Measuring macromolecular size distributions and interactions at high concentrations by sedimentation velocity

Abstract

In concentrated macromolecular solutions, weak physical interactions control the solution behavior including particle size distribution, aggregation, liquid-liquid phase separation, or crystallization. This is central to many fields ranging from colloid chemistry to cell biology and pharmaceutical protein engineering. Unfortunately, it is very difficult to determine macromolecular assembly states and polydispersity at high concentrations in solution, since all motion is coupled through long-range hydrodynamic, electrostatic, steric, and other interactions, and scattering techniques report on the solution structure when average interparticle distances are comparable to macromolecular dimensions. Here we present a sedimentation velocity technique that, for the first time, can resolve macromolecular size distributions at high concentrations, by simultaneously accounting for average mutual hydrodynamic and thermodynamic interactions. It offers high resolution and sensitivity of protein solutions up to 50 mg/ml, extending studies of macromolecular solution state closer to the concentration range of therapeutic formulations, serum, or intracellular conditions.

Fig. 1

Sedimentation velocity analysis of NISTmAb at 10 mg/ml. Interference data of NISTmAb stock solution in 25 mM histidine buffer, sedimenting at 45,000 rpm in 3 mm centerpieces, are shown with color temperature gradient indicating the boundary migrating from left to right (circles, for clarity only every 10th point is shown). The sedimentation model accounting for nonideality, c_NI(s₀), is shown as solid lines, leading to an rmsd of 0.015 fringes. For comparison, the best-fit standard ideal model c(s) is shown as dashed lines, leading to an rmsd of 0.098 fringes. In the nonideal model the frictional ratio is fixed to 1.6, whereas in the standard ideal model the frictional ratio is refined to a best-fit value of 3.5. The lower panel shows residuals of the c_NI(s₀) fit

Fig. 2

Sedimentation coefficient distribution of NISTmAb. The nonideal c_NI(s₀) model (magenta) associated with the fit shown in Fig. 1 has a monomer peak at 6.56 S, and a dimer peak comprising 2.7% of the material. For comparison, the best-fit standard c(s) model is shown as thin gray line

Fig. 3

Comparison of sedimentation coefficient distributions of apoferritin samples under ideal and nonideal conditions. Sedimentation data from the nonideal 12.6 mg/ml sample in PBS were analyzed with the nonideal c_NI(s₀) model (magenta). Raw data and fit are shown in Supplementary Fig. 4. The data from a dilute solution of apoferritin at 0.31 mg/ml (blue) were analyzed with the standard ideal c(s) model

Fig. 4

Impact of Johnston–Ogston effect on the detection of dimer populations. Sedimentation data were simulated for an antibody with different dimer populations at 5, 10, and 20 mg/ml total concentrations. Shown are the estimated dimer fractions from analysis using an empirical fit with the standard c(s) model (blue, cyan, green), and with the c_NI(s₀) model accounting for nonideality (red, orange, and magenta). The true dimer fractions are indicated by the dotted gray line

Fig. 5

Sedimentation analysis of BSA at 52 mg/ml in PBS. a Interference optical data were acquired in a 3 mm centerpiece (circles, showing every 10th data point of every third scan). The best-fit c_NI(s₀) model (solid lines) with a fixed frictional ratio of 1.45 results in an rmsd of 0.058 fringes, with k_S = 8.4 ml/g and k_D = 10 ml/g. b The associated sedimentation coefficient distribution at 52 mg/ml (magenta) and, for comparison, the distributions obtained in analogous analyses at 28 mg/ml (cyan), 9.8 mg/ml (blue), both also acquired in 3 mm centerpieces, and 1.6 mg/ml (green) acquired in a 12 mm centerpiece. The inset shows integrated dimer fractions at ~6.5 S (solid blue circles) and trimer fractions at ~8 S (solid green triangles) from these c_NI(s₀) analysis accounting for nonideality. The open circles are the apparent dimer fractions from empirical c(s) analyses of the same data neglecting nonideality contributions (Supplementary Fig. 7)