# Measurements of Protein-Protein Interactions by Size Exclusion Chromatography

$\frac{\Pi}{k_B T} = \rho + B_2(T)\rho^2 + ...$
where $\rho$ is the solute number density, $k_B$ is Boltzmann's constant and T is temperature. The second virial coefficient is $B_2$ and is defined as the pair of interaction potential between molecules. In 1994, it was shown that $B_2$ correlated to protein crystallizability. It was seen that proteins crystallized when $B_2$ became slightly negative because this indicated that the protein molecules had attractive interactions. Another type of liquid chromatography, frontal elution liquid chromatography, had previously been used to estimate the virial coefficients but this had several disadvantages (required large amounts of protein and took too long to run the columns). By using size exclusion HPLC, both the amount of protein required and the time to run the experiment were largely minimized.