Spatial structure increases the waiting time for cancer

Clonal interference, genetic variation and the speed of evolution in structured populations

When it comes to understanding the role that population structure plays in shaping rates of evolution, it is commonly accepted that interference between evolutionary innovations is more prevalent in structured populations compared to well-mixed, and that population structure reduces the rate of evolution, while simultaneously promoting maintenance of genetic variation. Prior models usually represent population structure using two or more connected demes or lattices with periodic boundary conditions. Fundamentally, the observed spatial evolutionary slow-down is rooted in the fact that these types of structures increase the time it takes for a selective sweep and therefore, increase the probability that multiple beneficial mutations will coexist and interfere. Here we show that systematically introducing more heterogeneity in population structure can reshape these prior conclusions and lead to a much wider range of observed evolutionary outcome, including increased rates of evolution. At a big picture level, our results showcase that the evolutionary effects of population structure crucially depend on the properties of the topology considered. Understanding these spatial properties is therefore requisite for making meaningful evolutionary comparisons across different topologies, for forming sensible null expectations about experimental or observational data or for developing an intuition for when well-mixed approximations, or approximations done using spatial models with a high degree of symmetry, might not apply.

Modeling tumors as complex ecosystems

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity or predict its consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), a standard tool to describe species-rich ecological communities, provides a suitable framework to model the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties provide a new understanding of the disease. We discuss potential extensions of the model and their application to phenotypic plasticity, cancer-immune interactions, and metastatic growth. Our work outlines a set of questions and a road map for further research in cancer ecology.

A modelling framework for cancer ecology and evolution

Cancer incidence increases rapidly with age, typically as a polynomial. The somatic mutation theory explains this increase through the waiting time for enough mutations to build up to generate cells with the full set of traits needed to grow without control. However, lines of evidence ranging from tumour reversion and dormancy to the prevalence of presumed cancer mutations in non-cancerous tissues argue that this is not the whole story, and that cancer is also an ecological process, and that mutations only lead to cancer when the systems of control within and across cells have broken down. Aging thus has two effects: the build-up of mutations and the breakdown of control. This paper presents a mathematical modelling framework to unify these theories with novel approaches to model the mutation and diversification of cell lineages and of the breakdown of the layers of control both within and between cells. These models correctly predict the polynomial increase of cancer with age, show how germline defects in control accelerate cancer initiation, and compute how the positive feedback between cell replication, ecology and layers of control leads to a doubly exponential growth of cell populations.

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.

Modeling tumors as species-rich ecological communities

Many advanced cancers resist therapeutic intervention. This process is fundamentally related to intra-tumor heterogeneity: multiple cell populations, each with different mutational and phenotypic signatures, coexist within a tumor and its metastatic nodes. Like species in an ecosystem, many cancer cell populations are intertwined in a complex network of ecological interactions. Most mathematical models of tumor ecology, however, cannot account for such phenotypic diversity nor are able to predict its consequences. Here we propose that the Generalized Lotka-Volterra model (GLV), a standard tool to describe complex, species-rich ecological communities, provides a suitable framework to describe the ecology of heterogeneous tumors. We develop a GLV model of tumor growth and discuss how its emerging properties, such as outgrowth and multistability, provide a new understanding of the disease. Additionally, we discuss potential extensions of the model and their application to three active areas of cancer research, namely phenotypic plasticity, the cancer-immune interplay and the resistance of metastatic tumors to treatment. Our work outlines a set of questions and a tentative road map for further research in cancer ecology.

Adding pattern and process to eco-evo theory and applications

Eco-evolutionary dynamics result when interacting biological forces simultaneously produce demographic and genetic population responses. Eco-evolutionary simulators traditionally manage complexity by minimizing the influence of spatial pattern on process. However, such simplifications can limit their utility in real-world applications. We present a novel simulation modeling approach for investigating eco-evolutionary dynamics, centered on the driving role of landscape pattern. Our spatially-explicit, individual-based mechanistic simulation approach overcomes existing methodological challenges, generates new insights, and paves the way for future investigations in four focal disciplines: Landscape Genetics, Population Genetics, Conservation Biology, and Evolutionary Ecology. We developed a simple individual-based model to illustrate how spatial structure drives eco-evo dynamics. By making minor changes to our landscape's structure, we simulated continuous, isolated, and semi-connected landscapes, and simultaneously tested several classical assumptions of the focal disciplines. Our results exhibit expected patterns of isolation, drift, and extinction. By imposing landscape change on otherwise functionally-static eco-evolutionary models, we altered key emergent properties such as gene-flow and adaptive selection. We observed demo-genetic responses to these landscape manipulations, including changes in population size, probability of extinction, and allele frequencies. Our model also demonstrated how demo-genetic traits, including generation time and migration rate, can arise from a mechanistic model, rather than being specified a priori. We identify simplifying assumptions common to four focal disciplines, and illustrate how new insights might be developed in eco-evolutionary theory and applications by better linking biological processes to landscape patterns that we know influence them, but that have understandably been left out of many past modeling studies.

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.

