Ultrasonic storage modulus as a novel parameter for analyzing protein-protein interactions in high protein concentration solutions: correlation with static and dynamic light scattering measurements

Abstract

The purpose of this work was to establish ultrasonic storage modulus (G') as a novel parameter for characterizing protein-protein interactions (PPI) in high concentration protein solutions. Using an indigenously developed ultrasonic shear rheometer, G' for 20-120 mg/ml solutions of a monoclonal antibody (IgG(2)), between pH 3.0 and 9.0 at 4 mM ionic strength, was measured at frequency of 10 MHz. Our understanding of ultrasonic rheology indicated decrease in repulsive and increase in attractive PPI with increasing solution pH. To confirm this behavior, dynamic (DLS) and static (SLS) light scattering measurements were conducted in dilute solutions. Due to technical limitations, light scattering measurements could not be conducted in concentrated solutions. Mutual-diffusion coefficient, measured by DLS, increased with IgG(2) concentration at pH 4.0 and this trend reversed as pH was increased to 9.0. Second virial coefficient, measured by SLS, decreased with increasing pH. These observations were consistent with the nature of PPI understood from G' measurements. Ultrasonic rheology, DLS, and SLS measurements were also conducted under conditions of increased ionic strength. The consistency between rheology and light scattering analysis under various solution conditions established the utility of ultrasonic G' measurements as a novel tool for analyzing PPI in high protein concentration systems.

FIGURE 1

Solution storage modulus (G′) for IgG₂ solutions at a frequency of 10 MHz measured using the ultrasonic shear rheometer (15) (a) as a function of IgG₂ concentration at different solution pH and (b) for 120 mg/ml IgG₂ solutions as a function of solution pH. The buffer ionic strength was 4 mM. The line in Fig. 1 b connects the points to guide the eye and is not a result of a model fitting to the data. The error bars if not visible are smaller than the symbols used.

FIGURE 2

(a) Hydrodynamic diameter (d_H) and (b) mutual-diffusion coefficient (D_m) for IgG₂ molecules as a function of concentration and solution pH at 4 mM ionic strength and 25 ± 0.1°C measured using DLS. The measurements were conducted in triplicate. D_m was back calculated from the measured d_H using the Stokes-Einstein equation (Eq. 9) and solution viscosities measured on the ultrasonic shear rheometer. In Fig. 2 a, lines connect the data points and are not a result of model fitting, and in Fig. 2 b, lines are linear best fits with the slope and intercept representing D_sk_D and D_s (self-diffusion coefficient), respectively (Eq. 7).

FIGURE 3

Debye plots for IgG₂ solutions as a function of solution pH at 4 mM ionic strength. The second virial coefficient and molecular weight calculated from the slope and intercept, respectively, of the Debye plots have been summarized in Table 1. The measurements were conducted at 25 ± 0.1°C in triplicate for each solution.

FIGURE 4

Solution G′ for IgG₂ solutions at a frequency of 10 MHz measured using the ultrasonic shear rheometer as a function of ionic strength and pH at (a) 120 mg/ml and (b) 40 mg/ml protein concentration. The ionic strength was adjusted using sodium chloride, and analysis was conducted at 25 ± 0.1°C in triplicate. The error bars if not visible are smaller than the symbols used. A scale break has been included in the x axis. The lines connect the points to guide the eye and are not a result of model fitting to the data.

FIGURE 5

Calculated k_D values for IgG₂ molecules in solution of different pH with ionic strength ranging from 4 mM to 300 mM. The ionic strength was adjusted using sodium chloride. The data points have been connected to guide the eye. A scale break has been included in the x axis. The lines do not represent the result of model fitting to the data.

FIGURE 6

B₂₂ values for IgG₂ molecules in solutions of different pH as a function of ionic strength. The results are an average of three measurements conducted at 25 ± 0.1°C. A scale break has been included in the x axis. The lines do not represent the result of a model fit to the data.

FIGURE 7

Solution G′ (♦), at 120 mg/ml IgG₂, and k_D values (⋄), calculated from relatively dilute solution measurements (4–12 mg/ml IgG₂), for IgG₂ solutions as a function of solution ionic strength. A scale break has been added in the x axis to focus on low and high ionic strength regions. The lines connect the points to guide the eye and are not a result of a model fit to the data.