Spatial structure governs the mode of tumour evolution

Simulations probe the role of space in the interplay between drug-sensitive and drug-resistant cancer cells

The interplay between drug-sensitive and drug-resistant cancer cells has been observed to impact cell-to-cell interactions in experimental settings. However, the role that space plays in these interactions remains unclear. In this study, we develop mathematical models to investigate how spatial factors affect cell-to-cell competition between drug-sensitive and drug-resistant cancer cells in silico. We develop two baseline models to study cells from the epithelial FaDu cell line subjected to two drugs, specifically the ATR inhibitor ceralasertib and the PARP inhibitor olaparib, that target DNA damage response pathways. Our baseline models are: (1) a temporally resolved ordinary differential equation (ODE) model, and (2) a spatio-temporally resolved agent-based model (ABM). The models simulate cells in well-mixed and spatially structured cell systems, respectively. The ODE model is calibrated against in vitro data and is thereafter mapped onto the baseline ABM which, in turn, is extended to enable a simulation-based investigation on how spatial factors impact cell-to-cell competition. Simulation results from the extended ABMs demonstrate that the in silico treatment responses are simultaneously affected by: (i) the initial spatial cell configurations, (ii) the initial fraction of drug-resistant cells, (iii) the drugs to which cells express resistance, (iv) drug combinations, (v) drug doses, and (vi) the doubling time of drug-resistant cells compared to the doubling time of drug-sensitive cells. These results reveal that spatial structures of the simulated cancer cells affect both cell-to-cell interactions, and the impact that these interactions have on the ensuing population dynamics. This leads us to suggest that the role that space plays in cell-to-cell interactions should be further investigated and quantified in experimental settings.

From morphology to single-cell molecules: high-resolution 3D histology in biomedicine

High-resolution three-dimensional (3D) tissue analysis has emerged as a transformative innovation in the life sciences, providing detailed insights into the spatial organization and molecular composition of biological tissues. This review begins by tracing the historical milestones that have shaped the development of high-resolution 3D histology, highlighting key breakthroughs that have facilitated the advancement of current technologies. We then systematically categorize the various families of high-resolution 3D histology techniques, discussing their core principles, capabilities, and inherent limitations. These 3D histology techniques include microscopy imaging, tomographic approaches, single-cell and spatial omics, computational methods and 3D tissue reconstruction (e.g. 3D cultures and spheroids). Additionally, we explore a wide range of applications for single-cell 3D histology, demonstrating how single-cell and spatial technologies are being utilized in the fields such as oncology, cardiology, neuroscience, immunology, developmental biology and regenerative medicine. Despite the remarkable progress made in recent years, the field still faces significant challenges, including high barriers to entry, issues with data robustness, ambiguous best practices for experimental design, and a lack of standardization across methodologies. This review offers a thorough analysis of these challenges and presents recommendations to surmount them, with the overarching goal of nurturing ongoing innovation and broader integration of cellular 3D tissue analysis in both biology research and clinical practice.

Ultra-deep sequencing of somatic mutations induced by a maize transposon

Cells accumulate mutations throughout development, contributing to cancer, aging, and evolution. Quantitative data on the abundance of de novo mutations within plants or animals are limited, as new mutations are often rare within a tissue and fall below the limits of current sequencing depths and error rates. Here, we show that mutations induced by the maize Mutator (Mu) transposon can be reliably quantified down to a detection limit of 1 part in 12,000. We measured the abundance of millions of de novo Mu insertions across four tissue types. Within a tissue, the distribution of de novo Mu allele frequencies was highly reproducible between plants, showing that, despite the stochastic nature of mutation, repeated statistical patterns of mutation abundance emerge. In contrast, there were significant differences in the allele frequency distribution between tissues. At the extremes, root was dominated by a small number of highly abundant de novo insertions, while endosperm was characterized by thousands of insertions at low allele frequencies. Finally, we used the measured pollen allele frequencies to reinterpret a classic genetic experiment, showing that evidence for late Mu activity in pollen are better explained by cell division statistics. These results provide insight into the complexity of mutation accumulation in multicellular organisms and a system to interrogate the factors that shape mutation abundance.

Evolutionary rescue model informs strategies for driving cancer cell populations to extinction

Cancers exhibit a remarkable ability to develop resistance to a range of treatments, often resulting in relapse following first-line therapies and significantly worse outcomes for subsequent treatments. While our understanding of the mechanisms and dynamics of the emergence of resistance during cancer therapy continues to advance, questions remain about how to minimize the probability that resistance will evolve, thereby improving long-term patient outcomes. Here, we present an evolutionary simulation model of a clonal population of cells that can acquire resistance mutations to one or more treatments. We leverage this model to examine the efficacy of a two-strike "extinction therapy" protocol, in which two treatments are applied sequentially to first contract the population to a vulnerable state and then push it to extinction, and compare it to a combination therapy protocol. We investigate how factors such as the timing of the switch between the two strikes, the rate of emergence of resistant mutations, the doses of the applied drugs, the presence of cross-resistance, and whether resistance is a binary or a quantitative trait affect the outcome. Our results show that the timing of switching to the second strike has a marked effect on the likelihood of driving the cancer to extinction, and that extinction therapy outperforms combination therapy when cross-resistance is present. We conduct an in silico trial that reveals when and why a second strike will succeed or fail. Finally, we demonstrate that our conclusions hold whether we model resistance as a binary trait or as a quantitative, multi-locus trait.

Establishment of a locally adaptive allele in multidimensional continuous space

Local adaptation is widely seen when species adapt to spatially heterogeneous environments. Although many theoretical studies have investigated the dynamics of local adaptation using 2-population models, there remains a need to extend the theoretical framework to continuous space settings, reflecting the real habitats of species. In this study, we use a multidimensional continuous space model and mathematically analyze the establishment process of local adaptation, with a specific emphasis on the relative roles of mutation and migration. First, the role of new mutations is evaluated by deriving the establishment probability of a locally adapted mutation using a branching process and a diffusion approximation. Next, the contribution of immigrants from a neighboring region with similar environmental conditions is considered. Theoretical predictions of the local adaptation rate agreed with the results of Wright-Fisher simulations in both mutation-driven and migration-driven cases. Evolutionary dynamics depend on several factors, including the strength of migration and selection, population density, habitat size, and spatial dimensions. These results offer a theoretical framework for assessing whether mutation or migration predominantly drives convergent local adaptation in spatially continuous environments in the presence of patchy regions with similar environmental conditions.