The role of spatial structures of tissues in cancer initiation dynamics

It is widely believed that biological tissues evolved to lower the risks of cancer development. One of the specific ways to minimize the chances of tumor formation comes from proper spatial organization of tissues. However, the microscopic mechanisms of underlying processes remain not fully understood. We present a theoretical investigation on the role of spatial structures in cancer initiation dynamics. In our approach, the dynamics of single mutation fixations are analyzed using analytical calculations and computer simulations by mapping them to Moran processes on graphs with different connectivity that mimic various spatial structures. It is found that while the fixation probability is not affected by modifying the spatial structures of the tissues, the fixation times can change dramatically. The slowest dynamics is observed in "quasi-one-dimensional" structures, while the fastest dynamics is observed in "quasi-three-dimensional" structures. Theoretical calculations also suggest that there is a critical value of the degree of graph connectivity, which mimics the spatial dimension of the tissue structure, above which the spatial structure of the tissue has no effect on the mutation fixation dynamics. An effective discrete-state stochastic model of cancer initiation is utilized to explain our theoretical results and predictions. Our theoretical analysis clarifies some important aspects on the role of the tissue spatial structures in the cancer initiation processes.

J-SPACE: a Julia package for the simulation of spatial models of cancer evolution and of sequencing experiments

Background

The combined effects of biological variability and measurement-related errors on cancer sequencing data remain largely unexplored. However, the spatio-temporal simulation of multi-cellular systems provides a powerful instrument to address this issue. In particular, efficient algorithmic frameworks are needed to overcome the harsh trade-off between scalability and expressivity, so to allow one to simulate both realistic cancer evolution scenarios and the related sequencing experiments, which can then be used to benchmark downstream bioinformatics methods.

Result

We introduce a Julia package for SPAtial Cancer Evolution (J-SPACE), which allows one to model and simulate a broad set of experimental scenarios, phenomenological rules and sequencing settings.Specifically, J-SPACE simulates the spatial dynamics of cells as a continuous-time multi-type birth-death stochastic process on a arbitrary graph, employing different rules of interaction and an optimised Gillespie algorithm. The evolutionary dynamics of genomic alterations (single-nucleotide variants and indels) is simulated either under the Infinite Sites Assumption or several different substitution models, including one based on mutational signatures. After mimicking the spatial sampling of tumour cells, J-SPACE returns the related phylogenetic model, and allows one to generate synthetic reads from several Next-Generation Sequencing (NGS) platforms, via the ART read simulator. The results are finally returned in standard FASTA, FASTQ, SAM, ALN and Newick file formats.

Conclusion

J-SPACE is designed to efficiently simulate the heterogeneous behaviour of a large number of cancer cells and produces a rich set of outputs. Our framework is useful to investigate the emergent spatial dynamics of cancer subpopulations, as well as to assess the impact of incomplete sampling and of experiment-specific errors. Importantly, the output of J-SPACE is designed to allow the performance assessment of downstream bioinformatics pipelines processing NGS data. J-SPACE is freely available at: https://github.com/BIMIB-DISCo/J-Space.jl.

Delineating the longitudinal tumor evolution using organoid models

Cancer is an evolutionary process fueled by genetic or epigenetic alterations in the genome. Understanding the evolutionary dynamics that are operative at different stages of tumor progression might inform effective strategies in early detection, diagnosis, and treatment of cancer. However, our understanding on the dynamics of tumor evolution through time is very limited since it is usually impossible to sample patient tumors repeatedly. The recent advances in in vitro 3D organoid culture technologies have opened new avenues for the development of more realistic human cancer models that mimic many in vivo biological characteristics in human tumors. Here, we review recent progresses and challenges in cancer genomic evolution studies and advantages of using tumor organoids to study cancer evolution. We propose to establish an experimental evolution model based on continuous passages of patient-derived organoids and longitudinal sampling to study clonal dynamics and evolutionary patterns over time. Development and integration of population genetic theories and computational models into time-course genomic data in tumor organoids will help to pinpoint the key cellular mechanisms underlying cancer evolutionary dynamics, thus providing novel insights on therapeutic strategies for highly dynamic and heterogeneous tumors.

Roles of phenotypic heterogeneity and microenvironment feedback in early tumor development

The local microenvironment of a tumor plays an important and commonly observed role in cancer development and progression. Dynamic changes in the tissue microenvironment are thought to epigenetically disrupt healthy cellular phenotypes and drive cancer incidence. Despite the experimental work in this area there are no conceptual models to understand the interplay between the epigenetic dysregulation in the microenvironment of early tumors and the appearance of cancer driver mutations. Here, we develop a minimal model of the tissue microenvironment which considers three interacting subpopulations: healthy, phenotypically dysregulated, and mutated cancer cells. Healthy cells can epigenetically (reversibly) transition to the dysregulated phenotype, and from there to the cancer state. The epigenetic transition rates of noncancer cells can be influenced by the number of cancer cells in the microenvironment (termed microenvironment feedback). Our model delineates the regime in which microenvironment feedback accelerates the rate of cancer initiation. In addition, the model shows when and how microenvironment feedback may inhibit cancer progression. We discuss how our framework may provide resolution to some of the puzzling experimental observations of slow cancer progression.

Shape of population interfaces as an indicator of mutational instability in coexisting cell populations

Cellular populations such as avascular tumors and microbial biofilms may 'invade' or grow into surrounding populations. The invading population is often comprised of a heterogeneous mixture of cells with varying growth rates. The population may also exhibit mutational instabilities, such as a heavy deleterious mutation load in a cancerous growth. We study the dynamics of a heterogeneous, mutating population competing with a surrounding homogeneous population, as one might find in a cancerous invasion of healthy tissue. We find that the shape of the population interface serves as an indicator for the evolutionary dynamics within the heterogeneous population. In particular, invasion front undulations become enhanced when the invading population is near a mutational meltdown transition or when the surrounding 'bystander' population is barely able to reinvade the mutating population. We characterize these interface undulations and the effective fitness of the heterogeneous population in one- and two-dimensional systems.

