Algorithms for Designing Therapeutic Oligonucleotides on Pangenome Graphs

Designing therapeutic oligonucleotides that act reliably across human genetic diversity requires more than alignment to a single reference genome. Binding affinity of an siRNA or ASO to a usually complementary site in an mRNA target molecule is one main determinant of drug efficacy. Thus, variation in sub-populations can lead to failures in drug development if this variation reduces binding affinity. We provide a first methodological step towards principled, variant-aware design of therapeutic oligonucleotides. The genetic diversity in target genes, or specific regions thereof, is represented as a pangenome graph. We define individual or small sets of suitable therapeutic oligonucleotides by their ability to cover all paths in a directed acyclic graph within a bounded edit distance <= k. Edit distance is used as an accepted proxy to the commonly used binding affinity. We formalize the resulting computational problem and provide complexity results: NP-hardness of identifying such minimal sets even for k =0, and coNP-completeness of verifying the validity of a given set of oligonucleotides. Further, we propose algorithmic approaches operating on a product graph of an automaton (an Aho-Corasick DFA or an Ukkonen DFA) and the pangenome graph, as well as a dynamic programming-based lossless filter. We evaluate the approaches on gene-specific subgraphs of human pangenome graphs and demonstrate favorable performance compared to naive brute-force computation. Our results show that candidate target sites with a threshold of k <= 3 can be identified even for large, complex graphs where the brute-force computation did not complete within 24h. We observe that the dynamic programming-based lossless filter outperforms both product-graph approaches as well as brute-force baselines while maintaining an average approximation ratio < 1.5 across more than a hundred evaluated subgraphs. We also present examples where a small set of oligonucleotides constitutes a feasible solution where no single oligonucleotide with a threshold of k <= 2 covers all paths.