A new universal system of tree shape indices

The comparison and categorization of tree diagrams is fundamental to large parts of biology, linguistics, computer science, and other fields, yet the indices currently applied to describing tree shape have important flaws that complicate their interpretation and limit their scope. Here we introduce a new system of indices with no such shortcomings. Our indices account for node sizes and branch lengths and are robust to small changes in either attribute. Unlike currently popular phylogenetic diversity, phylogenetic entropy, and tree balance indices, our definitions assign interpretable values to all rooted trees and enable meaningful comparison of any pair of trees. Our self-consistent definitions further unite measures of diversity, richness, balance, symmetry, effective height, effective outdegree, and effective branch count in a coherent system, and we derive numerous simple relationships between these indices. The main practical advantages of our indices are in 1) quantifying diversity in non-ultrametric trees; 2) assessing the balance of trees that have non-uniform branch lengths or node sizes; 3) comparing the balance of trees with different leaf counts or outdegrees; 4) obtaining a coherent, generic, multidimensional quantification of tree shape that is robust to sampling error and inferential error. We illustrate these features by comparing the shapes of trees representing the evolution of HIV and of Uralic languages, and trees generated by computational models of tumour evolution. Given the ubiquity of tree structures, we identify a wide range of applications across diverse domains.

Inferring allele-specific copy number aberrations and tumor phylogeography from spatially resolved transcriptomics

Analyzing somatic evolution within a tumor over time and across space is a key challenge in cancer research. Spatially resolved transcriptomics (SRT) measures gene expression at thousands of spatial locations in a tumor, but does not directly reveal genomic aberrations. We introduce CalicoST, an algorithm to simultaneously infer allele-specific copy number aberrations (CNAs) and reconstruct spatial tumor evolution, or phylogeography, from SRT data. CalicoST identifies important classes of CNAs-including copy-neutral loss of heterozygosity and mirrored subclonal CNAs-that are invisible to total copy number analysis. Using nine patients' data from the Human Tumor Atlas Network, CalicoST achieves an average accuracy of 86%, approximately 21% higher than existing methods. CalicoST reconstructs a tumor phylogeography in three-dimensional space for two patients with multiple adjacent slices. CalicoST analysis of multiple SRT slices from a cancerous prostate organ reveals mirrored subclonal CNAs on the two sides of the prostate, forming a bifurcating phylogeography in both genetic and physical space.

High-density sampling reveals volume growth in human tumours

In growing cell populations such as tumours, mutations can serve as markers that allow tracking the past evolution from current samples. The genomic analyses of bulk samples and samples from multiple regions have shed light on the evolutionary forces acting on tumours. However, little is known empirically on the spatio-temporal dynamics of tumour evolution. Here, we leverage published data from resected hepatocellular carcinomas, each with several hundred samples taken in two and three dimensions. Using spatial metrics of evolution, we find that tumour cells grow predominantly uniformly within the tumour volume instead of at the surface. We determine how mutations and cells are dispersed throughout the tumour and how cell death contributes to the overall tumour growth. Our methods shed light on the early evolution of tumours in vivo and can be applied to high-resolution data in the emerging field of spatial biology.

Tumor architecture and emergence of strong genetic alterations are bottlenecks for clonal evolution in primary prostate cancer

Prostate cancer (PCA) exhibits high levels of intratumoral heterogeneity. In this study, we developed a mathematical model to study the growth and genetic evolution of PCA. We explored the possible evolutionary patterns and demonstrated that tumor architecture represents a major bottleneck for divergent clonal evolution. Early consecutive acquisition of strong genetic alterations serves as a proxy for the formation of aggressive tumors. A limited number of clonal hierarchy patterns were identified. A biopsy study of synthetic tumors shows complex spatial intermixing of clones and delineates the importance of biopsy extent. Deep whole-exome multiregional next-generation DNA sequencing of the primary tumors from five patients was performed to validate the results, supporting our main findings from mathematical modeling. In conclusion, our model provides qualitatively realistic predictions of PCA genomic evolution, closely aligned with the evidence available from patient samples. We share the code of the model for further studies. A record of this paper's transparent peer review process is included in the supplemental information.

Single-cell and spatial omics unravel the spatiotemporal biology of tumour border invasion and haematogenous metastasis

Solid tumours exhibit a well-defined architecture, comprising a differentiated core and a dynamic border that interfaces with the surrounding tissue. This border, characterised by distinct cellular morphology and molecular composition, serves as a critical determinant of the tumour's invasive behaviour. Notably, the invasive border of the primary tumour represents the principal site for intravasation of metastatic cells. These cells, known as circulating tumour cells (CTCs), function as 'seeds' for distant dissemination and display remarkable heterogeneity. Advancements in spatial sequencing technology are progressively unveiling the spatial biological features of tumours. However, systematic investigations specifically targeting the characteristics of the tumour border remain scarce. In this comprehensive review, we illuminate key biological insights along the tumour body-border-haematogenous metastasis axis over the past five years. We delineate the distinctive landscape of tumour invasion boundaries and delve into the intricate heterogeneity and phenotype of CTCs, which orchestrate haematogenous metastasis. These insights have the potential to explain the basis of tumour invasion and distant metastasis, offering new perspectives for the development of more complex and precise clinical interventions and treatments.

Spatial interactions modulate tumor growth and immune infiltration

Direct observation of tumor-immune interactions is unlikely in tumors with currently available technology, but computational simulations based on clinical data can provide insight to test hypotheses. It is hypothesized that patterns of collagen evolve as a mechanism of immune escape, but the exact nature of immune-collagen interactions is poorly understood. Spatial data quantifying collagen fiber alignment in squamous cell carcinomas indicates that late-stage disease is associated with highly aligned fibers. Our computational modeling framework discriminates between two hypotheses: immune cell migration that moves (1) parallel or (2) perpendicular to collagen fiber orientation. The modeling recapitulates immune-extracellular matrix interactions where collagen patterns provide immune protection, leading to an emergent inverse relationship between disease stage and immune coverage. Here, computational modeling provides important mechanistic insights by defining a kernel cell-cell interaction function that considers a spectrum of local (cell-scale) to global (tumor-scale) spatial interactions. Short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects, while asymmetric tumor-immune interaction kernels lead to poor immune response. Thus, the length scale of tumor-immune interaction kernels drives tumor growth and infiltration.

Minimal cellular automaton model with heterogeneous cell sizes predicts epithelial colony growth

Regulation of cell proliferation is a crucial aspect of tissue development and homeostasis and plays a major role in morphogenesis, wound healing, and tumor invasion. A phenomenon of such regulation is contact inhibition, which describes the dramatic slowing of proliferation, cell migration and individual cell growth when multiple cells are in contact with each other. While many physiological, molecular and genetic factors are known, the mechanism of contact inhibition is still not fully understood. In particular, the relevance of cellular signaling due to interfacial contact for contact inhibition is still debated. Cellular automata (CA) have been employed in the past as numerically efficient mathematical models to study the dynamics of cell ensembles, but they are not suitable to explore the origins of contact inhibition as such agent-based models assume fixed cell sizes. We develop a minimal, data-driven model to simulate the dynamics of planar cell cultures by extending a probabilistic CA to incorporate size changes of individual cells during growth and cell division. We successfully apply this model to previous in-vitro experiments on contact inhibition in epithelial tissue: After a systematic calibration of the model parameters to measurements of single-cell dynamics, our CA model quantitatively reproduces independent measurements of emergent, culture-wide features, like colony size, cell density and collective cell migration. In particular, the dynamics of the CA model also exhibit the transition from a low-density confluent regime to a stationary postconfluent regime with a rapid decrease in cell size and motion. This implies that the volume exclusion principle, a mechanical constraint which is the only inter-cellular interaction incorporated in the model, paired with a size-dependent proliferation rate is sufficient to generate the observed contact inhibition. We discuss how our approach enables the introduction of effective bio-mechanical interactions in a CA framework for future studies.