When, why and how tumour clonal diversity predicts survival

The utility of intratumour heterogeneity as a prognostic biomarker is the subject of ongoing clinical investigation. However, the relationship between this marker and its clinical impact is mediated by an evolutionary process that is not well understood. Here, we employ a spatial computational model of tumour evolution to assess when, why and how intratumour heterogeneity can be used to forecast tumour growth rate and progression-free survival. We identify three conditions that can lead to a positive correlation between clonal diversity and subsequent growth rate: diversity is measured early in tumour development; selective sweeps are rare; and/or tumours vary in the rate at which they acquire driver mutations. Opposite conditions typically lead to negative correlation. In cohorts of tumours with diverse evolutionary parameters, we find that clonal diversity is a reliable predictor of both growth rate and progression-free survival. We thus offer explanations-grounded in evolutionary theory-for empirical findings in various cancers, including survival analyses reported in the recent TRACERx Renal study of clear-cell renal cell carcinoma. Our work informs the search for new prognostic biomarkers and contributes to the development of predictive oncology.

Application of simultaneous selective pressures slows adaptation

Beneficial mutations that arise in an evolving asexual population may compete or interact in ways that alter the overall rate of adaptation through mechanisms such as clonal or functional interference. The application of multiple selective pressures simultaneously may allow for a greater number of adaptive mutations, increasing the opportunities for competition between selectively advantageous alterations, and thereby reducing the rate of adaptation. We evolved a strain of Saccharomyces cerevisiae that could not produce its own histidine or uracil for ~500 generations under one or three selective pressures: limitation of the concentration of glucose, histidine, and/or uracil in the media. The rate of adaptation was obtained by measuring evolved relative fitness using competition assays. Populations evolved under a single selective pressure showed a statistically significant increase in fitness on those pressures relative to the ancestral strain, but the populations evolved on all three pressures did not show a statistically significant increase in fitness over the ancestral strain on any single pressure. Simultaneously limiting three essential nutrients for a population of S. cerevisiae effectively slows the rate of evolution on any one of the three selective pressures applied, relative to the single selective pressure cases. We identify possible mechanisms for fitness changes seen between populations evolved on one or three limiting nutrient pressures by high-throughput sequencing. Adding multiple selective pressures to evolving disease like cancer and infectious diseases could reduce the rate of adaptation and thereby may slow disease progression, prolong drug efficacy and prevent deaths.

Clonal evolution driven by superdriver mutations

Background

Tumors are widely recognized to progress through clonal evolution by sequentially acquiring selectively advantageous genetic alterations that significantly contribute to tumorigenesis and thus are termned drivers. Some cancer drivers, such as TP53 point mutation or EGFR copy number gain, provide exceptional fitness gains, which, in time, can be sufficient to trigger the onset of cancer with little or no contribution from additional genetic alterations. These key alterations are called superdrivers.

Results

In this study, we employ a Wright-Fisher model to study the interplay between drivers and superdrivers in tumor progression. We demonstrate that the resulting evolutionary dynamics follow global clonal expansions of superdrivers with periodic clonal expansions of drivers. We find that the waiting time to the accumulation of a set of superdrivers and drivers in the tumor cell population can be approximated by the sum of the individual waiting times.

Conclusions

Our results suggest that superdriver dynamics dominate over driver dynamics in tumorigenesis. Furthermore, our model allows studying the interplay between superdriver and driver mutations both empirically and theoretically.

Measuring the distribution of fitness effects in somatic evolution by combining clonal dynamics with dN/dS ratios

The distribution of fitness effects (DFE) defines how new mutations spread through an evolving population. The ratio of non-synonymous to synonymous mutations (dN/dS) has become a popular method to detect selection in somatic cells. However the link, in somatic evolution, between dN/dS values and fitness coefficients is missing. Here we present a quantitative model of somatic evolutionary dynamics that determines the selective coefficients of individual driver mutations from dN/dS estimates. We then measure the DFE for somatic mutant clones in ostensibly normal oesophagus and skin. We reveal a broad distribution of fitness effects, with the largest fitness increases found for TP53 and NOTCH1 mutants (proliferative bias 1-5%). This study provides the theoretical link between dN/dS values and selective coefficients in somatic evolution, and measures the DFE of mutations in human tissues.

Eleven grand challenges in single-cell data science

The recent boom in microfluidics and combinatorial indexing strategies, combined with low sequencing costs, has empowered single-cell sequencing technology. Thousands-or even millions-of cells analyzed in a single experiment amount to a data revolution in single-cell biology and pose unique data science problems. Here, we outline eleven challenges that will be central to bringing this emerging field of single-cell data science forward. For each challenge, we highlight motivating research questions, review prior work, and formulate open problems. This compendium is for established researchers, newcomers, and students alike, highlighting interesting and rewarding problems for the coming years.

Genetic heterogeneity and clonal evolution during metastasis in breast cancer patient-derived tumor xenograft models

Genetic heterogeneity within a tumor arises by clonal evolution, and patients with highly heterogeneous tumors are more likely to be resistant to therapy and have reduced survival. Clonal evolution also occurs when a subset of cells leave the primary tumor to form metastases, which leads to reduced genetic heterogeneity at the metastatic site. Although this process has been observed in human cancer, experimental models which recapitulate this process are lacking. Patient-derived tumor xenografts (PDX) have been shown to recapitulate the patient's original tumor's intra-tumor genetic heterogeneity, as well as its genomics and response to treatment, but whether they can be used to model clonal evolution in the metastatic process is currently unknown. Here, we address this question by following genetic changes in two breast cancer PDX models during metastasis. First, we discovered that mouse stroma can be a confounding factor in assessing intra-tumor heterogeneity by whole exome sequencing, thus we developed a new bioinformatic approach to correct for this. Finally, in a spontaneous, but not experimental (tail-vein) metastasis model we observed a loss of heterogeneity in PDX metastases compared to their orthotopic "primary" tumors, confirming that PDX models can faithfully mimic the clonal evolution process undergone in human patients during metastatic spreading.

