Bi-level diversity optimisation for representative protein panel selection

Selecting representative subsets from large protein sequence datasets is a common challenge in enzyme discovery and related tasks under limited screening capacity. In practice, candidate panels are often constructed using clustering-based redundancy reduction or manual selection guided by phylogenetic or similarity-network analyses, which do not directly optimise subset diversity and require threshold tuning or expert interpretation. Here, we present a bi-level diversity-optimisation framework for representative protein panel selection implemented using a local search heuristic that iteratively updates panel composition to improve diversity. The method formulates panel design as a combinatorial optimisation problem over pairwise distance matrices, combining a MaxMin objective to enforce minimum separation between selected sequences with a MaxSum objective to increase global dispersion. This formulation enables the direct construction of fixed-cardinality panels while remaining independent of the similarity representation used to compute pairwise distances. Benchmarking across four Pfam families shows that the bi-level formulation consistently reduces redundancy among selected sequences, lowering maximum pairwise identity by 43-46% relative to the previous MaxSum-based formulation, while maintaining comparable or improved EC-label coverage. The framework can incorporate sequence- or structure-based similarity measures, providing a flexible strategy for constructing diverse representative panels across homologous protein families.