Exploring the relationship between neutral and selective mutations in cancer

A war on many fronts: cross disciplinary approaches for novel cancer treatment strategies

Cancer is a disease characterized by uncontrolled cellular growth where cancer cells take advantage of surrounding cellular populations to obtain resources and promote invasion. Carcinomas are the most common type of cancer accounting for almost 90% of cancer cases. One of the major subtypes of carcinomas are adenocarcinomas, which originate from glandular cells that line certain internal organs. Cancers such as breast, prostate, lung, pancreas, colon, esophageal, kidney are often adenocarcinomas. Current treatment strategies include surgery, chemotherapy, radiation, targeted therapy, and more recently immunotherapy. However, patients with adenocarcinomas often develop resistance or recur after the first line of treatment. Understanding how networks of tumor cells interact with each other and the tumor microenvironment is crucial to avoid recurrence, resistance, and high-dose therapy toxicities. In this review, we explore how mathematical modeling tools from different disciplines can aid in the development of effective and personalized cancer treatment strategies. Here, we describe how concepts from the disciplines of ecology and evolution, economics, and control engineering have been applied to mathematically model cancer dynamics and enhance treatment strategies.

Cell competition and cancer from Drosophila to mammals

Throughout an individual's life, somatic cells acquire cancer-associated mutations. A fraction of these mutations trigger tumour formation, a phenomenon partly driven by the interplay of mutant and wild-type cell clones competing for dominance; conversely, other mutations function against tumour initiation. This mechanism of 'cell competition', can shift clone dynamics by evaluating the relative status of clonal populations, promoting 'winners' and eliminating 'losers'. This review examines the role of cell competition in the context of tumorigenesis, tumour progression and therapeutic intervention.

A Nexus model of cellular transition in cancer

The exact cause of cancer is one of the most immutable medical questions of the century. Cancer as an evolutionary disease must have a purpose and understanding the purpose is more important than decoding the cause. The model of cancer proposed herein, provides a link between the cellular biochemistry and cellular genetics of cancer evolution. We thus call this model as the “Nexus model” of cancer. The Nexus model is an effort to identify the most apparent route to the disease. We have tried to utilize existing cancer literature to identify the most plausible causes of cellular transition in cancer, where the primary cancer-causing agents (physical, chemical or biological) act as inducing factors to produce cellular impeders. These cellular impeders are further linked to the Nexus. The Nexus then generates codes for epigenetics and genetics in cancer development.

Genotype by random environmental interactions gives an advantage to non-favored minor alleles

Fixation probability, the probability that the frequency of a newly arising mutation in a population will eventually reach unity, is a fundamental quantity in evolutionary genetics. Here we use a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population where the fitness is a random function of both allelic state and spatial position, despite neither allele being favored on average. The concept of fitness varying with respect to both genotype and environment is important in models of cancer initiation and progression, bacterial dynamics, and drug resistance. Under our model spatial heterogeneity redefines the notion of neutrality for a newly arising mutation, as such mutations fix at a higher rate than that predicted under neutrality. The increased fixation probability appears to be due to rare alleles having an advantage. The magnitude of this effect can be large, and is an increasing function of the spatial variance and skew in fitness. The effect is largest when the fitness values of the mutants and wild types are anti-correlated across environments. We discuss results for both a spatial ring geometry of cells (such as that of a colonic crypt), a 2D lattice and a mass-action (complete graph) arrangement.

Modelling the evolution of genetic instability during tumour progression

The role of genetic instability in driving carcinogenesis remains controversial. Genetic instability should accelerate carcinogenesis by increasing the rate of advantageous driver mutations; however, genetic instability can also potentially retard tumour growth by increasing the rate of deleterious mutation. As such, it is unclear whether genetically unstable clones would tend to be more selectively advantageous than their genetically stable counterparts within a growing tumour. Here, we show the circumstances where genetic instability evolves during tumour progression towards cancer. We employ a Wright-Fisher type model that describes the evolution of tumour subclones. Clones can acquire both advantageous and deleterious mutations, and mutator mutations that increase a cell's intrinsic mutation rate. Within the model, cancers evolve with a mutator phenotype when driver mutations bestow only moderate increases in fitness: very strong or weak selection for driver mutations suppresses the evolution of a mutator phenotype. Genetic instability occurs secondarily to selectively advantageous driver mutations. Deleterious mutations have relatively little effect on the evolution of genetic instability unless selection for additional driver mutations is very weak or if deleterious mutations are very common. Our model provides a framework for studying the evolution of genetic instability in tumour progression. Our analysis highlights the central role of selection in shaping patterns of mutation in carcinogenesis.

