A noise and artifact suppression using resampling (NASR) method to facilitate de novo protein structure determination

The search of heavy atoms is crucial to the de novo determination of protein structures. Typically, the difference Patterson map is calculated as a first step to solve substructure. However, the pseudo-peaks and noises inherent in such maps arising from the high symmetry and large size of protein structures accompanied with the data collection errors inevitably pose a challenge in accurate real space-based substructure determination. In order to mitigate such pseudo-peaks and noises and further improve signal-to-noise ratio (SNR) of the difference Patterson map, the noise and artifact suppression using resampling (NASR) method originally proposed in nuclear magnetic resonance is introduced into protein crystallography in this work to optimize the difference Patterson map. The NASR method makes use of the statistical learning theory, which in this work repeatedly samples a fixed portion of diffraction data (sub-dataset) randomly followed by a statistical analysis of the multiple calculated difference Patterson maps to discard pseudo-peaks and noises. Its feasibility is based on the fact that the true vector peaks of the heavy atoms keep static in the multiple random sub-datasets, whereas the pseudo-peaks and noises fluctuate remarkably. And the key of this method lies in the design of a weighting function to distinguish true vector peaks from pseudo-peaks and noises, as well as a proper selection of the parameters associated with the function. The introduced NASR method is both numerically and experimentally demonstrated to be feasible in suppressing spurious peaks and non-correlative noises intrinsic to the difference Patterson maps. As a result, the SNR of the difference Patterson maps can be enhanced to some extent to facilitate real space-based substructure determination. It is therefore anticipated that the proposed method may provide a meaningful insight into how to denoise the difference Patterson maps, which in turn assists in locating heavy atoms and further facilitates de novo protein structure determination.