Crosstalk between tumor and microenvironment: Insights from spatial transcriptomics

Cancer is a dynamic disease, and clonal heterogeneity plays a fundamental role in tumor development, progression, and resistance to therapies. Single-cell and spatial multimodal technologies can provide a high-resolution molecular map of underlying genomic, epigenomic, and transcriptomic alterations involved in inter- and intra-tumor heterogeneity and interactions with the microenvironment. In this review, we provide a perspective on factors driving cancer heterogeneity, tumor evolution, and clonal states. We briefly describe spatial transcriptomic technologies and summarize recent literature that sheds light on the dynamical interactions between tumor states, cell-to-cell communication, and remodeling local microenvironment.

Oncotree2vec - a method for embedding and clustering of tumor mutation trees

MOTIVATION

Understanding the genomic heterogeneity of tumors is an important task in computational oncology, especially in the context of finding personalized treatments based on the genetic profile of each patient's tumor. Tumor clustering that takes into account the temporal order of genetic events, as represented by tumor mutation trees, is a powerful approach for grouping together patients with genetically and evolutionarily similar tumors and can provide insights into discovering tumor subtypes, for more accurate clinical diagnosis and prognosis.

RESULTS

Here, we propose oncotree2vec, a method for clustering tumor mutation trees by learning vector representations of mutation trees that capture the different relationships between subclones in an unsupervised manner. Learning low-dimensional tree embeddings facilitates the visualization of relations between trees in large cohorts and can be used for downstream analyses, such as deep learning approaches for single-cell multi-omics data integration. We assessed the performance and the usefulness of our method in three simulation studies and on two real datasets: a cohort of 43 trees from six cancer types with different branching patterns corresponding to different modes of spatial tumor evolution and a cohort of 123 AML mutation trees.

AVAILABILITY AND IMPLEMENTATION

https://github.com/cbg-ethz/oncotree2vec.

Nucleic acid-based drugs for patients with solid tumours

The treatment of patients with advanced-stage solid tumours typically involves a multimodality approach (including surgery, chemotherapy, radiotherapy, targeted therapy and/or immunotherapy), which is often ultimately ineffective. Nucleic acid-based drugs, either as monotherapies or in combination with standard-of-care therapies, are rapidly emerging as novel treatments capable of generating responses in otherwise refractory tumours. These therapies include those using viral vectors (also referred to as gene therapies), several of which have now been approved by regulatory agencies, and nanoparticles containing mRNAs and a range of other nucleotides. In this Review, we describe the development and clinical activity of viral and non-viral nucleic acid-based treatments, including their mechanisms of action, tolerability and available efficacy data from patients with solid tumours. We also describe the effects of the tumour microenvironment on drug delivery for both systemically administered and locally administered agents. Finally, we discuss important trends resulting from ongoing clinical trials and preclinical testing, and manufacturing and/or stability considerations that are expected to underpin the next generation of nucleic acid agents for patients with solid tumours.

LinG3D: visualizing the spatio-temporal dynamics of clonal evolution

BACKGROUND

Cancers are spatially heterogenous, thus their clonal evolution, especially following anti-cancer treatments, depends on where the mutated cells are located within the tumor tissue. For example, cells exposed to different concentrations of drugs, such as cells located near the vessels in contrast to those residing far from the vasculature, can undergo a different evolutionary path. However, classical representations of cell lineage trees do not account for this spatial component of emerging cancer clones. Here, we propose routines to trace spatial and temporal clonal evolution in computer simulations of the tumor evolution models.

RESULTS

The LinG3D (Lineage Graphs in 3D) is an open-source collection of routines (in MATLAB, Python, and R) that enables spatio-temporal visualization of clonal evolution in a two-dimensional tumor slice from computer simulations of the tumor evolution models. These routines draw traces of tumor clones in both time and space, and may include a projection of a selected microenvironmental factor, such as the drug or oxygen distribution within the tumor, if such a microenvironmental factor is used in the tumor evolution model. The utility of LinG3D has been demonstrated through examples of simulated tumors with different number of clones and, additionally, in experimental colony growth assay.

CONCLUSIONS

This routine package extends the classical lineage trees, that show cellular clone relationships in time, by adding the space component to show the locations of cellular clones within the 2D tumor tissue patch from computer simulations of tumor evolution models.

Spatial interactions modulate tumor growth and immune infiltration

Lenia, a cellular automata framework used in artificial life, provides a natural setting to implement mathematical models of cancer incorporating features such as morphogenesis, homeostasis, motility, reproduction, growth, stimuli response, evolvability, and adaptation. Historically, agent-based models of cancer progression have been constructed with rules that govern birth, death and migration, with attempts to map local rules to emergent global growth dynamics. In contrast, Lenia provides a flexible framework for considering a spectrum of local (cell-scale) to global (tumor-scale) dynamics by defining an interaction kernel governing density-dependent growth dynamics. Lenia can recapitulate a range of cancer model classifications including local or global, deterministic or stochastic, non-spatial or spatial, single or multi-population, and off or on-lattice. Lenia is subsequently used to develop data-informed models of 1) single-population growth dynamics, 2) multi-population cell-cell competition models, and 3) cell migration or chemotaxis. Mathematical modeling provides important mechanistic insights. First, short-range interaction kernels provide a mechanism for tumor cell survival under conditions with strong Allee effects. Next, we find that asymmetric interaction tumor-immune kernels lead to poor immune response. Finally, modeling recapitulates immune-ECM interactions where patterns of collagen formation provide immune protection, indicated by an emergent inverse relationship between disease stage and immune coverage.

Selective sweep probabilities in spatially expanding populations

Evolution during range expansions shapes biological systems from microbial communities and tumours up to invasive species. A fundamental question is whether, when a beneficial mutation arises during a range expansion, it will evade clonal interference and sweep through the population to fixation. However, most theoretical investigations of range expansions have been confined to regimes in which selective sweeps are effectively impossible, while studies of selective sweeps have either assumed constant population size or have ignored spatial structure. Here we use mathematical modelling and analysis to investigate selective sweep probabilities in the alternative yet biologically relevant scenario in which mutants can outcompete and displace a slowly spreading wildtype. Assuming constant radial expansion speed, we derive probability distributions for the arrival time and location of the first surviving mutant and hence find surprisingly simple approximate and exact expressions for selective sweep probabilities in one, two and three dimensions, which are independent of mutation rate. Namely, the selective sweep probability is approximately 1 - c w t / c m d , where c w t and c m are the wildtype and mutant radial expansion speeds, and d the spatial dimension. Using agent-based simulations, we show that our analytical results accurately predict selective sweep frequencies in the two-dimensional spatial Moran process. We further compare our results with those obtained for alternative growth laws. Parameterizing our model for human tumours, we find that selective sweeps are predicted to be rare except during very early solid tumour growth, thus providing a general, pan-cancer explanation for findings from recent sequencing studies.