Natural resistance to cancers: a Darwinian hypothesis to explain Peto's paradox

Background

Peto's paradox stipulates that there is no association between body mass (a surrogate of number of cells and longevity) and cancer prevalence in wildlife species. Resolving this paradox is a very promising research direction to understand mechanisms of cancer resistance. As of present, research has been focused on the consequences of these evolutionary pressures rather than of their causes.

Discussion

Here, we argue that evolution through natural selection may have shaped mechanisms of cancer resistance in wildlife species and that this can result in a threshold in body mass above which oncogenic and tumor suppressive mechanisms should be increasingly purified and positively selected, respectively.

Summary

We conclude that assessing wildlife species in their natural ecosystems, especially through theoretical modeling, is the most promising way to understand how evolutionary processes can favor one or the other pathway. This will provide important insights into mechanisms of cancer resistance.

Quasispecies Dynamics of RNA Viruses

RNA viruses, such as human immunodeficiency virus, hepatitis C virus, influenza virus, and poliovirus replicate with very high mutation rates and exhibit very high genetic diversity. The extremely high genetic diversity of RNA virus populations originates that they replicate as complex mutant spectra known as viral quasispecies. The quasispecies dynamics of RNA viruses are closely related to viral pathogenesis and disease, and antiviral treatment strategies. Over the past several decades, the quasispecies concept has been expanded to provide an adequate framework to explain complex behavior of RNA virus populations. Recently, the quasispecies concept has been used to study other complex biological systems, such as tumor cells, bacteria, and prions. Here, we focus on some questions regarding viral and theoretical quasispecies concepts, as well as more practical aspects connected to pathogenesis and resistance to antiviral treatments. A better knowledge of virus diversification and evolution may be critical in preventing and treating the spread of pathogenic viruses.

Quasispecies as a matter of fact: viruses and beyond

We review the origins of the quasispecies concept and its relevance for RNA virus evolution, viral pathogenesis and antiviral treatment strategies. We emphasize a critical point of quasispecies that refers to genome collectivities as the unit of selection, and establish parallels between RNA viruses and some cellular systems such as bacteria and tumor cells. We refer also to tantalizing new observations that suggest quasispecies behavior in prions, perhaps as a result of the same quantum-mechanical indeterminations that underlie protein conformation and error-prone replication in genetic systems. If substantiated, these observations with prions could lead to new research on the structure-function relationship of non-nucleic acid biological molecules.

Stochastic dynamics of cancer initiation

Most human cancer types result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Once the first change (or changes) have arisen, tumorigenesis is initiated and the subsequent emergence of additional alterations drives progression to more aggressive and ultimately invasive phenotypes. Elucidation of the dynamics of cancer initiation is of importance for an understanding of tumor evolution and cancer incidence data. In this paper, we develop a novel mathematical framework to study the processes of cancer initiation. Cells at risk of accumulating oncogenic mutations are organized into small compartments of cells and proliferate according to a stochastic process. During each cell division, an (epi)genetic alteration may arise which leads to a random fitness change, drawn from a probability distribution. Cancer is initiated when a cell gains a fitness sufficiently high to escape from the homeostatic mechanisms of the cell compartment. To investigate cancer initiation during a human lifetime, a 'race' between this fitness process and the aging process of the patient is considered; the latter is modeled as a second stochastic Markov process in an aging dimension. This model allows us to investigate the dynamics of cancer initiation and its dependence on the mutational fitness distribution. Our framework also provides a methodology to assess the effects of different life expectancy distributions on lifetime cancer incidence. We apply this methodology to colorectal tumorigenesis while considering life expectancy data of the US population to inform the dynamics of the aging process. We study how the probability of cancer initiation prior to death, the time until cancer initiation, and the mutational profile of the cancer-initiating cell depends on the shape of the mutational fitness distribution and life expectancy of the population.

