A quantitative model of cellular senescence influence on cancer and longevity

A Unified Model of Cohort Mortality

We propose a dynamic production function of population health and mortality from birth onward. Our parsimonious model provides an excellent fit for the mortality and survival curves for primate and human populations since 1816. The model sheds light on the dynamics behind many phenomena documented in the literature. Simple extensions of the model can reproduce (1) the existence and evolution of mortality gradients across socioeconomic statuses documented in the literature, (2) nonmonotonic dynamic effects of in utero shocks, (3) persistent or scarring effects of wars, and (4) mortality displacement after large temporary shocks, such as extreme weather.

Profound synchrony of age-specific incidence rates and tumor suppression for different cancer types as revealed by the multistage-senescence model of carcinogenesis

The age-specific trend of cancer incidence rates, but not its magnitude, is well described employing the multistage theory of carcinogenesis by Armitage and Doll in combination with the senescence model of Pompei and Wilson. We derived empirical parameters of the multistage-senescence model from U.S. Surveillance, Epidemiology, and End Results (SEER) incidence data from 2000–2003 and 2010–2013 for The Cancer Genome Atlas (TCGA) cancer types. Under the assumption of a constant tumor-specific transition rate between stages, there is an extremely strong linear relationship (P < 0.0001) between the number of stages and the stage transition rate. The senescence tumor suppression factor for 20 non-reproductive cancers is remarkably consistent (0.0099±0.0005); however, five female reproductive cancers have significantly higher tumor suppression. The peak incidence rate for non-reproductive cancers occurs at a younger age for cancers with fewer stages and their carcinogenic stages are of longer duration. Driver gene mutations are shown to contribute on average only about a third of the carcinogenic stages of different tumor types. A tumor’s accumulated incidence, calculated using a two-variable (age, stage) model, is strongly associated with intrinsic cancer risk. During both early adulthood and senescence, the pace of tumor suppression appears to be synchronized across most cancer types, suggesting the presence of overlapping evolutionary processes.

The multistage model of cancer development: some implications

The multistage model, introduced by Armitage and Doll, was very successful at describing many features of cancer development. Doll and Peto noted a significant departure below the prediction of the model and suggested that this could be due to undercounting of cases at older ages, or to the ‘biology of extreme old age.’ Moolgavkar pointed out that it could also be due to the approximation used. The recent observation that cancer incidence falls rapidly above age 80 has stimulated new modelling investigations, such as the Pompei-Wilson beta model (which does reproduce the rapid fall). In the present paper, we argue that Moolgavkar’s criticisms, while mathematically correct, do not affect the conclusions, particularly the constancy of the number of stages across different cancer registries (Cook, Doll and Fellingham. 1969: A mathematical model for the age distribution of cancer in man. International Journal of Cancer 4, 93-112). We discuss several exact solutions, compare them with the most recent data, and prove rigorously that the standard Armitage-Doll multistage model can never reproduce the sharp turnaround in cancer incidence at old age seen in the data. We discuss in detail multistage processes which have a property observed in many laboratory studies, namely that some stages progress much faster than the others. We verify mathematically the intuition that sufficiently fast stages do not appreciably affect the incidence rate of cancer, and discuss implications of this fact for cancer treatment strategies. We also show that the simplest possible modification of the Armitage-Doll model to incorporate cellular senescence just leads to the Pompei-Wilson beta model.

Minimizing second cancer risk following radiotherapy: current perspectives

Secondary cancer risk following radiotherapy is an increasingly important topic in clinical oncology with impact on treatment decision making and on patient management. Much of the evidence that underlies our understanding of secondary cancer risks and our risk estimates are derived from large epidemiologic studies and predictive models of earlier decades with large uncertainties. The modern era is characterized by more conformal radiotherapy technologies, molecular and genetic marker approaches, genome-wide studies and risk stratifications, and sophisticated biologically based predictive models of the carcinogenesis process. Four key areas that have strong evidence toward affecting secondary cancer risks are 1) the patient age at time of radiation treatment, 2) genetic risk factors, 3) the organ and tissue site receiving radiation, and 4) the dose and volume of tissue being irradiated by a particular radiation technology. This review attempts to summarize our current understanding on the impact on secondary cancer risks for each of these known risk factors. We review the recent advances in genetic studies and carcinogenesis models that are providing insight into the biologic processes that occur from tissue irradiation to the development of a secondary malignancy. Finally, we discuss current approaches toward minimizing the risk of radiation-associated secondary malignancies, an important goal of clinical radiation oncology.