A seven-step guide to spatial, agent-based modelling of tumour evolution

Spatial agent-based models are frequently used to investigate the evolution of solid tumours subject to localized cell-cell interactions and microenvironmental heterogeneity. As spatial genomic, transcriptomic and proteomic technologies gain traction, spatial computational models are predicted to become ever more necessary for making sense of complex clinical and experimental data sets, for predicting clinical outcomes, and for optimizing treatment strategies. Here we present a non-technical step by step guide to developing such a model from first principles. Stressing the importance of tailoring the model structure to that of the biological system, we describe methods of increasing complexity, from the basic Eden growth model up to off-lattice simulations with diffusible factors. We examine choices that unavoidably arise in model design, such as implementation, parameterization, visualization and reproducibility. Each topic is illustrated with examples drawn from recent research studies and state of the art modelling platforms. We emphasize the benefits of simpler models that aim to match the complexity of the phenomena of interest, rather than that of the entire biological system. Our guide is aimed at both aspiring modellers and other biologists and oncologists who wish to understand the assumptions and limitations of the models on which major cancer studies now so often depend.

Substrate geometry affects population dynamics in a bacterial biofilm

Biofilms inhabit a range of environments, such as dental plaques or soil micropores, often characterized by noneven surfaces. However, the impact of surface irregularities on the population dynamics of biofilms remains elusive, as most experiments are conducted on flat surfaces. Here, we show that the shape of the surface on which a biofilm grows influences genetic drift and selection within the biofilm. We culture Escherichia coli biofilms in microwells with a corrugated bottom surface and observe the emergence of clonal sectors whose size corresponds to that of the corrugations, despite no physical barrier separating different areas of the biofilm. The sectors are remarkably stable and do not invade each other; we attribute this stability to the characteristics of the velocity field within the biofilm, which hinders mixing and clonal expansion. A microscopically detailed computer model fully reproduces these findings and highlights the role of mechanical interactions such as adhesion and friction in microbial evolution. The model also predicts clonal expansion to be limited even for clones with a significant growth advantage-a finding which we confirm experimentally using a mixture of antibiotic-sensitive and antibiotic-resistant mutants in the presence of sublethal concentrations of the antibiotic rifampicin. The strong suppression of selection contrasts sharply with the behavior seen in range expansion experiments in bacterial colonies grown on agar. Our results show that biofilm population dynamics can be affected by patterning the surface and demonstrate how a better understanding of the physics of bacterial growth can be used to control microbial evolution.

Tumor phylogeography reveals block-shaped spatial heterogeneity and the mode of evolution in Hepatocellular Carcinoma

Solid tumors are complex ecosystems with heterogeneous 3D structures, but the spatial intra-tumor heterogeneity (sITH) at the macroscopic (i.e., whole tumor) level is under-explored. Using a phylogeographic approach, we sequence genomes and transcriptomes from 235 spatially informed sectors across 13 hepatocellular carcinomas (HCC), generating one of the largest datasets for studying sITH. We find that tumor heterogeneity in HCC segregates into spatially variegated blocks with large genotypic and phenotypic differences. By dissecting the transcriptomic heterogeneity, we discover that 30% of patients had a "spatially competing distribution" (SCD), where different spatial blocks have distinct transcriptomic subtypes co-existing within a tumor, capturing the critical transition period in disease progression. Interestingly, the tumor regions with more advanced transcriptomic subtypes (e.g., higher cell cycle) often take clonal dominance with a wider geographic range, rejecting neutral evolution for SCD patients. Extending the statistical tests for detecting natural selection to many non-SCD patients reveal varying levels of selective signal across different tumors, implying that many evolutionary forces including natural selection and geographic isolation can influence the overall pattern of sITH. Taken together, tumor phylogeography unravels a dynamic landscape of sITH, pinpointing important evolutionary and clinical consequences of spatial heterogeneity in cancer.

Visualizing the Spatio-Temporal Dynamics of Clonal Evolution with LinG3D software

Cancer clonal evolution, especially following anti-cancer treatments, depends on the locations of the mutated cells within the tumor tissue. Cells near the vessels, exposed to higher concentrations of drugs, will undergo a different evolutionary path than cells residing far from the vasculature in the areas of lower drug levels. However, classical representations of cell lineage trees do not account for this spatial component of emerging cancer clones. Here, we propose the LinG3D (Lineage Graphs in 3D) algorithms to trace clonal evolution in space and time. These are an open-source collection of routines (in MATLAB, Python, and R) that enables spatio-temporal visualization of clonal evolution in a two-dimensional tumor slice from computer simulations of the tumor evolution models. These routines draw traces of tumor clones in both time and space, with an option to include a projection of a selected microenvironmental factor, such as the drug or oxygen distribution within the tumor. The utility of LinG3D has been demonstrated through examples of simulated tumors with different number of clones and, additionally, in experimental colony growth assay. This routine package extends the classical lineage trees, that show cellular clone relationships in time, by adding the space component to show the locations of cellular clones within the 2D tumor tissue patch from computer simulations of tumor evolution models.

Tumour Growth Mechanisms Determine Effectiveness of Adaptive Therapy in Glandular Tumours

In cancer treatment, adaptive therapy holds promise for delaying the onset of recurrence through regulating the competition between drug-sensitive and drug-resistant cells. Adaptive therapy has been studied in well-mixed models assuming free mixing of all cells and spatial models considering the interactions of single cells with their immediate adjacent cells. Both models do not reflect the spatial structure in glandular tumours where intra-gland cellular interaction is high, while inter-gland interaction is limited. Here, we use mathematical modelling to study the effects of adaptive therapy on glandular tumours that expand using either glandular fission or invasive growth. A two-dimensional, lattice-based model of sites containing sensitive and resistant cells within individual glands is developed to study the evolution of glandular tumour cells under continuous and adaptive therapies. We found that although both growth models benefit from adaptive therapy's ability to prevent recurrence, invasive growth benefits more from it than fission growth. This difference is due to the migration of daughter cells into neighboring glands that is absent in fission but present in invasive growth. The migration resulted in greater mixing of cells, enhancing competition induced by adaptive therapy. By varying the initial spatial spread and location of the resistant cells within the tumour, we found that modifying the conditions within the resistant cells containing glands affect both fission and invasive growth. However, modifying the conditions surrounding these glands affect invasive growth only. Our work reveals the interplay between growth mechanism and tumour topology in modulating the effectiveness of cancer therapy.

