E.T. Adams

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.

[5] Membrane and vapor pressure osmometry

Publisher Summary Osmotic pressure, along with freezing point depression (cryoscopy), boiling point elevation (ebulliometry), vapor pressure lowering, dew point depression, and elasto-osmometry, is one of the colligative properties of solutions. This chapter is concerned with two of these colligative properties: membrane osmometry and vapor pressure osmometry. These techniques are useful for evaluating molecular weights or number average molecular weights and activity coefficients or osmotic pressure second virial coefficients for nonassociating solutes. For associating solutes, these techniques can be used to establish the type of association present, if that is not known beforehand, as well as nonideal terms. Vapor pressure osmometry is most useful for studying lower molecular weight solutes: solutes having molecular weights between 0 and 20,000 (grams/mole). Membrane osmometry, on the other hand, is more useful for the study of larger molecular weight solutes: macromolecules having molecular weights between 10,000 and 1,000,000.

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.

Osmotic pressure measurements of ovalbumin and lysozyme mixtures.

Ovalbumin and lysozyme have been reported to undergo a mixed association in solutions of low ionic strength. Osmotic pressure experiments were performed on ovalbumin and on lysozyme solutions in 0.06 M cacodylate buffer (I = 0.02, pH = 5.8) at 30 and at 37 degrees C. The individual proteins did not undergo any self-associations at either temperature; these measurements indicated that each of the solutions was nonideal. Osmotic pressure experiments on three blends of lysozyme and ovalbumin at 30 and 37 degrees C could be interpreted in two ways. One interpretation was that a nonideal, nonassociating mixture of A and B was present; for the three solutions the mixed nonideal term BAB was negative. A negative nonideal term is usually interpreted as indicating an association. The other interpretation of the data was as a quasi-ideal mixed association of the type A + B in equilibrium AB.

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.

Molecular weights and molecular-weight distributions from ultracentrifugation of nonideal solutions.

Ultracentrifugation, membrane osmometry and capillary viscometry experiments have been performed on two dextran samples, which have molecular-weight distributions (MWDs) similar to those of dextrans used as blood plasma extenders. The manufacturer reported values of Mn and MW, determined by end group analysis and by light scattering, respectively. Our values of Mn, determined by osmometry, and MW, calculated from ultracentrifugal and viscometry experiments, agreed quite well with the manufacturers results. Good agreement was obtained with values of MW and BLS (the light scattering second virial coefficient) obtained from sedimentation equilibrium experiments at different speeds using sector or nonsector-shaped centerpieces. Several ways of obtaining MW, MZ and BLS from sedimentation equilibrium experiments are presented. We have also shown how to obtain the speed-dependent term of the sedimentation equilibrium second virial coefficient. Both BLS and the speed-dependent nonideal terms could be used to correct the sedimentation equilibrium data, so that ideal values of d in c/d(r2) or dc/d(r2) could be estimated and used to obtain the MWDs of the dextran samples. Both Donnellys and Scholtes methods were used with the sedimentation equilibrium data. With both methods, unimodal MWDs were encountered, which gave good agreement with the manufacturers MWDs, obtained by a combination of analytical gel chromatography and light scattering. Uncorrected sedimentation equilibrium data gave MWDs quite different from the manufacturers results. The MWD calculated from the differential distribution of sedimentation coefficients also gave a unimodal MWD, but this MWD did not give a good agreement with the sedimentation equilibrium results or with the manufacturers results.

Some Modern Aspects of Ultracentrifugation

Abstract Shortly after the ultracentrifuge was developed, it was realized that molecular-weight distributions (MWDs) of polymers could be obtained from sedimentation equilibrium experiments. Although numerous attempts have been made to obtain MWDs from sedimentation equilibrium experiments, the results were not very satisfactory, and most MWDs were obtained from sedimentation velocity experiments. Only recently have some satisfactory methods been developed for sedimentation equilibrium experiments. These methods were restricted to ideal, dilute solutions and to ultracentrifuge cells with sector-shaped centerpieces. Both of these restrictions can now be removed. Methods for correcting for nonideal behavior are shown. Procedures for obtaining MWDs from sector—or nonsector—shaped centerpieces are shown. These procedures are illustrated with real examples, and a comparison between MWDs obtained by sedimentation velocity, sedimentation equilibrium, and gel permeation chromatography experiments is shown. Self-a...

Self-association of β-lactoglobulin c in acetate buffers

Abstract The self-association of β-lactoglobulin C at pH 4.65 (23° C) in acetate buffer has been studied at various temperatures, 10, 16, 20 and 25dg C, by a series of sedimentation equilibrium experiments. Two different buffers were used. Buffer I with an ionic strength of O.I consisted of 0.1M acetic acid and O.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, M a , with the total solute concentration, c , was characteristic of a self-association- In contrast to the behavior of β-lactoglobulin A in acetate buffer, the association of β-lactoglobulin C did not proceed beyond dimer. Furthermore, within the experimental error, the self-association of β-lactoglobulin C was independent of temperature and ionic strength; all experimental data could be put on the same M wa (or M 1 / M wa ) vs c plot! Several models were used to test the self-association, and a monomer—dimer association with K 2 = 2.10 × 10 3 dl/g and BM 1 = − 1.2 × 10 −2 dl/g seemed to give a good description of the M 1 /M wa vs c curve

Sedimentation coefficients of self-associating species: I. Basic theory

Abstract Under the same solution conditions, the apparent weight average sedimentation coefficient, swa, and some quantities obtained from it can be combined with the equilibrium constant or constants, Ki, and the monomer concentration, cI, obtained from sedimentation equilibrium, light scattering or osmotic pressure experiments on the same self-associating solute, so that the individual sedimentation coefficients, si, of the self-associating species, and also the hydrodynamic concentration dependence parameter,g or g , can be evaluated. Using two different models for the hydrodynamic concentration parameter, four different methods are presented for the evaluation of the sis. Methods for evaluating g or g , once the sis are known, are presented. A method for obtaining the number average sedimentation coefficient, sN, and its application to self-associations is presented. Methods are shown for the evaluation of Z average properties, xzc, as well as number average properties,xNc, of a self-associating solute from its weight average properties, xwc.

Mixed association of cholesterol with methyl cholate and methyl lithocholate in chloroform solutions

The concentration-dependent mixed association behavior of cholesterol with methyl cholate (MeC) and methyl lithocholate (MeLC) in chloroform at 37 degrees C has been studied by vapor pressure osmometry (VPO). This study is part of a larger project to investigate the effect of number and position of hydroxyl-bearing steroids. Using theories developed by Adams and by Steiner, the model and appropriate parameters for the nonideal mixed associations were elucidated. For the MeLC/cholesterol system, no mixed association was observed. For the MeC/cholesterol system, both methods of analysis indicate that a nonideal AB complex formation occurs. The best parameters to explain the experimental data are kAB = 0.04 1/g; BAB (the nonideal term) = 1.5 X 10(-5) 1 mol g-2.