New models of neoplastic progression in Barrett's oesophagus

Research in Barrett's oesophagus, and neoplastic progression to OAC (oesophageal adenocarcinoma), is hobbled by the lack of good pre-clinical models that capture the evolutionary dynamics of Barrett's cell populations. Current models trade off tractability for realism. Computational models are perhaps the most tractable and can be used both to interpret data and to develop intuitions and hypotheses for neoplastic progression. Tissue culture models include squamous cell lines, Barrett's oesophagus cell lines and OAC cell lines, although it was recognized recently that BIC-1, SEG-1 and TE-7 are not true OAC cell lines. Some of the unrealistic aspects of the micro-environment in two-dimensional tissue culture may be overcome with the development of three-dimensional organotypic cultures of Barrett's oesophagus. The most realistic, but least tractable, model is a canine surgical model that generates reflux and leads to an intestinal metaplasia. Alternatively, rat surgical models have gained popularity and should be tested for the common genetic features of Barrett's oesophagus neoplastic progression in humans including loss of CDKN2A (cyclin-dependent kinase inhibitor 2A) and TP53 (tumour protein 53), generation of aneuploidy and realistic levels of genetic diversity. This last feature will be important for studying the effects of cancer-prevention interventions. In order to study the dynamics of progression and the effects of an experimental intervention, there is a need to follow animals longitudinally, with periodic endoscopic biopsies. This is now possible and represents an exciting opportunity for the future.

New models of neoplastic progression in Barrett's oesophagus

Research in Barrett's oesophagus, and neoplastic progression to OAC (oesophageal adenocarcinoma), is hobbled by the lack of good pre-clinical models that capture the evolutionary dynamics of Barrett's cell populations. Current models trade off tractability for realism. Computational models are perhaps the most tractable and can be used both to interpret data and to develop intuitions and hypotheses for neoplastic progression. Tissue culture models include squamous cell lines, Barrett's oesophagus cell lines and OAC cell lines, although it was recognized recently that BIC-1, SEG-1 and TE-7 are not true OAC cell lines. Some of the unrealistic aspects of the micro-environment in two-dimensional tissue culture may be overcome with the development of three-dimensional organotypic cultures of Barrett's oesophagus. The most realistic, but least tractable, model is a canine surgical model that generates reflux and leads to an intestinal metaplasia. Alternatively, rat surgical models have gained popularity and should be tested for the common genetic features of Barrett's oesophagus neoplastic progression in humans including loss of CDKN2A (cyclin-dependent kinase inhibitor 2A) and TP53 (tumour protein 53), generation of aneuploidy and realistic levels of genetic diversity. This last feature will be important for studying the effects of cancer-prevention interventions. In order to study the dynamics of progression and the effects of an experimental intervention, there is a need to follow animals longitudinally, with periodic endoscopic biopsies. This is now possible and represents an exciting opportunity for the future.

Evolutionary dynamics of tumor progression with random fitness values

Most human tumors result from the accumulation of multiple genetic and epigenetic alterations in a single cell. Mutations that confer a fitness advantage to the cell are known as driver mutations and are causally related to tumorigenesis. Other mutations, however, do not change the phenotype of the cell or even decrease cellular fitness. While much experimental effort is being devoted to the identification of the functional effects of individual mutations, mathematical modeling of tumor progression generally considers constant fitness increments as mutations are accumulated. In this paper we study a mathematical model of tumor progression with random fitness increments. We analyze a multi-type branching process in which cells accumulate mutations whose fitness effects are chosen from a distribution. We determine the effect of the fitness distribution on the growth kinetics of the tumor. This work contributes to a quantitative understanding of the accumulation of mutations leading to cancer.