A computational model incorporating neural stem cell dynamics reproduces glioma incidence across the lifespan in the human population

Glioma is the most common form of primary brain tumor. Demographically, the risk of occurrence increases until old age. Here we present a novel computational model to reproduce the probability of glioma incidence across the lifespan. Previous mathematical models explaining glioma incidence are framed in a rather abstract way, and do not directly relate to empirical findings. To decrease this gap between theory and experimental observations, we incorporate recent data on cellular and molecular factors underlying gliomagenesis. Since evidence implicates the adult neural stem cell as the likely cell-of-origin of glioma, we have incorporated empirically-determined estimates of neural stem cell number, cell division rate, mutation rate and oncogenic potential into our model. We demonstrate that our model yields results which match actual demographic data in the human population. In particular, this model accounts for the observed peak incidence of glioma at approximately 80 years of age, without the need to assert differential susceptibility throughout the population. Overall, our model supports the hypothesis that glioma is caused by randomly-occurring oncogenic mutations within the neural stem cell population. Based on this model, we assess the influence of the (experimentally indicated) decrease in the number of neural stem cells and increase of cell division rate during aging. Our model provides multiple testable predictions, and suggests that different temporal sequences of oncogenic mutations can lead to tumorigenesis. Finally, we conclude that four or five oncogenic mutations are sufficient for the formation of glioma.

Similarities in the Age-Specific Incidence of Colon and Testicular Cancers

Colon cancers are thought to be an inevitable result of aging, while testicular cancers are thought to develop in only a small fraction of men, beginning in utero. These models of carcinogenesis are, in part, based upon age-specific incidence data. The specific incidence for colon cancer appears to monotonically increase with age, while that of testicular cancer increases to a maximum value at about 35 years of age, then declines to nearly zero by the age of 80. We hypothesized that the age-specific incidence for these two cancers is similar; the apparent difference is caused by a longer development time for colon cancer and the lack of age-specific incidence data for people over 84 years of age. Here we show that a single distribution can describe the age-specific incidence of both colon carcinoma and testicular cancer. Furthermore, this distribution predicts that the specific incidence of colon cancer should reach a maximum at about age 90 and then decrease. Data on the incidence of colon carcinoma for women aged 85–99, acquired from SEER and the US Census, is consistent with this prediction. We conclude that the age specific data for testicular cancers and colon cancers is similar, suggesting that the underlying process leading to the development of these two forms of cancer may be similar.

Radiation-induced carcinogenesis: mechanistically based differences between gamma-rays and neutrons, and interactions with DMBA

Different types of ionizing radiation produce different dependences of cancer risk on radiation dose/dose rate. Sparsely ionizing radiation (e.g. γ-rays) generally produces linear or upwardly curving dose responses at low doses, and the risk decreases when the dose rate is reduced (direct dose rate effect). Densely ionizing radiation (e.g. neutrons) often produces downwardly curving dose responses, where the risk initially grows with dose, but eventually stabilizes or decreases. When the dose rate is reduced, the risk increases (inverse dose rate effect). These qualitative differences suggest qualitative differences in carcinogenesis mechanisms. We hypothesize that the dominant mechanism for induction of many solid cancers by sparsely ionizing radiation is initiation of stem cells to a pre-malignant state, but for densely ionizing radiation the dominant mechanism is radiation-bystander-effect mediated promotion of already pre-malignant cell clone growth. Here we present a mathematical model based on these assumptions and test it using data on the incidence of dysplastic growths and tumors in the mammary glands of mice exposed to high or low dose rates of γ-rays and neutrons, either with or without pre-treatment with the chemical carcinogen 7,12-dimethylbenz-alpha-anthracene (DMBA). The model provides a mechanistic and quantitative explanation which is consistent with the data and may provide useful insight into human carcinogenesis.

Age-specific incidence data indicate four mutations are required for human testicular cancers

Normal human cells require a series of genetic alterations to undergo malignant transformation. Direct sequencing of human tumors has identified hundreds of mutations in tumors, but many of these are thought to be unnecessary and a result of, rather than a cause of, the tumor. The exact number of mutations to transform a normal human cell into a tumor cell is unknown. Here I show that male gonadal germ cell tumors, the most common form of testicular cancers, occur after four mutations. I infer this by constructing a mathematical model based upon the multi-hit hypothesis and comparing it to the age-specific incidence data. This result is consistent with the multi-hit hypothesis, and implies that these cancers are genetically or epigenetically predetermined at birth or an early age.

A new view of radiation-induced cancer

Biologically motivated mathematical models are important for understanding the mechanisms of radiation-induced carcinogenesis. Existing models fall into two categories: (1) short-term formalisms, which focus on the processes taking place during and shortly after irradiation (effects of dose, radiation quality, dose rate and fractionation), and (2) long-term formalisms, which track background cancer risks throughout the entire lifetime (effects of age at exposure and time since exposure) but make relatively simplistic assumptions about radiation effects. Grafting long-term mechanisms on to short-term models is badly needed for modelling radiogenic cancer. A combined formalism was developed and applied to cancer risk data in atomic bomb survivors and radiotherapy patients and to background cancer incidence. The data for nine cancer types were described adequately with a set of biologically meaningful parameters for each cancer. These results suggest that the combined short-long-term approach is a potentially promising method for predicting radiogenic cancer risks and interpreting the underlying biological mechanisms.