Evolutionary Rescue from a Wave of Biological Invasion

Evolution can potentially rescue populations from being driven extinct by biological invasions, but predictions for this occurrence are generally lacking. Here I derive theoretical predictions for evolutionary rescue of a resident population experiencing invasion from an introduced competitor that spreads over its introduced range as a traveling spatial wave that displaces residents. I compare the likelihood of evolutionary rescue from invasion for two modes of competition: exploitation and interference competition. I find that, all else equal, evolutionary rescue is less effective at preventing extinction caused by interference-driven invasions than by exploitation-driven invasions. Rescue from interference-driven invasions is, surprisingly, independent of invader dispersal rate or the speed of invasion and is more weakly dependent on range size than in the exploitation-driven case. In contrast, rescue from exploitation-driven invasions strongly depends on range size and is less likely during fast invasions. The results presented here have potential applications for conserving endemic species from nonnative invaders and for ensuring extinction of pests using intentionally introduced biocontrol agents.

Evolutionary Dynamics in Structured Populations Under Strong Population Genetic Forces

In the long-term neutral equilibrium, high rates of migration between subpopulations result in little population differentiation. However, in the short-term, even very abundant migration may not be enough for subpopulations to equilibrate immediately. In this study, we investigate dynamical patterns of short-term population differentiation in adapting populations via stochastic and analytical modeling through time. We characterize a regime in which selection and migration interact to create non-monotonic patterns of population differentiation over time when migration is weaker than selection, but stronger than drift. We demonstrate how these patterns can be leveraged to estimate high migration rates using approximate Bayesian computation. We apply this approach to estimate fast migration in a rapidly adapting intra-host Simian-HIV population sampled from different anatomical locations. We find differences in estimated migration rates between different compartments, even though all are above [Formula: see text] = 1. This work demonstrates how studying demographic processes on the timescale of selective sweeps illuminates processes too fast to leave signatures on neutral timescales.

Collective motion conceals fitness differences in crowded cellular populations

Many cellular populations are tightly-packed, such as microbial colonies and biofilms, or tissues and tumors in multicellular organisms. Movement of one cell in those crowded assemblages requires motion of others, so that cell displacements are correlated over many cell diameters. Whenever movement is important for survival or growth, these correlated rearrangements could couple the evolutionary fate of different lineages. Yet, little is known about the interplay between mechanical forces and evolution in dense cellular populations. Here, by tracking slower-growing clones at the expanding edge of yeast colonies, we show that the collective motion of cells prevents costly mutations from being weeded out rapidly. Joint pushing by neighboring cells generates correlated movements that suppress the differential displacements required for selection to act. This mechanical screening of fitness differences allows slower-growing mutants to leave more descendants than expected under non-mechanical models, thereby increasing their chance for evolutionary rescue. Our work suggests that, in crowded populations, cells cooperate with surrounding neighbors through inevitable mechanical interactions. This effect has to be considered when predicting evolutionary outcomes, such as the emergence of drug resistance or cancer evolution.

Emergence of evolutionarily stable communities through eco-evolutionary tunnelling

Ecological and evolutionary dynamics of communities are inexorably intertwined. The ecological state determines the fate of newly arising mutants, and mutations that increase in frequency can reshape the ecological dynamics. Evolutionary game theory and its extensions within adaptive dynamics have been the mathematical frameworks for understanding this interplay, leading to notions such as evolutionarily stable states (ESS) in which no mutations are favoured, and evolutionary branching points near which the population diversifies. A central assumption behind these theoretical treatments has been that mutations are rare so that the ecological dynamics has time to equilibrate after every mutation. A fundamental question is whether qualitatively new phenomena can arise when mutations are frequent. Here, we describe an adaptive diversification process that robustly leads to complex ESS, despite the fact that such communities are unreachable through a step-by-step evolutionary process. Rather, the system as a whole tunnels between collective states over a short timescale. The tunnelling rate is a sharply increasing function of the rate at which mutations arise in the population. This makes the emergence of ESS communities virtually impossible in small populations, but generic in large ones. Moreover, communities emerging through this process can spatially spread as single replication units that outcompete other communities. Overall, this work provides a qualitatively new mechanism for adaptive diversification and shows that complex structures can generically evolve even when no step-by-step evolutionary path exists.

Harnessing Tumor Evolution to Circumvent Resistance

High-throughput sequencing can be used to measure changes in tumor composition across space and time. Specifically, comparisons of pre- and post-treatment samples can reveal the underlying clonal dynamics and resistance mechanisms. Here, we discuss evidence for distinct modes of tumor evolution and their implications for therapeutic strategies. In addition, we consider the utility of spatial tissue sampling schemes, single-cell analysis, and circulating tumor DNA to track tumor evolution and the emergence of resistance, as well as approaches that seek to forestall resistance by targeting tumor evolution. Ultimately, characterization of the (epi)genomic, transcriptomic, and phenotypic changes that occur during tumor progression coupled with computational and mathematical modeling of tumor evolutionary dynamics may inform personalized treatment strategies.

