Evolutionary Multi Objective Optimisation with Diversity as Objective for the Protein Structure Similarity Problem

In biology, the subject of protein structure prediction is of continued interest, not only to keep charting the molecular map of the living cell, but also to design pro-teins with new functions. Given a reference protein and its corresponding tertiary (3D) structure, this work is concerned with finding 1) the most diverse nucleotide sequences which 2) produce very similar 3D structures. This task is different from conventional 3D prediction seeking to predict the structure of one given sequence. In order to effi-ciently evaluate the protein structure similarity objective we introduce a fast evaluation method based on an approximate prediction of its secondary structure. This permits to use a Genetic Algorithm (GA) to efficiently probe the enormous search space of possible sequences. Since we are additionally interested in finding as many different sequences as possible, we use the diversity-as-objective (DAO) approach [1] to push the algorithm farther into wide-spread areas of the solution-space. The problem is consequently bi-objective and tackled with a Multi-Objective GA (MOGA). To cir-cumvent the possible dominance of the diversity objective over the similarity objective, the Quantile Constraint (QC) is introduced in which the worse quantile of the pop