The evolutionary impact of androgen levels on prostate cancer in a multi-scale mathematical model

Background

Androgens bind to the androgen receptor (AR) in prostate cells and are essential survival factors for healthy prostate epithelium. Most untreated prostate cancers retain some dependence upon the AR and respond, at least transiently, to androgen ablation therapy. However, the relationship between endogenous androgen levels and cancer etiology is unclear. High levels of androgens have traditionally been viewed as driving abnormal proliferation leading to cancer, but it has also been suggested that low levels of androgen could induce selective pressure for abnormal cells. We formulate a mathematical model of androgen regulated prostate growth to study the effects of abnormal androgen levels on selection for pre-malignant phenotypes in early prostate cancer development.

Results

We find that cell turnover rate increases with decreasing androgen levels, which may increase the rate of mutation and malignant evolution. We model the evolution of a heterogeneous prostate cell population using a continuous state-transition model. Using this model we study selection for AR expression under different androgen levels and find that low androgen environments, caused either by low serum testosterone or by reduced 5α-reductase activity, select more strongly for elevated AR expression than do normal environments. High androgen actually slightly reduces selective pressure for AR upregulation. Moreover, our results suggest that an aberrant androgen environment may delay progression to a malignant phenotype, but result in a more dangerous cancer should one arise.

Conclusions

The model represents a useful initial framework for understanding the role of androgens in prostate cancer etiology, and it suggests that low androgen levels can increase selection for phenotypes resistant to hormonal therapy that may also be more aggressive. Moreover, clinical treatment with 5α-reductase inhibitors such as finasteride may increase the incidence of therapy resistant cancers.

Reviewers

This article was reviewed by Ariosto S. Silva (nominated by Marek Kimmel) and Marek Kimmel.

Unfinished stories on viral quasispecies and Darwinian views of evolution

Experimental evidence that RNA virus populations consist of distributions of mutant genomes, termed quasispecies, was first published 31 years ago. This work provided the earliest experimental support for a theory to explain a system that replicated with limited fidelity and to understand the self-organization and adaptability of early life forms on Earth. High mutation rates and quasispecies dynamics of RNA viruses are intimately related to both viral disease and antiviral treatment strategies. Moreover, the quasispecies concept is being applied to other biological systems such as cancer research in which cellular mutant spectra can be also detected. This review addresses some of the unanswered questions regarding viral and theoretical quasispecies concepts as well as more practical aspects concerning resistance to antiviral treatments and pathogenesis.

Evolutionary theory of cancer

As Theodosius Dobzhansky famously noted in 1973, "Nothing in biology makes sense except in the light of evolution," and cancer is no exception to this rule. Our understanding of cancer initiation, progression, treatment, and resistance has advanced considerably by regarding cancer as the product of evolutionary processes. Here we review the literature of mathematical models of cancer evolution and provide a synthesis and discussion of the field.

Animal cell differentiation patterns suppress somatic evolution

Cell differentiation in multicellular organisms has the obvious function during development of creating new cell types. However, in long-lived organisms with extensive cell turnover, cell differentiation often continues after new cell types are no longer needed or produced. Here, we address the question of why this is true. It is believed that multicellular organisms could not have arisen or been evolutionarily stable without possessing mechanisms to suppress somatic selection among cells within organisms, which would otherwise disrupt organismal integrity. Here, we propose that one such mechanism is a specific pattern of ongoing cell differentiation commonly found in metazoans with cell turnover, which we call "serial differentiation." This pattern involves a sequence of differentiation stages, starting with self-renewing somatic stem cells and proceeding through several (non-self-renewing) transient amplifying cell stages before ending with terminally differentiated cells. To test the hypothesis that serial differentiation can suppress somatic evolution, we used an agent-based computer simulation of cell population dynamics and evolution within tissues. The results indicate that, relative to other, simpler patterns, tissues organized into serial differentiation experience lower rates of detrimental cell-level evolution. Self-renewing cell populations are susceptible to somatic evolution, while those that are not self-renewing are not. We find that a mutation disrupting differentiation can create a new self-renewing cell population that is vulnerable to somatic evolution. These results are relevant not only to understanding the evolutionary origins of multicellularity, but also the causes of pathologies such as cancer and senescence in extant metazoans, including humans.

