The majority of macromolecular crystal structures are determined using the method of molecular replacement, in which known related structures are rotated and translated to provide an initial atomic model for the new structure. A theoretical understanding of the signal-to-noise ratio in likelihood-based molecular replacement searches has been developed to account for the influence of model quality and completeness, as well as the resolution of the diffraction data. Here we show that, contrary to current belief, molecular replacement need not be restricted to the use of models comprising a substantial fraction of the unknown structure. Instead, likelihood-based methods allow a continuum of applications depending predictably on the quality of the model and the resolution of the data. Unexpectedly, our understanding of the signal-to-noise ratio in molecular replacement leads to the finding that, with data to sufficiently high resolution, fragments as small as single atoms of elements usually found in proteins can yield ab initio solutions of macromolecular structures, including some that elude traditional direct methods.This research was supported by a Principal Research Fellowship from the Wellcome Trust (082961/Z/07/Z to R.J.R.), and grants from the NIH (Grant P01GM063210 to R.J.R.), the Swedish Research Council (Grant 521-2014-1833 to K.T. and Grant 2007-5648 to B.L.), the Knut and Alice Wallenberg Foundation (K.T.), the Novo Nordisk Foundation (K.T.), and the Röntgen Ångström Cluster (Grant 349-2013-597 to B.L.). The research was facilitated by Wellcome Trust Strategic Award 100140 to the Cambridge Institute for Medical Research
