Analysis of nonideality: insights from high concentration simulations of sedimentation velocity data

The Aviv fluorescence detection system (Aviv-FDS) has allowed the performance of sedimentation velocity experiments on therapeutic antibodies in highly concentrated environments like formulation buffers and serum. Methods were implemented in the software package SEDANAL for the analysis of nonideal, weakly associating AUC data acquired on therapeutic antibodies and proteins (Wright et al. Eur Biophys J 47:709–722, 2018, Anal Biochem 550:72–83, 2018). This involved fitting both hydrodynamic, ks, and thermodynamic, BM1, nonideality where concentration dependence is expressed as s = so/(1 + ksc) and D = Do(1 + 2BM1c)/(1 + ksc) and so and Do are values extrapolated to c = 0 (mg/ml). To gain insight into the consequences of these phenomenological parameters, we performed simulations with SEDANAL of a monoclonal antibody as a function of ks (0–100 ml/g) and BM1 (0–100 ml/g). This provides a visual understanding of the separate and joint impact of ks and BM1 on the shape of high-concentration sedimentation velocity boundaries and the challenge of their unique determination by finite element methods. In addition, mAbs undergo weak self- and hetero-association (Yang et al. Prot Sci 27:1334–1348, 2018) and thus we have simulated examples of nonideal weak association over a wide range of concentrations (1–120 mg/ml). Here we demonstrate these data are best analyzed by direct boundary global fitting to models that account for ks, BM1 and weak association. Because a typical clinical dose of mAb is 50–200 mg/ml, these results have relevance for biophysical understanding of concentrated therapeutic proteins. Electronic supplementary material The online version of this article (10.1007/s00249-020-01474-5) contains supplementary material, which is available to authorized users.

SEDANAL models that include hydrodynamic ks and thermodynamic nonideality BM1 allow three fitting options: fit, hold, or matrix. The fit option allows a single value to be varied in a NLLS sense, but that value applies to all column elements in the implied matrix. Matrix allows the user to enter different values for each ij element in the matrix. The hold option allows a constant value to be used during the fit or simulation. This corresponds to the ks and BM1 items in the first column A in Figure 1, indicated by the blue color. The yellow colors indicate that values are derived or copied from the blue box to their left. Currently matrix elements cannot be fit individually due to 1) the reasonable assumption that backflow for each species is constant, and 2) that they are underdetermined. Future versions of SEDANAL will cautiously allow fitting of select matrix elements. Similar considerations apply to the BijMj matrix, Table S2.

Figure S2
A) Plot of concentration vs radius for a monomer-dimer-trimer model for the 80 th scan (SEDANAL output option) during a simulation with ks = BM1 = 10 ml/g and monomer concentration = 40 mg/ml. Note the JO effect in the monomer concentration distribution. B) The plot shows s/so and D/Do for these data, as calculated using equations 3 and 4, plotted vs radius. This demonstrates the change in nonideality as a function of radial position and component concentrations. Claverie options under the advanced control button allows limitations on min s/so, max D/Do and max concentration at the base.

Figure S3
Wide Distribution (WD) Analysis (Stafford and Braswell, 2004) of an ABC model for 10 mg/ml Simponi and 10% dimeric (B/A) and 5% trimeric (C/A) aggregates. Panel A shows speed dependence and suggests that ABC or monomer-dimer-trimer species resolve better at higher speeds (larger σ, reduced molecular weight). Panel B shows WD analysis at 40K where different radial positions are averaged. This demonstrates data at high radial positions are preferred for best resolution. Radial positions greater than 6.5 cm clearly give the best separation and resolution for dimers and trimers. Data from 6.8 to 7.0 cm are typically used in the Figures 2-9, S4.

Figure S4
DCDT + and WD Analysis of an ABC model for 10 mg/ml Simponi and 10% dimeric and 5% trimeric aggregates. Panel A) shows DCDT + g(s*) vs s* plots while panel B) on the right shows WDA s*g(s*) vs log(s*) plots averaged from 6.8 to 7.0 cm. The use of large radial positions and the log scale in the WDA plot accentuates boundary sharpening and component separation.

Figure S5
Screen dump of pre-processor images of Simponi simulation at 120 mg/ml with A) BM1 = 0 ml/g and B) BM1 = 10 ml/g. The y-axis is signal or absorbance while the x-axis is radial position in cm. Panel A) The BM1 0 ml/g sample generates a pellet up to an absorbance of 38,000, or 27,142 mg/ml. Panel B) The BM1 10 ml/g sample generates a pellet up to an absorbance or 2623, or 1873 mg/ml. This high concentration in the pellet spreads into the plateau region in a thermodynamically nonideal manner: at BM1 = 0 ml/g the plateau is zero at 7.16 cm in the 400 th scan; at BM1 = 10 ml/g the plateau approaches zero at < 7.0 cm in the 400 th scan. This behavior of an expanded back diffusion region is diagnostic of samples with large thermodynamic nonideality.

Figure S6
Panel A) DCDT + analysis, normalized g(s*) vs s*, of the concentration data presented in Figure 5. Panel B) is Figure 5 copied here for direct comparison. Analysis with g(s*) is typically presented vs s*. It is clear these data are not as well resolved at the data in Figure 5, panel B, especially the dimer and trimer aggregate peaks. The integrated results from these data are plotted as 1/sw vs c in Figure 6.

Figure S7
Panel A is DCDT + analysis, normalized g(s*) vs s*, of the concentration data presented in Figure 8. Panel B is Figure 9 copied here for direct comparison. DCDT+ analysis for g(s*) is typically presented vs s*. It is clear these data are not as well resolved as the data in Figure 9, panel B, especially the dimer and trimer aggregate peaks. The integrated results from these data are plotted as 1/sw vs c in Figure 10.

Figure S8
Panel A is a WDA plot of the ABCksBM1 FDS data fit in Figure 7. Panel B is a WDA plot of the AA2BCksBM1K2 FDS data fit in Figure 11. The data is plotted in unnormalzed mode because the signal is the same in each sample in a tracer experiment.