Cellular automaton simulation examining progenitor hierarchy structure effects on mammary ductal carcinoma in situ

A computer simulation is used to model ductal carcinoma in situ, a form of non-invasive breast cancer. The simulation uses known histological morphology, cell types, and stochastic cell proliferation to evolve tumorous growth within a duct. The ductal simulation is based on a hybrid cellular automaton design using genetic rules to determine each cell's behavior. The genetic rules are a mutable abstraction that demonstrate genetic heterogeneity in a population. Our goal was to examine the role (if any) that recently discovered mammary stem cell hierarchies play in genetic heterogeneity, DCIS initiation and aggressiveness. Results show that simpler progenitor hierarchies result in greater genetic heterogeneity and evolve DCIS significantly faster. However, the more complex progenitor hierarchy structure was able to sustain the rapid reproduction of a cancer cell population for longer periods of time.

Positive selection in the evolution of cancer

We hypothesize that forms of antagonistic coevolution have forged strong links between positive selection at the molecular level and increased cancer risk. By this hypothesis, evolutionary conflict between males and females, mothers and foetuses, hosts and parasites, and other parties with divergent fitness interests has led to rapid evolution of genetic systems involved in control over fertilization and cellular resources. The genes involved in such systems promote cancer risk as a secondary effect of their roles in antagonistic coevolution, which generates evolutionary disequilibrium and maladaptation. Evidence from two sources: (1) studies on specific genes, including SPANX cancer/testis antigen genes, several Y-linked genes, the pem homebox gene, centromeric histone genes, the breast cancer gene BRCA1, the angiogenesis gene ANG, cadherin genes, cytochrome P450 genes, and viral oncogenes; and (2) large-scale database studies of selection on different functional categories of genes, supports our hypothesis. These results have important implications for understanding the evolutionary underpinnings of cancer and the dynamics of antagonistically-coevolving molecular systems.

Simulating the hallmarks of cancer

Cancer can be viewed as the loss of cooperative cell behaviors that normally facilitate multicellularity, including the formation of tissues and organs. Hanahan and Weinberg describe the phenotypic differences between healthy and cancerous cells in an article titled "The Hallmarks of Cancer" (Cell, 100, 57-70, 2000). Here the authors propose six phenotypic changes at the cellular level as the essential hallmarks of cancer. They investigate the dynamics and interactions of these hallmarks in a model known as CancerSim. They describe how CancerSim implements the hallmarks in an agent-based simulation which can help test the hypotheses put forth by Hanahan and Weinberg. Experiments with CancerSim are described that study the interactions of cell phenotype alterations, and in particular, the likely sequences of precancerous mutations, known as pathways. The experiments show that sequencing is an important factor in tumorigenesis, as some mutations have preconditions--they are selectively advantageous only in combination with other mutations. CancerSim enables a modeler to study the dynamics of a developing tumor and simulate how progression can be altered by tuning model parameters.

Evolutionary biology of cancer

Cancer is driven by the somatic evolution of cell lineages that have escaped controls on replication and by the population-level evolution of genes that influence cancer risk. We describe here how recent evolutionary ecological studies have elucidated the roles of predation by the immune system and competition among normal and cancerous cells in the somatic evolution of cancer. Recent analyses of the evolution of cancer at the population level show how rapid changes in human environments have augmented cancer risk, how strong selection has frequently led to increased cancer risk as a byproduct, and how anticancer selection has led to tumor-suppression systems, tissue designs that slow somatic evolution, constraints on morphological evolution and even senescence itself. We discuss how applications of the tools of ecology and evolutionary biology are poised to revolutionize our understanding and treatment of this disease.

