Population risk and physiological rate parameters for colon cancer. The union of an explicit model for carcinogenesis with the public health records of the United States

Shape-specific characterization of colorectal adenoma growth and transition to cancer with stochastic cell-based models

Colorectal adenoma are precursor lesions on the pathway to cancer. Their removal in screening colonoscopies has markedly reduced rates of cancer incidence and death. Generic models of adenoma growth and transition to cancer can guide the implementation of screening strategies. But adenoma shape has rarely featured as a relevant risk factor. Against this backdrop we aim to demonstrate that shape influences growth dynamics and cancer risk. Stochastic cell-based models are applied to a data set of 197,347 Bavarian outpatients who had colonoscopies from 2006-2009, 50,649 patients were reported with adenoma and 296 patients had cancer. For multi-stage clonal expansion (MSCE) models with up to three initiating stages parameters were estimated by fits to data sets of all shapes combined, and of sessile (70% of all adenoma), peduncular (17%) and flat (13%) adenoma separately for both sexes. Pertinent features of adenoma growth present themselves in contrast to previous assumptions. Stem cells with initial molecular changes residing in early adenoma predominantly multiply within two-dimensional structures such as crypts. For these cells mutation and division rates decrease with age. The absolute number of initiated cells in an adenoma of size 1 cm is small around 103, related to all bulk cells they constitute a share of about 10-5. The notion of very few proliferating stem cells with age-decreasing division rates is supported by cell marker experiments. The probability for adenoma transiting to cancer increases with squared linear size and shows a shape dependence. Compared to peduncular and flat adenoma, it is twice as high for sessile adenoma of the same size. We present a simple mathematical expression for the hazard ratio of interval cancers which provides a mechanistic understanding of this important quality indicator. We conclude that adenoma shape deserves closer consideration in screening strategies and as risk factor for transition to cancer.

A mechanistic mathematical model of initiation and malignant transformation in sporadic vestibular schwannoma

BACKGROUND

A vestibular schwannoma (VS) is a relatively rare, benign tumour of the eighth cranial nerve, often involving alterations to the gene NF2. Previous mathematical models of schwannoma incidence have not attempted to account for alterations in specific genes, and could not distinguish between nonsense mutations and loss of heterozygosity (LOH).

METHODS

Here, we present a mechanistic approach to modelling initiation and malignant transformation in schwannoma. Each parameter is associated with a specific gene or mechanism operative in Schwann cells, and can be determined by combining incidence data with empirical frequencies of pathogenic variants and LOH.

RESULTS

This results in new estimates for the base-pair mutation rate u = 4.48 × 10-10 and the rate of LOH = 2.03 × 10-6/yr in Schwann cells. In addition to new parameter estimates, we extend the approach to estimate the risk of both spontaneous and radiation-induced malignant transformation.

DISCUSSION

We conclude that radiotherapy is likely to have a negligible excess risk of malignancy for sporadic VS, with a possible exception of rapidly growing tumours.

Periodic Fluctuations in the Incidence of Gastrointestinal Cancer

Purpose

Native stem cells can be periodically replaced during short and long epigenetic intervals. Cancer-prone new stem cells might bring about periodic (non-stochastic) carcinogenic events rather than stochastic events. We investigated the epigenetic non-stochastic carcinogenesis by analyzing regular fluctuations in lifelong cancer incidence.

Materials and Methods

Korean National Cancer Screening Program data were collected between 2009 and 2016. Non-linear and log-linear regression models were applied to comparatively evaluate non-stochastic and stochastic increases in cancer incidence. Prediction performances of regression models were measured by calculating the coefficient of determination, R².

Results

The incidence of gastric and colorectal cancers fluctuated regularly during both short (8 years) and long (20 years) intervals in the non-linear regression model and increased stochastically in the log-linear regression model. In comparison between the 20-year interval fluctuation model and the stochastic model, R² values were higher in the 20-year interval fluctuation model of men with gastric cancer (0.975 vs. 0.956), and in the stochastic model of men with colorectal cancer (0.862 vs. 0.877) and women with gastric cancer (0.837 vs. 0.890) and colorectal cancer (0.773 vs. 0.809). Men with gastric cancer showed a high R² value (0.973) in the 8-year interval fluctuation model as well.

Conclusion

Lifelong incidence of gastrointestinal cancer tended to fluctuate during short and long intervals, especially in men with gastric cancer, suggesting the influence of an epigenetic schedule.

