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.     

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.     

A case study and use of sedimentation equilibrium analytical ultracentrifugation as a tool for biopharmaceutical development

Analytical ultracentrifugation (AUC) has re-emerged as a powerful technique for protein characterisation. We report the pivotal role sedimentation equilibrium AUC has played in the development of macrophage inflammatory protein-1α (MIP-1α) as a protein therapeutic. MIP-1α has potential clinical applications in cancer but its clinical use is limited, since it associates to form large insoluble aggregates in physiological buffers. Using AUC as a screening technique, we have produced a biologically active variant of MIP-1α, BB-10010, which has a reduced tendency to aggregate in physiological buffers. The aggregation of protein based pharmaceuticals is routinely monitored by size exclusion chromatography (SEC). Comparison of the data acquired by SEC and AUC, demonstrates that owing to the complexity of BB-10010, AUC analysis is required in addition to SEC to provide a rigorous characterisation of molecular association. This work has been extended to include the use of AUC as an analytical tool to monitor the quality of BB-10010 during formulation and stability studies. Accepted: 6 October 1996     

The equilibrium sedimentation of hyaluronic acid and of two synthetic polymers

1. The method of equilibrium sedimentation has been investigated as an alternative to osmotic-pressure measurement for determining thermodynamic properties of polymer solutions at relatively high concentrations. 2. The simplifications that must be made in the theoretical treatment are discussed. 3. Measurements have been made on samples of polyethylene glycol, neutralized polymethacrylic acid and hyaluronic acid. With the first and third, values of the ;non-ideality coefficients' have been obtained that agree with those obtained from osmotic measurements on the same materials. 4. Evidence has been obtained of the presence in hyaluronic acid preparations of a fraction that has either a lower degree of thermodynamic non-ideality or a higher density increment than the bulk of the sample. This fraction is not protein.     

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).     

An extrapolation method for reducing equilibration times in sedimentation equilibrium experiments.

We present a detailed investigation of the use of an extrapolation technique to decrease running times of sedimentation equilibrium experiments. If concentration profiles are available at time delta tau, 2delta tau, 3delta tau,...., cn(r) = c(r, n delta tau), then the Aitken transformation replaces the cn(r) + ĉn(r) = [cn + 1(r) cn - 1(r) - c2n(r)]/[cn + 1(r) + cn - 1(r) - 2cn(r)]. We show that the ĉn(r) converge to the equilibrium values c infinity (r) much more quickly than the cn(r). Savings in time are shown to range from a factor of approximately 2 for meniscus depletion experiments to factors of between 4 and 8 for lower speeds or smaller molecular weights. It is also shown that the technique is quite sensitive to noise, so that an accurate optical system is required to allow its optimal use.     

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.     

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.     

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, I(M) 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 8 mg/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.     

The direct analysis of sedimentation equilibrium results obtained with polymerizing systems.

Theory is presented in relation to sedimentation equilibrium results obtained with polymerizing systems, which permits evaluation of the activity of the monomer as a function of total weight concentration. In contrast to established methods, the suggested procedure does not involve the solution of simultaneous equations which are sums of exponentials or the determination of weight-average molecular weights. A major advantage of the method is that it avoids errors inherent in differentiation and integration steps. An extrapolation to infinite filution is involved, but this is to a defined limit and is uncomplicated by the existence of critical points in the relevant plot. The method is capable of detecting possible volume changes inherent on polymer formation, of treating systems where activity coefficients of solute species are functions of total concentration and of describing the system in terms of relevant equilibrium constants. These points and comparisons with existing methods of analysis are illustrated with numerical examples and with results obtained with lysozyme at pH 6.7. The lysozyme results are interpretable in terms of either a non-ideal monomer-dimer system or a monomer-dimer-trimer system.     

Scaling of the equilibrium sedimentation distribution in dense DNA solutions

DNA molecules, several persistence lengths long in sedimentation equilibrium at speeds high enough to maintain fairly close packing, show a dense, sharply-bounded turbid phase and an isotropic phase (as with shorter fragments) and also an intermediate, somewhat turbid region. The concentration distribution in the isotropic phase is in satisfactory agreement with a simple extension of scaled particle theory in which semiflexible chains are equivalent to straight rods of the same length. The net intermolecular interactions, as inferred from the Zimm cluster integral, are purely repulsive. As in our previous study with short fragments, the results are compatible with a hard-core electrostatic radius, decreasing with increasing salt concentration. However, for the longer fragments it is necessary to infer either a slightly greater mass per unit length or a slightly smaller electrostatic radius for closest agreement with scaled particle theory. The properties of the solution at the boundary with the turbid, presumably strongly ordered phase are consistent with those found for shorter fragments and with theoretical scaling expectation for a hard, asymmetric particle.     

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.