Estimating probabilistic context-free grammars for proteins using contact map constraints.

Interactions between amino acids that are close in the spatial structure, but not necessarily in the sequence, play important structural and functional roles in proteins. These non-local interactions ought to be taken into account when modeling collections of proteins. Yet the most popular representations of sets of related protein sequences remain the profile Hidden Markov Models. By modeling independently the distributions of the conserved columns from an underlying multiple sequence alignment of the proteins, these models are unable to capture dependencies between the protein residues. Non-local interactions can be represented by using more expressive grammatical models. However, learning such grammars is difficult. In this work, we propose to use information on protein contacts to facilitate the training of probabilistic context-free grammars representing families of protein sequences. We develop the theory behind the introduction of contact constraints in maximum-likelihood and contrastive estimation schemes and implement it in a machine learning framework for protein grammars. The proposed framework is tested on samples of protein motifs in comparison with learning without contact constraints. The evaluation shows high fidelity of grammatical descriptors to protein structures and improved precision in recognizing sequences. Finally, we present an example of using our method in a practical setting and demonstrate its potential beyond the current state of the art by creating a grammatical model of a meta-family of protein motifs. We conclude that the current piece of research is a significant step towards more flexible and accurate modeling of collections of protein sequences. The software package is made available to the community.