Predicting colorectal cancer risk from adenoma detection via a two-type branching process model

Despite advances in the modeling and understanding of colorectal cancer development, the dynamics of the progression from benign adenomatous polyp to colorectal carcinoma are still not fully resolved. To take advantage of adenoma size and prevalence data in the National Endoscopic Database of the Clinical Outcomes Research Initiative (CORI) as well as colorectal cancer incidence and size data from the Surveillance Epidemiology and End Results (SEER) database, we construct a two-type branching process model with compartments representing adenoma and carcinoma cells. To perform parameter inference we present a new large-size approximation to the size distribution of the cancer compartment and validate our approach on simulated data. By fitting the model to the CORI and SEER data, we learn biologically relevant parameters, including the transition rate from adenoma to cancer. The inferred parameters allow us to predict the individualized risk of the presence of cancer cells for each screened patient. We provide a web application which allows the user to calculate these individual probabilities at https://ccrc-eth.shinyapps.io/CCRC/. For example, we find a 1 in 100 chance of cancer given the presence of an adenoma between 10 and 20mm size in an average risk patient at age 50. We show that our two-type branching process model recapitulates the early growth dynamics of colon adenomas and cancers and can recover epidemiological trends such as adenoma prevalence and cancer incidence while remaining mathematically and computationally tractable.

Colorectal cancer is a major public health burden. The development of colorectal cancer starts with the mutational initiation of non-cancerous growths in the form of benign adenomatous polyps. These adenomas grow over time with the potential to develop into carcinomas. Many mathematical and simulation-based models have been used to gain insight into this process. We aimed to understand rates of adenoma growth and transition into carcinomas, to enable better planning of colorectal cancer screening strategies. To this end, we expand the two-type branching process model, and fit it on data describing the frequency of sizes of adenomas and carcinomas. The results provide new, data-based, estimates of the rates of development for colorectal cancer.

Genomic instability and radiation risk in molecular pathways to colon cancer

Colon cancer is caused by multiple genomic alterations which lead to genomic instability (GI). GI appears in molecular pathways of microsatellite instability (MSI) and chromosomal instability (CIN) with clinically observed case shares of about 15–20% and 80–85%. Radiation enhances the colon cancer risk by inducing GI, but little is known about different outcomes for MSI and CIN. Computer-based modelling can facilitate the understanding of the phenomena named above. Comprehensive biological models, which combine the two main molecular pathways to colon cancer, are fitted to incidence data of Japanese a-bomb survivors. The preferred model is selected according to statistical criteria and biological plausibility. Imprints of cell-based processes in the succession from adenoma to carcinoma are identified by the model from age dependences and secular trends of the incidence data. Model parameters show remarkable compliance with mutation rates and growth rates for adenoma, which has been reported over the last fifteen years. Model results suggest that CIN begins during fission of intestinal crypts. Chromosomal aberrations are generated at a markedly elevated rate which favors the accelerated growth of premalignant adenoma. Possibly driven by a trend of Westernization in the Japanese diet, incidence rates for the CIN pathway increased notably in subsequent birth cohorts, whereas rates pertaining to MSI remained constant. An imbalance between number of CIN and MSI cases began to emerge in the 1980s, whereas in previous decades the number of cases was almost equal. The CIN pathway exhibits a strong radio-sensitivity, probably more intensive in men. Among young birth cohorts of both sexes the excess absolute radiation risk related to CIN is larger by an order of magnitude compared to the MSI-related risk. Observance of pathway-specific risks improves the determination of the probability of causation for radiation-induced colon cancer in individual patients, if their exposure histories are known.

Mutator/Hypermutable fetal/juvenile metakaryotic stem cells and human colorectal carcinogenesis

Adult age-specific colorectal cancer incidence rates increase exponentially from maturity, reach a maximum, then decline in extreme old age. Armitage and Doll (1) postulated that the exponential increase resulted from "n" mutations occurring throughout adult life in normal "cells at risk" that initiated the growth of a preneoplastic colony in which subsequent "m" mutations promoted one of the preneoplastic "cells at risk" to form a lethal neoplasia. We have reported cytologic evidence that these "cells at risk" are fetal/juvenile organogenic, then preneoplastic metakaryotic stem cells. Metakaryotic cells display stem-like behaviors of both symmetric and asymmetric nuclear divisions and peculiarities such as bell shaped nuclei and amitotic nuclear fission that distinguish them from embryonic, eukaryotic stem cells. Analyses of mutant colony sizes and numbers in adult lung epithelia supported the inferences that the metakaryotic organogenic stem cells are constitutively mutator/hypermutable and that their contributions to cancer initiation are limited to the fetal/juvenile period. We have amended the two-stage model of Armitage and Doll and incorporated these several inferences in a computer program CancerFit v.5.0. We compared the expectations of the amended model to adult (15-104 years) age-specific colon cancer rates for European-American males born 1890-99 and observed remarkable concordance. When estimates of normal colonic fetal/juvenile APC and OAT gene mutation rates (∼2-5 × 10(-5) per stem cell doubling) and preneoplastic colonic gene loss rates (∼8 × 10(-3)) were applied, the model was in accordance only for the values of n = 2 and m = 4 or 5.