Modeling the Effect of Spatial Structure on Solid Tumor Evolution and Circulating Tumor DNA Composition

Circulating tumor DNA (ctDNA) monitoring, while sufficiently advanced to reflect tumor evolution in real time and inform cancer diagnosis, treatment, and prognosis, mainly relies on DNA that originates from cell death via apoptosis or necrosis. In solid tumors, chemotherapy and immune infiltration can induce spatially variable rates of cell death, with the potential to bias and distort the clonal composition of ctDNA. Using a stochastic evolutionary model of boundary-driven growth, we study how elevated cell death on the edge of a tumor can simultaneously impact driver mutation accumulation and the representation of tumor clones and mutation detectability in ctDNA. We describe conditions in which invasive clones are over-represented in ctDNA, clonal diversity can appear elevated in the blood, and spatial bias in shedding can inflate subclonal variant allele frequencies (VAFs). Additionally, we find that tumors that are mostly quiescent can display similar biases but are far less detectable, and the extent of perceptible spatial bias strongly depends on sequence detection limits. Overall, we show that spatially structured shedding might cause liquid biopsies to provide highly biased profiles of tumor state. While this may enable more sensitive detection of expanding clones, it could also increase the risk of targeting a subclonal variant for treatment. Our results indicate that the effects and clinical consequences of spatially variable cell death on ctDNA composition present an important area for future work.

Mapping cancer biology in space: applications and perspectives on spatial omics for oncology

Technologies to decipher cellular biology, such as bulk sequencing technologies and single-cell sequencing technologies, have greatly assisted novel findings in tumor biology. Recent findings in tumor biology suggest that tumors construct architectures that influence the underlying cancerous mechanisms. Increasing research has reported novel techniques to map the tissue in a spatial context or targeted sampling-based characterization and has introduced such technologies to solve oncology regarding tumor heterogeneity, tumor microenvironment, and spatially located biomarkers. In this study, we address spatial technologies that can delineate the omics profile in a spatial context, novel findings discovered via spatial technologies in oncology, and suggest perspectives regarding therapeutic approaches and further technological developments.

Mutation divergence over space in tumour expansion

Mutation accumulation in tumour evolution is one major cause of intra-tumour heterogeneity (ITH), which often leads to drug resistance during treatment. Previous studies with multi-region sequencing have shown that mutation divergence among samples within the patient is common, and the importance of spatial sampling to obtain a complete picture in tumour measurements. However, quantitative comparisons of the relationship between mutation heterogeneity and tumour expansion modes, sampling distances as well as the sampling methods are still few. Here, we investigate how mutations diverge over space by varying the sampling distance and tumour expansion modes using individual-based simulations. We measure ITH by the Jaccard index between samples and quantify how ITH increases with sampling distance, the pattern of which holds in various sampling methods and sizes. We also compare the inferred mutation rates based on the distributions of variant allele frequencies under different tumour expansion modes and sampling sizes. In exponentially fast expanding tumours, a mutation rate can always be inferred for any sampling size. However, the accuracy compared with the true value decreases when the sampling size decreases, where small sampling sizes result in a high estimate of the mutation rate. In addition, such an inference becomes unreliable when the tumour expansion is slow, such as in surface growth.

Growth Dynamics of Ductal Carcinoma in Situ Recapitulate Normal Breast Development

Ductal carcinoma in situ (DCIS) and invasive breast cancer share many morphologic, proteomic, and genomic alterations. Yet in contrast to invasive cancer, many DCIS tumors do not progress and may remain indolent over decades. To better understand the heterogenous nature of this disease, we reconstructed the growth dynamics of 18 DCIS tumors based on the geo-spatial distribution of their somatic mutations. The somatic mutation topographies revealed that DCIS is multiclonal and consists of spatially discontinuous subclonal lesions. Here we show that this pattern of spread is consistent with a new 'Comet' model of DCIS tumorigenesis, whereby multiple subclones arise early and nucleate the buds of the growing tumor. The discontinuous, multiclonal growth of the Comet model is analogous to the branching morphogenesis of normal breast development that governs the rapid expansion of the mammary epithelium during puberty. The branching morphogenesis-like dynamics of the proposed Comet model diverges from the canonical model of clonal evolution, and better explains observed genomic spatial data. Importantly, the Comet model allows for the clinically relevant scenario of extensive DCIS spread, without being subjected to the selective pressures of subclone competition that promote the emergence of increasingly invasive phenotypes. As such, the normal cell movement inferred during DCIS growth provides a new explanation for the limited risk of progression in DCIS and adds biologic rationale for ongoing clinical efforts to reduce DCIS overtreatment.

Single-cell phylogenies reveal changes in the evolutionary rate within cancer and healthy tissues

Cell lineages accumulate somatic mutations during organismal development, potentially leading to pathological states. The rate of somatic evolution within a cell population can vary due to multiple factors, including selection, a change in the mutation rate, or differences in the microenvironment. Here, we developed a statistical test called the Poisson Tree (PT) test to detect varying evolutionary rates among cell lineages, leveraging the phylogenetic signal of single-cell DNA sequencing (scDNA-seq) data. We applied the PT test to 24 healthy and cancer samples, rejecting a constant evolutionary rate in 11 out of 15 cancer and five out of nine healthy scDNA-seq datasets. In six cancer datasets, we identified subclonal mutations in known driver genes that could explain the rate accelerations of particular cancer lineages. Our findings demonstrate the efficacy of scDNA-seq for studying somatic evolution and suggest that cell lineages often evolve at different rates within cancer and healthy tissues.

Modeling the effect of acquired resistance on cancer therapy outcomes

Adaptive therapy (AT) is an evolution-based treatment strategy that exploits cell-cell competition. Acquired resistance can change the competitive nature of cancer cells in a tumor, impacting AT outcomes. We aimed to determine if adaptive therapy can still be effective with cell's acquiring resistance. We developed an agent-based model for spatial tumor growth considering three different types of acquired resistance: random genetic mutations during cell division, drug-induced reversible (plastic) phenotypic changes, and drug-induced irreversible phenotypic changes. These three resistance mechanisms lead to different spatial distributions of resistant cells. To quantify the spatial distribution, we propose an extension of Ripley's K-function, Sampled Ripley's K-function (SRKF), which calculates the non-randomness of the resistance distribution over the tumor domain. Our model predicts that the emergent spatial distribution of resistance can determine the time to progression under both adaptive and continuous therapy (CT). Notably, a high rate of random genetic mutations leads to quicker progression under AT than CT due to the emergence of many small clumps of resistant cells. Drug-induced phenotypic changes accelerate tumor progression irrespective of the treatment strategy. Low-rate switching to a sensitive state reduces the benefits of AT compared to CT. Furthermore, we also demonstrated that drug-induced resistance necessitates aggressive treatment under CT, regardless of the presence of cancer-associated fibroblasts. However, there is an optimal dose that can most effectively delay tumor relapse under AT by suppressing resistance. In conclusion, this study demonstrates that diverse resistance mechanisms can shape the distribution of resistance and thus determine the efficacy of adaptive therapy.

