The classic analysis of Rayleigh light scattering (LS) is re-examined for multi-component protein solutions, within the context of Kirkwood-Buff (KB) theory as well as a more generalized canonical treatment. Significant differences arise when traditional treatments that approximate constant pressure and neglect concentration fluctuations in one or more (co)solvent/co-solute species are compared with more rigorous treatments at constant volume and with all species free to fluctuate. For dilute solutions, it is shown that LS can be used to rigorously and unambiguously obtain values for the osmotic second virial coefficient (B 22 ), in contrast with recent arguments regarding protein interactions deduced from LS experiments. For more concentrated solutions, it is shown that conventional analysis over(under)-estimates the magnitude of B 22 for significantly repulsive(attractive) conditions, and that protein-protein KB integrals (G 22 ) are the more relevant quantity obtainable from LS. Published data for α-chymotrypsinogen A and a series of monoclonal antibodies at different pH and salt concentrations are re-analyzed using traditional and new treatments. The results illustrate that while traditional analysis may be sufficient if one is interested in only the sign of B 22 or G 22 , the quantitative values can be significantly in error. A simple approach is illustrated for determining whether protein concentration (c 2 ) is sufficiently dilute for B 22 to apply, and for correcting B 22 values from traditional LS regression at higher c 2 values. The apparent molecular weight M 2,app obtained from LS is shown to generally not be equal to the true molecular weight, with the differences arising from a combination of protein-solute and protein-cosolute interactions that may, in principle, also be determined from LS.
Reversible protein cluster formation is an important initial step in the processes of native and non-native protein aggregation, but involves relatively long time and length scales for detailed atomistic simulations and extensive mapping of free energy landscapes. A coarse-grained (CG) model is presented to semi-quantitatively characterize the thermodynamics and key configurations involved in the landscape for protein oligomerization, as well as experimental measures of interactions such as the osmotic second virial coefficient (B22). Based on earlier work, this CG model treats proteins as rigid bodies composed of one bead per amino acid, with each amino acid having specific parameters for its size, hydrophobicity, and charge. The net interactions are a combination of steric repulsions, short-range attractions, and screened long-range charge-charge interactions. Model parametrization was done by fitting simulation results against experimental values of the B22 as a function of solution ionic strength for α-chymotrypsinogen A and γD-crystallin (gD-Crys). The CG model is applied to characterize the pairwise interactions and dimerization of gD-Crys and the dependance on temperature, protein concentration, and ionic strength. The results illustrate that at experimentally relevant conditions where stable dimers do not form, the entropic contributions are predominant in the free-energy of protein cluster formation and colloidal protein interactions, arguing against interpretations that treat B22 primarily from energetic considerations alone. Additionally, the results suggest that electrostatic interactions help to modulate the population of the different stable configurations for protein nearest-neighbor pairs, while short-range attractions determine the relative orientations of proteins within these configurations. Finally, simulation results are combined with Principal Component Analysis to identify those amino-acids / surface patches that form inter-protein contacts at conditions that favor dimerization of gD-Crys. The resulting regions agree with previously found aggregation-prone sites, as well as suggesting new ones that may be important.
Nonspecific protein−protein interactions of a monoclonal antibody were quantified experimentally using light scattering from low to high protein concentrations (c 2 ) and compared with prior work for a different antibody that yielded qualitatively different behavior. The c 2 dependence of the excess Rayleigh ratio (R ex ) provided the osmotic second virial coefficient (B 22 ) at low c 2 and the static structure factor (S q=0 ) at high c 2 , as a function of solution pH, total ionic strength (TIS), and sucrose concentration. Net repulsive interactions were observed at pH 5, with weaker repulsions at higher TIS. Conversely, attractive electrostatic interactions were observed at pH 6.5, with weaker attractions at higher TIS. Refined coarse-grained models were used to fit model parameters using experimental B 22 versus TIS data. The parameters were used to predict high-c 2 R ex values via Monte Carlo simulations and separately with Mayer-sampling calculations of higher-order virial coefficients. For both methods, predictions for repulsive to mildly attractive conditions were quantitatively accurate. However, only qualitatively accurate predictions were practical for strongly attractive conditions. An alternative, higher resolution model was used to show semiquantitatively and quantitatively accurate predictions of strong electrostatic attractions at low c 2 and low ionic strength.
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