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.

Cell selection as driving force in lung and colon carcinogenesis

Carcinogenesis is the result of mutations and subsequent clonal expansions of mutated, selectively advantageous cells. To investigate the relative contributions of mutation versus cell selection in tumorigenesis, we compared two mathematical models of carcinogenesis in two different cancer types: lung and colon. One approach is based on a population genetics model, the Wright-Fisher process, whereas the other approach is the two-stage clonal expansion model. We compared the dynamics of tumorigenesis predicted by the two models in terms of the time period until the first malignant cell appears, which will subsequently form a tumor. The mean waiting time to cancer has been calculated approximately for the evolutionary colon cancer model. Here, we derive new analytic approximations to the median waiting time for the two-stage lung cancer model and for a multistage approximation to the Wright-Fisher process. Both equations show that the waiting time to cancer is dominated by the selective advantage per mutation and the net clonal expansion rate, respectively, whereas the mutation rate has less effect. Our comparisons support the idea that the main driving force in lung and colon carcinogenesis is Darwinian cell selection.

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

Background

The purpose of this article is to present a relatively easy to understand cancer model where transformation occurs when the first cell, among many at risk within a colon, accumulates a set of driver mutations. The analysis of this model yields a simple algebraic equation, which takes as inputs the number of stem cells, mutation and division rates, and the number of driver mutations, and makes predictions about cancer epidemiology.

Methods

The equation [p = 1 - (1 - (1 - (1 - u)^d)^k)^Nm ] calculates the probability of cancer (p) and contains five parameters: the number of divisions (d), the number of stem cells (N × m), the number of critical rate-limiting pathway driver mutations (k), and the mutation rate (u). In this model progression to cancer "starts" at conception and mutations accumulate with cell division. Transformation occurs when a critical number of rate-limiting pathway mutations first accumulates within a single stem cell.

Results

When applied to several colorectal cancer data sets, parameter values consistent with crypt stem cell biology and normal mutation rates were able to match the increase in cancer with aging, and the mutation frequencies found in cancer genomes. The equation can help explain how cancer risks may vary with age, height, germline mutations, and aspirin use. APC mutations may shorten pathways to cancer by effectively increasing the numbers of stem cells at risk.

Conclusions

The equation illustrates that age-related increases in cancer frequencies may result from relatively normal division and mutation rates. Although this equation does not encompass all of the known complexity of cancer, it may be useful, especially in a teaching setting, to help illustrate relationships between small and large cancer features.

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.

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.

Age-specific incidence of cancer: Phases, transitions, and biological implications

The observation that the age-specific incidence curve of many carcinomas is approximately linear on a double logarithmic plot has led to much speculation regarding the number and nature of the critical events involved in carcinogenesis. By a consideration of colorectal and pancreatic cancers in the Surveillance Epidemiology and End Results (SEER) registry we show that the log-log model provides a poor description of the data, and that a much better description is provided by a multistage model that predicts two basic phases in the age-specific incidence curves, a first exponential phase until the age of approximately 60 followed by a linear phase after that age. These two phases in the incidence curve reflect two phases in the process of carcinogenesis. Paradoxically, the early-exponential phase reflects events between the formation (initiation) of premalignant clones in a tissue and the clinical detection of a malignant tumor, whereas the linear phase reflects events leading to initiated cells that give rise to premalignant lesions because of abrogated growth/differentiation control. This model is consistent with Knudson's idea that renewal tissue, such as the colon, is converted into growing tissue before malignant transformation. The linear phase of the age-specific incidence curve represents this conversion, which is the result of recessive inactivation of a gatekeeper gene, such as the APC gene in the colon and the CDKN2A gene in the pancreas.

Fetal-juvenile origins of point mutations in the adult human tracheal-bronchial epithelium: absence of detectable effects of age, gender or smoking status

Allele-specific mismatch amplification mutation assays (MAMA) of anatomically distinct sectors of the upper bronchial tracts of nine nonsmokers revealed many numerically dispersed clusters of the point mutations C742T, G746T, G747T of the TP53 gene, G35T of the KRAS gene and G508A of the HPRT1 gene. Assays of these five mutations in six smokers have yielded quantitatively similar results. One hundred and eighty four micro-anatomical sectors of 0.5-6x10(6) tracheal-bronchial epithelial cells represented en toto the equivalent of approximately 1.7 human smokers' bronchial trees to the fifth bifurcation. Statistically significant mutant copy numbers above the 95% upper confidence limits of historical background controls were found in 198 of 425 sector assays. No significant differences (P=0.1) for negative sector fractions, mutant fractions, distributions of mutant cluster size or anatomical positions were observed for smoking status, gender or age (38-76 year). Based on the modal cluster size of mitochondrial point mutants, the size of the adult bronchial epithelial maintenance turnover unit was estimated to be about 32 cells. When data from all 15 lungs were combined the log2 of nuclear mutant cluster size plotted against log2 of the number of clusters of a given cluster size displayed a slope of approximately 1.1 over a range of cluster sizes from approximately 2(6) to 2(15) mutant copies. A parsimonious interpretation of these nuclear and previously reported data for lung epithelial mitochondrial point mutant clusters is that they arose from mutations in stem cells at a high but constant rate per stem cell doubling during at least ten stem cell doublings of the later fetal-juvenile period. The upper and lower decile range of summed point mutant fractions among lungs was about 7.5-fold, suggesting an important source of stratification in the population with regard to risk of tumor initiation.

