Assessment of Fragmentation Strategies for Large Proteins Using the Multilayer Molecules-in-Molecules Approach

We present a rigorous evaluation of the potential for the multilayer Molecules-in-Molecules (MIM) fragmentation method to be applied to large biomolecules. Density functional total energies of a test set of 8 peptides, sizes ranging from 107 to 721 atoms, were evaluated with MIM and compared to unfragmented energies to help develop a protocol for the treatment of large proteins. Fragmentation schemes involving subsystems of 4 to 5 covalently bonded fragments (tetramer or pentamer schemes) were tested with a single level of theory (MIM1) and produced errors on the order of 100 kcal/mol due to the relatively small size of the subsystems and the neglect of nonbonded interactions. Supplementing the two schemes with nonbonded dimer subsystems, formed from fragments within a specified cutoff distance (3.0 Å), nearly cut the MIM1 errors in half, leading us to employ these new schemes as starting points in multilayer calculations. When employing a DFT low level with a substantially smaller basis set (MIM2), the dimer-supplemented schemes produce errors below our target accuracy of 2 kcal/mol in the majority of cases. However, for the larger test systems, such as the 45 residue slice of a human protein kinase with over 10,000 basis functions in the high level, the low level calculation over the full molecule becomes the bottleneck for MIM2 calculations. To overcome any associated limitations, we explored, for the first time, 3-layer MIM methods (MIM3) with a distance-based medium level of fragmentation and dispersion-corrected semiempirical methods (e.g., PM6-D3) as the low level. A modestly sized cutoff distance in the medium level (3.0-3.5 Å), leading to subsystems of 30-50 atoms treated at the medium and low levels of theory, was able to match the low errors of the MIM2 calculations. These results allow us to develop a general prescription for 3-layer calculations wherein a much cheaper low level can be used, while fragment sizes in the high layer stay modest, allowing the MIM method to be applied to very large proteins in the future.