A simple algebraic cancer equation: calculating how cancers may arise with normal mutation rates

Cancer Prevalence across Vertebrates

Cancer is pervasive across multicellular species, but what explains the differences in cancer prevalence across species? Using 16,049 necropsy records for 292 species spanning three clades of tetrapods (amphibians, sauropsids, and mammals), we found that neoplasia and malignancy prevalence increases with adult mass (contrary to Peto's paradox) and somatic mutation rate but decreases with gestation time. The relationship between adult mass and malignancy prevalence was only apparent when we controlled for gestation time. Evolution of cancer susceptibility appears to have undergone sudden shifts followed by stabilizing selection. Outliers for neoplasia prevalence include the common porpoise (<1.3%), the Rodrigues fruit bat (<1.6%), the black-footed penguin (<0.4%), ferrets (63%), and opossums (35%). Discovering why some species have particularly high or low levels of cancer may lead to a better understanding of cancer syndromes and novel strategies for the management and prevention of cancer. Significance: Evolution has discovered mechanisms for suppressing cancer in a wide variety of species. By analyzing veterinary necropsy records, we can identify species with exceptionally high or low cancer prevalence. Discovering the mechanisms of cancer susceptibility and resistance may help improve cancer prevention and explain cancer syndromes. See related commentary by Metzger, p. 14.

Revealing endogenous conditions for Peto's paradox via an ordinary differential equation model

Cancer, a disease intimately linked to cellular mutations, is commonly believed to exhibit a positive association with the cell count and lifespan of a species. Despite this assumption, the observed uniformity in cancer rates across species, referred to as the Peto's paradox, presents a conundrum. Recognizing that tumour progression is not solely dependent on cancer cells but involves intricate interactions among various cell types, this study employed a Lotka-Volterra (LV) ordinary differential equation model to analyze the evolution of cancerous cells and the cancer incidence in an immune environment. As a result, this study uncovered the sufficient conditions underlying the absence of correlation in Peto's paradox and provide insights into the reasons for the equitable distribution of cancer incidence across diverse species by applying nondimensionalization and drawing an analogy between the characteristic time interval for the variation of cell populations in the ODE model and that of cell cycles of a species.

Cancer Prevalence Across Vertebrates

Cancer is pervasive across multicellular species, but what explains differences in cancer prevalence across species? Using 16,049 necropsy records for 292 species spanning three clades (amphibians, sauropsids and mammals) we found that neoplasia and malignancy prevalence increases with adult weight (contrary to Petos Paradox) and somatic mutation rate, but decreases with gestation time. Evolution of cancer susceptibility appears to have undergone sudden shifts followed by stabilizing selection. Outliers for neoplasia prevalence include the common porpoise (<1.3%), the Rodrigues fruit bat (<1.6%) the black-footed penguin (<0.4%), ferrets (63%) and opossums (35%). Discovering why some species have particularly high or low levels of cancer may lead to a better understanding of cancer syndromes and novel strategies for the management and prevention of cancer.

Cancer Prevalence Across Vertebrates

Cancer is pervasive across multicellular species, but what explains differences in cancer prevalence across species? Using 16,049 necropsy records for 292 species spanning three clades (amphibians, sauropsids and mammals) we found that neoplasia and malignancy prevalence increases with adult weight (contrary to Peto's Paradox) and somatic mutation rate, but decreases with gestation time. Evolution of cancer susceptibility appears to have undergone sudden shifts followed by stabilizing selection. Outliers for neoplasia prevalence include the common porpoise (<1.3%), the Rodrigues fruit bat (<1.6%) the black-footed penguin (<0.4%), ferrets (63%) and opossums (35%). Discovering why some species have particularly high or low levels of cancer may lead to a better understanding of cancer syndromes and novel strategies for the management and prevention of cancer.

A mathematical model for cancer risk and accumulation of mutations caused by replication errors and external factors

Replication errors influence mutations, and thus, lifetime cancer risk can be explained by the number of stem-cell divisions. Additionally, mutagens also affect cancer risk, for instance, high-dose radiation exposure increases lifetime cancer risk. However, the influence of low-dose radiation exposure is still unclear because this influence, if any, is very slight. We can assess the minimal influence of the mutagen by virtually comparing the states with and without mutagen using a mathematical model. Here, we constructed a mathematical model to assess the influence of replication errors and mutagens on cancer risk. In our model, replication errors occur with a certain probability during cell division. Mutagens cause mutations at a constant rate. Cell division is arrested when the number of cells reaches the capacity of the cell pool. When the number of cells decreases because of cell death or other reasons, cells resume division. It was assumed that the mutations of cancer driver genes occur stochastically with each mutation and that cancer occurs when the number of cancer driver gene mutations exceeds a certain threshold. We approximated the number of mutations caused by errors and mutagens. Then, we examined whether cancer registry data on cancer risk can be explained only through replication errors. Although the risk of leukemia was not fitted to the model, the risks of esophageal, liver, thyroid, pancreatic, colon, breast, and prostate cancers were explained only by replication errors. Even if the risk was explained by replication errors, the estimated parameters did not always agree with previously reported values. For example, the estimated number of cancer driver genes in lung cancer was larger than the previously reported values. This discrepancy can be partly resolved by assuming the influence of mutagen. First, the influence of mutagens was analyzed using various parameters. The model predicted that the influence of mutagens will appear earlier, when the turnover rate of the tissue is higher and fewer mutations of cancer driver genes were necessary for carcinogenesis. Next, the parameters of lung cancer were re-estimated assuming the influence of mutagens. The estimated parameters were closer to the previously reported values. than when considering only replication errors. Although it may be useful to explain cancer risk by replication errors, it would be biologically more plausible to consider mutagens in cancers in which the effects of mutagens are apparent.