Adaptive therapy achieves long-term control of chemotherapy resistance in high grade ovarian cancer

Drug resistance results in poor outcomes for most patients with metastatic cancer. Adaptive Therapy (AT) proposes to address this by exploiting presumed fitness costs incurred by drug-resistant cells when drug is absent, and prescribing dose reductions to allow fitter, sensitive cells to re-grow and re-sensitise the tumour. However, empirical evidence for treatment-induced fitness change is lacking. We show that fitness costs in chemotherapy-resistant ovarian cancer cause selective decline and apoptosis of resistant populations in low-resource conditions. Moreover, carboplatin AT caused fluctuations in sensitive/resistant tumour population size in vitro and significantly extended survival of tumour-bearing mice. In sequential blood-derived cell-free DNA and tumour samples obtained longitudinally from ovarian cancer patients during treatment, we inferred resistant cancer cell population size through therapy and observed it correlated strongly with disease burden. These data have enabled us to launch a multicentre, phase 2 randomised controlled trial (ACTOv) to evaluate AT in ovarian cancer.

Unraveling the Drivers of Tumorigenesis in the Context of Evolution: Theoretical Models and Bioinformatics Tools

Cancer originates from somatic cells that have accumulated mutations. These mutations alter the phenotype of the cells, allowing them to escape homeostatic regulation that maintains normal cell numbers. The emergence of malignancies is an evolutionary process in which the random accumulation of somatic mutations and sequential selection of dominant clones cause cancer cells to proliferate. The development of technologies such as high-throughput sequencing has provided a powerful means to measure subclonal evolutionary dynamics across space and time. Here, we review the patterns that may be observed in cancer evolution and the methods available for quantifying the evolutionary dynamics of cancer. An improved understanding of the evolutionary trajectories of cancer will enable us to explore the molecular mechanism of tumorigenesis and to design tailored treatment strategies.

Toward a systems-level probing of tumor clonality

Cancer has been described as a genetic disease that clonally evolves in the face of selective pressures imposed by cell-intrinsic and extrinsic factors. Although classical models based on genetic data predominantly propose Darwinian mechanisms of cancer evolution, recent single-cell profiling of cancers has described unprecedented heterogeneity in tumors providing support for alternative models of branched and neutral evolution through both genetic and non-genetic mechanisms. Emerging evidence points to a complex interplay between genetic, non-genetic, and extrinsic environmental factors in shaping the evolution of tumors. In this perspective, we briefly discuss the role of cell-intrinsic and extrinsic factors that shape clonal behaviors during tumor progression, metastasis, and drug resistance. Taking examples of pre-malignant states associated with hematological malignancies and esophageal cancer, we discuss recent paradigms of tumor evolution and prospective approaches to further enhance our understanding of this spatiotemporally regulated process.

Spatial Positioning of Immune Hotspots Reflects the Interplay between B and T Cells in Lung Squamous Cell Carcinoma

Beyond tertiary lymphoid structures, a significant number of immune-rich areas without germinal center-like structures are observed in non-small cell lung cancer. Here, we integrated transcriptomic data and digital pathology images to study the prognostic implications, spatial locations, and constitution of immune rich areas (immune hotspots) in a cohort of 935 patients with lung cancer from The Cancer Genome Atlas. A high intratumoral immune hotspot score, which measures the proportion of immune hotspots interfacing with tumor islands, was correlated with poor overall survival in lung squamous cell carcinoma but not in lung adenocarcinoma. Lung squamous cell carcinomas with high intratumoral immune hotspot scores were characterized by consistent upregulation of B-cell signatures. Spatial statistical analyses conducted on serial multiplex IHC slides further revealed that only 4.87% of peritumoral immune hotspots and 0.26% of intratumoral immune hotspots were tertiary lymphoid structures. Significantly lower densities of CD20+CXCR5+ and CD79b+ B cells and less diverse immune cell interactions were found in intratumoral immune hotspots compared with peritumoral immune hotspots. Furthermore, there was a negative correlation between the percentages of CD8+ T cells and T regulatory cells in intratumoral but not in peritumoral immune hotspots, with tertiary lymphoid structures excluded. These findings suggest that the intratumoral immune hotspots reflect an immunosuppressive niche compared with peritumoral immune hotspots, independent of the distribution of tertiary lymphoid structures. A balance toward increased intratumoral immune hotspots is indicative of a compromised antitumor immune response and poor outcome in lung squamous cell carcinoma.

SIGNIFICANCE

Intratumoral immune hotspots beyond tertiary lymphoid structures reflect an immunosuppressive microenvironment, different from peritumoral immune hotspots, warranting further study in the context of immunotherapies.

Agent-based methods facilitate integrative science in cancer

In this opinion, we highlight agent-based modeling as a key tool for exploration of cell-cell and cell-environment interactions that drive cancer progression, therapeutic resistance, and metastasis. These biological phenomena are particularly suited to be captured at the cell-scale resolution possible only within agent-based or individual-based mathematical models. These modeling approaches complement experimental work (in vitro and in vivo systems) through parameterization and data extrapolation but also feed forward to drive new experiments that test model-generated predictions.

State-dependent evolutionary models reveal modes of solid tumour growth

Spatial properties of tumour growth have profound implications for cancer progression, therapeutic resistance and metastasis. Yet, how spatial position governs tumour cell division remains difficult to evaluate in clinical tumours. Here, we demonstrate that faster division on the tumour periphery leaves characteristic genetic patterns, which become evident when a phylogenetic tree is reconstructed from spatially sampled cells. Namely, rapidly dividing peripheral lineages branch more extensively and acquire more mutations than slower-dividing centre lineages. We develop a Bayesian state-dependent evolutionary phylodynamic model (SDevo) that quantifies these patterns to infer the differential division rates between peripheral and central cells. We demonstrate that this approach accurately infers spatially varying birth rates of simulated tumours across a range of growth conditions and sampling strategies. We then show that SDevo outperforms state-of-the-art, non-cancer multi-state phylodynamic methods that ignore differential sequence evolution. Finally, we apply SDevo to single-time-point, multi-region sequencing data from clinical hepatocellular carcinomas and find evidence of a three- to six-times-higher division rate on the tumour edge. With the increasing availability of high-resolution, multi-region sequencing, we anticipate that SDevo will be useful in interrogating spatial growth restrictions and could be extended to model non-spatial factors that influence tumour progression.

