The Distance and Median Problems in the Single-Cut-Or-Join Model with Single-Gene Duplications

Background. In the field of genome rearrangement algorithms, models accounting for gene duplication lead often to hard problems. For example, while computing the pairwise distance is tractable in most duplication-free models, the problem is NP-complete for most extensions of these models accounting for duplicated genes. Moreover, problems involving more than two genomes, such as the genome median and the Small Parsimony problem, are intractable for most duplication-free models, with some exceptions, for example the Single-Cut-or-Join (SCJ) model. Results. We introduce a variant of the SCJ distance that accounts for duplicated genes, in the context of directed evolution from an ancestral genome to a descendant genome where orthology relations between ancestral genes and their descendant are known. Our model includes two duplication mechanisms: single-gene tandem duplication and the creation of single-gene circular chromosomes. We prove that in this model, computing the directed distance and a parsimonious evolutionary scenario in terms of SCJ and single-gene duplication events can be done in linear time. We also show that the directed median problem is tractable for this distance, while the rooted median problem, where we assume that one of the given genomes is ancestral to the median, is NP-complete. We also describe an Integer Linear Program for solving this problem. We evaluate the directed distance and rooted median algorithms on simulated data. Conclusion. Our results provide a simple genome rearrangement model, extending the SCJ model to account for single-gene duplications, for which we prove a mix of tractability and hardness results. For the NP-complete rooted median problem, we design a simple Integer Linear Program. Our publicly available implementation of these algorithms for the directed distance and median problems allow to solve efficiently these problems on large instances

The Clinically Actionable Molecular Profile of Early versus Late-Stage Non-Small Cell Lung Cancer, an Individual Age and Sex Propensity-Matched Pair Analysis

Background: Despite meticulous surgery for non-small cell lung cancer (NSCLC), relapse is as high as 70% at 5 years. Many institutions do not conduct reflexive molecular testing on early stage specimens, although targeted gene therapy may extend life by years in the event of recurrence. This ultimately delays definitive treatment with additional biopsy risking suboptimal tissue acquisition and quality for molecular testing. Objective: To compare molecular profiles of genetic alterations in early and late NSCLC to provide evidence that reflexive molecular testing provides clinically valuable information. Methods: A single-center propensity matched retrospective analysis was conducted using prospectively collected data. Adults with early and late-stage NSCLC had tissue subject to targeted panel-based NGS. Frequencies of putative drivers were compared, with 1:3 matching on the propensity score; p < 0.05 deemed statistically significant. Results: In total, 635 NSCLC patients underwent NGS (59 early, 576 late); 276 (43.5%) females; age 70.9 (±10.2) years; never smokers 140 (22.0%); 527 (83.0%) adenocarcinomas. Unadjusted frequencies of EGFR mutations were higher in the early cohort (30% vs. 18%). Following adjustment for sex and smoking status, similar frequencies for both early and late NSCLC were observed for variants in EGFR, KRAS, ALK, MET, and ROS1. Conclusion: The frequency of clinically actionable variants in early and late-stage NSCLC was found to be similar, providing evidence that molecular profiling should be performed on surgical specimens. This pre-determined profile is essential to avoid treatment delay for patients who will derive clinical benefit from targeted systemic therapy, in the high likelihood of subsequent relapse