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Kornelia Polyak, Franziska Michor and colleagues report a novel method, STAR-FISH, for combined in situ single-cell analysis of point mutations and copy number alterations in archived tissue samples. They apply STAR-FISH to clinically relevant PIK3CA mutations and HER2 amplifications and observe associations between intratumoral diversity and clinical outcome.

Analysis of global remethylation in mouse embryos at several developmental stages identifies an epigenetic landscape that partitions extraembryonic tissues within the embryo and resembles a frequent, global departure in genome regulation in human cancers.

Copy-number changes in cancer genomes may be caused by errors during the replication of colocalized DNA regions. De and Michor provide genome-wide evidence for this model by integrating data on DNA replication timing, the three-dimensional organization of the genome and copy-number alterations in cancer.

Osimertinib and dacomitinib are approved as first-line treatment of EGFR-mutant NSCLC but resistance can arise. Here, the authors use a computational model to identify an optimal dosing schedule for osimertinib and dacomitinib combination therapy that was confirmed tolerable and effective in an ongoing phase I clinical trial.

The role of mTORC1 in AML has not yet been proven due to the mixed results of its inhibitors in clinical trials. Here the authors show the real-time dynamics of the mTORC1 pathway in association with AML growth and response to chemotherapy with fluorescent markers, providing guidance for timed intervention with pathway-specific inhibitors.

Human cancer genomes often contain large amounts of single-nucleotide substitutions (SNS). Liu et al. catalogued SNS signatures across various cancer and normal genomes, demonstrating coordinative effects between replication timing and nuclear architecture on SNS patterns in cancer genomes.

A computational model of the spatiotemporal dynamics of the perivascular niche that incorporates relevant cellular and tissue-level phenomena can be used to optimize treatment schedules for glioblastoma.

KDM4C regulates cathepsin L-mediated histone H3 N-terminal tail clipping through grainyhead-like 2 (GRHL2) methylation in breast cancer. This link between the cellular redox state and chromatin remodeling might represent a therapeutic target in KDM4C-amplified tumors.

The phenotypic consequence of 3D genome boundary disruption on developmental processes remains insufficiently understood. Here, the authors show that perturbation of a SOX17 boundary in human pluripotent stem cells interferes with proper differentiation and that germline variations affecting such boundaries are subject to selection, resulting in underrepresentation in the human population.

Although human cancers exhibit intratumour heterogeneity, the influence of the tumour environment on this property is unclear. Single basal-like mammary epithelial cells are now shown to engage a dynamic TGFBR3–JUND signalling circuit in an extracellular-matrix-dependent manner. Cell transition between the distinct gene expression states underlying this circuit alters their properties and may modulate their propensity to malignancy.

TGFβ signalling is reported to regulate hormone-responsive mammary epithelial progenitors that are associated with breast cancer risk. Here, the authors find that short-term TGFBR1 inhibition prevents tumour formation in rat breast cancer models and identify a TGFBR1 inhibition-responsive sub-population of mammary epithelial cells, which is associated with human breast cancer risk.

Single-cell analysis of genomes from primary human breast tumours and cell lines shows that chromosomal aberrations continue to evolve during primary tumour expansion, resulting in a milieu of subclones within the tumour.

Janiszewska et al. show that minor subpopulations expressing IL11 and FIGF in breast cancer cells promote metastasis through altering local and systemic tumour microenvironments including neutrophils.

Effective combination therapies to improve the efficacy of BET inhibitors are currently under investigation. Here, the authors examine palbociclib and paclitaxel as two promising candidates for combination therapies with BET inhibition in breast cancer and investigate the dynamics of resistance to these combinations through DNA barcoding and mathematical modelling.

To investigate the role of sub-clonal tumour heterogeneity in cancer progression, a mouse xenograft model was used which revealed that tumour growth can be driven by a minor cell subpopulation by a non-cell-autonomous mechanism, although this minor subpopulation can be outcompeted by faster proliferating competitors.

