Extracting Orientation and Distance-Dependent Interaction\nPotentials between Proteins in Solutions Using Small-Angle X‑ray/Neutron\nScattering

Nonspecific protein–protein\ninteractions (PPIs) are key\nto understanding the behavior of proteins in solutions. However, experimentally\nmeasuring anisotropic PPIs as a function of orientation and distance\nhas been challenging. Here, we propose to measure a new parameter,\nthe generalized second virial coefficient, <i>B</i><sub>22</sub>(<i>Q</i>), to address this challenge. <i>B</i><sub>22</sub>(<i>Q</i>) can be measured by using\nsmall-angle X-ray/neutron scattering (SAXS/SANS) at finite <i>Q</i> values, where <i>Q</i> is the magnitude of the\nscattering wave vector. We develop the analytical theory here to calculate <i>B</i><sub>22</sub>(<i>Q</i>) with any known interprotein\npotentials including anisotropic interaction potentials. This method\novercomes the challenges and limitations of commonly used methods\nfor extracting PPI information, namely, using integral approximations\nto solve the Ornstein–Zernike equation by fitting SAXS/SANS\ndata. The accuracy of this analytical theory is further evaluated\nwith computer simulations using a model system. Not only can our method\ngreatly extend the capability of SAXS/SANS to investigate PPIs of\nmany proteins, but it is also applicable to a wide variety of colloidal\nsystems where anisotropic interaction potentials are important.