Integral equation models for solvent in macromolecular crystals

Solvent can occupy up to ~70% of macromolecular crystals and hence having models that predict solvent distributions in periodic systems could improve in the interpretation of crystallographic data. Yet there are few implicit solvent models applicable to periodic solutes while crystallographic structures are commonly solved assuming a flat solvent model. Here we present a newly-developed periodic version of the 3D-RISM integral equation method that is able to solve for efficiently and describe accurately water and ions distributions in periodic systems; the code can compute accurate gradients that can be used in minimizations or molecular dynamics simulations. The new method includes an extension of the OZ equation needed to yield charge neutrality for charged solutes which requires an additional contribution to the excess chemical potential that has not been previously identified; this is an important consideration for nucleic acids or any other charged system where most or all of the counter- and co-ions are part of the "disordered" solvent. We present of several calculations of protein, RNA and small molecule crystals to show that X-ray scattering intensities and solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with experiment than are intensities computed using the default flat solvent model in the refmac5 or phenix refinement programs, with the greatest improvement in the 2 to 4 {\AA} range. Prospects for incorporating integral equation models into crystallographic refinement are discussed.