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.     

The analysis of macromolecular interactions by sedimentation equilibrium

The study of macromolecular interactions by sedimentation equilibrium is a highly technical method that requires great care in both the experimental design and data analysis. The complexity of the interacting system that can be analyzed is only limited by the ability to deconvolute the exponential contributions of each of the species to the overall concentration gradient. This is achieved in part through the use of multi-signal data collection and the implementation of soft mass conservation. We illustrate the use of these constraints in SEDPHAT through the study of an A+B+B?AB+B?ABB system and highlight some of the technical challenges that arise. We show that both the multi-signal analysis and mass conservation result in a precise and robust data analysis and discuss improvements that can be obtained through the inclusion of data from other methods such as sedimentation velocity and isothermal titration calorimetry.     

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.     

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 alpha-chymotrypsin (pH 4.0, I 0.05 M).     

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 sedimentation equilibrium of heterogeneously associating systems and mixtures of non-interacting solutes: analysis without determination of molecular weight averages

Sedimentation equilibrium is first considered of a system in which a ligand of any size binds to an acceptor at p sites, the experimental result, obtained with either interference or absorption optics, being a distribution of total solute concentration as a function of radial distance. Theory illustrated by a numerical example, is presented which shows that this distribution may be analysed to give the activity of the unbound ligand as a function of total weight concentration. It is shown that this information may be used together with conservation of mass equations written in terms of the initial mixing composition to evaluate the equilibrium constant(s) relevant to the system. Correlation with composition evaluation by use of absorption optics (when possible) is also discussed. The procedure does not involve solution of simultaneous equations which are sums of exponentials nor differentiation of experimental results to obtain apparent weight-average molecular weights. It is general in that it leads to the evaluation of the activity of the species characterized by the smallest M(l-$\text{v}$π) product and, accordingly, is shown to be useful in the analysis of non-interacting as well as of interacting systems.     

Analyses of sedimentation equilibrium data

A numerical procedure is presented which can quite adequately compute the molecular weight averages as a function of solute concentration from sedimentation equilibrium data for homogeneous systems and for monomer-dimer associating systems with a possible extension to heterogeneous systems where monotonic variation in the weight average molecular weight is observed such as in weakly associating or dissociating systems. The procedure utilizes the method of orthogonal polynomials for curve fitting which allows for a rapid determination of best fit with minimal round off error. The procedure is particularly applicable in cases where the concentration of solute at the meniscus can be considered to be neither appreciable and reasonably well determined as in low speed sedimentation equilibrium experiments, nor essentially zero as in high speed sedimentation equilibrium experiments where the calculations become somewhat more simplified. The use of moderate speed sedimentation equilibrium has the advantage of providing a more broad concentration distribution in the centrifuge cell which yields more extensive information concerning dissociating systems yet still provides results at low solute concentrations where most solutes can be considered to be behaving ideally.     

Concentration dependence in three-component systems in sedimentation equilibrium in buoyant density gradients

The data on the band widths and band shapes of several DNA's at various concentrations in sedimentation equilibrium in a CsCl density gradient have recently become available. In the present report, these literature data are treated in the following manner: (1) based on a theory of isotope-substitution, calculations are made of the molecular weights at infinite dilution, and (2) to explain the concentration dependence of band widths and band shapes, a theory of charge and hydration is put forth, and it is shown that by retaining the terms involving the charge of the macromolecules, it is possible to account for most of the concentration dependence.     

Digitization of sedimentation equilibrium and velocity data for analysis by minicomputer

A procedure is described whereby phosphorylated seryl residues may be unequivocally identified during the sequential degradation of a polypeptide chain by the Edman technique. The phosphoseryl residue, Ser(P), was first converted by treatment with methylamine in dilute alkali to a β-methylaminoalanyl residue which was split from the polypeptide by the degradative procedure as the derived phenylthiohydantoin. This was identified by high-performance liquid chromatography. The procedure was highly effective when the Ser(P) occupied an isolated position in a polypeptide chain but was less so when grouped consecutively with other Ser(P).     

Urea-induced structural changes in chromatin obtained by sedimentation.

Sedimentation coefficients have been determined for fractionated preparations of whole and stripped (depleted of very lysine-rich histones and non-histone proteins) chicken erythrocyte chromatin fragments in 0-10 M urea. Significant differences in urea effects are observed between these preparations; differences which can be interpreted structurally by use of Kirkwood's dynamical theory of the translational frictional coefficient. This type of analysis implies that urea-induced chain-swelling in stripped chromatin is due largely to the urea effect upon the constituent nu-bodies, whereas the much larger swelling observed in whole chromatin appears to involve also the effect of urea upon the region between adjacent nu-bodies.     

The proteoglycans of bovine nasal cartilage and human articular cartilage: a sedimentation equilibrium analysis

Cartilage proteoglycan was isolated from bovine nasal septum and fractionated according to buoyant density after dissociative CsCl density gradient centrifugation. Gel-exclusion chromatography showed that hyaluronic acid was present in fractions of density lower than 1.69 g/mL. The molecular weight, assessed by sedimentation equilibrium analysis, of the proteoglycan present in the fractions with density > 1.69 g/mL, which appeared chromatographically homogeneous and constituted 54% of the preparation, ranged from 1.0 to 2.6 × 10⁶ for v = 0.55 cm³ g^?1. Carbodiimide-induced modification of the carboxyl groups by methylamine resulted in a reduction of the molecular weight to 0.74 – 1.25 × 10⁶. An analogous reduction in molecular weight was obtained after equilibration of this proteoglycan fraction with hyaluronic acid oligomers containing five disaccharide units. Since both procedures are known to cause inhibition of the interaction between proteoglycans and hyaluronic acid, it is suggested that this lower molecular-weight range represents the true degree of polydispersity of the sub-units of hyaline cartilage proteoglycan constituting this fraction, while the higher values obtained for the intact proteoglycan are the result of the presence of hyaluronic acid in the sample. The molecular-weight range of the whole proteoglycan subunit preparation, assessed after carboxyl group modification, was 0.5–1.2 × 10⁶. Apparently normal and abnormal cartilage was excised from single human osteoarthrosic femoral heads. Proteoglycans extracted by 4M guanidine hydrochloride were isolated after dissociative density gradient centrifugation and subjected to carboxyl group modification. Preparations from normal tissue exhibited molecular-weight averages ranging from 5 to 9 × 10⁵. A molecular-weight reduction was observed with proteoglycans isolated from abnormal areas.     

Determination of the asymptotic shapes of sedimentation velocity patterns for reversibly polymerizing solutes

A simple method is described for the determination of the asymptotic boundary shape from a series of schlieren patterns taken during a sedimentation velocity experiment on a rapidly and reversibly associating solute. The form of the boundary so obtained reflects effects of sedimentation and chemical reaction but is free from effects of diffusion. The procedure is illustrated with analyses of experiments on diisopropyl fluorophosphate-inhibited α-chymotrypsin in 0.29 I phosphate, pH 7.9 (a monomer-dimer system), and on β-lactoglobulin A in 0.1 I acetate, pH 4.65 (a monomer-dimer-trimer-tetramer system). Asymptotic patterns so determined exhibit close agreement with those predicted by Gilbert theory.