A survey of open questions in adaptive therapy: Bridging mathematics and clinical translation

Adaptive therapy is a dynamic cancer treatment protocol that updates (or 'adapts') treatment decisions in anticipation of evolving tumor dynamics. This broad term encompasses many possible dynamic treatment protocols of patient-specific dose modulation or dose timing. Adaptive therapy maintains high levels of tumor burden to benefit from the competitive suppression of treatment-sensitive subpopulations on treatment-resistant subpopulations. This evolution-based approach to cancer treatment has been integrated into several ongoing or planned clinical trials, including treatment of metastatic castrate resistant prostate cancer, ovarian cancer, and BRAF-mutant melanoma. In the previous few decades, experimental and clinical investigation of adaptive therapy has progressed synergistically with mathematical and computational modeling. In this work, we discuss 11 open questions in cancer adaptive therapy mathematical modeling. The questions are split into three sections: (1) integrating the appropriate components into mathematical models (2) design and validation of dosing protocols, and (3) challenges and opportunities in clinical translation.

The role of physics in multiomics and cancer evolution

Complex interactions between the physical environment and phenotype of a tumour, and genomics, transcriptomics, proteomics and epigenomics, are increasingly known to have a significant influence on cancer development, progression and evolution. For example, mechanical stress can alter both genome maintenance and histone modifications, which consequently affect transcription and the epigenome. Increased stiffness has been linked to genetic heterogeneity and is responsible for heterochromatin accumulations. Stiffness thereby leads to deregulation in gene expression, disrupts the proteome and can impact angiogenesis. Several studies have shown how the physics of cancer can influence diverse cancer hallmarks such as resistance to cell death, angiogenesis and evasion from immune destruction. In this review, we will explain the role that physics of cancer plays in cancer evolution and explore how multiomics are being used to elucidate the mechanisms underpinning them.

SMITH: spatially constrained stochastic model for simulation of intra-tumour heterogeneity

MOTIVATION

Simulations of cancer evolution are highly useful to study the effects of selection and mutation rates on cellular fitness. However, most methods are either lattice-based and cannot simulate realistically sized tumours, or they omit spatial constraints and lack the clonal dynamics of real-world tumours.

RESULTS

Stochastic model of intra-tumour heterogeneity (SMITH) is an efficient and explainable model of cancer evolution that combines a branching process with a new confinement mechanism limiting clonal growth based on the size of the individual clones as well as the overall tumour population. We demonstrate how confinement is sufficient to induce the rich clonal dynamics observed in spatial models and cancer samples across tumour types, while allowing for a clear geometric interpretation and simulation of 1 billion cells within a few minutes on a desktop PC.

AVAILABILITY AND IMPLEMENTATION

SMITH is implemented in C# and freely available at https://bitbucket.org/schwarzlab/smith. For visualizations, we provide the accompanying Python package PyFish at https://bitbucket.org/schwarzlab/pyfish.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Spatial biology of cancer evolution

The natural history of cancers can be understood through the lens of evolution given that the driving forces of cancer development are mutation and selection of fitter clones. Cancer growth and progression are spatial processes that involve the breakdown of normal tissue organization, invasion and metastasis. For these reasons, spatial patterns are an integral part of histological tumour grading and staging as they measure the progression from normal to malignant disease. Furthermore, tumour cells are part of an ecosystem of tumour cells and their surrounding tumour microenvironment. A range of new spatial genomic, transcriptomic and proteomic technologies offers new avenues for the study of cancer evolution with great molecular and spatial detail. These methods enable precise characterizations of the tumour microenvironment, cellular interactions therein and micro-anatomical structures. In conjunction with spatial genomics, it emerges that tumours and microenvironments co-evolve, which helps explain observable patterns of heterogeneity and offers new routes for therapeutic interventions.

Overcoming biophysical barriers with innovative therapeutic delivery approaches

Cancer is often conceptualized as principally a cellular process, one initiated by genetic mutations in a progenitor cell that result in dysregulated cell proliferation. Accordingly, investigations into mechanisms of treatment resistance to cancer therapies often revolve around the biologic barriers to the therapies. However, there is a growing appreciation for the unique biomechanical properties for tumors and the role they play in treatment resistance for conventional, molecularly targeted, and immune-mediated cancer therapies. This understanding has inspired the development of pharmacologic and interventional approaches to overcome these barriers. Of particular promise are perfusion-enhanced drug delivery (PEDD) approaches that potentially allow for comprehensive tumor coverage with increased delivery pressure and prevention of reflux to drive therapeutics into the tumor parenchyma. In this review, we summarize the key features of the tumor microenvironment that drive tumor progression and impose barriers to anti-cancer therapies. We highlight the rationale and application of pharmacologic approaches and interventional drug delivery devices designed to overcome these impediments. We additionally contextualize these concepts by illustrating their application to the treatment of uveal melanoma liver metastases.

Phenotypic plasticity and genetic control in colorectal cancer evolution

Genetic and epigenetic variation, together with transcriptional plasticity, contribute to intratumour heterogeneity1. The interplay of these biological processes and their respective contributions to tumour evolution remain unknown. Here we show that intratumour genetic ancestry only infrequently affects gene expression traits and subclonal evolution in colorectal cancer (CRC). Using spatially resolved paired whole-genome and transcriptome sequencing, we find that the majority of intratumour variation in gene expression is not strongly heritable but rather 'plastic'. Somatic expression quantitative trait loci analysis identified a number of putative genetic controls of expression by cis-acting coding and non-coding mutations, the majority of which were clonal within a tumour, alongside frequent structural alterations. Consistently, computational inference on the spatial patterning of tumour phylogenies finds that a considerable proportion of CRCs did not show evidence of subclonal selection, with only a subset of putative genetic drivers associated with subclone expansions. Spatial intermixing of clones is common, with some tumours growing exponentially and others only at the periphery. Together, our data suggest that most genetic intratumour variation in CRC has no major phenotypic consequence and that transcriptional plasticity is, instead, widespread within a tumour.

Spatial transcriptomics technology in cancer research

In recent years, spatial transcriptomics (ST) technologies have developed rapidly and have been widely used in constructing spatial tissue atlases and characterizing spatiotemporal heterogeneity of cancers. Currently, ST has been used to profile spatial heterogeneity in multiple cancer types. Besides, ST is a benefit for identifying and comprehensively understanding special spatial areas such as tumor interface and tertiary lymphoid structures (TLSs), which exhibit unique tumor microenvironments (TMEs). Therefore, ST has also shown great potential to improve pathological diagnosis and identify novel prognostic factors in cancer. This review presents recent advances and prospects of applications on cancer research based on ST technologies as well as the challenges.

Chromosomal Instability, Selection and Competition: Factors That Shape the Level of Karyotype Intra-Tumor Heterogeneity

Intra-tumor heterogeneity (ITH) is a pan-cancer predictor of survival, with high ITH being correlated to a dismal prognosis. The level of ITH is, hence, a clinically relevant characteristic of a malignancy. ITH of karyotypes is driven by chromosomal instability (CIN). However, not all new karyotypes generated by CIN are viable or competitive, which limits the amount of ITH. Here, we review the cellular processes and ecological properties that determine karyotype ITH. We propose a framework to understand karyotype ITH, in which cells with new karyotypes emerge through CIN, are selected by cell intrinsic and cell extrinsic selective pressures, and propagate through a cancer in competition with other malignant cells. We further discuss how CIN modulates the cell phenotype and immune microenvironment, and the implications this has for the subsequent selection of karyotypes. Together, we aim to provide a comprehensive overview of the biological processes that shape the level of karyotype heterogeneity.

