Characterization of macromolecular heterogeneity by equilibrium sedimentation techniques

New graphical procedures have been developed to investigate the heterogeneity of protein preparations using sedimentation equilibrium. The heterogeneous systems that can be studied include self-associating systems contaminated by incompetent monomer, self-associating systems contaminated by non-dissociating oligomer and simple non-interacting monomer-oligmer disperse systems. The new procedures are based on the concentration dependence of the apparent association constants estimated by a non-linear least square fitting program (NONLIN), on the assumption of conservation of mass during sedimentation and on the applications of several standard techniques for statistical inferences of NONLIN estimations. The procedures outlined here can detect various types of heterogeneity, discriminate amongst different types of heterogeneity, estimate the amount of contaminant causing heterogeneity and determine the true equilibrium constant of the self-associating components. The procedures appear to be sensitive, accurate and easily applicable when tested using both protein samples and computer simulated data.     

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= 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.     

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.     

Analytical ultracentrifugation as a tool for studying protein interactions

The last two decades have led to significant progress in the field of analytical ultracentrifugation driven by instrumental, theoretical, and computational methods. This review will highlight key developments in sedimentation equilibrium (SE) and sedimentation velocity (SV) analysis. For SE, this includes the analysis of tracer sedimentation equilibrium at high concentrations with strong thermodynamic non-ideality, and for ideally interacting systems, the development of strategies for the analysis of heterogeneous interactions towards global multi-signal and multi-speed SE analysis with implicit mass conservation. For SV, this includes the development and applications of numerical solutions of the Lamm equation, noise decomposition techniques enabling direct boundary fitting, diffusion deconvoluted sedimentation coefficient distributions, and multi-signal sedimentation coefficient distributions. Recently, effective particle theory has uncovered simple physical rules for the co-migration of rapidly exchanging systems of interacting components in SV. This has opened new possibilities for the robust interpretation of the boundary patterns of heterogeneous interacting systems. Together, these SE and SV techniques have led to new approaches to study macromolecular interactions across the entire spectrum of affinities, including both attractive and repulsive interactions, in both dilute and highly concentrated solutions, which can be applied to single-component solutions of self-associating proteins as well as the study of multi-protein complex formation in multi-component solutions.     

Analysis of protein self-association under conditions of the thermodynamic non-ideality

Analysis of protein-protein interactions in highly concentrated solutions requires a consideration of the non-ideality in such solutions which is expressed by the virial coefficients. Different equations are presented to estimate effects of the thermodynamic non-ideality on the macromolecular interaction of self-associating proteins in sedimentation equilibrium experiments. Usually the influence of thermodynamic non-ideal behavior are described by concentration power series. The convergence of such power series is limited at high solute concentration. When expressing the thermodynamic non-ideality by an activity power series this disadvantage can be minimized. The developed centrifuge equations are the basis for a global analysis to estimate equilibrium constants and the corresponding thermodynamic activities of the reactants. Based on fit analysis of synthetic concentration profiles it was established that marked deviations from the expected association constants are observed for proteins with strong association forces between solute molecules. Considerable differences were also observed in weakly interacting systems. This was due to the excluded volume of the protein which is similar in magnitude to the binding constant. For interactions with moderate affinities values extremely close to the true binding values were obtained, as confirmed by experimental results with concanavalin A.     

A comparison of weight average and direct boundary fitting of sedimentation velocity data for indefinite polymerizing systems

Analysis of sedimentation velocity data for indefinite self-associating systems is often achieved by fitting of weight average sedimentation coefficients (s(20,w)) However, this method discriminates poorly between alternative models of association and is biased by the presence of inactive monomers and irreversible aggregates. Therefore, a more robust method for extracting the binding constants for indefinite self-associating systems has been developed. This approach utilizes a set of fitting routines (SedAnal) that perform global non-linear least squares fits of up to 10 sedimentation velocity experiments, corresponding to different loading concentrations, by a combination of finite element simulations and a fitting algorithm that uses a simplex convergence routine to search parameter space. Indefinite self-association is analyzed with the software program isodesfitter, which incorporates user provided functions for sedimentation coefficients as a function of the degree of polymerization for spherical, linear and helical polymer models. The computer program hydro was used to generate the sedimentation coefficient values for the linear and helical polymer assembly mechanisms. Since this curve fitting method directly fits the shape of the sedimenting boundary, it is in principle very sensitive to alternative models and the presence of species not participating in the reaction. This approach is compared with traditional fitting of weight average data and applied to the initial stages of Mg(2+)-induced tubulin self-associating into small curved polymers, and vinblastine-induced tubulin spiral formation. The appropriate use and limitations of the methods are discussed.     

