Sedimentation Equilibrium Distributions Research Articles

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization

This reexamination of a high-speed sedimentation equilibrium distribution for α-chymotrypsin under slightly acidic conditions (pH 4.1, IM 0.05) has provided experimental support for the adequacy of nearest-neighbor considerations in the allowance for effects of thermodynamic nonideality in the characterization of protein self-association over a moderate concentration range (up to 8mg/mL). A widely held but previously untested notion about allowance for thermodynamic nonideality effects is thereby verified experimentally. However, it has also been shown that a greater obstacle to better characterization of protein self-association is likely to be the lack of a reliable estimate of monomer net charge, a parameter that has a far more profound effect on the magnitude of the measured equilibrium constant than any deficiency in current procedures for incorporating the effects of thermodynamic nonideality into the analysis of sedimentation equilibrium distributions reflecting reversible protein self-association.

Allowance for the effect of protein charge in the characterization of nonideal solute self-association by sedimentation equilibrium

This theoretical investigation explores the use of statistical–mechanical approaches to characterize the reversible tetramerization of a protein monomer with the size and charge characteristics of serum albumin under conditions where consideration of nearest-neighbor interactions suffices to describe effects of thermodynamic non-ideality. Such analysis of simulated sedimentation equilibrium distributions points to the adequacy of both the scaled particle theory and potential-of-mean-force methods for determining the self-association constant. Although the latter method usually entails the assignment of a magnitude to monomer net charge, this requirement can be obviated to some extent by repeating the analysis for a range of monomer charges and identifying the most appropriate value as that associated with a minimum in the sum-of-squares-of-residuals (SSR) of the best-fit descriptions of the sedimentation equilibrium distribution. Reasonable estimates of the association constant are usually obtained from corresponding analyses of the same sedimentation equilibrium distributions with activity coefficients obtained by scaled particle theory, an approach which also involves the identification of parameters on the basis of a minimum in SSR. However, the value of monomer charge determined must be regarded as a curve-fitting parameter rather than a true measure of monomer charge. Similar qualifications are shown to prevail in the scaled particle theory approach, which also involves the identification of parameters (the effective monomer volume and the polymer/monomer volume ratio) on the basis of a minimum in SSR. We therefore recommend discontinuation of the practice whereby quite precise distinction between modes of self-association has been attempted on the grounds of the physical credibility of the magnitudes of these additional curve-fitting parameters.

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.

Reconsideration of sedimentation equilibrium distributions reflecting the effects of small inert cosolutes on the dimerization of α-chymotrypsin

A reported discrepancy between quantitative estimates of the extent of enhanced α-chymotrypsin dimerization in the presence of sucrose is traced to different consequences of using an incorrect value of the buoyant molecular weight in the analysis of sedimentation equilibrium distributions. Support is thereby provided for the earlier contention that the effect of sucrose, as well as of glucose and raffinose, on dimerization may be rationalized quantitatively in terms of molecular crowding by an inert cosolute.

Characterization of weak protein dimerization by direct analysis of sedimentation equilibrium distributions: The INVEQ approach

Closer scrutiny has been accorded a recently reported procedure for characterizing weak protein dimerization by sedimentation equilibrium (INVEQ) in which the equilibrium distribution is analyzed as a dependence of radial distance on solute concentration rather than of solute concentration on radial distance. By demonstrating theoretically that the fundamental parameter derived from the analysis is simply the difference between the dimerization constant and the osmotic second virial coefficient for monomer-monomer interaction, this investigation refutes the original claim that independent estimates of these two parameters can be obtained by nonlinear curve fitting of the sedimentation equilibrium distribution. This criticism also applies to conventional analyses of sedimentation distributions by the commonly employed Beckman Origin and NONLIN software. Numerically simulated distributions are then analyzed to demonstrate limitations of the procedure and also to indicate a means of improving the reliability of the returned estimate of the dimerization constant. These features are illustrated by applying the original and revised analytical procedures to a sedimentation equilibrium distribution for α-chymotrypsin (pH 4.0, I 0.05 M).

Nonequivalence of second virial coefficients from sedimentation equilibrium and static light scattering studies of protein solutions

Experimental data for ovalbumin and lysozyme are presented to highlight the nonequivalence of second virial coefficients obtained for proteins by sedimentation equilibrium and light scattering. Theoretical considerations confirm that the quantity deduced from sedimentation equilibrium distributions is B 22, the osmotic second virial coefficient describing thermodynamic nonideality arising solely from protein self-interaction. On the other hand, the virial coefficient determined by light scattering is shown to reflect the combined contributions of protein–protein and protein–buffer interactions to thermodynamic nonideality of the protein solution. Misidentification of the light scattering parameter as B 22 accounts for published reports of negative osmotic second virial coefficients as indicators of conditions conducive to protein crystal growth. Finally, textbook assertions about the equivalence of second virial coefficients obtained by sedimentation equilibrium and light scattering reflect the restriction of consideration to single-solute systems. Although sedimentation equilibrium distributions for buffered protein solutions are, indeed, amenable to interpretation in such terms, the same situation does not apply to light scattering measurements because buffer constituents cannot be regarded as part of the solvent: instead they must be treated as non-scattering cosolutes.