Heterogeneity in multistage carcinogenesis and mixture modeling

Carcinogenesis is commonly described as a multistage process, in which stem cells are transformed into cancer cells via a series of mutations. In this article, we consider extensions of the multistage carcinogenesis model by mixture modeling. This approach allows us to describe population heterogeneity in a biologically meaningful way. We focus on finite mixture models, for which we prove identifiability. These models are applied to human lung cancer data from several birth cohorts. Maximum likelihood estimation does not perform well in this application due to the heavy censoring in our data. We thus use analytic graduation instead. Very good fits are achieved for models that combine a small high risk group with a large group that is quasi immune.

DNA damage, a biomarker of carcinogenesis: its measurement and modulation by diet and environment

Free radicals and other reactive oxygen or nitrogen species are constantly generated in vivo and can cause oxidative damage to DNA. This damage has been implicated to be important in many diseases, including cancer. The assessment of damage in various biological matrices, such as tissues, cells, and urine, is vital to understanding this role and subsequently devising intervention strategies. During the last 20 years, many analytical techniques have been developed to monitor oxidative DNA base damage. High-performance liquid chromatography-electrochemical detection and gas chromatography-mass spectrometry are the two pioneering contributions to the field. Currently, the arsenal of methods available include the promising high-performance liquid chromatography-tandem mass spectrometry technique, capillary electrophoresis, 32P-postlabeling, antibody-base immunoassays, and assays involving the use of DNA repair glycosylases such as the comet assay. The objective of this review is to discuss the biological significance of oxidative DNA damage, evaluate the effectiveness of several techniques for measurement of oxidative DNA damage in various biological samples and review current research on factors (dietary and non-dietary) that influence DNA oxidative damage using these techniques.

Stem cell stages and the origins of colon cancer: a multidisciplinary perspective

Analysis of historical age-specific colorectal cancer rates, present day age-specific colonic adenoma prevalence and the few reports of direct measurements of genetic change in human tissues as a function of age in adults have led to a new set of hypotheses about carcinogenesis. A key observation, that the calculated rate of growth of preneoplasia is equal to the calculated growth rate of the juvenile colon, suggested that tumor initiation blocks the developmental step by which growing juvenile stem cells are transformed into or replaced by adult maintenance stem cells. In this hypothesis the slowly growing adenomatous polyps would simply be patches of highly organized juvenile tissue modified by the mechanical constraints of surrounding nongrowing adult tissue. As juvenile tissue presumably grows by net increase in stem cells creating crypts, tumor promotion could be achieved by transformation of an initiated stem cell into a fetal stem cell that would express the program of rapid net growth and differentiation into the heterogeneous cell types of fetal colonic organogenesis. (One additional interpretation of data from observations of point mutations in adult lung epithelium is that rates of genetic change in juvenile stem cells are markedly higher than in adult maintenance stem cells.) Unfortunately, the concept of a "stem cell" undergoing staged transitions in organ development and blocked or reverse transitions in carcinogenesis has lacked the physical embodiment of a cell that could be recognized, isolated, and analyzed. In an attempt to overcome this impediment we set reexamined fetal and adult colonic tissue, adenomas, and adenocarcinomas using a novel histological preparation method. Gostjeva then discovered that fetal and neoplastic tissues share a set of cells distinguished by specific nuclear morphotypes that appear to cooperate in creating the elements of the fetal organ, preneoplastic, and neoplastic lesions. In particular, microscopic examination of fetal gut at 5-7 wk gestation reveals tubular syncytia containing opened-mouthed, bell-shaped nuclei that account for some 30% of the nuclei in the protoorgan. These peculiar nuclei undergo both symmetric and asymmetric nuclear fissions, the latter creating all of the other nuclear morphotypes. These nuclear fissions are "amitotic" insofar as no general chromosome condensation is observed. Bell-shaped nuclei are rarely found in adult colonic crypt bases but are found in preneoplasia and neoplasia.

