A smooth and differentiable bulk-solvent model for macromolecular diffraction

Inclusion of low-resolution data in macromolecular crystallography requires a model for the bulk solvent. Previous methods have used a binary mask to accomplish this, which has proven to be very effective, but the mask is discontinuous at the solute-solvent boundary (i.e. the mask value jumps from zero to one) and is not differentiable with respect to atomic parameters. Here, two algorithms are introduced for computing bulk-solvent models using either a polynomial switch or a smoothly thresholded product of Gaussians, and both models are shown to be efficient and differentiable with respect to atomic coordinates. These alternative bulk-solvent models offer algorithmic improvements, while showing similar agreement of the model with the observed amplitudes relative to the binary model as monitored using R, R(free) and differences between experimental and model phases. As with the standard solvent models, the alternative models improve the agreement primarily with lower resolution (>6 A) data versus no bulk solvent. The models are easily implemented into crystallographic software packages and can be used as a general method for bulk-solvent correction in macromolecular crystallography.