Assessing sedimentation equilibrium profiles in analytical ultracentrifugation experiments on macromolecules: from simple average molecular weight analysis to molecular weight distribution and interaction analysis

Abstract

Molecular weights (molar masses), molecular weight distributions, dissociation constants and other interaction parameters are fundamental characteristics of proteins, nucleic acids, polysaccharides and glycoconjugates in solution. Sedimentation equilibrium analytical ultracentrifugation provides a powerful method with no supplementary immobilization, columns or membranes required. It is a particularly powerful tool when used in conjunction with its sister technique, namely sedimentation velocity. Here, we describe key approaches now available and their application to the characterization of antibodies, polysaccharides and glycoconjugates. We indicate how major complications, such as thermodynamic non-ideality, can now be routinely dealt with, thanks to a great extent to the extensive contribution of Professor Don Winzor over several decades of research.

Keywords: COVOL; Extended Fujita; Non-ideality; SEDFIT-MSTAR.

Fig. 1

Output of the SEDFIT-MSTAR procedure for analysis on a solution of a monodisperse preparation of the human/murine hybrid antibody immunoglobulin G1 known as “Erbitux” at a loading concentration of 1 mg/ml. True M _w is ∼150,000 Da. a Log concentration lnc(r)) vs. r ² plot, where r is the radial distance from the centre of rotation. b M* versus r plot (open squares): the value of M* extrapolated to the cell base = M _w,app, the apparent weight-average molecular weight for the whole distribution. c Point or local apparent weight-average molecular weight M _w,_app(c) at radial position r and corresponding local concentration c(r)) plotted against the local concentration. d Molecular weight distribution c(M) vs. M plot. Red line shows the fit, dot-dashed lines show the position of the hinge point (a) and the corresponding estimation of the M _w,app value (c). Retrieved M _w from extrapolation of M* to the cell base = 148,000 (±2000) Da, and from the hinge point = ∼147,500 Da. Figure is from Schuck et al. (2014), with permission

Fig. 2

As in Fig. 1 a–d but for analysis of a polydisperse solution of the marine seaweed polysaccharide λ-carrageenan at a loading concentration of 0.3 mg/ml. b Retrieved value for M _w,app = 310,000 Da from extrapolation of M* to the cell base. c Retrieved value for M _w,app from the hinge point method ∼ 320,000 Da. Both retrieved values for M _w,app are in agreement with each other and with SEC-MALS. Figure is from Schuck et al. (2014), with permission

Fig. 3

Extended Fujita method estimate of the molecular weight (expressed as molar mass, g/mol) distribution f(M) vs. M for alginate at a loading concentration of 0.03 mg/ml in 0.3 M NaCl. Transformation from a g(s) vs. s plot (inset) using a value for b of ∼0.33 (Harding et al. 2011) and κ_s = 0.0685, with the latter calculated from M _w = 280,000 g/mol (from SEC-MALS) and s  = s _20,w (at 0.03 mg/ml) = 4.3S. Estimates for M _z/M _w (the ratio of the z-average to the weight average molar mass) and M _w/M _n (the ratio of the weight average to the number average molar mass) are also given

Fig. 4

Extended Fujita method estimate of the molecular weight (expressed as molar mass, g/mol) distribution for a large glycoconjugate vaccine. The plot shows the distribution for two different values of the power law coefficient b

Fig. 5

Sedimentation equilibrium analysis of the heterodimerization of the electron transfer flavoprotein ETF. The dimerization is of two equimolar components of molecular weight (M ) 28,900 and 33,700 Da, respectively. a The apparent weight-average molecular weight (M _w,app) averaged over all radial positions in the ultracentrifuge cell from meniscus to cell base plotted against c for four different cell loading concentrations c showing a monomer–dimer system with a dimer molecular weight of ∼63 kDa (including FAD and AMP cofactors of collective M = 1120 Da) dissociating at lower concentration. b Plot of the ‘point’ apparent weight-average, M_w,_app(r), evaluated at individual radial positions r as a function of concentration [expressed as UV-absorbance A(r) values at 280 nm] at those radial positions. Data sets for two loading concentrations are shown. Within error, they overlap, demonstrating a reversible interaction. c Modelling the concentration distribution in terms of an ideal dimerization. d As (c), but in terms of the radial function ψ(r). The fitted data in both c and d correspond to a K_d ∼ (1.5 ± 0.1) × 10⁻⁶ M, a strong interaction. Again, the overlap at two different loading concentrations is commensurate with a reversible association. Figure is from Cölfen et al. (1997), with kind permission of the European Biophysics Journal (Springer Science + Business Media)

Fig. 6

Apparent weight-average molecular weight (M _w,app) of the CD2 and CD48 proteins and of the CD2–CD48 heterodimer as determined using sedimentation equilibrium × CD2, ● CD48 and O the CD2–CD48 heterodimer. Non-linear least-square fits to data for CD2 (dotted line) and CD48 (dashed line). Continuous line Predicted regression for a value of 2BM (from COVOL) of 10.4 ml/g. Dotted–dashed line Fit to CD2–CD48 heterodimer data. Using the COVOL value of 2BM = 10.4 ml/g, a value for the dissociation constant K_d ∼ (1.0 ± 0.3) × 10⁻⁴ M is obtained, a weak interaction. Figure is from Silkowski et al. (1997), with kind permission of the European Biophysics Journal (Springer Science + Business Media)