The Erlang distribution approximates the age distribution of incidence of childhood and young adulthood cancers

Background

It is widely believed that cancers develop upon acquiring a particular number of (epi) mutations in driver genes, but the law governing the kinetics of this process is not known. We have previously shown that the age distribution of incidence for the 20 most prevalent cancers of old age is best approximated by the Erlang probability distribution. The Erlang distribution describes the probability of several successive random events occurring by the given time according to the Poisson process, which allows an estimate for the number of critical driver events.

Methods

Here we employ a computational grid search method to find global parameter optima for five probability distributions on the CDC WONDER dataset of the age distribution of childhood and young adulthood cancer incidence.

Results

We show that the Erlang distribution is the only classical probability distribution we found that can adequately model the age distribution of incidence for all studied childhood and young adulthood cancers, in addition to cancers of old age.

Conclusions

This suggests that the Poisson process governs driver accumulation at any age and that the Erlang distribution can be used to determine the number of driver events for any cancer type. The Poisson process implies the fundamentally random timing of driver events and their constant average rate. As waiting times for the occurrence of the required number of driver events are counted in decades, and most cells do not live this long, it suggests that driver mutations accumulate silently in the longest-living dividing cells in the body—the stem cells.

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.

A speculative discussion of four animal carcinogens endogenously produced in humans and a formula for cancer development

The major factors (macro) which cause human cancer have been elucidated and include tobacco use, diet, infection, reproductive and sexual behavior and, to a lesser extent, alcohol consumption and occupational factors. Several reports have been published about endogenous chemicals made in humans which produce DNA adducts; however, few have linked them to possible carcinogenic activity. This paper discussed four chemicals made in humans (formaldehyde, acetaldehyde, isoprene and ethylene oxide), pathways of their formation, their animal carcinogenicity and questions about these and other endogenous chemicals’ possible role in human cancer. In addition, the author posits a simplified formula for development of cancer and a formula for causing mutations by various agents.

Predation shapes the impact of cancer on population dynamics and the evolution of cancer resistance

Cancer is a widespread disease that affects most of the metazoans. However, cancer development is a slow process and, long before causing the death of the individual, may weaken organisms' capacities and impair their interactions with other species. Yet, the impact of cancer development on biotic interactions, and over the dynamics of the whole ecosystem, is still largely unexplored. As well, the feedback of altered biotic interactions on the evolution of resistance against cancer in the context of community ecology has not been investigated. From this new perspective, we theoretically investigate how cancer can challenge expected interaction outcomes in a predator-prey model system, and how, in return, these altered interaction outcomes could affect evolution of resistance mechanism against cancer. First, we demonstrate a clear difference between prey and predator vulnerability to cancer, with cancer having a limited impact on prey populations. Second, we show that biotic interactions can surprisingly lead to a null or positive effect of cancer on population densities. Finally, our evolutionary analysis sheds light on how biotic interactions can lead to diverse resistance levels in predator populations. While its role in ecosystems is mostly unknown, we demonstrate that cancer in wildlife is an important ecological and evolutionary force to consider.

Context-dependent selection as the keystone in the somatic evolution of cancer

Somatic evolution of cancer involves a series of mutations, and attendant changes, in one or more clones of cells. A “bad luck” type model assumes chance accumulation of mutations. The clonal expansion model assumes, on the other hand, that any mutation leading to partial loss of regulation of cell proliferation will give a selective advantage to the mutant. However, a number of experiments show that an intermediate pre-cancer mutant has only a conditional selective advantage. Given that tissue microenvironmental conditions differ across individuals, this selective advantage to a mutant could be widely distributed over the population. We evaluate three models, namely “bad luck”, context-independent, and context-dependent selection, in a comparative framework, on their ability to predict patterns in total incidence, age-specific incidence, stem cell number-incidence relationship and other known phenomena associated with cancers. Results show that among the factors considered in the model, context dependence is necessary and sufficient to explain observed epidemiological patterns, and that cancer evolution is largely selection-limited, rather than mutation-limited. A wide range of physiological, genetic and behavioural factors influence the tissue micro-environment, and could therefore be the source of this context dependence in somatic evolution of cancer. The identification and targeting of these micro-environmental factors that influence the dynamics of selection offer new possibilities for cancer prevention.

Sensitivity analysis methods in the biomedical sciences

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presentation of their results.

