  Static light scattering is a popular physical chemistry technique that
enables calculation of physical attributes such as the radius of gyration and
the second virial coefficient for a macromolecule (e.g., a polymer or a
protein) in solution. The second virial coefficient is a physical quantity that
characterizes the magnitude and sign of pairwise interactions between
particles, and hence is related to aggregation propensity, a property of
considerable scientific and practical interest. Estimating the second virial
coefficient from experimental data is challenging due both to the degree of
precision required and the complexity of the error structure involved. In
contrast to conventional approaches based on heuristic OLS estimates, Bayesian
inference for the second virial coefficient allows explicit modeling of error
processes, incorporation of prior information, and the ability to directly test
competing physical models. Here, we introduce a fully Bayesian model for static
light scattering experiments on small-particle systems, with joint inference
for concentration, index of refraction, oligomer size, and the second virial
coefficient. We apply our proposed model to study the aggregation behavior of
hen egg-white lysozyme and human gammaS-crystallin using in-house experimental
data. Based on these observations, we also perform a simulation study on the
primary drivers of uncertainty in this family of experiments, showing in
particular the potential for improved monitoring and control of concentration
to aid inference.
