Glioblastoma (GBM) constitutes the most common and aggressive primary brain tumor. To better understand how GBM evolves we analyzed longitudinal genomic and transcriptomic data of 114 patients. The analysis reveals a highly branched evolutionary pattern in which 63% of patients experience expression-based subtype changes. The branching pattern together with estimates of evolutionary rates suggest that the relapse associated clone typically preexisted years before diagnosis. 15% of tumors present hypermutations at relapse in highly expressed genes with a clear mutational signature. We find that 11% of recurrent tumors harbor mutations in LTBP4, a protein binding to TGF-β. Silencing LTBP4 in GBM cells leads to TGF-β activity suppression and decreased proliferation. In IDH1-wild-type recurrent GBM, high LTBP4 expression is associated with worse prognosis, highlighting the TGF-β pathway as a potential therapeutic target in GBM.

We used 20 de novo genome assemblies to probe the speciation history and architecture of gene flow in rapidly radiating Heliconius butterflies. Our tests to distinguish incomplete lineage sorting from introgression indicate that gene flow has obscured several ancient phylogenetic relationships in this group over large swathes of the genome. Introgressed loci are underrepresented in low-recombination and gene-rich regions, consistent with the purging of foreign alleles more tightly linked to incompatibility loci. Here, we identify a hitherto unknown inversion that traps a color pattern switch locus. We infer that this inversion was transferred between lineages by introgression and is convergent with a similar rearrangement in another part of the genus. These multiple de novo genome sequences enable improved understanding of the importance of introgression and selective processes in adaptive radiation.

In this paper we establish a universal characterization of higher algebraic K-theory in the setting of small stable infinity categories. Specifically, we prove that connective algebraic K-theory is the universal additive invariant, i.e., the universal functor with values in spectra which inverts Morita equivalences, preserves filtered colimits, and satisfies Waldhausen's additivity theorem. Similarly, we prove that non-connective algebraic K-theory is the universal localizing invariant, i.e., the universal functor that moreover satisfies the "Thomason-Trobaugh-Neeman" localization theorem. To prove these results, we construct and study two stable infinity categories of "noncommutative motives"; one associated to additivity and another to localization. In these stable infinity categories, Waldhausen's S. construction corresponds to the suspension functor and connective and non-connective algebraic K-theory spectra become corepresentable by the noncommutative motive of the sphere spectrum. In particular, the algebraic K-theory of every scheme, stack, and ring spectrum can be recovered from these categories of noncommutative motives. In order to work with these categories of noncommutative motives, we establish comparison theorems between the category of spectral categories localized at the Morita equivalences and the category of small idempotent-complete stable infinity categories. We also explain in detail the comparison between the infinity categorical version of Waldhausen K-theory and the classical definition. As an application of our theory, we obtain a complete classification of the natural transformations from higher algebraic K-theory to topological Hochschild homology (THH) and topological cyclic homology (TC). Notably, we obtain an elegant conceptual description of the cyclotomic trace map.Comment: Various revisions and correction

We here pioneer a low-cost assembly strategy for 20 Heliconiini genomes to characterize the evolutionary history of the rapidly radiating genus Heliconius. A bifurcating tree provides a poor fit to the data, and we therefore explore a reticulate phylogeny for Heliconius. We probe the genomic architecture of gene flow, and develop a new method to distinguish incomplete lineage sorting from introgression. We find that most loci with non-canonical histories arose through introgression, and are strongly underrepresented in regions of low recombination and high gene density. This is expected if introgressed alleles are more likely to be purged in such regions due to tighter linkage with incompatibility loci. Finally, we identify a hitherto unrecognized inversion, and show it is a convergent structural rearrangement that captures a known color pattern switch locus within the genus. Our multi-genome assembly approach enables an improved understanding of adaptive radiation.

Precision medicine in cancer proposes that genomic characterization of tumors can inform personalized targeted therapies1–5. This proposition, however, is complicated by spatial and temporal heterogeneity6–14. Here we study genomic and expression profiles across 127 multi-sector or longitudinal specimens from 52 glioblastoma (GBM) patients. Using bulk and single-cell data, we find that samples from the same tumor mass share genomic and expression signatures, while geographically separated multifocal tumors and/or long-term recurrent tumors are seeded from different clones. Chemical screening of patient-derived glioma cells (PDCs) shows that therapeutic response is associated to genetic similarity, and multifocal tumors enriched with PIK3CA mutations have a heterogeneous drug response pattern. Importantly, we show that targeting truncal events is more efficacious in reducing tumor burden. In summary, this work demonstrates that evolutionary inference from integrated genomic analysis in multi-sector biopsies can inform targeted therapeutic interventions for GBM patients.