Accelerated Evolution in Distinctive Species Reveals Candidate Elements for Clinically Relevant Traits, Including Mutation and Cancer Resistance

The identity of most functional elements in the mammalian genome and the phenotypes they impact are unclear. Here, we perform a genomewide comparative analysis of patterns of accelerated evolution in species with highly distinctive traits to discover candidate functional elements for clinically important phenotypes. We identify accelerated regions (ARs) in the elephant, hibernating bat, orca, dolphin, naked mole rat, and thirteen-lined ground squirrel lineages in mammalian conserved regions, uncovering ~33,000 elements that bind hundreds of different regulatory proteins in humans and mice. ARs in the elephant, the largest land mammal, are uniquely enriched near elephant DNA damage response genes. The genomic hotspot for elephant ARs is the E3 ligase subunit of the Fanconi anemia complex, a master regulator of DNA repair. Additionally, ARs in the six species are associated with specific human clinical phenotypes that have apparent concordance with overt traits in each species.

Risk Factors for Development of Canine and Human Osteosarcoma: A Comparative Review

Osteosarcoma is the most common primary tumor of bone. Osteosarcomas are rare in humans, but occur more commonly in dogs. A comparative approach to studying osteosarcoma has highlighted many clinical and biologic aspects of the disease that are similar between dogs and humans; however, important species-specific differences are becoming increasingly recognized. In this review, we describe risk factors for the development of osteosarcoma in dogs and humans, including height and body size, genetics, and conditions that increase turnover of bone-forming cells, underscoring the concept that stochastic mutational events associated with cellular replication are likely to be the major molecular drivers of this disease. We also discuss adaptive, cancer-protective traits that have evolved in large, long-lived mammals, and how increasing size and longevity in the absence of natural selection can account for the elevated bone cancer risk in modern domestic dogs.

Multi-stage models for the failure of complex systems, cascading disasters, and the onset of disease

Complex systems can fail through different routes, often progressing through a series of (rate-limiting) steps and modified by environmental exposures. The onset of disease, cancer in particular, is no different. Multi-stage models provide a simple but very general mathematical framework for studying the failure of complex systems, or equivalently, the onset of disease. They include the Armitage-Doll multi-stage cancer model as a particular case, and have potential to provide new insights into how failures and disease, arise and progress. A method described by E.T. Jaynes is developed to provide an analytical solution for a large class of these models, and highlights connections between the convolution of Laplace transforms, sums of random variables, and Schwinger/Feynman parameterisations. Examples include: exact solutions to the Armitage-Doll model, the sum of Gamma-distributed variables with integer-valued shape parameters, a clonal-growth cancer model, and a model for cascading disasters. Applications and limitations of the approach are discussed in the context of recent cancer research. The model is sufficiently general to be used in many contexts, such as engineering, project management, disease progression, and disaster risk for example, allowing the estimation of failure rates in complex systems and projects. The intended result is a mathematical toolkit for applying multi-stage models to the study of failure rates in complex systems and to the onset of disease, cancer in particular.

A generalized theory of age-dependent carcinogenesis

The Multi-Stage Model of Carcinogenesis (MMC), developed in the 1950 s-70s, postulated carcinogenesis as a Darwinian somatic selection process. The cellular organization of tissues was then poorly understood, with almost nothing known about cancer drivers and stem cells. The MMC paradigm was later confirmed, and cancer incidence was explained as a function of mutation occurrence. However, the MMC has never been tested for its ability to account for the discrepancies in the number of driver mutations and the organization of the stem cell compartments underlying different cancers that still demonstrate nearly universal age-dependent incidence patterns. Here we demonstrate by Monte Carlo modeling the impact of key somatic evolutionary parameters on the MMC performance, revealing that two additional major mechanisms, aging-dependent somatic selection and life history-dependent evolution of species-specific tumor suppressor mechanisms, need to be incorporated into the MMC to make it capable of generalizing cancer incidence across tissues and species.

Editorial note

This article has been through an editorial process in which the authors decide how to respond to the issues raised during peer review. The Reviewing Editor's assessment is that all the issues have been addressed (see decision letter).

Systemic Metabolism, Its Regulators, and Cancer: Past Mistakes and Future Potential

There has been a resurgence of interest in cancer metabolism; primarily in the resetting of metabolism within malignant cells. Metabolism within cells has always been a tightly regulated process; initially in protozoans due to metabolic enzymes, and the intracellular signaling pathways that regulate these, being directly sensitive to the availability of nutrients. With the evolution of metazoans many of these controls had been overlaid by extra-cellular regulators that ensured coordinated regulation of metabolism within the community of cells that comprised the organism. Central to these systemic regulators is the insulin/insulin-like growth factor (IGF) system that throughout evolution has integrated the control of tissue growth with metabolic status. Oncological interest in the main systemic metabolic regulators greatly subsided when pharmaceutical strategies designed to treat cancers failed in the clinic. During the same period, however the explosion of new information from genetics has revealed the complexity and heterogeneity of advanced cancers and helped explain the problems of managing cancer when it reaches such a stage. Evidence has also accumulated implying that the setting of the internal environment determines whether cancers progress to advanced disease and metabolic status is clearly an important component of this local ecology. We are in the midst of an epidemic of metabolic disorders and there is considerable research into strategies for controlling metabolism. Integrating these new streams of information suggests new possibilities for cancer prevention; both primary and secondary.

