Polarizable atomic multipole X-ray refinement: weighting schemes for macromolecular diffraction

In the past, weighting between the sum of chemical and data-based targets in macromolecular crystallographic refinement was based on comparing the gradients or Hessian diagonal terms of the two potential functions. Here, limitations of this scheme are demonstrated, especially in the context of a maximum-likelihood target that is inherently weighted by the model and data errors. In fact, the congruence between the maximum-likelihood target and a chemical potential based on polarizable atomic multipole electrostatics evaluated with Ewald summation has opened the door to a transferable static weight. An optimal static weight is derived from first principles and is demonstrated to be transferable across a broad range of data resolutions in the context of a recent implementation of X-ray crystallographic refinement using the polarizable AMOEBA force field and it is shown that the resulting models are balanced with respect to optimizing both R(free) and MolProbity scores. Conversely, the classical automatic weighting scheme is shown to lead to underfitting or overfitting of the data and poor model geometry. The benefits of this approach for low-resolution diffraction data, where the need for prior chemical information is of particular importance, are also highlighted. It is demonstrated that this method is transferable between low- and high-resolution maximum-likelihood-based crystallographic refinement, which proves for the first time that resolution-dependent parameterization of either the weight or the chemical potential is unnecessary.