Protein-protein interactions in dilute to concentrated solutions: α-chymotrypsinogen in acidic conditions

Abstract

Protein-protein interactions were investigated for α-chymotrypsinogen by static and dynamic light scattering (SLS and DLS, respectively), as well as small-angle neutron scattering (SANS), as a function of protein and salt concentration at acidic conditions. Net protein-protein interactions were probed via the Kirkwood-Buff integral G22 and the static structure factor S(q) from SLS and SANS data. G22 was obtained by regressing the Rayleigh ratio versus protein concentration with a local Taylor series approach, which does not require one to assume the underlying form or nature of intermolecular interactions. In addition, G22 and S(q) were further analyzed by traditional methods involving fits to effective interaction potentials. Although the fitted model parameters were not always physically realistic, the numerical values for G22 and S(q → 0) were in good agreement from SLS and SANS as a function of protein concentration. In the dilute regime, fitted G22 values agreed with those obtained via the osmotic second virial coefficient B22 and showed that electrostatic interactions are the dominant contribution for colloidal interactions in α-chymotrypsinogen solutions. However, as protein concentration increases, the strength of protein-protein interactions decreases, with a more pronounced decrease at low salt concentrations. The results are consistent with an effective "crowding" or excluded volume contribution to G22 due to the long-ranged electrostatic repulsions that are prominent even at the moderate range of protein concentrations used here (<40 g/L). These apparent crowding effects were confirmed and quantified by assessing the hydrodynamic factor H(q → 0), which is obtained by combining measurements of the collective diffusion coefficient from DLS data with measurements of S(q → 0). H(q → 0) was significantly less than that for a corresponding hard-sphere system and showed that hydrodynamic nonidealities can lead to qualitatively incorrect conclusions regarding B22, G22, and static protein-protein interactions if one uses only DLS to assess protein interactions.

Figure 1

Rayleigh scattering (R₉₀/K) as a function of protein concentration for α-chymotrypsinogen at pH = 3.5 and different salt concentrations. Symbols represent the different NaCl concentrations evaluated here: (blue circles) 0; (red squares) 10; (green diamonds) 50; and (gray triangles) 100 mM. Error bars (95% confidence intervals) are smaller than the size of the symbols.

Figure 2

Osmotic second virial coefficient, B₂₂, or protein–protein KB integral, G₂₂ (panel a), and apparent molecular weight (M_w) (panel b) for α-chymotrypsinogen at pH = 3.5 as a function of NaCl concentration. B₂₂ and M_w are obtained by fitting R₉₀/K versus c₂ to eq 2 for c₂ ≤ 7 g/L, while G₂₂ is obtained by fitting the same data to eq 4. B₂₂ and G₂₂ are reported relative to the hard-sphere second virial coefficient (i.e., B₂₂^* = B₂₂/B₂^HS and G₂₂^* = −G₂₂/2B₂^HS). Error bars correspond to 95% confidence intervals for the fitted parameters. The dashed line in panel b indicates the true value for the protein molecular weight.

Figure 3

Fitted values of G₂₂ as a function of protein concentration for α-chymotrypsinogen at pH = 3.5 and different salt concentrations. Symbols represent the different NaCl concentrations evaluated here: (blue circles) 0; (red squares) 10; (green diamonds) 50; and (gray triangles) 100 mM. G₂₂ is obtained by regressing R₉₀/K versus c₂ to eq 4 over concentration windows of 3–7 data points using the local Taylor series approach. G₂₂ is reported relative to the hard-sphere second virial coefficient (i.e., G₂₂^* = −G₂₂/2B₂^HS). Error bars correspond to 95% confidence intervals in the fitted values.

Figure 4

SANS scattering intensities as a function of the wave vector Q from α-chymotrypsinogen solutions at pH 3.5 and different salt concentrations: (a) 0; (b) 10; (c) 50; and (d) 100 mM NaCl. Symbols correspond to three different protein concentrations: (circles) 40; (squares) 10; and (triangles) 2 g/L. Lines represent the best fitted curves to I(Q) for the working conditions. All of the models consider the form factor as that of a spherical particle and differ by the structure factor S(Q), with S(Q) given by (solid line) a two-Yukawa potential (2Y); (dashed line) a screened Coulomb repulsion (SC); and (dotted-dashed line) a hard-sphere potential (HS). Labels in each panel indicate different models. In cases where models were indistinguishable (e.g., panel d), only the fit to the simplest model is shown.

Figure 5

Comparison of of the zero-q limit static structure factor S(q → 0) as a function of protein concentration for α-chymotrypsinogen obtained from SLS (open symbols) and SANS (close symbols). Symbols correspond to different salt concentrations: (circles) 0; (squares) 10; (diamonds) 50; and (triangles) 100 mM. In the case of SLS, the structure factor was calculated from fitted values of G₂₂ because S(q → 0) = 1 + c₂G₂₂.

Figure 6

Values of the collective (or mutual) diffusion coefficient D_c (panel a) and the self-diffusion coefficient D_s (panel b) as a function of protein concentration for α-chymotrypsinogen. Symbols correspond to the different salt concentrations: (circles) 0; (squares) 10; (diamonds) 50; and (triangles) 100 mM. D_s was calculated from combining D_c with R₉₀/K (cf. Figure 1) via eq 9. The dashed line in panel b corresponds to the theoretical D_s for a system of suspended hard spheres 4 nm in diameter.