Spatial mutation patterns as markers of early colorectal tumor cell mobility

A growing body of evidence suggests that a subset of human cancers grows as single clonal expansions. In such a nearly neutral evolution scenario, it is possible to infer the early ancestral tree of a full-grown tumor. We hypothesized that early tree reconstruction can provide insights into the mobility phenotypes of tumor cells during their first few cell divisions. We explored this hypothesis by means of a computational multiscale model of tumor expansion incorporating the glandular structure of colorectal tumors. After calibrating the model to multiregional and single gland data from 19 human colorectal tumors using approximate Bayesian computation, we examined the role of early tumor cell mobility in shaping the private mutation patterns of the final tumor. The simulations showed that early cell mixing in the first tumor gland can result in side-variegated patterns where the same private mutations could be detected on opposite tumor sides. In contrast, absence of early mixing led to nonvariegated, sectional mutation patterns. These results suggest that the patterns of detectable private mutations in colorectal tumors may be a marker of early cell movement and hence the invasive and metastatic potential of the tumor at the start of the growth. In alignment with our hypothesis, we found evidence of early abnormal cell movement in 9 of 15 invasive colorectal carcinomas ("born to be bad"), but in none of 4 benign adenomas. If validated with a larger dataset, the private mutation patterns may be used for outcome prediction among screen-detected lesions with unknown invasive potential.

Big Bang Tumor Growth and Clonal Evolution

The advent and application of next-generation sequencing (NGS) technologies to tumor genomes has reinvigorated efforts to understand clonal evolution. Although tumor progression has traditionally been viewed as a gradual stepwise process, recent studies suggest that evolutionary rates in tumors can be variable with periods of punctuated mutational bursts and relative stasis. For example, Big Bang dynamics have been reported, wherein after transformation, growth occurs in the absence of stringent selection, consistent with effectively neutral evolution. Although first noted in colorectal tumors, effective neutrality may be relatively common. Additionally, punctuated evolution resulting from mutational bursts and cataclysmic genomic alterations have been described. In this review, we contrast these findings with the conventional gradualist view of clonal evolution and describe potential clinical and therapeutic implications of different evolutionary modes and tempos.

The Heterogeneity of Prostate Cancer: A Practical Approach

Prostate cancer is a paradigm tumor model for heterogeneity in almost every sense. Its clinical, spatial, and morphological heterogeneity divided by the high-level molecular genetic diversity outline the complexity of this disease in the clinical and research settings. In this review, we summarize the main aspects of prostate cancer heterogeneity at different levels, with special attention given to the spatial heterogeneity within the prostate, and to the standard morphological heterogeneity, with respect to tumor grading and modern classifications. We also cover the complex issue of molecular genetic heterogeneity, discussing it in the context of the current evidence of the genetic characterization of prostate carcinoma; the interpatient, intertumoral (multifocal disease), and intratumoral heterogeneity; tumor clonality; and metastatic disease. Clinical and research implications are summarized and serve to address the most pertinent problems stemming from the extreme heterogeneity of prostate cancer.

An evolutionary perspective on field cancerization

Tumorigenesis begins long before the growth of a clinically detectable lesion and, indeed, even before any of the usual morphological correlates of pre-malignancy are recognizable. Field cancerization, which is the replacement of the normal cell population by a cancer-primed cell population that may show no morphological change, is now recognized to underlie the development of many types of cancer, including the common carcinomas of the lung, colon, skin, prostate and bladder. Field cancerization is the consequence of the evolution of somatic cells in the body that results in cells that carry some but not all phenotypes required for malignancy. Here, we review the evidence of field cancerization across organs and examine the biological mechanisms that drive the evolutionary process that results in field creation. We discuss the clinical implications, principally, how measurements of the cancerized field could improve cancer risk prediction in patients with pre-malignant disease.

Evolution of Premalignant Disease

Where does cancer come from? Although the cell-of-origin is difficult to pinpoint, cancer clones harbor information about their clonal ancestries. In an effort to find cells before they evolve into a life-threatening cancer, physicians currently diagnose premalignant diseases at frequencies that substantially exceed those of clinical cancers. Cancer risk prediction relies on our ability to distinguish between which premalignant features will lead to cancer mortality and which are characteristic of inconsequential disease. Here, we review the evolution of cancer from premalignant disease, and discuss the concept that even phenotypically normal cell progenies inherently gain more malignant potential with age. We describe the hurdles of prognosticating cancer risk in premalignant disease by making reference to the underlying continuous and multivariate natures of genotypes and phenotypes and the particular challenge inherent in defining a cell lineage as "cancerized."

A population genetics perspective on the determinants of intra-tumor heterogeneity

Cancer results from the acquisition of somatic alterations in a microevolutionary process that typically occurs over many years, much of which is occult. Understanding the evolutionary dynamics that are operative at different stages of progression in individual tumors might inform the earlier detection, diagnosis, and treatment of cancer. Although these processes cannot be directly observed, the resultant spatiotemporal patterns of genetic variation amongst tumor cells encode their evolutionary histories. Such intra-tumor heterogeneity is pervasive not only at the genomic level, but also at the transcriptomic, phenotypic, and cellular levels. Given the implications for precision medicine, the accurate quantification of heterogeneity within and between tumors has become a major focus of current research. In this review, we provide a population genetics perspective on the determinants of intra-tumor heterogeneity and approaches to quantify genetic diversity. We summarize evidence for different modes of evolution based on recent cancer genome sequencing studies and discuss emerging evolutionary strategies to therapeutically exploit tumor heterogeneity. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Should tissue structure suppress or amplify selection to minimize cancer risk?