The combination of genetic instability and clonal expansion predicts progression to esophageal adenocarcinoma

There is debate in the literature over the relative importance of genetic instability and clonal expansion during progression to cancer. Barrett's esophagus is a uniquely suited model to investigate neoplastic progression prospectively because periodic endoscopic biopsy surveillance is recommended for early detection of esophageal adenocarcinoma. We hypothesized that expansion of clones with genetic instability would predict progression to esophageal adenocarcinoma. We measured p16 (CDKN2A/INK4A) lesions (loss of heterozygosity, mutations, and CpG island methylation), p53 (TP53) lesions (loss of heterozygosity, mutation) and ploidy abnormalities (aneuploidy, tetraploidy) within each Barrett's esophagus segment of a cohort of 267 research participants, who were followed prospectively with cancer as an outcome. We defined the size of a lesion as the fraction of cells with the lesion multiplied by the length of the Barrett's esophagus segment. A Cox proportional hazards regression indicates that the sizes of clones with p53 loss of heterozygosity (relative risk = 1.27(x) for an x cm clone; 95% confidence interval, 1.07-1.50) or ploidy abnormalities (relative risk = 1.31(x) for an x cm clone; 95% confidence interval, 1.07-1.60) predict progression to esophageal adenocarcinoma better than the mere presence of such clones (likelihood ratio test, P < 0.01). Controlling for length of the Barrett's esophagus segment had little effect. The size of a clone with a p16 lesion is not a significant predictor of esophageal adenocarcinoma when we controlled for p53 loss of heterozygosity status. The combination of clonal expansion and genetic instability is a better predictor of cancer outcome than either alone. This implies that interventions that limit expansion of genetically unstable clones may reduce risk of progression to cancer.

Selectively advantageous mutations and hitchhikers in neoplasms: p16 lesions are selected in Barrett's esophagus

Neoplastic progression is an evolutionary process characterized by genomic instability and waves of clonal expansions carrying genetic and epigenetic lesions to fixation (100% of the cell population). However, an evolutionarily neutral lesion may also reach fixation if it spreads as a hitchhiker on a selective sweep. We sought to distinguish advantageous lesions from hitchhikers in the premalignant condition Barrett's esophagus. Patients (211) had biopsies taken at 2-cm intervals in their Barrett's segments. Purified epithelial cells were assayed for loss of heterozygosity and microsatellite shifts on chromosomes 9 and 17, sequence mutations in CDKN2A/MTS1/INK4a (p16) and TP53 (p53), and methylation of the p16 promoter. We measured the expanse of a lesion in a Barrett's segment as the proportion of proliferating cells that carried a lesion in that locus. We then selected the lesion having expanses >90% in the greatest number of patients as our first putative advantageous lesion. We filtered out hitchhikers by removing all expanses of other lesions that did not occur independent of the advantageous lesion. The entire process was repeated on the remaining expanses to identify additional advantageous lesions. p16 loss of heterozygosity, promoter methylation, and sequence mutations have strong, independent, advantageous effects on Barrett's cells early in progression. Second lesions in p16 and p53 are associated with later selective sweeps. Virtually all of the other lesion expansions, including microsatellite shifts, could be explained as hitchhikers on p16 lesion clonal expansions. These techniques can be applied to any neoplasm.

Cancer Prevention Strategies That Address the Evolutionary Dynamics of Neoplastic Cells: Simulating Benign Cell Boosters and Selection for Chemosensitivity

Cells in neoplasms evolve by natural selection. Traditional cytotoxic chemotherapies add further selection pressure to the evolution of neoplastic cells, thereby selecting for cells resistant to the therapies. An alternative proposal is a benign cell booster. Rather than trying to kill the highly dysplastic or malignant cells directly, a benign cell booster increases the fitness of the more benign cells, which may be either normal or benign clones, so that they may outcompete more advanced or malignant cells in a neoplasm. In silico simulations of benign cell boosters in neoplasms with evolving clones show benign cell boosters to be effective at destroying advanced or malignant cells and preventing relapse even when applied late in progression. These results are conditional on the benign cell boosters giving a competitive advantage to the benign cells in the neoplasm. Furthermore, the benign cell boosters must be applied over a long period of time in order for the benign cells to drive the dysplastic cells to extinction or near extinction. Most importantly, benign cell boosters based on this strategy must target a characteristic of the benign cells that is causally related to the benign state to avoid relapse. Another promising strategy is to boost cells that are sensitive to a cytotoxin, thereby selecting for chemosensitive cells, and then apply the toxin. Effective therapeutic and prevention strategies will have to alter the competitive dynamics of a neoplasm to counter progression toward invasion, metastasis, and death.