Parallel routes of human carcinoma development: implications of the age-specific incidence data

Background

The multi-stage hypothesis suggests that cancers develop through a single defined series of genetic alterations. This hypothesis was first suggested over 50 years ago based upon age-specific incidence data. However, recent molecular studies of tumors indicate that multiple routes exist to the formation of cancer, not a single route. This parallel route hypothesis has not been tested with age-specific incidence data.

Methodology/Principal Findings

To test the parallel route hypothesis, I formulated it in terms of a mathematical equation and then tested whether this equation was consistent with age-specific incidence data compiled by the Surveillance Epidemiology and End Results (SEER) cancer registries since 1973. I used the chi-squared goodness of fit test to measure consistency. The age-specific incidence data from most human carcinomas, including those of the colon, lung, prostate, and breast were consistent with the parallel route hypothesis. However, this hypothesis is only consistent if an immune sub-population exists, one that will never develop carcinoma. Furthermore, breast carcinoma has two distinct forms of the disease, and one of these occurs at significantly different rates in different racial groups.

Conclusions/Significance

I conclude that the parallel route hypothesis is consistent with the age-specific incidence data only if carcinoma occurs in a distinct sub population, while the multi-stage hypothesis is inconsistent with this data.

A new view of radiation-induced cancer: integrating short- and long-term processes. Part I: approach

Mathematical models of radiation carcinogenesis are important for understanding mechanisms and for interpreting or extrapolating risk. There are two classes of such models: (1) long-term formalisms that track pre-malignant cell numbers throughout an entire lifetime but treat initial radiation dose-response simplistically and (2) short-term formalisms that provide a detailed initial dose-response even for complicated radiation protocols, but address its modulation during the subsequent cancer latency period only indirectly. We argue that integrating short- and long-term models is needed. As an example of this novel approach, we integrate a stochastic short-term initiation/inactivation/repopulation model with a deterministic two-stage long-term model. Within this new formalism, the following assumptions are implemented: radiation initiates, promotes, or kills pre-malignant cells; a pre-malignant cell generates a clone, which, if it survives, quickly reaches a size limitation; the clone subsequently grows more slowly and can eventually generate a malignant cell; the carcinogenic potential of pre-malignant cells decreases with age.

Cancer suppression at old age

Increased age is regularly linked with heightened cancer risk, but recent research suggests a flattening around age 80. We report that, independent of cancer site or time period, most incidence rates decrease in the more elderly and drop to or toward zero near the ceiling of human life span. For all major organ sites, male and female, we use 1979 to 2003 Surveillance, Epidemiology, and End Results registry records (8-26% of the U.S. population) to construct three sequential cross-sections at 10-year intervals, totaling 129 sets of age-specific cancer data. To compute incidence rates, we estimate older populations at risk with census counts and NIH life tables. This article provides both a minimal and a more comprehensive extension of Surveillance, Epidemiology, and End Results cancer rates to those above 85. Almost all cancers peak at age approximately 80. Generally, it seems that centenarians are asymptomatic or untargeted by cancers. We suggest that the best available justification for this pattern of incidence is a link between increased senescence and decreased proliferative potential among cancers. Then, thus far, as senescence may be a carcinogen, it might also be considered an anticarcinogen in the elderly. We model rising and falling incidence rates with a beta curve obtained by appending a linearly decreasing factor to the well-known Armitage-Doll multistage model of cancer. Taken at face value, the beta model implies that medical, diet, or lifestyle interventions restricting carcinogenesis ought to be examined for possible effects on longevity.

Cellular senescence, cancer, and organismal aging: a paradigm shift

Cellular senescence is an anti-cancer mechanism and may contribute to organismal aging. A change in paradigm has been proposed that cellular senescence may reduce cancer mortality rather than promote it late in life, and thus positively contributes to longevity in organisms with renewable tissues as a common mechanism across the species.

SIRT1: tumor promoter or tumor suppressor?

Over the past decade, an intensive research on the basic biology of aging has identified individual genes either directly or indirectly involved in regulating the aging process in various model organisms. This allows us to garner all the information available from studies of model organisms and to apply them to better understand aging and cancer in human. Among many genes thus far reported contributing to aging process, the yeast silent information regulator-2 (SIR2) and its homologues in other species, which belong to the family of type III histone and protein deacetylases, have been the subject of active discussion. The demonstrated roles of SIRT1, the mammalian counterpart of the yeast SIR2, reveal that SIRT1 regulates important cellular processes including anti-apoptosis, neuronal protection, cellular senescence, aging and longevity. Based on the observations that SIRT1 is upregulated in tumor cells, the hypothesis is that deregulation of SIRT1 expression may promote tumorigenesis by altering cellular signaling or by inducing modulation of chromatin remodeling leading to promotion of tumorigenesis. Further studies will shed new light on the underlying mechanisms of tumorigenesis mediated by SIRT1.