Background

It has been frequently argued that tissues evolved to suppress the accumulation of growth enhancing cancer inducing mutations. A prominent example is the hierarchical structure of tissues with high cell turnover, where a small number of tissue specific stem cells produces a large number of specialized progeny during multiple differentiation steps. Another well known mechanism is the spatial organization of stem cell populations and it is thought that this organization suppresses fitness enhancing mutations. However, in small populations the suppression of advantageous mutations typically also implies an increased accumulation of deleterious mutations. Thus, it becomes an important question whether the suppression of potentially few advantageous mutations outweighs the combined effects of many deleterious mutations.

Results

We argue that the distribution of mutant fitness effects, e.g. the probability to hit a strong driver compared to many deleterious mutations, is crucial for the optimal organization of a cancer suppressing tissue architecture and should be taken into account in arguments for the evolution of such tissues.

Conclusion

We show that for systems that are composed of few cells reflecting the typical organization of a stem cell niche, amplification or suppression of selection can arise from subtle changes in the architecture. Moreover, we discuss special tissue structures that can suppress most types of non-neutral mutations simultaneously.

Reviewers

This article was reviewed by Benjamin Allen, Andreas Deutsch and Ignacio Rodriguez-Brenes. For the full reviews, please go to the Reviewers’ comments section.

Solutions to Peto's paradox revealed by mathematical modelling and cross-species cancer gene analysis

Whales have 1000-fold more cells than humans and mice have 1000-fold fewer; however, cancer risk across species does not increase with the number of somatic cells and the lifespan of the organism. This observation is known as Peto's paradox. How much would evolution have to change the parameters of somatic evolution in order to equalize the cancer risk between species that differ by orders of magnitude in size? Analysis of previously published models of colorectal cancer suggests that a two- to three-fold decrease in the mutation rate or stem cell division rate is enough to reduce a whale's cancer risk to that of a human. Similarly, the addition of one to two required tumour-suppressor gene mutations would also be sufficient. We surveyed mammalian genomes and did not find a positive correlation of tumour-suppressor genes with increasing body mass and longevity. However, we found evidence of the amplification of TP53 in elephants, MAL in horses and FBXO31 in microbats, which might explain Peto's paradox in those species. Exploring parameters that evolution may have fine-tuned in large, long-lived organisms will help guide future experiments to reveal the underlying biology responsible for Peto's paradox and guide cancer prevention in humans.

Spatial Moran models, II: cancer initiation in spatially structured tissue

We study the accumulation and spread of advantageous mutations in a spatial stochastic model of cancer initiation on a lattice. The parameters of this general model can be tuned to study a variety of cancer types and genetic progression pathways. This investigation contributes to an understanding of how the selective advantage of cancer cells together with the rates of mutations driving cancer, impact the process and timing of carcinogenesis. These results can be used to give insights into tumor heterogeneity and the "cancer field effect," the observation that a malignancy is often surrounded by cells that have undergone premalignant transformation.

A Computational Modeling Approach for Deriving Biomarkers to Predict Cancer Risk in Premalignant Disease

The lack of effective biomarkers for predicting cancer risk in premalignant disease is a major clinical problem. There is a near-limitless list of candidate biomarkers, and it remains unclear how best to sample the tissue in space and time. Practical constraints mean that only a few of these candidate biomarker strategies can be evaluated empirically, and there is no framework to determine which of the plethora of possibilities is the most promising. Here, we have sought to solve this problem by developing a theoretical platform for in silico biomarker development. We construct a simple computational model of carcinogenesis in premalignant disease and use the model to evaluate an extensive list of tissue sampling strategies and different molecular measures of these samples. Our model predicts that (i) taking more biopsies improves prognostication, but with diminishing returns for each additional biopsy; (ii) longitudinally collected biopsies provide slightly more prognostic information than a single biopsy collected at the latest possible time point; (iii) measurements of clonal diversity are more prognostic than measurements of the presence or absence of a particular abnormality and are particularly robust to confounding by tissue sampling; and (iv) the spatial pattern of clonal expansions is a particularly prognostic measure. This study demonstrates how the use of a mechanistic framework provided by computational modeling can diminish empirical constraints on biomarker development.

Tumour Cell Heterogeneity

The population of cells that make up a cancer are manifestly heterogeneous at the genetic, epigenetic, and phenotypic levels. In this mini-review, we summarise the extent of intra-tumour heterogeneity (ITH) across human malignancies, review the mechanisms that are responsible for generating and maintaining ITH, and discuss the ramifications and opportunities that ITH presents for cancer prognostication and treatment.

Experimental evolution in biofilm populations

Biofilms are a major form of microbial life in which cells form dense surface associated communities that can persist for many generations. The long-life of biofilm communities means that they can be strongly shaped by evolutionary processes. Here, we review the experimental study of evolution in biofilm communities. We first provide an overview of the different experimental models used to study biofilm evolution and their associated advantages and disadvantages. We then illustrate the vast amount of diversification observed during biofilm evolution, and we discuss (i) potential ecological and evolutionary processes behind the observed diversification, (ii) recent insights into the genetics of adaptive diversification, (iii) the striking degree of parallelism between evolution experiments and real-life biofilms and (iv) potential consequences of diversification. In the second part, we discuss the insights provided by evolution experiments in how biofilm growth and structure can promote cooperative phenotypes. Overall, our analysis points to an important role of biofilm diversification and cooperation in bacterial survival and productivity. Deeper understanding of both processes is of key importance to design improved antimicrobial strategies and diagnostic techniques.

This review paper provides an overview of (i) the different experimental models used to study biofilm evolution, (ii) the vast amount of diversification observed during biofilm evolution (including potential causes and consequences) and (iii) recent insights in how growth in biofilms can lead to the evolution of cooperative phenotypes.

Do cell-autonomous and non-cell-autonomous effects drive the structure of tumor ecosystems?

