CCK* (Convex Closure K*): A Suite of Algorithms for De Novo L- and D-peptide Design

The computational design of L-peptides and their mirror-image counterparts, D-peptides, is an active area in drug design. Peptide therapeutics offer exceptional structural diversity and high binding specificity, while D-peptides additionally confer critical advantages such as proteolytic resistance. Progress in de novo D-peptide design has been hindered by the absence of evolutionary context and limited structural data, both of which underpin the deep learning methods widely used in L-peptide design. Consequently, a robust framework capable of designing both L- and D-peptides should integrate data-driven inference with first-principles, physics-based modeling. Here, we introduce a unified computational framework that supports de novo design of both L- and D-peptides, thereby expanding the accessible design space across both chiral spaces. Convex Closure K* (CCK*) is a suite of chirality-agnostic algorithms: SCOPE, MONTAGE, and ARISE. SCOPE uses geometry as a proxy for chemical energetics, computing convex hull representations of rotameric states to rapidly generate multi-sequence protein contact maps. MONTAGE employs geometric hashing in conjunction with the K* algorithm to generate and rank backbone scaffolds according to their suitability for sequence design. ARISE is a K*-based sequence design algorithm that performs iterative residue assignment in an undirected graph to design high-affinity peptide sequences. We apply the full CCK* suite to six de novo design tasks, benchmarking chirality-preserving and chirality-inverting designs in both homochiral and heterochiral complexes.