Integral equation models for solvent in macromolecular crystals

The solvent can occupy up to similar to 70% of macromolecular crystals, and hence, having models that predict solvent distributions in periodic systems could improve the interpretation of crystallographic data. Yet, there are few implicit solvent models applicable to periodic solutes, and crystallographic structures are commonly solved assuming a flat solvent model. Here, we present a newly developed periodic version of the 3D-reference interaction site model (RISM) integral equation method that is able to solve efficiently and describe accurately water and ion 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 Ornstein-Zernike 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 the counter- and co-ions are part of the disordered solvent. We present several calculations of proteins, RNAs, and small molecule crystals to show that x-ray scattering intensities and the solvent structure predicted by the periodic 3D-RISM solvent model are in closer agreement with the 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 A range. Prospects for incorporating integral equation models into crystallographic refinement are discussed. (c) 2022 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

In this study, a new periodic version of the 3D-reference interaction site model (RISM) integral equation method is presented, which can accurately describe the distributions of water and ions in periodic systems. The method outperforms the traditional flat solvent model in interpreting crystallographic data, as demonstrated by calculations on proteins, RNAs, and small molecule crystals.