Non-local Parabolic and Hyperbolic Models for Cell Polarisation in Heterogeneous Cancer Cell Populations

Tumours consist of heterogeneous populations of cells. The sub-populations can have different features, including cell motility, proliferation and metastatic potential. The interactions between clonal sub-populations are complex, from stable coexistence to dominant behaviours. The cell–cell interactions, i.e. attraction, repulsion and alignment, processes critical in cancer invasion and metastasis, can be influenced by the mutation of cancer cells. In this study, we develop a mathematical model describing cancer cell invasion and movement for two polarised cancer cell populations with different levels of mutation. We consider a system of non-local hyperbolic equations that incorporate cell–cell interactions in the speed and the turning behaviour of cancer cells, and take a formal parabolic limit to transform this model into a non-local parabolic model. We then investigate the possibility of aggregations to form, and perform numerical simulations for both hyperbolic and parabolic models, comparing the patterns obtained for these models.

Cancer Risks Linked to the Bad Luck Hypothesis and Epigenomic Mutational Signatures

Exposure to pathogen infection, and occupational and environmental agents, contributes to induction of most types of cancer through different mechanisms. Cancer is defined and characterized by accumulation of mutations and epimutations that lead to changes in the cellular genome and epigenome. According to a recent Bad Luck Hypothesis, random error mutations during DNA replication in a small population of stem cells may be implicated in two-thirds of variation of cancer risk in 25 organs and tissues. What determines stem cell vulnerability and risk of malignancy across the spectrum of organs, such as the brain, bone marrow, skeletal muscles, skin, and liver? Have stem cells pooled in particular tissues or organs evolved some critical ability to deal with DNA damage in the presence of extrinsic environmental factors? This paper describes how the complex replication and repair DNA systems control mutational events. In addition, recent advances on cancer epigenomic signatures and epigenetic mechanisms are discussed, which will guide future investigation of the origin of cancer initiating cells in tissue and organs in a clinical setting.

Bioenergetics of life, disease and death phenomena

In this article, some new aspects of unified cell bioenergetics are presented. From the perspective of unified cell bioenergetics certain subsequent stages of cancer development, from initiation stage, through transformation to metastasis, are analyzed. Here we show that after transformation, cancer cells are permanently exposed to reactive oxygen species, that causes continual random DNA mutations and as a result genome and chromosomal destabilizations. The modern cancer attractor hypothesis has been extended in explaining cancer development. Discussion is conducted in light of current cancerogenesis research, including bioenergetic cancer initiation, the somatic mutation theory and the tissue organization field theory. In the article reasons complicating the discovery of patterns of cancer genome changes and cancer evolution are presented. In addition certain cancer therapeutic aspects are given attention to.

A Simple 3-Parameter Model for Cancer Incidences

We propose a simple 3-parameter model that provides very good fits for incidence curves of 18 common solid cancers even when variations due to different locations, races, or periods are taken into account. From a data perspective, we use model selection (Akaike information criterion) to show that this model, which is based on the Weibull distribution, outperforms other simple models like the Gamma distribution. From a modeling perspective, the Weibull distribution can be justified as modeling the accumulation of driver events, which establishes a link to stem cell division based cancer development models and a connection to a recursion formula for intrinsic cancer risk published by Wu et al. For the recursion formula a closed form solution is given, which will help to simplify future analyses. Additionally, we perform a sensitivity analysis for the parameters, showing that two of the three parameters can vary over several orders of magnitude. However, the shape parameter of the Weibull distribution, which corresponds to the number of driver mutations required for cancer onset, can be robustly estimated from epidemiological data.

The Biology of Aging and Cancer: A Brief Overview of Shared and Divergent Molecular Hallmarks

Aging is the inevitable time-dependent decline in physiological organ function and is a major risk factor for cancer development. Due to advances in health care, hygiene control and food availability, life expectancy is increasing and the population in most developed countries is shifting to an increasing proportion of people at a cancer susceptible age. Mechanisms of aging are also found to occur in carcinogenesis, albeit with shared or divergent end-results. It is now clear that aging and cancer development either share or diverge in several disease mechanisms. Such mechanisms include the role of genomic instability, telomere attrition, epigenetic changes, loss of proteostasis, decreased nutrient sensing and altered metabolism, but also cellular senescence and stem cell function. Cancer cells and aged cells are also fundamentally opposite, as cancer cells can be thought of as hyperactive cells with advantageous mutations, rapid cell division and increased energy consumption, while aged cells are hypoactive with accumulated disadvantageous mutations, cell division inability and a decreased ability for energy production and consumption. Nonetheless, aging and cancer are tightly interconnected and many of the same strategies and drugs may be used to target both, while in other cases antagonistic pleiotrophy come into effect and inhibition of one can be the activation of the other. Cancer can be considered an aging disease, though the shared mechanisms underpinning the two processes remain unclear. Better understanding of the shared and divergent pathways of aging and cancer is needed.

Size, longevity and cancer: age structure

There is significant recent interest in Peto's paradox and the related problem of the evolution of large, long-lived organisms in terms of cancer robustness. Peto's paradox refers to the expectation that large, long-lived organisms have a higher lifetime cancer risk, which is not the case: a paradox. This paradox, however, is circular: large, long-lived organisms are large and long-lived because they are cancer robust. Lifetime risk, meanwhile, depends on the age distributions of both cancer and competing risks: if cancer strikes before competing risks, then lifetime risk is high; if not, not. Because no set of competing risks is generally prevalent, it is instructive to temporarily dispose of competing risks and investigate the pure age dynamics of cancer under the multistage model of carcinogenesis. In addition to augmenting earlier results, I show that in terms of cancer-free lifespan large organisms reap greater benefits from an increase in cellular cancer robustness than smaller organisms. Conversely, a higher cellular cancer robustness renders cancer-free lifespan more resilient to an increase in size. This interaction may be an important driver of the evolution of large, cancer-robust organisms.