Identification and interpretation of complexity in sedimentation velocity boundaries.

Synthetic sedimentation velocity boundaries were generated using finite-element solutions to the original and modified forms of the Lamm equation. Situations modeled included ideal single- and multicomponent samples, concentration-dependent samples, noninteracting multicomponent samples, and reversibly self-associating samples. Synthetic boundaries subsequently were analyzed using the method of van Holde and Weischet, and results were compared against known input parameters. Results indicate that this analytical method provides rigorous diagnostics for virtually every type of sample complexity encountered experimentally. Accordingly, both the power and utility of sedimentation velocity experiments have been significantly expanded.     

Studies on buffalo pituitary lutropin (LH): Physicochemical and immunological properties

Physicochemical and immunological properties of buffalo pituitary lutropin (buffalo LH) are reported here. The preparation was shown to be homogeneous by several physicochemical criteria. The molecular weight was found to be 30,000–40,000 by SDS-PAGE, GP-HPLC, and ultracentrifugation analyses. It showed certain interesting features, such as anomalous sedimentation behavior, microheterogeneity due to sugar-linked sulfate, and weak immunogenicity in rabbits. The subunit nature of the hormone has been confirmed. Sugar composition showed similarities as well as differences with LH of other species. Preliminary data on the homologous and heterologous RIAs, using iodinated sheep LH and buffalo LH and the respective antisera, have also been given.     

Preparation of unilamellar liposomes of intermediate size (0.1-0.2 mumol) by a combination of reverse phase evaporation and extrusion through polycarbonate membranes

The mixed association between two self-associating systems, human apolipoproteins A-I and A-II, has been evaluated by fluorescence spectroscopy and sedimentation equilibrium. The combined results are consistent with the formation of specific mixed oligomers between apolipoproteins A-I and A-II in aqueous solution. The data are discussed in terms of the role of protein-protein versus protein-lipid interactions in the quaternary organization of plasma lipoproteins.     

Osmotic pressure measurements on insulin: anomalous results indicate that the monomer is preferentially adsorbed

The concentration dependence of the number average molecular weight of insulin at pH 2, ionic strength 0.05, and 20 degrees C as determined by osmotic pressure measurements indicates that the hormone is a homogeneous protein of molecular weight close to that of the dimer. Since sedimentation equilibrium experiments confirm what is well known, namely that insulin is a self-associating protein dissociating to monomer under these conditions, an explanation for the anomaly was sought in the possible loss of protein from solution by adsorption. Analysis of the results strongly supports this conclusion and consideration of the adsorption properties of insulin in terms of hydrophobic interactions shows them to be consistent with the behaviour of insulin as a self-associating protein. The monomer appears to be the primary molecular species responsible for insulin adsorption.     

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

Under the same solution conditions, the apparent weight average sedimentation coefficient, s_wa, and some quantities obtained from it can be combined with the equilibrium constant or constants, K_i, and the monomer concentration, c_I, obtained from sedimentation equilibrium, light scattering or osmotic pressure experiments on the same self-associating solute, so that the individual sedimentation coefficients, s_i, of the self-associating species, and also the hydrodynamic concentration dependence parameter,g or $\text{g}$, can be evaluated. Using two different models for the hydrodynamic concentration parameter, four different methods are presented for the evaluation of the s_i's. Methods for evaluating g or $\text{g}$, once the s_i's are known, are presented. A method for obtaining the number average sedimentation coefficient, s_N, and its application to self-associations is presented. Methods are shown for the evaluation of Z average properties, x_zc, as well as number average properties,x_Nc, of a self-associating solute from its weight average properties, x_wc.     