Low-LET-induced radioprotective mechanisms within a stochastic two-stage cancer model

A stochastic two-stage cancer model with clonal expansion was used to investigate the potential impact on human lung cancer incidence of some aspects of the hormesis mechanisms suggested by Feinendegen (Health Phys. 52 663-669, 1987). The model was applied to low doses of low-LET radiation delivered at low dose rates. Non-linear responses arise in the model because radiologically induced adaptations in radical scavenging and DNA repair may reduce the biological consequences of DNA damage formed by endogenous processes and ionizing radiation. Sensitivity studies were conducted to identify critical model inputs and to help define the changes in cellular defense mechanisms necessary to produce a lifetime probability for lung cancer that deviates from a linear no-threshold (LNT) type of response. Our studies suggest that lung cancer risk predictions may be very sensitive to the induction of DNA damage by endogenous processes. For doses comparable to background radiation levels, endogenous DNA damage may account for as much as 50 to 80% of the predicted lung cancers. For an additional lifetime dose of 1 Gy from low-LET radiation, endogenous processes may still account for as much as 20% of the predicted cancers (Fig. 2). When both repair and scavengers are considered as inducible, radiation must enhance DNA repair and radical scavenging in excess of 30 to 40% of the baseline values to produce lifetime probabilities for lung cancer outside the range expected for endogenous processes and background radiation.

Bell-shaped nuclei dividing by symmetrical and asymmetrical nuclear fission have qualities of stem cells in human colonic embryogenesis and carcinogenesis

Large cell nuclei with at least eight distinct morphologies have been discovered throughout the fetal gut (5-7 weeks), colonic adenomas, and adenocarcinomas, five of which are not present in the normal adult colon. The most remarkable nuclear forms are hollow bells, approximately 10-15 microns in height and about 7-10 microns in bell mouth diameter. When encased in tubular syncytia, these bell-shaped structures divide symmetrically by an amitotic nuclear fission process resembling the separation of two paper cups. Seven other nuclear morphotypes emerge from the bell-shaped nuclei within the syncytia by asymmetrical amitotic nuclear fission. Cells containing these differentiated nuclear forms subsequently divide extra-syncytially by mitoses that form clonal populations of cells with identical nuclear morphotypes in embryos, adenomas, adenocarcinomas, and metastases. Cells with bell-shaped nuclei thus appear to be responsible for both net growth and differentiation in the embryonic gut, adenomas, and adenocarcinomas, and fulfill the requirements for post-embryonic stem cells in colon organogenesis and carcinogenesis.

Numbers of mutations to different types of colorectal cancer

Background

The numbers of oncogenic mutations required for transformation are uncertain but may be inferred from how cancer frequencies increase with aging. Cancers requiring more mutations will tend to appear later in life. This type of approach may be confounded by biologic heterogeneity because different cancer subtypes may require different numbers of mutations. For example, a sporadic cancer should require at least one more somatic mutation relative to its hereditary counterpart.

Methods

To better estimate numbers of mutations before transformation, 1,022 colorectal cancers were classified with respect to microsatellite instability (MSI) and germline DNA mismatch repair mutations characteristic of hereditary nonpolyposis colorectal cancer (HNPCC). MSI- cancers were also classified with respect to clinical stage. Ages at cancer and a Bayesian algorithm were used to estimate the numbers of oncogenic mutations required for transformation for each cancer subtype.

Results

Ages at MSI+ cancers were consistent with five or six oncogenic mutations for hereditary (HNPCC) cancers, and seven or eight mutations for its sporadic counterpart. Ages at cancer were consistent with seven mutations for sporadic MSI- cancers, and were similar (six to eight mutations) regardless of clinical cancer stage.

Conclusion

Different biologic subtypes of colorectal cancer appear to require different numbers of oncogenic mutations before transformation. Sporadic MSI+ cancers may require more than a single additional somatic alteration compared to hereditary MSI+ cancers because the epigenetic inactivation of MLH1 commonly observed in sporadic MSI+ cancers may be a multistep process. Interestingly, estimated numbers of MSI- cancer mutations were similar (six to eight mutations) regardless of clinical cancer stage, suggesting a propensity to spread or metastasize does not require additional mutations after transformation. Estimates of oncogenic mutation numbers may help explain some of the biology underlying different cancer subtypes.

Stochastic tunnels in evolutionary dynamics

We study a situation that arises in the somatic evolution of cancer. Consider a finite population of replicating cells and a sequence of mutations: type 0 can mutate to type 1, which can mutate to type 2. There is no back mutation. We start with a homogeneous population of type 0. Mutants of type 1 emerge and either become extinct or reach fixation. In both cases, they can generate type 2, which also can become extinct or reach fixation. If mutation rates are small compared to the inverse of the population size, then the stochastic dynamics can be described by transitions between homogeneous populations. A "stochastic tunnel" arises, when the population moves from all 0 to all 2 without ever being all 1. We calculate the exact rate of stochastic tunneling for the case when type 1 is as fit as type 0 or less fit. Type 2 has the highest fitness. We discuss implications for the elimination of tumor suppressor genes and the activation of genetic instability. Although our theory is developed for cancer genetics, stochastic tunnels are general phenomena that could arise in many circumstances.

