Transferable kriging machine learning models for the multipolar electrostatics of helical deca-alanine

We exploit the transferability of quantum topological atoms in the construction of a multipolar polarizable protein force field QCTFF. A helical oligopeptide of 10 alanine residues (103 atoms) has its total electrostatic energy predicted using the kriging machine learning method with a mean error of 6.4 kJ mol−1. This error is similar to that found in smaller molecules presented in past QCTFF publications. Kriging relates the molecular geometry to atomic multipole moments that describe the ab initio electron density. Atom types are constructed from similar atoms within the helix. As the atoms within a given atom type share a local chemical environment, they can share a kriging model with a reduced number of input descriptors (i.e. features). The feature reduction decreases the kriging training times by more than 23 times but increases the prediction error by only 1.3 %. In transferability tests, transferable models give a 5.7 % error when predicting moments of an atom outside the training set, compared to the 3.9 % error when tested against data belonging to atoms included in the training data. The transferable kriging models successfully predict atomic multipole moments with useful accuracy, opening an avenue to QCTFF modelling of a whole protein.