Orientation-averaged pair potentials between dipolar proteins or colloids

Potentials of mean force between nonuniformly charged colloids or globular proteins are often estimated as a pairwise sum of distinct orientation averages for charge-dipole and dipole-dipole interactions. In systems with dipole-related interactions comparable to or exceeding the thermal energy, however, correlations between charge-dipole and dipole-dipole terms can render the additivity assumption highly inaccurate. On the basis of the third-order cumulant expansion of intercolloidal interactions. we derive an asymptotically exact relation for the potential of mean force that includes the correlation between distinct contributions. Using a simple discrete-orientation model, we obtain an approximate expression for the nonadditivity correction that reproduces correct behavior in weak and strong coupling limits and is sufficiently accurate for practical calculations over a wide range of interaction strengths including those characteristic of aqueous protein solutions.