Model-informed experimental design recommendations for distinguishing intrinsic and acquired targeted therapeutic resistance in head and neck cancer

The promise of precision medicine has been limited by the pervasive resistance to many targeted therapies for cancer. Inferring the timing (i.e., pre-existing or acquired) and mechanism (i.e., drug-induced) of such resistance is crucial for designing effective new therapeutics. This paper studies cetuximab resistance in head and neck squamous cell carcinoma (HNSCC) using tumor volume data obtained from patient-derived tumor xenografts. We ask if resistance mechanisms can be determined from this data alone, and if not, what data would be needed to deduce the underlying mode(s) of resistance. To answer these questions, we propose a family of mathematical models, with each member of the family assuming a different timing and mechanism of resistance. We present a method for fitting these models to individual volumetric data, and utilize model selection and parameter sensitivity analyses to ask: which member(s) of the family of models best describes HNSCC response to cetuximab, and what does that tell us about the timing and mechanisms driving resistance? We find that along with time-course volumetric data to a single dose of cetuximab, the initial resistance fraction and, in some instances, dose escalation volumetric data are required to distinguish among the family of models and thereby infer the mechanisms of resistance. These findings can inform future experimental design so that we can best leverage the synergy of wet laboratory experimentation and mathematical modeling in the study of novel targeted cancer therapeutics.

Modeling age-specific incidence of colon cancer via niche competition

Cancer development is a multistep process often starting with a single cell in which a number of epigenetic and genetic alterations have accumulated thus transforming it into a tumor cell. The progeny of such a single benign tumor cell expands in the tissue and can at some point progress to malignant tumor cells until a detectable tumor is formed. The dynamics from the early phase of a single cell to a detectable tumor with billions of tumor cells are complex and still not fully resolved, not even for the well-known prototype of multistage carcinogenesis, the adenoma-adenocarcinoma sequence of colorectal cancer. Mathematical models of such carcinogenesis are frequently tested and calibrated based on reported age-specific incidence rates of cancer, but they usually require calibration of four or more parameters due to the wide range of processes these models aim to reflect. We present a cell-based model, which focuses on the competition between wild-type and tumor cells in colonic crypts, with which we are able reproduce epidemiological incidence rates of colon cancer. Additionally, the fraction of cancerous tumors with precancerous lesions predicted by the model agree with clinical estimates. The correspondence between model and reported data suggests that the fate of tumor development is majorly determined by the early phase of tumor growth and progression long before a tumor becomes detectable. Due to the focus on the early phase of tumor development, the model has only a single fit parameter, the time scale set by an effective replacement rate of stem cells in the crypt. We find this effective rate to be considerable smaller than the actual replacement rate, which implies that the time scale is limited by the processes succeeding clonal conversion of crypts.

Cancer development is a multistep process often starting with a single cell turning into a tumor cell whose progeny growths via clonal expansion into a macroscopic tumor with billions of cells. While experimental insight exists on the cellular scale and cancer registries provide statistics on detectable tumors, the complex dynamics leading from the microscopic cellular scale to a macroscopic tumor is still not fully resolved. Models of cancer biology are commonly used to explain incidence rates but usually require the fit of several biological parameters due to the complexity of the incorporated processes. We employ a cell-based model based on the competition in colonic crypts, to reproduce epidemiological age-specific incidence rates of colon cancer. Due to the focus on the early stage of tumor development, only the time scale in the model has to be calibrated. The agreement between theoretical prediction and epidemiological observation suggests that the fate of tumor development is dominated by the early phase of tumor development long before a tumor becomes detectable.

Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet, existing indices are not defined for all rooted trees, are unreliable for comparing trees with different numbers of leaves, and are sensitive to the presence or absence of rare types. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless' index but can account for population sizes, are defined for trees with any degree distribution, and enable meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalized reciprocal of Sackin's index. Hence, we both unify and generalize the two most popular existing tree balance indices. Our indices are intrinsically normalized and can be computed in linear time. We conclude that these more widely applicable indices have the potential to supersede those in current use. [Cancer; clone tree; Colless index; Sackin index; species tree; tree balance.].

Single cell cancer epigenetics

Bulk sequencing methodologies have allowed us to make great progress in cancer research. Unfortunately, these techniques lack the resolution to fully unravel the epigenetic mechanisms that govern tumor heterogeneity. Consequently, many novel single cell-sequencing methodologies have been developed over the past decade, allowing us to explore the epigenetic components that regulate different aspects of cancer heterogeneity, namely: clonal heterogeneity, tumor microenvironment (TME), spatial organization, intratumoral differentiation programs, metastasis, and resistance mechanisms. In this review, we explore the different sequencing techniques that enable researchers to study different aspects of epigenetics (DNA methylation, chromatin accessibility, histone modifications, DNA-protein interactions, and chromatin 3D architecture) at the single cell level, their potential applications in cancer, and their current technical limitations.

An Updated Review on EPR-Based Solid Tumor Targeting Nanocarriers for Cancer Treatment

The enhanced permeability and retention (EPR) effect in cancer treatment is one of the key mechanisms that enables drug accumulation at the tumor site. However, despite a plethora of virus/inorganic/organic-based nanocarriers designed to rely on the EPR effect to effectively target tumors, most have failed in the clinic. It seems that the non-compliance of research activities with clinical trials, goals unrelated to the EPR effect, and lack of awareness of the impact of solid tumor structure and interactions on the performance of drug nanocarriers have intensified this dissatisfaction. As such, the asymmetric growth and structural complexity of solid tumors, physicochemical properties of drug nanocarriers, EPR analytical combination tools, and EPR description goals should be considered to improve EPR-based cancer therapeutics. This review provides valuable insights into the limitations of the EPR effect in therapeutic efficacy and reports crucial perspectives on how the EPR effect can be modulated to improve the therapeutic effects of nanomedicine.

Branching structure of genealogies in spatially growing populations and its implications for population genetics inference

Spatial models where growth is limited to the population edge have been instrumental to understanding the population dynamics and the clone size distribution in growing cellular populations, such as microbial colonies and avascular tumours. A complete characterization of the coalescence process generated by spatial growth is still lacking, limiting our ability to apply classic population genetics inference to spatially growing populations. Here, we start filling this gap by investigating the statistical properties of the cell lineages generated by the two dimensional Eden model, leveraging their physical analogy with directed polymers. Our analysis provides quantitative estimates for population measurements that can easily be assessed via sequencing, such as the average number of segregating sites and the clone size distribution of a subsample of the population. Our results not only reveal remarkable features of the genealogies generated during growth, but also highlight new properties that can be misinterpreted as signs of selection if non-spatial models are inappropriately applied.