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Significance Evolution of drug resistance, as observed in bacteria, viruses, parasites, and cancer, is a key challenge for global health. We approach the problem using the mathematical concepts of stochastic optimal control to study what is needed to control evolving populations. We focus on the detrimental effect of imperfect information and the loss of control it entails, thus quantifying the intuition that to control, one must monitor. We apply these concepts to cancer therapy to derive protocols where decisions are based on monitoring the response of the tumor, which can outperform established therapy paradigms. Populations can evolve to adapt to external changes. The capacity to evolve and adapt makes successful treatment of infectious diseases and cancer difficult. Indeed, therapy resistance has become a key challenge for global health. Therefore, ideas of how to control evolving populations to overcome this threat are valuable. Here we use the mathematical concepts of stochastic optimal control to study what is needed to control evolving populations. Following established routes to calculate control strategies, we first study how a polymorphism can be maintained in a finite population by adaptively tuning selection. We then introduce a minimal model of drug resistance in a stochastically evolving cancer cell population and compute adaptive therapies. When decisions are in this manner based on monitoring the response of the tumor, this can outperform established therapy paradigms. For both case studies, we demonstrate the importance of high-resolution monitoring of the target population to achieve a given control objective, thus quantifying the intuition that to control, one must monitor.

Cancer development is characterized by chromosomal instability, manifesting in frequent occurrences of different genomic alteration mechanisms ranging in extent and impact. Mathematical modeling can help evaluate the role of each mutational process during tumor progression, however existing frameworks can only capture certain aspects of chromosomal instability (CIN). We present CINner, a mathematical framework for modeling genomic diversity and selection during tumor evolution. The main advantage of CINner is its flexibility to incorporate many genomic events that directly impact cellular fitness, from driver gene mutations to copy number alterations (CNAs), including focal amplifications and deletions, missegregations and whole-genome duplication (WGD). We apply CINner to find chromosome-arm selection parameters that drive tumorigenesis in the absence of WGD in chromosomally stable cancer types from the Pan-Cancer Analysis of Whole Genomes (PCAWG, n = 718 ). We found that the selection parameters predict WGD prevalence among different chromosomally unstable tumors, hinting that the selective advantage of WGD cells hinges on their tolerance for aneuploidy and escape from nullisomy. Analysis of inference results using CINner across cancer types in The Cancer Genome Atlas ( n = 8207 ) further reveals that the inferred selection parameters reflect the bias between tumor suppressor genes and oncogenes on specific genomic regions. Direct application of CINner to model the WGD proportion and fraction of genome altered (FGA) in PCAWG uncovers the increase in CNA probabilities associated with WGD in each cancer type. CINner can also be utilized to study chromosomally stable cancer types, by applying a selection model based on driver gene mutations and focal amplifications or deletions (chronic lymphocytic leukemia in PCAWG, n = 95 ). Finally, we used CINner to analyze the impact of CNA probabilities, chromosome selection parameters, tumor growth dynamics and population size on cancer fitness and heterogeneity. We expect that CINner will provide a powerful modeling tool for the oncology community to quantify the impact of newly uncovered genomic alteration mechanisms on shaping tumor progression and adaptation.

Dysregulated DNA replication is a cause and a consequence of aneuploidy in cancer, yet the interplay between copy number alterations (CNAs), replication timing (RT) and cell cycle dynamics remain understudied in aneuploid tumors. We developed a probabilistic method, PERT, for simultaneous inference of cell-specific replication and copy number states from single-cell whole genome sequencing (scWGS) data. We used PERT to investigate clone-specific RT and proliferation dynamics in  >50,000 cells obtained from aneuploid and clonally heterogeneous cell lines, xenografts and primary cancers. We observed bidirectional relationships between RT and CNAs, with CNAs affecting X-inactivation producing the largest RT shifts. Additionally, we found that clone-specific S-phase enrichment positively correlated with ground-truth proliferation rates in genomically stable but not unstable cells. Together, these results demonstrate robust computational identification of S-phase cells from scWGS data, and highlight the importance of RT and cell cycle properties in studying the genomic evolution of aneuploid tumors. Here the authors develop a probabilistic model for single-cell DNA sequencing of aneuploid tumors that infers clone-specific replication timing and S-phase fractions, unveiling their relationships with copy number evolution and clonal fitness.