Towards cancer-aware life-history modelling

Studies of body size evolution, and life-history theory in general, are conducted without taking into account cancer as a factor that can end an organism's reproductive lifespan. This reflects a tacit assumption that predation, parasitism and starvation are of overriding importance in the wild. We argue here that even if deaths directly attributable to cancer are a rarity in studies of natural populations, it remains incorrect to infer that cancer has not been of importance in shaping observed life histories. We present first steps towards a cancer-aware life-history theory, by quantifying the decrease in the length of the expected reproductively active lifespan that follows from an attempt to grow larger than conspecific competitors. If all else is equal, a larger organism is more likely to develop cancer, but, importantly, many factors are unlikely to be equal. Variations in extrinsic mortality as well as in the pace of life—larger organisms are often near the slow end of the fast–slow life-history continuum—can make realized cancer incidences more equal across species than what would be observed in the absence of adaptive responses to cancer risk (alleviating the so-called Peto's paradox). We also discuss reasons why patterns across species can differ from within-species predictions. Even if natural selection diminishes cancer susceptibility differences between species, within-species differences can remain. In many sexually dimorphic cases, we predict males to be more cancer-prone than females, forming an understudied component of sexual conflict.

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.

Sporadic colorectal cancer: Studying ways to an end

INTRODUCTION

Although colorectal cancer (CRC) has often been regarded as a single entity, different pathways may lead to macroscopically similar cancers. These pathways may evolve into a patchy colonic field defect that we aimed to study in consecutive CRC patients.

METHODS

In a single-center, observational, prospective study, consecutive CRC patients were included if surgery and a perioperative colonoscopy were planned. Personal and familial history data were collected. Tumors were studied for microsatellite instability (MSI) status, DNA repair protein expression (DRPE) and presence of BRAF and/or APC mutations. Macroscopically normal mucosa samples were tested for APC mutations. Presence and location of synchronous and metachronous adenomas and patient follow-up were analyzed. The association of two categorical variables was tested through the Fisher's exact test (SPSS 19).

RESULTS

Twenty-four patients (12 male, mean age 69 years) were studied. High-grade MSI (MSI-H) was found in eight tumors-these were significantly more common in the right colon (p = 0.047) and more likely to have an altered DRPE (p = 0.007). BRAF mutation was found in two of six tested MSI-H tumors. APC gene mutations were found in nine of 16 non-MSI-H tumors and absent in normal mucosa samples. There was a nonsignificant co-localization of CRC and synchronous adenomas and a significant co-localization (p = 0.05) of synchronous and metachronous adenomas.

DISCUSSION

Sporadic CRCs evolve through distinct pathways, evidenced only by pathological and molecular analysis, but clinically relevant both for patients and their families. In non-MSI-H tumors, the expected APC gene mutations were not detected by the most commonly used techniques in a high number of cases. More studies are needed to fully characterize these tumors and to search for common early events in normal mucosa patches, which might explain the indirect evidence found here for a field defect in the colon.

Potential Mechanisms for Cancer Resistance in Elephants and Comparative Cellular Response to DNA Damage in Humans

IMPORTANCE

Evolutionary medicine may provide insights into human physiology and pathophysiology, including tumor biology.

OBJECTIVE

To identify mechanisms for cancer resistance in elephants and compare cellular response to DNA damage among elephants, healthy human controls, and cancer-prone patients with Li-Fraumeni syndrome (LFS).

DESIGN, SETTING, AND PARTICIPANTS

A comprehensive survey of necropsy data was performed across 36 mammalian species to validate cancer resistance in large and long-lived organisms, including elephants (n = 644). The African and Asian elephant genomes were analyzed for potential mechanisms of cancer resistance. Peripheral blood lymphocytes from elephants, healthy human controls, and patients with LFS were tested in vitro in the laboratory for DNA damage response. The study included African and Asian elephants (n = 8), patients with LFS (n = 10), and age-matched human controls (n = 11). Human samples were collected at the University of Utah between June 2014 and July 2015.

EXPOSURES

Ionizing radiation and doxorubicin.

MAIN OUTCOMES AND MEASURES

Cancer mortality across species was calculated and compared by body size and life span. The elephant genome was investigated for alterations in cancer-related genes. DNA repair and apoptosis were compared in elephant vs human peripheral blood lymphocytes.