By definition, a driver mutation confers a growth advantage to the cancer cell in which it occurs, while a passenger mutation does not: the former is usually considered as the engine of cancer progression, while the latter is not. Actually, the effects of a given mutation depend on the genetic background of the cell in which it appears, thus can differ in the subclones that form a tumor. In addition to cell-autonomous effects generated by the mutations, non-cell-autonomous effects shape the phenotype of a cancer cell. Here, we review the evidence that a network of biological interactions between subclones drives cancer cell adaptation and amplifies intra-tumor heterogeneity. Integrating the role of mutations in tumor ecosystems generates innovative strategies targeting the tumor ecosystem's weaknesses to improve cancer treatment.

Gene expression variability in clonal populations: Causes and consequences

During the last decade it has been shown that among cell variation in gene expression plays an important role within clonal populations. Here, we provide an overview of the different mechanisms contributing to gene expression variability in clonal populations. These are ranging from inherent variations in the biochemical process of gene expression itself, such as intrinsic noise, extrinsic noise and bistability to individual responses to variations in the local micro-environment, a phenomenon called phenotypic plasticity. Also genotypic variations caused by clonal evolution and phase variation can contribute to gene expression variability. Consequently, gene expression studies need to take these fluctuations in expression into account. However, frequently used techniques for expression quantification, such as microarrays, RNA sequencing, quantitative PCR and gene reporter fusions classically determine the population average of gene expression. Here, we discuss how these techniques can be adapted towards single cell analysis by integration with single cell isolation, RNA amplification and microscopy. Alternatively more qualitative selection-based techniques, such as mutant screenings, in vivo expression technology (IVET) and recombination-based IVET (RIVET) can be applied for detection of genes expressed only within a subpopulation. Finally, differential fluorescence induction (DFI), a protocol specially designed for single cell expression is discussed.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

Spatial evolution of tumors with successive driver mutations

We study the influence of driver mutations on the spatial evolutionary dynamics of solid tumors. We start with a cancer clone that expands uniformly in three dimensions giving rise to a spherical shape. We assume that cell division occurs on the surface of the growing tumor. Each cell division has a chance to give rise to a mutation that activates an additional driver gene. The resulting clone has an enhanced growth rate, which generates a local ensemble of faster growing cells, thereby distorting the spherical shape of the tumor. We derive formulas for the abundance and diversity of additional driver mutations as function of time. Our model is semi-deterministic: the spatial growth of cancer clones is deterministic, while mutants arise stochastically.

Can a minimal replicating construct be identified as the embodiment of cancer?

Genomic instability is a hallmark of cancer. Cancer cells that exhibit abnormal chromosomes are characteristic of most advanced tumours, despite the potential threat represented by accumulated genetic damage. Carcinogenesis involves a loss of key components of the genetic and signalling molecular networks; hence some authors have suggested that this is part of a trend of cancer cells to behave as simple, minimal replicators. In this study, we explore this conjecture and suggest that, in the case of cancer, genomic instability has an upper limit that is associated with a minimal cancer cell network. Such a network would include (for a given microenvironment) the basic molecular components that allow cells to replicate and respond to selective pressures. However, it would also exhibit internal fragilities that could be exploited by appropriate therapies targeting the DNA repair machinery. The implications of this hypothesis are discussed.

Survival probabilities at spherical frontiers

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: R(t) = R0(1 + t/t(∗))Θ, where Θ is a growth exponent, R0 is the initial radius, and t(∗) is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters t(∗) and Θ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary Θ. We compare our results to simulations of linearly inflating expansions (Θ = 1 spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations (Θ = 0, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" (Θ = 1/2) expansions.

Clonal interference and Muller's ratchet in spatial habitats

Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Muller's ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio [Formula: see text] between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using, again, an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation.

Multifocality and recurrence risk: a quantitative model of field cancerization

Primary tumors often emerge within genetically altered fields of premalignant cells that appear histologically normal but have a high chance of progression to malignancy. Clinical observations have suggested that these premalignant fields pose high risks for emergence of recurrent tumors if left behind after surgical removal of the primary tumor. In this work, we develop a spatio-temporal stochastic model of epithelial carcinogenesis, combining cellular dynamics with a general framework for multi-stage genetic progression to cancer. Using the model, we investigate how various properties of the premalignant fields depend on microscopic cellular properties of the tissue. In particular, we provide analytic results for the size-distribution of the histologically undetectable premalignant fields at the time of diagnosis, and investigate how the extent and the geometry of these fields depend upon key groups of parameters associated with the tissue and genetic pathways. We also derive analytical results for the relative risks of local vs. distant secondary tumors for different parameter regimes, a critical aspect for the optimal choice of post-operative therapy in carcinoma patients. This study contributes to a growing literature seeking to obtain a quantitative understanding of the spatial dynamics in cancer initiation.