Computer stimulation of sedimentation in the ultracentrifuge. VII. Solutes undergoing indefinite self-association

The velocity sedimentation of solutes involved in self-association equilibria of the indefinite type was simulated using a computer model. The changes in boundary shape that resulted from varying the association constant and the molecular weight of the self-associating monomer were examined. Both ideally and nonideally sedimenting solutes were considered, and several alternative treatments of the variation of the frictional ratio with molecular size were used. All of the calculated boundaries were skewed, with the leading limb of the gradient profile steeper than the trailing limb. For relatively tightly self-associating solutes, the boundaries were very broad and strongly skewed. No shoulders or subsidiary peaks were observed for any of the model solutes used.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. II. Two protein components

Relations describing sedimentation equilibrium in solutions containing two macromolecular solute components are derived for the following cases: (1) two nonassociating proteins at arbitrary concentration, (2) one dilute self-associating protein in the presence of a second inert protein at arbitrary concentration, and (3) two proteins at arbitrary concentration that can associate to form a single heterocomplex of arbitrary composition. As in earlier work (R. C. Chatelier and A. P. Minton (1987) Biopolymers, 26, 507–524), the relations are obtained by using scaled particle theory to calculate the thermodynamic activity of each species present at a given radial distance in the centrifuge. The results of numerical simulations of sedimentation equilibrium are presented as the dependence of apparent molecular weights, or apparent weight-average molecular weights, upon solution composition. Semiempirical methods are presented, by means of which the weight-average molecular weights of self- and heteroassociating proteins in highly nonideal solutions may be estimated from experimental data. It is found that the semiempirical methods yield reasonably accurate estimates of the true weight-average molecular weight over a broad range of experimental conditions, providing that the partial specific volumes of two components in a heteroassociating system do not differ by more than about 0.05 mL/g.     

An ultracentrifugal study of the self-association of canine apolipoprotein A-I in solution.

The sedimentation behavior of canine apolipoprotein (apo) A-I in 0.02 M EDTA, pH 8.6, was studied as a function of protein concentration by the techniques of sedimentation velocity and sedimentation equilibrium in the analytical ultracentrifuge. At concentrations of less than 1 g/liter, apo-A-I exhibited a monomodal sedimentation pattern, with apparent sedimentation coefficients which varied from 2.3 to 3.5 S with increasing protein concentrations. Above 1.5 g/liter, apo-A-I had two well resolved peaks with s20,w values of 4.15 S and 5.75 S. The proportion of the 5.75 S component increased with increasing apo-A-I concentrations, with a concomitant decrease of the 4.15 S component. By sedimentation equilibrium ultracentrifugation with both the conventional and meniscus-depletion methods, the apparent weight-average molecular weight of apo-A-I was found to be concentration-dependent. At a protein concentration of 5.25 g/liter, an apparent weight average molecular weight of 138,000 was determined, indicating that molecular species larger than a tetramer (monomer molecular weight = 28,000) were present in solution. When analyzed in terms of a reversible self-associating system, the experimental data could best be described according to a monomer-dimer-tetramer-octamer model, as previously reported from human apo-A-I (Vitello, L. B., and Scanu, A. M. (1975) J. Biol. Chem. 251, 1131-1136). The equilibrium constants were: K2 = 4.5 liters/g, K4 = 470 liters3/g3, and K8 = 41,600 liters7/g7, respectively.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

A Double-Isotope Procedure for Examining Protein Microheterogeneity: Multiple Forms of Fast-Transported Glycoproteins and Sulfoproteins Possess a Common Polypeptide Chain

Several fast-transported proteins that appear as single bands after sodium dodecyl sulfate-polyacrylamide gel electrophoresis resolve into multiple spots during isoelectric focusing. A method was devised for determining if such microheterogeneity in net charge indicates that individual polypeptides have been posttranslationally modified to differing extents. Dorsal root ganglia were pulse-labeled with [35S]methionine and either [3H]leucine or [3H]proline, proteins fast-transported into peripheral sensory axons were separated by two-dimensional gel electrophoresis, and isotope incorporation ratios of proteins associated with individual gel spots were determined. When four microheterogeneous glycoproteins were analyzed, each protein "family" showed markedly similar isotope ratios for its three to seven characteristic spots. Such ratios differed between families by almost twofold. In addition, a group of nonglycosylated, sulfate-containing proteins was identified as a family on the basis of the similar isotope incorporation ratios of its component spots. These results suggest that protein microheterogeneity can result from variable sulfation of tyrosine residues as well as from variation in sialic acid-containing oligosaccharide side-chains. More generally, the method can be utilized to test for protein microheterogeneity in cases where the amounts of protein are too low to permit peptide mapping analysis and where the nature of the charge-altering modification is unknown.     

