  We present a general theory for predicting the interaction potentials between
DNA-coated colloids, and more broadly, any particles that interact via
valence-limited ligand-receptor binding. Our theory correctly incorporates the
configurational and combinatorial entropic factors that play a key role in
valence-limited interactions. By rigorously enforcing self-consistency, it
achieves near-quantitative accuracy with respect to detailed Monte Carlo
calculations. With suitable approximations and in particular geometries, our
theory reduces to previous successful treatments, which are now united in a
common and extensible framework. We expect our tools to be useful to other
researchers investigating ligand-mediated interactions. A complete and
well-documented Python implementation is freely available at
http://github.com/patvarilly/DNACC .