Analysis of thermodynamic non-ideality in terms of protein solvation

The effects of thermodynamic non-ideality on the forms of sedimentation equilibrium distributions for several isoelectric proteins have been analysed on the statistical–mechanical basis of excluded volume to obtain an estimate of the extent of protein solvation. Values of the effective solvation parameter δ are reported for ellipsoidal as well as spherical models of the proteins, taken to be rigid, impenetrable macromolecular structures. The dependence of the effective solvated radius upon protein molecular mass exhibits reasonable agreement with the relationship calculated for a model in which the unsolvated protein molecule is surrounded by a 0.52-nm solvation shell. Although the observation that this shell thickness corresponds to a double layer of water molecules may be of questionable relevance to mechanistic interpretation of protein hydration, it augurs well for the assignment of magnitudes to the second virial coefficients of putative complexes in the quantitative characterization of protein–protein interactions under conditions where effects of thermodynamic non-ideality cannot justifiably be neglected.

Ultracentrifugal studies of the effect of molecular crowding by trimethylamine N-oxide on the self-association of muscle glycogen phosphorylase b.

The suitability of sedimentation equilibrium for characterizing the self-association of muscle glycogen phosphorylase b has been reappraised. Whereas sedimentation equilibrium distributions for phosphorylase b in 40 mM Hepes buffer (pH 6.8) supplemented with 1 mM AMP signify a lack of chemical equilibrium attainment, those in buffer supplemented additionally with potassium sulfate conform with the requirements of a dimerizing system in chemical as well as sedimentation equilibrium. Because the rate of attainment of chemical equilibrium under the former conditions is sufficiently slow to allow resolution of the dimeric and tetrameric enzyme species by sedimentation velocity, this procedure has been used to examine the effects of thermodynamic nonideality arising from molecular crowding by trimethylamine N-oxide on the self-association behaviour of phosphorylase b. In those terms the marginally enhanced extent of phosphorylase b self-association observed in the presence of high concentrations of the cosolute is taken to imply that the effects of thermodynamic nonideality on the dimer-tetramer equilibrium are being countered by those displacing the T<==>R isomerization equilibrium for dimer towards the smaller, nonassociating T state. Because the R state is the enzymically active form, an inhibitory effect is the predicted consequence of molecular crowding by high concentrations of unrelated solutes. Thermodynamic nonideality thus provides an alternative explanation for the inhibitory effects of high concentrations of glycerol, sucrose and ethylene glycol on phosphorylase b activity, phenomena that have been attributed to extremely weak interaction of these cryoprotectants with the T state of the enzyme.

Interpretation of thermodynamic non-ideality in sedimentation equilibrium experiments on proteins

This investigation re-examines theoretical aspects of the allowance for effects of thermodynamic non-ideality on the sedimentation equilibrium distribution for a single macromolecular solute, and thereby resolves the question of the constraints that pertain to the definition of the activity coefficient term in the basic sedimentation equilibrium expression. Sedimentation equilibrium results for ovalbumin are then presented to illustrate a simple procedure for evaluating the net charge (valence) of a protein from the magnitude of the second virial coefficient in situations where the effective radius of the protein can be assigned. Finally, published sedimentation equilibrium results on lysozyme are reanalysed to demonstrate the feasibility of employing the dependence of the second virial coefficient upon ionic strength to evaluate both the valence and the effective radius of the non-interacting solute.

Direct analysis of sedimentation equilibrium distributions reflecting complex formation between cytochrome c and ovalbumin.

Conference Article| November 01 1998 Direct analysis of sedimentation equilibrium distributions reflecting complex formation between cytochrome c and ovalbumin Donald J. Winzor; Donald J. Winzor *Department of Biochemistry, University of Queensland, Brisbane, Queensland 4072, Australia Search for other works by this author on: This Site PubMed Google Scholar Michael P. Jacobsen; Michael P. Jacobsen *Department of Biochemistry, University of Queensland, Brisbane, Queensland 4072, Australia Search for other works by this author on: This Site PubMed Google Scholar Peter R. Wills Peter R. Wills †Department of Physics, University of Auckland, Auckland, New Zealand Search for other works by this author on: This Site PubMed Google Scholar Biochem Soc Trans (1998) 26 (4): 741–745. https://doi.org/10.1042/bst0260741 Article history Received: July 28 1998 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Facebook Twitter LinkedIn MailTo Cite Icon Cite Get Permissions Citation Donald J. Winzor, Michael P. Jacobsen, Peter R. Wills; Direct analysis of sedimentation equilibrium distributions reflecting complex formation between cytochrome c and ovalbumin. Biochem Soc Trans 1 November 1998; 26 (4): 741–745. doi: https://doi.org/10.1042/bst0260741 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsBiochemical Society Transactions Search Advanced Search This content is only available as a PDF. © 1998 Biochemical Society1998 Article PDF first page preview Close Modal You do not currently have access to this content.

