A Novel Multi-objectivisation Approach for Optimising the Protein Inverse Folding Problem

In biology, the subject of protein structure prediction is of continued interest, not only to chart the molecular map of the living cell, but also to design proteins of new functions. The Inverse Folding Problem (IFP) is in itself an important research problem, but also at the heart of most rational protein design approaches. In brief, the IFP consists in finding sequences that will fold into a given structure, rather than determining the structure for a given sequence - as in conventional structure prediction. In this work we present a Multi Objective Genetic Algorithm (MOGA) using the diversity-as-objective (DAO) variant of multi-objectivisation, to optimise secondary structure similarity and sequence diversity at the same time, hence pushing the search farther into wide-spread areas of the sequence solution-space. To control the high diversity generated by the DAO approach, we add a novel Quantile Constraint (QC) mechanism to discard an adjustable worst quantile of the population. This DAO-QC approach can efficiently emphasise exploitation rather than exploration to a selectable degree achieving a trade-off producing both better and more diverse sequences than the standard Genetic Algorithm (GA). To validate the final results, a subset of the best sequences was selected for tertiary structure prediction. The super-positioning with the original protein structure demonstrated that meaningful sequences are generated underlining the potential of this work.