Molecular characteristics of the major scrapie prion protein

A major protein was identified that purifies with the scrapie agent extracted from infected hamster brains. The protein, designated PrP 27-30, was differentiated from other proteins in purified fractions containing the scrapie agent by its microheterogeneity (Mr 27000-30000) and its unusual resistance to protease digestion. PrP 27-30 was found in all fractions enriched for scrapie prions by discontinuous sucrose gradient sedimentation or sodium dodecyl sarcosinate-agarose gel electrophoresis. It is unlikely that PrP 27-30 is a pathologic product because it was found in fractions isolated from the brains of hamsters sacrificed prior to the appearance of histopathology. If PrP 27-30 is present in normal brain, its concentration must be 100-fold lower than that found in equivalent fractions from scrapie-infected hamsters. Three protease-resistant proteins similar to PrP 27-30 were found in fractions obtained by discontinuous sucrose gradient sedimentation of scrapie-infected mouse brain. These proteins were not evident in corresponding fractions prepared from normal mouse brain. One-dimensional peptide maps comparing PrP 27-30 and normal hamster brain proteins of similar molecular weight demonstrated that PrP 27-30 has a primary structure which is distinct from these normal proteins. Heating substantially purified scrapie fractions to 100 degrees C in sodium dodecyl sulfate inactivated the prion and rendered PrP 27-30 susceptible to protease digestion. Though the scrapie agent appears to be hydrophobic, PrP 27-30 remained in the aqueous phase after extraction with organic solvents, indicating that it is probably not a proteolipid. PrP 27-30 is the first structural component of the scrapie prion to be identified.     

An unusual cysteine-containing histone H1-like protein and two protamine-like proteins are the major nuclear proteins of the sperm of the bivalve mollusc Macoma nasuta

The sperm-specific protamine-like (PL) components PL-I, PL-II, and PL-III from the sperm of the bent-nose clam Macoma nasuta have been isolated and characterized for the first time. These proteins coexist in the sperm nuclei with a small percentage of a full histone complement. All of them have a very similar amino acid composition, following what seems to be the general composition prototype for the class Bivalvia (Ausió, J. (1986) Comp. Biochem. Physiol. B Comp. Biochem. 85, 439-449). Nevertheless, they have different molecular weights (PL-I = 23,500, PL-II = 15,600, and PL-III = 7,900) as measured by sedimentation equilibrium in the analytical ultracentrifuge. Furthermore, the PL-I component shares common features with the proteins of the histone H1 family. Yet, it is very unusual, for it contains 2 cysteine residues that are located in the trypsin-resistant core of this protein. The protamine-like fraction PL-III exhibits intraspecific microheterogeneity which is reflected by the presence of two protein variants which most probably are the result of an allelic polymorphism.     

Sedimentation equilibrium: a valuable tool to study homologous and heterogeneous interactions of proteins or proteins and nucleic acids

We present a short overview of our experience in analyzing the affinity and stoichiometry of self-associating and heterologous interactions by using the sedimentation equilibrium technique. Data acquisition and the fitting procedure employing the computer programs that we have developed, Polymole and Virial, are utilized for obtaining reliable results under ideal as well as non-ideal conditions. Such data derived from biologically important macromolecules find utility in understanding physiological events such as cell regulation.     

MSTARA and MSTARI: interactive PC algorithms for simple, model independent evaluation of sedimentation equilibrium data

This paper describes a program available for PC's for the evaluation of molecular weights from sedimentation equilibrium. This program, in its two forms – MSTARA for absorption optical records and MSTARI for interference optical records – requires no prior assumption of the nature of the system (ideal, non-ideal, monodisperse, polydisperse, self-associating etc.) and takes into consideration the whole solute distribution (i.e. from solution meniscus to cell base) in the ultracentrifuge cell rather than just a selected data-set. MSTARA or MSTARI are therefore recommended as a first analysis programme of sedimentation equilibrium data coming off an absorption or interference based analytical ultracentrifuge. These programmes are therefore particularly well suited if heterogeneity (polydispersity or interaction phenomena) or non-ideality is suspected. Their use is demonstrated for a series of data-set types (ideal, non-ideal, polydisperse and self-associating). Although MSTARA and MSTARI are model independent, they provide the basis for more detailed analysis of interactions, polydisperse distributions or non-ideality via easy export of ASCII datafiles to model dependent routines. Received: 4 November 1996 / Accepted: 15 November 1996