Challenges in Predicting Protein-Protein Interactions from Measurements of Molecular Diffusivity

Abstract

Dynamic light scattering can be used to measure the diffusivity of a protein within a formulation. The dependence of molecular diffusivity on protein concentration (traditionally expressed in terms of the interaction parameter k_D) is often used to infer whether protein-protein interactions are repulsive or attractive, resulting in solutions that are colloidally stable or unstable, respectively. However, a number of factors unrelated to intermolecular forces can also impact protein diffusion, complicating this interpretation. Here, we investigate the influence of multicomponent diffusion in a ternary protein-salt-water system on protein diffusion and k_D in the context of Nernst-Planck theory. This analysis demonstrates that large changes in protein diffusivity with protein concentration can result even for hard-sphere systems in the absence of protein-protein interactions. In addition, we show that dynamic light scattering measurements of diffusivity made at low ionic strength cannot be reliably used to detect protein conformational changes. We recommend comparing experimentally determined k_D values to theoretically predicted excluded-volume contributions, which will allow a more accurate assessment of protein-protein interactions.

Figure 1

DLS data for lysozyme (A) and mAb (B) in 2 mM KCl (circles), 5 mM KCl (diamonds), 10 mM KCl (triangles), and 90 mM KCl (inverted triangles) at pH 6.0. Error bars represent the standard deviation of triplicate measurements. Most error bars are smaller than symbols. Lines show the fit of the model D_m,2 versus c, calculated using Eq. 3 in 2 mM KCl (solid line), 5 mM KCl (dashed line), 10 mM KCl (dash-dotted line), and 90 mM KCl (dotted line) at pH 6.0. The inset in (B) shows a zoomed-out version of the model to demonstrate curvature.

Figure 2

The self-diffusion coefficient, D_s,2, as a function of ionic strength calculated by linear extrapolation of DLS data for lysozyme (A) and mAb (B). Results are obtained by finding the intercept of the linear portion of DLS data in Fig. 1. Error bars represent the standard deviation of triplicate measurements and extrapolation to zero protein concentration.

Figure 3

Normalized far-UV CD spectra in KCl at pH 6.0 for lysozyme (A) and the mAb (B) at 2 mM KCl (solid black line), 10 mM KCl (dashed gray line), and 90 mM KCl (dashed black line), at pH 6.0. Each curve represents the average of triplicates of 10 scans each. Error bars are not shown, for clarity.

Figure 4

Excluded-volume contribution to k_D calculated using Eq. 8 for an HS with S = 2.5 and k = 1.35 (thin black line), for lysozyme modeled as a prolate ellipsoid with S = 3.01 and k = 2.91 (thick line), and for the mAb with S = 2.6 and k = 2.3 (dashed line).

Figure 5

Theoretical k_D values as a function of lysozyme concentration calculated by contributions from excluded volume and electrostatics using Eqs. 3 and 8, with 2 mM KCl (solid line), 5 mM KCl (dashed line), 10 mM KCl (dash-dotted line), and 90 mM KCl (dotted line) at pH 6.0.