The Physical Sciences–Oncology Centers in the US bring together scientists from all backgrounds to tackle some of the most important questions in cancer research.

The origins of lineage correlations and heterogeneity in division and apoptosis times among single cells are incompletely understood. Here, a new lineage tracking data analysis approach reveals that circadian oscillations may underlie cell fate control and explain the observed correlation structures.

Triple-negative breast cancer is highly heterogeneous and aggressive. Here, the authors utilise single-cell RNA sequencing to investigate this heterogeneity, and discover a subpopulation of cells associated with metastasis and treatment resistance signatures, and linked to long term survival outcomes.

This Review discusses mathematical modelling approaches in cancer research. These models can complement experimental and clinical studies, but can also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research.

Hoetker et al. show that H3K36 methylation exerts a dual role in cell identity maintenance: it integrates TGFβ signals at mesenchymal targets to keep them active and prevents the activation of alternative lineage programmes via enhancer methylation.

Stereotactic needle biopsies are currently performed for diagnosis only in glioblastoma; this study highlights the depth of information available through multi-omics analysis.

To investigate genomic diversity within tumours, a new type of whole-genome and exome single cell sequencing has been developed using G2/M nuclei; the technique was used to sequence single nuclei from an oestrogen-positive breast cancer and a triple-negative ductal carcinoma—aneuploidy rearrangements emerged as early events in tumour formation and then point mutations evolved gradually over time.

Cancer is a complex disease, as has been amply shown by the mass of recently generated 'omics' data. Can the new US National Cancer Institute Physical Sciences-Oncology Centers initiative help us to better understand the complexity of this disease?

Amplification of PDGFRα is a common alteration in glioblastoma. In this study, the authors develop a genetically engineered mouse model of GBM based on autocrine, chronic stimulation of overexpressed PDGFR and discover Stathmin1 as an important PDGFRα regulated-protein involved in the response to vinstabline.

Nicholas Navin and colleagues use highly multiplexed single-nucleus sequencing to investigate DNA copy number evolution in patients with triple-negative breast cancer. Their data suggest that most copy number alterations are acquired at the earliest stages of tumor evolution in short punctuated bursts, followed by stable clonal expansions that form the tumor mass.

New computational tools reveal the contribution of microsatellite insertions and deletions to the mutational landscape in human cancer.

The authors have developed a barcoded library that enables the high-throughput tracking of tumor cell dynamics and clonal evolution in response to therapy.

In game theory, 'loners' who choose not to participate in fact promote cooperation between players. The dynamics of the game show phase transitions and complex phenomena reminiscent of statistical physics.

The location of DNA breakpoints associated with somatic copy-number alterations in cancer genomes is analyzed, revealing an enrichment of sequences with propensity to adopt G-quadruplex conformation, often near transcription start sites, and a correlation with hypomethylation. The analysis indicates that G4 formation contributes to cancer genome instability.

Genome-wide analyses of somatic mutations across six cancer types show that mutation frequencies differ between chromosomal regions located at the nuclear core versus the periphery, and thus mutational patterns are influenced by nuclear architecture.

Mathematical modelling provides a means of understanding cancer evolution and optimizing cancer treatment response. This Review outlines different computational methods of modelling cancer treatment response and identifying optimal treatment strategies.

In vitro evolution experiments on haploid, diploid, and tetraploid yeast strains show that adaptation is faster in tetraploids, providing direct quantitative evidence that in some environments polyploidy can accelerate evolutionary adaptation.

Debra Van Egeren et al. present a stochastic computational model of the dynamics of an asexually reproducing population, such as somatic or cancer cells, crossing a fitness valley. They find that fitness variation persisting across generations promotes weaker selection against deleterious intermediates, thereby increasing the rate of valley crossing.

This tutorial outlines common strategies for analysis of bulk RNA-sequencing (RNA-seq) data in the context of tumor immunity and immunotherapy response and presents a comprehensive computational pipeline integrating these tools to streamline RNA-seq analysis.