RESULTS

Across mammals, cancer mortality did not increase with body size and/or maximum life span (eg, for rock hyrax, 1% [95% CI, 0%-5%]; African wild dog, 8% [95% CI, 0%-16%]; lion, 2% [95% CI, 0%-7%]). Despite their large body size and long life span, elephants remain cancer resistant, with an estimated cancer mortality of 4.81% (95% CI, 3.14%-6.49%), compared with humans, who have 11% to 25% cancer mortality. While humans have 1 copy (2 alleles) of TP53, African elephants have at least 20 copies (40 alleles), including 19 retrogenes (38 alleles) with evidence of transcriptional activity measured by reverse transcription polymerase chain reaction. In response to DNA damage, elephant lymphocytes underwent p53-mediated apoptosis at higher rates than human lymphocytes proportional to TP53 status (ionizing radiation exposure: patients with LFS, 2.71% [95% CI, 1.93%-3.48%] vs human controls, 7.17% [95% CI, 5.91%-8.44%] vs elephants, 14.64% [95% CI, 10.91%-18.37%]; P < .001; doxorubicin exposure: human controls, 8.10% [95% CI, 6.55%-9.66%] vs elephants, 24.77% [95% CI, 23.0%-26.53%]; P < .001).

CONCLUSIONS AND RELEVANCE

Compared with other mammalian species, elephants appeared to have a lower-than-expected rate of cancer, potentially related to multiple copies of TP53. Compared with human cells, elephant cells demonstrated increased apoptotic response following DNA damage. These findings, if replicated, could represent an evolutionary-based approach for understanding mechanisms related to cancer suppression.

Peto's paradox and the promise of comparative oncology

The past several decades have seen a paradigm shift with the integration of evolutionary thinking into studying cancer. The evolutionary lens is most commonly employed in understanding cancer emergence, tumour growth and metastasis, but there is an increasing realization that cancer defences both between tissues within the individual and between species have been influenced by natural selection. This special issue focuses on discoveries of these deeper evolutionary phenomena in the emerging area of 'comparative oncology'. Comparing cancer dynamics in different tissues or species can lead to insights into how biology and ecology have led to differences in carcinogenesis, and the diversity, incidence and lethality of cancers. In this introduction to the special issue, we review the history of the field and outline how the contributions use empirical, comparative and theoretical approaches to address the processes and patterns associated with 'Peto's paradox', the lack of a statistical relationship of cancer incidence with body size and longevity. This burgeoning area of research can help us understand that cancer is not only a disease but is also a driving force in biological systems and species life histories. Comparative oncology will be key to understanding globally important health issues, including cancer epidemiology, prevention and improved therapies.

Cell size and cancer: a new solution to Peto's paradox?

Cancer, one of the leading health concerns for humans, is by no means a human-unique malady. Accumulating evidence shows that cancer kills domestic and wild animals at a similar rate to humans and can even pose a conservation threat to certain species. Assuming that each physiologically active and proliferating cell is at risk of malignant transformation, any evolutionary increase in the number of cells (and thus body mass) will lead to a higher cancer frequency, all else being equal. However, available data fail to support the prediction that bigger animals are affected by cancer more than smaller ones. The unexpected lack of correlation between body size (and life span) and cancer risk across taxa was dubbed Peto's paradox. In this perspective, several plausible explanations of Peto's paradox are presented, with the emphasis on a largely underappreciated relation of cell size to both metabolism and cell division rates across species, which we believe are key factors underlying the paradox. We conclude that larger organisms have bigger and slowly dividing cells with lower energy turnover, all significantly reducing the risk of cancer initiation. Solving Peto's paradox will enhance our understanding the evolution of cancer and may provide new implications for cancer prevention and treatment.

Evolution of ibrutinib resistance in chronic lymphocytic leukemia (CLL)

The Bruton tyrosine kinase inhibitor (BTKi) ibrutinib is a new targeted therapy for patients with chronic lymphocytic leukemia (CLL). Ibrutinib is given orally on a continuous schedule and induces durable remissions in the majority of CLL patients. However, a small proportion of patients initially responds to the BTKi and then develops resistance. Estimating the frequency, timing, and individual risk of developing resistance to ibrutinib, therefore, would be valuable for long-term management of patients. Computational evolutionary models, based on measured kinetic parameters of patients, allow us to approach these questions and to develop a roadmap for personalized prognosis and treatment management. Our kinetic models predict that BTKi-resistant mutants exist before initiation of ibrutinib therapy, although they only comprise a minority of the overall tumor burden. Furthermore, we can estimate the time required for resistant cells to grow to detectable levels. We predict that this can be highly variable, depending mostly on growth and death rates of the individual CLL cell clone. For a specific patient, this time can be predicted with a high degree of certainty. Our model can thus be used to predict for how long ibrutinib can suppress the disease in individual patients. Furthermore, the model can suggest whether prior debulking of the tumor with chemo-immunotherapy can prolong progression-free survival under ibrutinib. Finally, by applying the models to data that document progression during ibrutinib therapy, we estimated that resistant mutants might have a small (<2%) mean fitness advantage in the absence of treatment, compared with sensitive cells.

The protective role of symmetric stem cell division on the accumulation of heritable damage

Stem cell divisions are either asymmetric—in which one daughter cell remains a stem cell and one does not—or symmetric, in which both daughter cells adopt the same fate, either stem or non-stem. Recent studies show that in many tissues operating under homeostatic conditions stem cell division patterns are strongly biased toward the symmetric outcome, raising the question of whether symmetry confers some benefit. Here, we show that symmetry, via extinction of damaged stem-cell clones, reduces the lifetime risk of accumulating phenotypically silent heritable damage (mutations or aberrant epigenetic changes) in individual stem cells. This effect is greatest in rapidly cycling tissues subject to accelerating rates of damage accumulation over time, a scenario that describes the progression of many cancers. A decrease in the rate of cellular damage accumulation may be an important factor favoring symmetric patterns of stem cell division.

