Experimental support for reclassification of the light scattering second virial coefficient from macromolecular solutions as a hydrodynamic parameter

Abstract

This investigation examines the source of the disparity between experimental values of the light scattering second virial coefficient [Formula: see text] (mL.mol/g²) for proteins and those predicted on the statistical mechanical basis of excluded volume. A much better theoretical description of published results for lysozyme is obtained by considering the experimental parameters to monitor the difference between the thermodynamic excluded volume term and its hydrodynamic counterpart. This involves a combination of parameters quantifying concentration dependence of the translational diffusion coefficient obtained from dynamic light scattering measurements. That finding is shown to account for observations of a strong correlation between [Formula: see text] (mL/g), where M₂ is the molar mass (molecular weight) of the macromolecule and the diffusion concentration parameter [Formula: see text] (mL/g). On the grounds that [Formula: see text] is regarded as a hydrodynamic parameter, the same status should be accorded the light scattering second virial coefficient rather than its current incorrect thermodynamic designation as [Formula: see text] (mL.mol/g²), or just B, the osmotic second virial coefficient for protein self-interaction.

Keywords: Dynamic light scattering; Hydrodynamics; Lysozyme; Monoclonal IgG antibodies; Second virial coefficient; Static light scattering; Statistical mechanics; Thermodynamic nonideality.

Fig. 1

Electrostatic map calculated using the Poisson–Boltzmann equation of hen egg white lysozyme (PDB: 1AKI) at pH 7.0. It can be clearly seen that there is an even distribution of charge across the surface (positive: blue; negative: red). Hydrophobic patches are shown in grey: the only patch visible was c.a. 5 angstroms in diameter seen in the bottom right of the molecule, and is unlikely to contribute to aggregation due to the large electrostatic shadow cast by the other residues in the molecule. No other patches were visible on the molecule (data not shown) (color figure online)

Fig. 2

Analysis of static light scattering data for lysozyme solutions at pH 4.7 (from data of Muschol and Rosenberger 1995). a Experimental results $\left(\bullet \right)$ for the dependence of the second virial coefficient $A_2{M}_2$ upon ionic strength, together with theoretical dependence predicted either on the basis of its consideration as the equivalent of the osmotic second virial coefficient for protein self-interaction, ${\lambda }_T{v}_s/2$ $\left(---\right)$, or the combination of that parameter and its hydrodynamic counterpart (—), as in Eq. (16) for the diffusion concentration dependence coefficient, $\left({\lambda }_T,-,{\lambda }_H\right)v_s/2$. b Demonstration of the correlation between $k_D$ and $A_2{M}_2$. [Data for ${\lambda }_T$ and ${\lambda }_H$ calculated from Table 2 of Muschol and Rosenberger (1995)]

Fig. 3

Further evidence for correlation between the diffusion concentration dependence coefficient $k_D$ and the light scattering second virial coefficient $A_2{M}_2$ for monoclonal IgG antibodies. a Combined results for five monoclonal IgG antibodies (pH 6.0) at high and low ionic strengths. [Data taken from Lehermayr et al (2011)] b Corresponding dependence for a single monoclonal antibody at pH 5.0 and pH 5.75 and a range of ionic strengths. [Data from Roberts et al. (2014)]