Calculating Structure Factors of Protein Solutions by Atomistic Modeling of Protein-Protein Interactions

We present a method, FMAPS(q), for calculating the structure factor, $S\left(q\right)$ , of a protein solution, by extending our fast Fourier transform-based modeling of atomistic protein-protein interactions (FMAP) approach. The interaction energy consists of steric, nonpolar attractive, and electrostatic terms that are additive among all pairs of atoms between two protein molecules. In the present version, we invoke the free-rotation approximation, such that the structure factor is given by the Fourier transform of the protein center-center distribution function $g_C\left(R\right)$ . At low protein concentrations, $g_C\left(R\right)$ can be approximated as $e^{-\beta W\left(R\right)}$ , where $W\left(R\right)$ is the potential of mean force along the center-center distance $R$ . We calculate $W\left(R\right)$ using FMAPB2, a member of the FMAP class of methods that is specialized for the second virial coefficient [Qin and Zhou, J Phys Chem B 123 (2019) 8203-8215]. For higher protein concentrations, we obtain $S\left(q\right)$ by a modified random-phase approximation, which is a perturbation around the steric-only energy function. Without adjusting any parameters, the calculated structure factors for lysozyme and bovine serum albumin at various ionic strengths, temperatures, and protein concentrations are all in reasonable agreement with those measured by small-angle X-ray or neutron scattering. This initial success motivates further developments, including removing approximations and parameterizing the interaction energy function.