Recently, highly symmetric patterns of stem cell division have been observed in a variety of adult mammalian somatic tissues. Here we identify conditions under which this behavior serves as a strategy to protect the organism against mutation accumulation. First, we find that a sufficient number of lifetime stem cell divisions must occur, potentially explaining why stem cell pools with the most symmetric divisions are rapidly cycling. Second, we find that late-occurring mutations must occur rapidly, a scenario known in cancer biology as genetic instability. These findings provide a potential explanation for the observation that cancer risks among large, long-lived organisms fail to rise as expected with lifespan and body size.

Epithelial cancers in the post-genomic era: should we reconsider our lifestyle?

The age-related epithelial cancers of the breast, colorectum and prostate are the most prevalent and are increasing in our aging populations. Epithelial cells turnover rapidly and mutations naturally accumulate throughout life. Most epithelial cancers arise from this normal mutation rate. All elderly individuals will harbour many cells with the requisite mutations and most will develop occult neoplastic lesions. Although essential for initiation, these mutations are not sufficient for the progression of cancer to a life-threatening disease. This progression appears to be dependent on context: the tissue ecosystem within individuals and lifestyle exposures across populations of individuals. Together, this implies that the seeds may be plentiful but they only germinate in the right soil. The incidence of these cancers is much lower in Eastern countries but is increasing with Westernisation and increases more acutely in migrants to the West. A Western lifestyle is strongly associated with perturbed metabolism, as evidenced by the epidemics of obesity and diabetes: this may also provide the setting enabling the progression of epithelial cancers. Epidemiology has indicated that metabolic biomarkers are prospectively associated with cancer incidence and prognosis. Furthermore, within cancer research, there has been a rediscovery that a switch in cell metabolism is critical for cancer progression but this is set within the metabolic status of the host. The seed may only germinate if the soil is fertile. This perspective brings together the different avenues of investigation implicating the role that metabolism may play within the context of post-genomic concepts of cancer.

Defining stem cell dynamics in models of intestinal tumor initiation

Cancer is a disease in which cells accumulate genetic aberrations that are believed to confer a clonal advantage over cells in the surrounding tissue. However, the quantitative benefit of frequently occurring mutations during tumor development remains unknown. We quantified the competitive advantage of Apc loss, Kras activation, and P53 mutations in the mouse intestine. Our findings indicate that the fate conferred by these mutations is not deterministic, and many mutated stem cells are replaced by wild-type stem cells after biased, but still stochastic events. Furthermore, P53 mutations display a condition-dependent advantage, and especially in colitis-affected intestines, clones harboring mutations in this gene are favored. Our work confirms the previously theoretical notion that the tissue architecture of the intestine suppresses the accumulation of mutated lineages.

Monoallelic expression of TMPRSS2/ERG in prostate cancer stem cells

While chromosomal translocations have a fundamental role in the development of several human leukaemias, their role in solid tumour development has been somewhat more controversial. Recently, it was shown that up to 80% of prostate tumours harbour at least one such gene fusion, and that the most common fusion event, between the prostate-specific TMPRSS2 gene and the ERG oncogene, is a critical, and probably early factor in prostate cancer development. Here we demonstrate the presence and expression of this significant chromosomal rearrangement in prostate cancer stem cells. Moreover, we show that in the prostate epithelial hierarchy from both normal and tumour tissues, TMPRSS2 transcription is subjected to tight monoallelic regulation, which is retained upon asymmetric division and relaxed during epithelial cell differentiation. The presence and expression of TMPRSS2/ERG in prostate stem cells would provide ERG-driven survival advantages, allowing maintenance of this mutated genotype.

Direct measurements of human colon crypt stem cell niche genetic fidelity: the role of chance in non-darwinian mutation selection

Perfect human stem cell genetic fidelity would prevent aging and cancer. However, perfection would be difficult to achieve, and aging is universal and cancers common. A hypothesis is that because mutations are inevitable over a human lifetime, downstream mechanisms have evolved to manage the deleterious effects of beneficial and lethal mutations. In the colon, a crypt stem cell architecture reduces the number of mitotic cells at risk for mutation accumulation, and multiple niche stem cells ensure that a lethal mutation within any single stem cell does not lead to crypt death. In addition, the architecture of the colon crypt stem cell niche may harness probability or chance to randomly discard many beneficial mutations that might lead to cancer. An analysis of somatic chromosome copy number alterations (CNAs) reveals a lack of perfect fidelity in individual normal human crypts, with age-related increases and higher frequencies in ulcerative colitis, a proliferative, inflammatory disease. The age-related increase in somatic CNAs appears consistent with relatively normal replication error and cell division rates. Surprisingly, and similar to point mutations in cancer genomes, the types of crypt mutations were more consistent with random fixation rather than selection. In theory, a simple “non-Darwinian” way to nullify selection is to reduce the size of the reproducing population. Fates are more determined by chance rather than selection in very small populations, and therefore selection may be minimized within small crypt niches. The desired effect is that many beneficial mutations that might lead to cancer are randomly lost by drift rather than fixed by selection. The subdivision of the colon into multiple very small stem cell niches may trade Darwinian evolution for non-Darwinian somatic cell evolution, capitulating to aging but reducing cancer risks.

