The beta subunit, in spite of an apparently simple sedimentation coefficient-concentration curve, showed molecular weights varying from well below 14 000 to beyond 20 000. There is evidence to suggest that the isolated alpha and beta subunits, even on standing as dry solid, are not stable but give rise to lower molecular weight products. Aged freeze-dried hLH did not show such impurity.

Self-association of beta-lactoglobulin c in acetate buffers

The self-association of beta-lactoglobulin C at pH 4.65 (23 degrees C) in acetate buffer has been studied at various temperatures, 10, 16, 20 and 25 degrees C, by a series of sedimentation equilibrium experiments. Two different buffers were used. Buffer I with an ionic strength of 0.1 consisted of 0.1M acetic acid and 0.1M sodium acetate; buffer II had 0.1M KCl in addiation so that its ionic strength was 0.2. The variation of the apparent weight average molecular weight, Mwa, with the total solute concentration, c, was characteristic of a self-association. In contrast to the behavior of beta-lactoglobulin A in acetate buffer, the association of beta-lactoglobulin C did not proceed beyond dimer. Furthermore, within the experimental error, the self-association of beta-lactoglobulin C was independent of temperature and ionic strength; all experimental data could be put on the same Mwa (or M1/Mwa) vs. c plot! Several models were used to test the self-association, and a monomer--dimer association with K2 = 2.10 X 10(3) dl/g and BM1 =- 1.2 X 10(-2) dl/g seemed to give a good description of the M1/Mwa vs. c curve.

Determination of the equilibrium constants of self-associating protein systems. XI. The application of C-(r) in graphical analysis and the enumeration of interacting species in the ultracentrifuge

A greatly simplified procedure is proposed which employs C equals f(r) as determined from sedimentation equilibrium measurements in graphical analysis of self-associating protein systems and in the enumeration of interacting species in the ultracentrifuge. Basic equations given here are applicable to any self-associating system. A procedure is outlined for enumeration of interacting components independent of non-ideal behavior, using principal component analysis.