Radon-induced lung cancer in French and Czech miner cohorts described with a two-mutation cancer model

A two-mutation carcinogenesis model with clonal expansion of pre-malignant cells is used to describe lung cancer mortality data from studies on French and Czech miners with relatively low exposures to radon. The aim was to derive radon-induced lung cancer risk estimates applicable to different populations using a model description consistent with both cellular dose-response relationships, and previous model analyses of animal and human epidemiological data. The significantly different baseline lung cancer risks for the two cohorts that include the effects from the unknown smoking habits, are described with different background model parameters. A uniform description of the effect of radon for both miner cohorts is achieved by applying the same multiplicative effect for radon on the background mutation rates in the model. Incorporating the effects of decreased cellular proliferation at very advanced age improves the description of the baseline lung cancer risk, but does not lead to significant changes in the estimated radiation parameters. Here, a multi-stage model demonstrates the possibility of transferring radon-induced lung cancer risks across populations. The inherent age-time dose-rate relationships in the model allow for extrapolation to lifelong exposures to residential radon concentrations. The resulting cumulated (lifetime) risks from continuous exposure to low-level radon concentrations were found to agree with the results of the BEIR VI models.

[Risk factors for lymphatic metastasis from pT1 colorectal adenocarcinoma]

During the last 20 years, endoscopic removal of colorectal adenoma has become widely accepted as a replacement for removal by open surgery. Even colorectal adenocarcinomas are not excluded. The key question is when surgical treatment should still be preferred over endoscopic removal as the primary treatment. One good indicator is the frequency of lymph node metastasis, which should be compared with the overall risk involved in the surgical procedure itself. Histological examination allows subdivision of early colorectal adenocarcinomas into low-risk and high-risk groups. Classical parameters for a high-risk situation are lymphatic invasion, poor differentiation, and incomplete removal (R1). Additional risk factors that have recently been discussed are infiltration into the lower third of the submucosal layer (sm3) and dissociation (budding) of the tumour cells at the invasion front. Drawing on the literature and an analysis of our own patients, we demonstrate a positive correlation between these new markers and an elevated risk of the presence of lymph node metastasis.

Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability

In this paper, we derive analytic solutions of stochastic mutation-selection networks that describe early events of cancer formation. A main assumption is that cancer is initiated in tissue compartments, where only a relatively small number of cells are at risk of mutating into cells that escape from homeostatic regulation. In this case, the evolutionary dynamics can be approximated by a low-dimensional stochastic process with a linear Kolmogorov forward equation that can be solved analytically. Most of the time, the cell population is homogeneous with respect to relevant mutations. Occasionally, such homogeneous states are connected by 'stochastic tunnels'. We give a precise analysis of the existence of tunnels and calculate the rate of tunneling. Finally, we calculate the conditions for chromosomal instability (CIN) to precede inactivation of the first tumor suppressor gene. In this case, CIN is an early event and a driving force of cancer progression. The techniques developed in this paper can be used to study arbitrarily complex mutation-selection networks of the somatic evolution of cancer.

Have environmental mutagens caused oncomutations in people?

Age-specific cancer rates show large historical increases that indict environmental risk factors. But these environmental factors did not necessarily act by increasing oncomutation rates. Mathematical analyses suggest selective effects on pre-existing oncomutants. The widely held hypothesis that environmental chemicals induce a substantial fraction of human point mutations has not been supported by observation. Direct measurement of the kinds and numbers of point mutations in human tissues have, in fact, found no clear relationship with exposure to environmental agents, save for sunlight in the skin. Alternative hypotheses that point mutations arise primarily as errors during turnover of undamaged DNA and that environmental conditions select rather than induce oncomutants seem to better explain the facts of environmental carcinogenesis in humans.