Direct analysis of sedimentation equilibrium distributions reflecting complex formation between dissimilar reactants.

Procedures are developed for the characterization of thermodynamically ideal complex formation between dissimilar macromolecular reactants by direct analysis of sedimentation equilibrium distributions. Studies of an electrostatic interaction between ovalbumin and cytochrome c are used to illustrate the application of analyses pertaining to (i) the situation in which separate sedimentation equilibrium distributions for the two macromolecular constituents are available, (ii) that in which the experimental record reflects the distribution of only one constituent, and (iii) the situation in which a composite distribution for both constituents is the sole experimental record. An association constant of 63 000 (+/- 2000) M-1 is obtained for the 1:1 interaction between ovalbumin and cytochrome c under the conditions examined (pH 6.3, I 0.03). Because of their inherent simplicity, these direct analytical procedures offer potential for accommodating the effects of thermodynamic nonideality in dissimilar reactant systems.

Low temperature solution behaviour of Methylophilus methylotrophus electron transferring flavoprotein: a study by analytical ultracentrifugation

The solution behaviour of electron transferring flavoprotein (ETF) from Methylophilus methylotrophus was investigated at low temperature (4 °C) by analytical ultracentrifugation. The concentration dependence of the apparent weight average molecular weight, Mw,app, established the existence of the protein in heterodimeric state (M = 63,700 Da), but also signified the possible dissociation of the heterodimer at lower concentrations into its constituent subunits (M = 28,900 Da and 33,700 Da, together with FAD and AMP cofactors of collective M = 1120 Da). This similarity in subunit size allows approximate quantification of the dissociation in terms of expressions for a monomer-dimer equilibrium. The dissociative behaviour was confirmed by determination of the point average molecular weight, Mw,app(r), as a function of the ETF concentration, c(r), throughout the sedimentation equilibrium distributions obtained with loading concentrations of 0.4 and 0.7 mg/ml. By means of the recently formulated ``psi'' procedure for direct analysis of solute self-association a value of (1.5 ± 0.1) µM has been obtained for the dissociation constant Kd. Sedimentation velocity experiments yielded an estimate of the heterodimer sedimentation coefficient, s020,w, of (4.5 ± 0.2) S which for M = 63,700 Da suggests a globular structure.

Cytoskeleton-membrane connections in the human erythrocyte membrane: band 4.1 binds to tetrameric band 3 protein

Band 4.1 provides, besides ankyrin, the main linkage between the erythrocyte membrane and its cytoskeleton. Its predominant binding sites in the membrane are located on the glycophorins. However, the cytoplasmic domain of band 3 can also bind band 4.1. We have studied which of the different band 3 oligomers observed (monomers, dimers, tetramers) can act as band 4.1 binding sites, by equilibrium sedimentation experiments on mixtures of purified band 3 and dye-labelled band 4.1 in solutions of a nonionic detergent. At low molar ratios of band 4.1 and band 3, the sedimentation equilibrium distributions obtained could all be perfectly fitted assuming that only two dye-labelled particles were present: uncomplexed band 4.1 and a complex formed between one band 4.1 molecule and one band 3 tetramer. The presence of small amounts of complexes containing band 3 monomers or dimers could not be completely ruled out but is unlikely. On the other hand, stabilized band 3 dimers effectively bound band 4.1. At higher molar band 4.1/band 3 ratio, the band 3 tetramer apparently could bind up to at least four band 4.1 molecules. The band 4.1/band 3 tetramer complex was found to be unstable. The results described, together with those reported previously, point at a prominent role of tetrameric band 3 in ligand binding.

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.

Thermodynamic analysis of the effects of small inert cosolutes in the ultracentrifugation of noninteracting proteins.

Considerations of the effect of a small cosolute on the sedimentation equilibrium distribution for a noninteracting protein have led to the development of a simple procedure for evaluating both the molecular weight of the protein and the second virial coefficient describing the excluded volume interaction between protein and cosolute. Its application is illustrated by analysis of sedimentation equilibrium distributions for bovine thyroglobulin and horse liver alcohol dehydrogenase in the presence of a range of sucrose concentrations, and also of those for aldolase in the presence of urea to obtain the subunit molecular weight of this tetrameric enzyme. The effects of sucrose concentration on the sedimentation coefficients of thyroglobulin, catalase, and horse liver alcohol dehydrogenase are also examined to demonstrate that the second virial coefficients for protein-cosolute excluded volume interaction may be determined, albeit with less precision, from the cosolute concentration required to render the sedimentation coefficient zero by virtue of its effect on the buoyancy term. These findings serve to reinforce the fact that the effects of small cosolutes usually ascribed to changes in "protein solvation" are envisaged more realistically in terms of excluded volume.