The real war on cancer: the evolutionary dynamics of cancer suppression

Cancer is a disease of multicellular animals caused by unregulated cell division. The prevailing model of cancer (multistage carcinogenesis) is based on the view that cancer results after a series of (generally somatic) mutations that knock out the genetic mechanisms suppressing unregulated cell growth. The chance of these mutations occurring increases with size and longevity, leading to Peto's paradox: why don't large animals have a higher lifetime incidence of cancer than small animals? The solution to this paradox is evolution. From an evolutionary perspective, an increasing frequency of prereproductive cancer deaths results in natural selection for enhanced cancer suppression. The expected result is a prereproductive risk of cancer across species that is independent of life history. However, within species, we still expect cancer risk to increase with size and longevity. Here, I review the evolutionary model of cancer suppression and some recent empirical evidence supporting it. Data from humans and domestic dogs confirm the expected intraspecific association between size and cancer risk, while results from interspecific comparisons between rodents provide the best evidence to date of the predicted recruitment of additional cancer suppression mechanisms as species become larger or longer lived.

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.

Spatial structure increases the waiting time for cancer

Cancer results from a sequence of genetic and epigenetic changes which lead to a variety of abnormal phenotypes including increased proliferation and survival of somatic cells, and thus, to a selective advantage of pre-cancerous cells. The notion of cancer progression as an evolutionary process has been experiencing increasing interest in recent years. Many efforts have been made to better understand and predict the progression to cancer using mathematical models; these mostly consider the evolution of a well-mixed cell population, even though pre-cancerous cells often evolve in highly structured epithelial tissues. In this study, we propose a novel model of cancer progression that considers a spatially structured cell population where clones expand via adaptive waves. This model is used to assess two different paradigms of asexual evolution that have been suggested to delineate the process of cancer progression. The standard scenario of periodic selection assumes that driver mutations are accumulated strictly sequentially over time. However, when the mutation supply is sufficiently high, clones may arise simultaneously on distinct genetic backgrounds, and clonal adaptation waves interfere with each other. We find that in the presence of clonal interference, spatial structure increases the waiting time for cancer, leads to a patchwork structure of non-uniformly sized clones, decreases the survival probability of virtually neutral (passenger) mutations, and that genetic distance begins to increase over a characteristic length scale L(c). These characteristic features of clonal interference may help to predict the onset of cancers with pronounced spatial structure and to interpret spatially-sampled genetic data obtained from biopsies. Our estimates suggest that clonal interference likely occurs in the progression of colon cancer, and possibly other cancers where spatial structure matters.

Peto's Paradox: evolution's prescription for cancer prevention

The evolution of multicellularity required the suppression of cancer. If every cell has some chance of becoming cancerous, large, long-lived organisms should have an increased risk of developing cancer compared with small, short-lived organisms. The lack of correlation between body size and cancer risk is known as Peto's paradox. Animals with 1000 times more cells than humans do not exhibit an increased cancer risk, suggesting that natural mechanisms can suppress cancer 1000 times more effectively than is done in human cells. Because cancer has proven difficult to cure, attention has turned to cancer prevention. In this review, similar to pharmaceutical companies mining natural products, we seek to understand how evolution has suppressed cancer to develop ultimately improved cancer prevention in humans.

Recent advances in understanding the role of diet and obesity in the development of colorectal cancer

Colorectal cancer (CRC) is a major cause of premature death in the UK and many developed countries. However, the risk of developing CRC is well recognised to be associated not only with diet but also with obesity and lack of exercise. While epidemiological evidence shows an association with factors such as high red meat intake and low intake of vegetables, fibre and fish, the mechanisms underlying these effects are only now being elucidated. CRC develops over many years and is typically characterised by an accumulation of mutations, which may arise as a consequence of inherited polymorphisms in key genes, but more commonly as a result of spontaneously arising mutations affecting genes controlling cell proliferation, differentiation, apoptosis and DNA repair. Epigenetic changes are observed throughout the progress from normal morphology through formation of adenoma, and the subsequent development of carcinoma. The reasons why this accumulation of loss of homoeostatic controls arises are unclear but chronic inflammation has been proposed to play a central role. Obesity is associated with increased plasma levels of chemokines and adipokines characteristic of chronic systemic inflammation, and dietary factors such as fish oils and phytochemicals have been shown to have anti-inflammatory properties as well as modulating established risk factors such as apoptosis and cell proliferation. There is also some evidence that diet can modify epigenetic changes. This paper briefly reviews the current state of knowledge in relation to CRC development and considers evidence for potential mechanisms by which diet may modify risk.

Mutation and epigenetic molecular clocks in cancer

A quandary of evolution is how to measure change over time. A natural inclination is to use morphologic criteria-the greater the differences between two phenotypes, the greater amount of time needed to evolve these differences. However, appearances may be deceiving, and another approach to infer time is with molecular clocks. Here, the greater the differences between two genomes, on average the greater the time since a common ancestor. Recent advances in DNA sequencing shed new light on how human cancers might evolve.