Stability of 2'-deoxyxanthosine in DNA

The deamination of nucleobases in DNA occurs by a variety of mechanisms and results in the formation of hypoxanthine from adenine, uracil from cytosine, and xanthine and oxanine from guanine. 2'-Deoxyxanthosine (dX) has been assumed to be an unstable lesion in cells, yet no study has been performed under biological conditions. We now report that dX is a relatively stable lesion at pH 7, 37 degrees C and 110 mM ionic strength, with a half-life (t(1/2)) of 2.4 years in double-stranded DNA. The stability of dX as a 2'-deoxynucleoside (t(1/2) = 3.7 min at pH 2; 1104 h at pH 6) was increased substantially upon incorporation into a single-stranded oligodeoxynucleotide, in which the half-life of dX at different pH values was found to range from 7.7 h at pH 2 to 17 700 h at pH 7. Incorporation of dX into a double-stranded oligodeoxynucleotide resulted in a statistically insignificant increase in the half-life to 20 900 h at pH 7. Data for the pH dependence of the stability of dX in single-stranded DNA were used to determine the rate constants for the acid-catalyzed (2.6 x 10(-5) x s(-1)) and pH-independent (1.4 x 10(-8) x s(-1)) depurination reactions for dX as well as the dissociation constant for the N7 position of dX (6.1 x 10(-4) M). We conclude that dX is a relatively stable lesion that could play a role in deamination-induced mutagenesis.

Multistage carcinogenesis and the incidence of colorectal cancer

We use general multistage models to fit the age-specific incidence of colorectal cancers in the Surveillance, Epidemiology, and End Results registry, which covers approximately 10% of the U.S. population, while simultaneously adjusting for birth cohort and calendar year effects. The incidence of colorectal cancers in the Surveillance, Epidemiology, and End Results registry is most consistent with a model positing two rare events followed by a high-frequency event in the conversion of a normal stem cell into an initiated cell that expands clonally to give rise to an adenomatous polyp. Only one more rare event appears to be necessary for malignant transformation. The two rare events involved in initiation are interpreted to represent the homozygous loss of adenomatous polyposis coli gene function. The subsequent transition of a preinitiated stem cell into an initiated cell capable of clonal expansion via symmetric division is predicted to occur with a frequency too high for a mutational event but may reflect a positional effect in colonic crypts. Our results suggest it is not necessary to invoke genomic instability to explain colorectal cancer incidence rates in human populations. Temporal trends in the incidence of colon cancer appear to be dominated by calendar year effects. The model also predicts that interventions, such as administration of nonsteroidal anti-inflammatory drugs, designed to decrease the growth rate of adenomatous polyps, are very efficient at lowering colon cancer risk substantially, even when begun later in life. By contrast, interventions that decrease the rate of mutations at the adenomatous polyposis coli locus are much less effective in reducing the risk of colon cancer.

The overrated role of 'promotion' in mechanistic modelling of radiation carcinogenesis

It is argued that the 'cellular' dose-response relationships of model parameters cannot be determined from mechanistic model fits to experimental or epidemiologic cancer data. Baseline population cancer incidence data show conclusions about intermediate cell kinetics to be especially questionable. Here we recommend that mechanistic models should be applied solely in one direction: by starting from known cellular dose-response relationships the models aim at providing a biologically motivated consistent description of the development of radiation-induced cancer for different exposures, which is very important for low-dose risk estimation.

Age-incidence relationships and time trends in cervical cancer in Sweden

Age-incidence relationships are informative of carcinogenic mechanisms. These have been previously assessed for cervical squamous cell carcinoma (SCC) but not for adenocarcinoma. The aim was to assess by means of age-, period- and cohort-specific analyses and Poisson regression modelling whether the two types of cervical cancer show an age-incidence maximum at a relatively young age, as shown in cross-sectional analyses. The Swedish Family-Cancer Database was used to analyse age-incidence relationships in cervical SCC and adenocarcinoma diagnosed in years 1958-1996, including a total of 15,118 and 1866 cases, respectively. Area of residence and socio-economic status were included in analyses because they were risk factors of cervical cancer. The analysis of cervical SCC confirmed an incidence maximum at ages 35-39 years. The data for adenocarcinoma also suggested a similar early age maximum but the curves differed extensively by birth cohort. The incidence of adenocarcinoma increased substantially at young age groups towards the end of follow-up. Endometrial adenocarcinoma and vaginal and vulvar SCC, which share some risk factors with cervical cancer, did not show an early age incidence maximum. The results also showed that there was a decrease in the incidence of cervical SCC around year 1960, almost 10 years before the organized population screening, probably due to introduced opportunistic pap testing. The benefits of the organized screening were observed as a further decline in the incidence rates. The unique age-incidence relationships in cervical cancer call for biological explanations.

The in vivo levels of DNA alkylation products in human lymphocytes are not age dependent: an assay of 7-methyl- and 7-(2-hydroxyethyl)-guanine DNA adducts

Endogenous DNA damage is assumed to be a major contributor to aging and cancer. This study compares the steady-state levels of 7-methyl- and 7-(2-hydroxyethyl)-guanine DNA adducts in lymphocytes isolated from the younger (mean age 39.8 years) and the older (mean age 82.8 years) healthy subjects. Using a 32P-post-labelling method, these adducts were measured in lymphocyte DNA from a total of 34 subjects. The results show that the amount of both 7-methyl- and 7-(2-hydroxyethyl)-guanine adducts in the younger age group was similar to that in the older age group. Our findings show that at steady-state the levels of DNA alkylation products are independent of age, suggesting that endogenous DNA damage, through methylation or lipid peroxidation, and the repair of such damage may not be deficient in lymphocytes of older individuals.