Stabilizing effect of sucrose against irreversible denaturation of rabbit muscle lactate dehydrogenase

Measurements of the kinetics of activity loss by rabbit muscle lactate dehydrogenase in acetate-chloride buffer, pH 5.0, I 0.20, have shown that the enzyme exhibits greater stability against irreversible inactivation when the buffer is supplemented with sucrose (0.1 M–0.5 M). On the basis of sedimentation equilibrium distributions obtained for enzyme in the absence and presence of sucrose (0.5 M), the lactate dehydrogenase is essentially dimeric in both environments. The observed stabilization of enzyme activity has therefore been considered in terms of the space-filling effects of sucrose on an isomerization equilibrium between native and unfolded forms of dimeric lactate dehydrogenase, which precedes irreversible inactivation of the unfolded isomer. Interpretation of the kinetic results on that basis has led to the conclusion that the initial stage of enzyme unfolding entails a minor change in volume and/or asymmetry of the lactate dehydrogenase that gives rise to a 4% increase in the second virial coefficient describing excluded volume interactions between dimeric enzyme and sucrose.

Association of Structural Repeats in the α-Actinin Rod Domain. Alignment of Inter-subunit Interactions

Fragments of the rod domain of chicken α-actinin, which comprises four spectrin-like repeat sequences, have been prepared by expression in Escherichia coli. Electron microscopy reveals that all products containing three or four complete repeats are rod-like. Self-association of fragments was detected by chemical cross-linking and analytical equilibrium sedimentation. The intact rod domain forms a stable dimer, which does not dissociate measureably in the accessible concentration range. Elimination of either terminal repeat (repeat 1 or repeat 4) greatly diminishes the extent of dimerisation. The fragment comprising repeats 1-3 dimerises appreciably, with an association constant estimated from the sedimentation equilibrium distribution of approximately 5|mult|10 5M −1. The fragment made up of repeats 2-4 dimerises to a small extent, but also forms aggregates at high concentrations. The results are most easily reconciled with an aligned structure for the rod domain in solution, in which repeat 1 associates with repeat 4 of the partnering chain, and repeat 2 with repeat 3, rather than with a staggered structure, in which one of the terminal repeats does not participate in dimerisation. Possible explanations for the apparent difference observed between the α-actinin rod structure in solution and in two-dimensional crystalline arrays are examined.

Allowance for composition dependence of activity coefficients in the analysis of sedimentation equilibrium results obtained with heterogeneously associating systems

An iterative procedure is described that permits analysis of sedimentation equilibrium distributions obtained with heterogeneously associating systems, account being taken of the dependence of each activity coefficient on the composition of the solution, which varies with radial distance. The procedure is illustrated with treatment of distributions simulated for a system of the type A + B ⇌ C, and comment is made on its applicability to systems involving higher order complexes.

Computer Simulation of Sedimentation Equilibrium Distributions for Systems Involving Heterogeneous Associations: THE INTERACTION OF N-ACETYLGLUCOSAMINE WITH LYSOZYME

Two methods are presented for computing the concentration of a species at sedimentation equilibrium as a function of radial distance, for systems wherein the species is involved in a set of chemical equilibria. The treatments are exemplified with a system involving a polymerizing acceptor and a series of acceptor-ligand complexes. It is shown that analytical expressions are available for the computation of exact distributions even in cases where volume changes accompany the several interactions, provided the activity coefficient of each species is taken as unity. This aspect of the work extends previously reported simulation procedures pertaining to simple interacting systems considered thermodynamically ideal. Secondly, a numerical integration procedure is presented for the solution of cases where both volume changes and non-ideality effects operate. The potential use of computer-simulated sedimentation equilibrium distributions is illustrated in relation to experimental results obtained with interacting mixtures of lysozyme (monomer and dimer) and N-acetylglucosamine at pH 8.0, Γ/2 = 0.15, and 15°. First, it is shown that the apparent weight average molecular weight approaches that of the monomer-inhibitor complex at saturating concentrations of the inhibitor, behavior consistent with the effective loss of binding sites on dimer formation. Further analysis involves the direct comparison of simulated distributions with those obtained experimentally using different inhibitor concentrations. The results indicate that the monomeric and dimeric forms of lysozyme bear one binding site with essentially identical affinity for the inhibitor.