A tumour grows when the total division (birth) rate of its cells exceeds their total mortality (death) rate. The capability for uncontrolled growth within the host tissue is acquired via the accumulation of driver mutations which enable the tumour to progress through various hallmarks of cancer. We present a mathematical model of the penultimate stage in such a progression. We assume the tumour has reached the limit of its present growth potential due to cell competition that either results in total birth rate reduction or death rate increase. The tumour can then progress to the final stage by either seeding a metastasis or acquiring a driver mutation. We influence the ensuing evolutionary dynamics by cytotoxic (increasing death rate) or cytostatic (decreasing birth rate) therapy while keeping the effect of the therapy on net growth reduction constant. Comparing the treatments head to head we derive conditions for choosing optimal therapy. We quantify how the choice and the related gain of optimal therapy depends on driver mutation, metastasis, intrinsic cell birth and death rates, and the details of cell competition. We show that detailed understanding of the cell population dynamics could be exploited in choosing the right mode of treatment with substantial therapy gains.

High-grade serous ovarian cancer (HGSOC) is an archetypal cancer of genomic instability 1 – 4 patterned by distinct mutational processes 5 , 6 , tumour heterogeneity 7 – 9 and intraperitoneal spread 7 , 8 , 10 . Immunotherapies have had limited efficacy in HGSOC 11 – 13 , highlighting an unmet need to assess how mutational processes and the anatomical sites of tumour foci determine the immunological states of the tumour microenvironment. Here we carried out an integrative analysis of whole-genome sequencing, single-cell RNA sequencing, digital histopathology and multiplexed immunofluorescence of 160 tumour sites from 42 treatment-naive patients with HGSOC. Homologous recombination-deficient HRD-Dup ( BRCA1 mutant-like) and HRD-Del ( BRCA2 mutant-like) tumours harboured inflammatory signalling and ongoing immunoediting, reflected in loss of HLA diversity and tumour infiltration with highly differentiated dysfunctional CD8 + T cells. By contrast, foldback-inversion-bearing tumours exhibited elevated immunosuppressive TGFβ signalling and immune exclusion, with predominantly naive/stem-like and memory T cells. Phenotypic state associations were specific to anatomical sites, highlighting compositional, topological and functional differences between adnexal tumours and distal peritoneal foci. Our findings implicate anatomical sites and mutational processes as determinants of evolutionary phenotypic divergence and immune resistance mechanisms in HGSOC. Our study provides a multi-omic cellular phenotype data substrate from which to develop and interpret future personalized immunotherapeutic approaches and early detection research. Multi-modal analysis of genomically unstable ovarian tumours characterizes the contribution of anatomical sites and mutational processes to evolutionary phenotypic divergence and immune resistance mechanisms.

Patients with high-grade serous ovarian carcinoma (HGSC) are usually diagnosed with advanced-stage disease, and the tumors often have immunosuppressive characteristics. Together, these factors are important for disease progression, drug resistance, and mortality. In this study, we used a combination of single-cell sequencing and spatial transcriptomics to identify the molecular mechanisms that lead to immunosuppression in HGSC. Primary tumors consistently showed a more active immune microenvironment than did omental tumors. In addition, we found that untreated primary tumors were mostly populated by dysfunctional CD4 and CD8 T cells in later stages of differentiation; this, in turn, was correlated with expression changes in the interferon α and γ pathways in epithelial cells, showing that cross-communication between the epithelial and immune compartments is important for immune suppression in HGSC. These findings could have implications for the design of clinical trials with immune-modulating drugs.

Patients with high-grade serous ovarian cancer suffer poor prognosis and variable response to treatment. Known prognostic factors for this disease include homologous recombination deficiency status, age, pathological stage and residual disease status after debulking surgery. Recent work has highlighted important prognostic information captured in computed tomography and histopathological specimens, which can be exploited through machine learning. However, little is known about the capacity of combining features from these disparate sources to improve prediction of treatment response. Here, we assembled a multimodal dataset of 444 patients with primarily late-stage high-grade serous ovarian cancer and discovered quantitative features, such as tumor nuclear size on staining with hematoxylin and eosin and omental texture on contrast-enhanced computed tomography, associated with prognosis. We found that these features contributed complementary prognostic information relative to one another and clinicogenomic features. By fusing histopathological, radiologic and clinicogenomic machine-learning models, we demonstrate a promising path toward improved risk stratification of patients with cancer through multimodal data integration.