Quantifying the role of population subdivision in evolution on rugged fitness landscapes

Natural selection drives populations towards higher fitness, but crossing fitness valleys or plateaus may facilitate progress up a rugged fitness landscape involving epistasis. We investigate quantitatively the effect of subdividing an asexual population on the time it takes to cross a fitness valley or plateau. We focus on a generic and minimal model that includes only population subdivision into equivalent demes connected by global migration, and does not require significant size changes of the demes, environmental heterogeneity or specific geographic structure. We determine the optimal speedup of valley or plateau crossing that can be gained by subdivision, if the process is driven by the deme that crosses fastest. We show that isolated demes have to be in the sequential fixation regime for subdivision to significantly accelerate crossing. Using Markov chain theory, we obtain analytical expressions for the conditions under which optimal speedup is achieved: valley or plateau crossing by the subdivided population is then as fast as that of its fastest deme. We verify our analytical predictions through stochastic simulations. We demonstrate that subdivision can substantially accelerate the crossing of fitness valleys and plateaus in a wide range of parameters extending beyond the optimal window. We study the effect of varying the degree of subdivision of a population, and investigate the trade-off between the magnitude of the optimal speedup and the width of the parameter range over which it occurs. Our results, obtained for fitness valleys and plateaus, also hold for weakly beneficial intermediate mutations. Finally, we extend our work to the case of a population connected by migration to one or several smaller islands. Our results demonstrate that subdivision with migration alone can significantly accelerate the crossing of fitness valleys and plateaus, and shed light onto the quantitative conditions necessary for this to occur.

Experimental evidence has recently been accumulating to suggest that fitness landscape ruggedness is common in a variety of organisms. Rugged landscapes arise from interactions between genetic variants, called epistasis, which can lead to fitness valleys or plateaus. The time needed to cross such fitness valleys or plateaus exhibits a rich dependence on population size, since stochastic effects have higher importance in small populations, increasing the probability of fixation of neutral or deleterious mutants. This may lead to an advantage of population subdivision, a possibility which has been strongly debated for nearly one hundred years. In this work, we quantitatively determine when, and to what extent, population subdivision accelerates valley and plateau crossing. Using the simple model of an asexual population subdivided into identical demes connected by gobal migration, we derive the conditions under which crossing by a subdivided population is driven by its fastest deme, thus giving rise to the maximal speedup. Our analytical predictions are verified using stochastic simulations. We investigate the effect of varying the degree of subdivision of a population. We generalize our results to weakly beneficial intermediates and to different population structures. We discuss the magnitude and robustness of the effect for realistic parameter values.

Catastrophic shifts and lethal thresholds in a propagating front model of unstable tumor progression

Unstable dynamics characterizes the evolution of most solid tumors. Because of an increased failure of maintaining genome integrity, a cumulative increase in the levels of gene mutation and loss is observed. Previous work suggests that instability thresholds to cancer progression exist, defining phase transition phenomena separating tumor-winning scenarios from tumor extinction or coexistence phases. Here we present an integral equation approach to the quasispecies dynamics of unstable cancer. The model exhibits two main phases, characterized by either the success or failure of cancer tissue. Moreover, the model predicts that tumor failure can be due to either a reduced selective advantage over healthy cells or excessive instability. We also derive an approximate, analytical solution that predicts the front speed of aggressive tumor populations on the instability space.

Turning ecology and evolution against cancer

The fight against cancer has drawn researchers from a wide variety of disciplines, ranging from molecular biology to physics, but the perspective of an ecological theorist has been mostly overlooked. By thinking about the cells that make up a tumour as an endangered species, cancer vulnerabilities become more apparent. Studies in conservation biology and microbial experiments indicate that extinction is a complex phenomenon, which is often driven by the interaction of ecological and evolutionary processes. Recent advances in cancer research have shown that tumours, like species striving for survival, harbour intricate population dynamics, which suggests the possibility to exploit the ecology of tumours for treatment.

Effect of dedifferentiation on time to mutation acquisition in stem cell-driven cancers

Accumulating evidence suggests that many tumors have a hierarchical organization, with the bulk of the tumor composed of relatively differentiated short-lived progenitor cells that are maintained by a small population of undifferentiated long-lived cancer stem cells. It is unclear, however, whether cancer stem cells originate from normal stem cells or from dedifferentiated progenitor cells. To address this, we mathematically modeled the effect of dedifferentiation on carcinogenesis. We considered a hybrid stochastic-deterministic model of mutation accumulation in both stem cells and progenitors, including dedifferentiation of progenitor cells to a stem cell-like state. We performed exact computer simulations of the emergence of tumor subpopulations with two mutations, and we derived semi-analytical estimates for the waiting time distribution to fixation. Our results suggest that dedifferentiation may play an important role in carcinogenesis, depending on how stem cell homeostasis is maintained. If the stem cell population size is held strictly constant (due to all divisions being asymmetric), we found that dedifferentiation acts like a positive selective force in the stem cell population and thus speeds carcinogenesis. If the stem cell population size is allowed to vary stochastically with density-dependent reproduction rates (allowing both symmetric and asymmetric divisions), we found that dedifferentiation beyond a critical threshold leads to exponential growth of the stem cell population. Thus, dedifferentiation may play a crucial role, the common modeling assumption of constant stem cell population size may not be adequate, and further progress in understanding carcinogenesis demands a more detailed mechanistic understanding of stem cell homeostasis.

Recent evidence suggests that, like many normal tissues, many cancers are maintained by a small population of immortal stem cells that divide indefinitely to produce many differentiated cells. Cancer stem cells may come directly from mutation of normal stem cells, but this route demands high mutation rates, because there are few normal stem cells. There are, however, many differentiated cells, and mutations can cause such cells to “dedifferentiate” into a stem-like state. We used mathematical modeling to study the effects of dedifferentiation on the time to cancer onset. We found that the effect of dedifferentiation depends critically on how stem cell numbers are controlled by the body. If homeostasis is very tight (due to all divisions being asymmetric), then dedifferentiation has little effect, but if homeostatic control is looser (allowing both symmetric and asymmetric divisions), then dedifferentiation can dramatically hasten cancer onset and lead to exponential growth of the cancer stem cell population. Our results suggest that dedifferentiation may be a very important factor in cancer and that more study of dedifferentiation and stem cell control is necessary to understand and prevent cancer onset.