High frequency of homoplasmic mitochondrial DNA mutations in human tumors can be explained without selection

Researchers in several laboratories have reported a high frequency of homoplasmic mitochondrial DNA (mtDNA) mutations in human tumors. This observation has been interpreted to reflect a replicative advantage for mutated mtDNA copies, a growth advantage for a cell containing certain mtDNA mutations, and/or tumorigenic properties of mtDNA mutations. We consider another possibility-that the observed homoplasmy arose entirely by chance in tumor progenitor cells, without any physiological advantage or tumorigenic requirement. Through extensive computer modeling, we demonstrate that there is sufficient opportunity for a tumor progenitor cell to achieve homoplasmy through unbiased mtDNA replication and sorting during cell division. To test our model in vivo, we analyzed mtDNA homoplasmy in healthy human epithelial tissues and discovered that the model correctly predicts the considerable observed frequency of homoplasmic cells. Based on the available data on mitochondrial mutant fractions and cell division kinetics, we show that the predicted frequency of homoplasmy in tumor progenitor cells in the absence of selection is similar to the reported frequency of homoplasmic mutations in tumors. Although a role for other mechanisms is not excluded, random processes are sufficient to explain the incidence of homoplasmic mtDNA mutations in human tumors.

Genetic epidemiology of multistage carcinogenesis

It is commonly believed that cancer is a multistage, polygenic disease. Even though conceptually appealing, the evidence supporting the multistage theory remains limited. Most known tumor suppresser genes are associated with monogenic dominant cancers following a two-hit pathway. We review results from a recent twin study on 90000 individuals that give support to the multistage theory. Statistically significant heritability estimates were shown for cancers of the colorectum (35%), breast (27%), and prostate (42%). These estimates are much higher than those obtained from family studies in which parents and offspring, or sibs are compared. The difference can be accounted for by the involvement of many genes. A polygenic cancer would show small effects in family studies but large effects in twin studies. We present calculations on the decrease in familial risks when the number of genes involved increases or when the penetrance decreases. We test the apparent number of stages involved in the main cancers from the Swedish Family-Cancer Database. The logarithms of the slopes suggest large differences in the apparent numbers of mutations involved in different cancers. The number of mutations required appears to be less in familial breast cancer compared to sporadic breast cancer. Study designs for gene identification should be revised to accommodate polygenic cancers.

Multiple primary cancers of the colon, breast and skin (melanoma) as models for polygenic cancers

To assess the role of family history in the development of multiple primary cancer, the Swedish Family-Cancer Database was used to analyze second primary cancer in patients born in 1935 to 1996 with an initial primary cancer of the colon, breast and skin (melanoma) by familial cancer in first-degree relatives. Standardized incidence ratios (SIRs) were calculated from site-, sex- and age-specific rates for all persons (offspring) born in 1935 to 1996. Familial risk (SIR) was calculated for the first and second primary cancers in offspring. A Poisson regression analysis was also performed to assess the risk factors for occurrence of second primary cancer. The familial proportion of multiple primary cancers was 29.0% (9/31) for colon, 16.3% (122/747) for female breast and 14.5% (17/117) for melanoma. Compared with all offspring, patients with family history were at a much higher and significantly increased risk for subsequent primary cancer at colon (SIR = 59.1), skin (SIR = 48.2) and female breast (SIR = 7.9). The corresponding SIRs in patients without family history were 13.8, 10.5 and 5.2 at the three sites. The ratios for incidence of second primary to first primary were highest when diagnosis age was less than 40 years. A Poisson regression analysis showed that family history was one of the major risk factors for occurrence of multiple primary cancers at colon, breast and skin. The high risk of second cancer, even in the absence of family history, would be consistent with a polygenic model of carcinogenesis.

Different mechanisms in the tumorigenesis of proximal and distal colon cancers

Environment or genetic constitutions can lead to an increase of genetic or epigenetic events and increase the risk for malignancy. Genomic instability is seen in most types of malignancies. Two forms of genetic instability have been described in colorectal cancer: chromosomal instability (CIN), and microsatellite instability (MIN). Almost all sporadic MIN tumors occur in the proximal colon, whereas most sporadic CIN tumors are distributed in the distal colon. The two familial syndromes, familial adenomatous polyposis and Lynch syndrome, constitute models for the different carcinogenic mechanisms in CIN and MIN tumors, respectively. This article reviews the principal differences between CIN and MIN tumors, evidence for a proximal and distal route in carcinogenesis, gender differences, and aspects of methylation in CIN and MIN colorectal tumorigenesis.