Pre-existing and de novo genetic variants can both drive adaptation to environmental changes, but their relative contributions and interplay remain poorly understood. Here we investigated the evolutionary dynamics in drug-treated yeast populations with different levels of pre-existing variation by experimental evolution coupled with time-resolved sequencing and phenotyping. We found a doubling of pre-existing variation alone boosts the adaptation by 64.1% and 51.5% in hydroxyurea and rapamycin, respectively. The causative pre-existing and de novo variants were selected on shared targets: RNR4 in hydroxyurea and TOR1, TOR2 in rapamycin. Interestingly, the pre-existing and de novo TOR variants map to different functional domains and act via distinct mechanisms. The pre-existing TOR variants from two domesticated strains exhibited opposite rapamycin resistance effects, reflecting lineage-specific functional divergence. This study provides a dynamic view on how pre-existing and de novo variants interactively drive adaptation and deepens our understanding of clonally evolving populations.

Missense driver mutations in cancer are concentrated in a few hotspots 1 . Various mechanisms have been proposed to explain this skew, including biased mutational processes 2 , phenotypic differences 3 – 6 and immunoediting of neoantigens 7 , 8 ; however, to our knowledge, no existing model weighs the relative contribution of these features to tumour evolution. We propose a unified theoretical ‘free fitness’ framework that parsimoniously integrates multimodal genomic, epigenetic, transcriptomic and proteomic data into a biophysical model of the rate-limiting processes underlying the fitness advantage conferred on cancer cells by driver gene mutations. Focusing on TP53 , the most mutated gene in cancer 1 , we present an inference of mutant p53 concentration and demonstrate that TP53 hotspot mutations optimally solve an evolutionary trade-off between oncogenic potential and neoantigen immunogenicity. Our model anticipates patient survival in The Cancer Genome Atlas and patients with lung cancer treated with immunotherapy as well as the age of tumour onset in germline carriers of TP53 variants. The predicted differential immunogenicity between hotspot mutations was validated experimentally in patients with cancer and in a unique large dataset of healthy individuals. Our data indicate that immune selective pressure on TP53 mutations has a smaller role in non-cancerous lesions than in tumours, suggesting that targeted immunotherapy may offer an early prophylactic opportunity for the former. Determining the relative contribution of immunogenicity and oncogenic function to the selective advantage of hotspot mutations thus has important implications for both precision immunotherapies and our understanding of tumour evolution. A mathematical framework to estimate the fitness of cancer driver mutations by integrating mutational bias, oncogenicity and immunogenicity finds fundamental trade-offs in cancer evolution.

Subclonal reconstruction algorithms use bulk DNA sequencing data to quantify parameters of tumor evolution, allowing an assessment of how cancers initiate, progress and respond to selective pressures. We launched the ICGC–TCGA (International Cancer Genome Consortium–The Cancer Genome Atlas) DREAM Somatic Mutation Calling Tumor Heterogeneity and Evolution Challenge to benchmark existing subclonal reconstruction algorithms. This 7-year community effort used cloud computing to benchmark 31 subclonal reconstruction algorithms on 51 simulated tumors. Algorithms were scored on seven independent tasks, leading to 12,061 total runs. Algorithm choice influenced performance substantially more than tumor features but purity-adjusted read depth, copy-number state and read mappability were associated with the performance of most algorithms on most tasks. No single algorithm was a top performer for all seven tasks and existing ensemble strategies were unable to outperform the best individual methods, highlighting a key research need. All containerized methods, evaluation code and datasets are available to support further assessment of the determinants of subclonal reconstruction accuracy and development of improved methods to understand tumor evolution. Benchmarking of tumor subclonal reconstruction algorithms finds that interalgorithm variability overwhelms intertumor variability and identifies key quality metrics.