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

A stochastic carcinogenesis model incorporating multiple types of genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little [Little, M.P. (1995). Are two mutations sufficient to cause cancer? Some generalizations of the two-mutation model of carcinogenesis of Moolgavkar, Venzon, and Knudson, and of the multistage model of Armitage and Doll. Biometrics 51, 1278-1291] and Little and Wright [Little, M.P., Wright, E.G. (2003). A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data. Math. Biosci. 183, 111-134] is developed; the model incorporates multiple types of progressive genomic instability and an arbitrary number of mutational stages. The model is fitted to US Caucasian colon cancer incidence data. On the basis of the comparison of fits to the population-based data, there is little evidence to support the hypothesis that the model with more than one type of genomic instability fits better than models with a single type of genomic instability. Given the good fit of the model to this large dataset, it is unlikely that further information on presence of genomic instability or of types of genomic instability can be extracted from age-incidence data by extensions of this model.

Biological applications of the theory of birth-and-death processes

In this review, we discuss applications of the theory of birth-and-death processes to problems in biology, primarily, those of evolutionary genomics. The mathematical principles of the theory of these processes are briefly described. Birth-and-death processes, with some straightforward additions such as innovation, are a simple, natural and formal framework for modeling a vast variety of biological processes such as population dynamics, speciation, genome evolution, including growth of paralogous gene families and horizontal gene transfer and somatic evolution of cancers. We further describe how empirical data, e.g. distributions of paralogous gene family size, can be used to choose the model that best reflects the actual course of evolution among different versions of birth-death-and-innovation models. We conclude that birth-and-death processes, thanks to their mathematical transparency, flexibility and relevance to fundamental biological processes, are going to be an indispensable mathematical tool for the burgeoning field of systems biology.

Selective pressures for and against genetic instability in cancer: a time-dependent problem

Genetic instability in cancer is a two-edge sword. It can both increase the rate of cancer progression (by increasing the probability of cancerous mutations) and decrease the rate of cancer growth (by imposing a large death toll on dividing cells). Two of the many selective pressures acting upon a tumour, the need for variability and the need to minimize deleterious mutations, affect the tumour's 'choice' of a stable or unstable 'strategy'. As cancer progresses, the balance of the two pressures will change. In this paper, we examine how the optimal strategy of cancerous cells is shaped by the changing selective pressures. We consider the two most common patterns in multistage carcinogenesis: the activation of an oncogene (a one-step process) and an inactivation of a tumour-suppressor gene (a two-step process). For these, we formulate an optimal control problem for the mutation rate in cancer cells. We then develop a method to find optimal time-dependent strategies. It turns out that for a wide range of parameters, the most successful strategy is to start with a high rate of mutations and then switch to stability. This agrees with the growing biological evidence that genetic instability, prevalent in early cancers, turns into stability later on in the progression. We also identify parameter regimes where it is advantageous to keep stable (or unstable) constantly throughout the growth.

Spindle assembly checkpoint and centrosome abnormalities in oral cancer

Like many solid tumours, oral squamous cell carcinomas (OSCC) invariably exhibit chromosomal instability (CIN) leading to aneuploidy. The mechanisms responsible for CIN in OSCC, however, are largely unknown. This study examined the fidelity of the spindle checkpoint, together with the number, structure and function of centrosomes in a series of well-characterised aneuploid immortal OSCC-derived cell lines that harbour p53 and p16(INK4A) defects. The spindle checkpoints were fully functional in 2 of 7 cell lines and attenuated in the remaining 5 cell lines. Overexpression of the spindle checkpoint protein, Cdc20, was observed in 2 of the cell lines with attenuated checkpoints. Defects in centrosome number, size and localisation were detected in 5 of the cell lines. Clonal cell populations contained cells with both normal and abnormal numbers of centrosomes, suggesting that the control of centrosome number may be inherently unstable in OSCC-derived cell lines. Centrosomal abnormalities were then examined in tissue samples of oral epithelial dysplasias and carcinomas. Abnormal centrosomes were detected in all the tissues examined albeit in a low percentage of cells (<1% to >5%). The percentage of cells containing centrosome abnormalities was significantly higher in the carcinomas than in the dysplasias (p<0.02) and in the poorly differentiated SCCs relative to their moderately differentiated (p<0.04) and well-differentiated (p<0.01) counterparts. We suggest that the genetic alterations associated with the development of the immortal phenotype, together with spindle checkpoint and centrosome defects, are responsible, albeit in part, for the complex karyotypes observed in OSCC. The presence of centrosome abnormalities in oral dysplasias raises the possibility that such defects might contribute to malignant progression.

An evolutionary hybrid cellular automaton model of solid tumour growth

We propose a cellular automaton model of solid tumour growth, in which each cell is equipped with a micro-environment response network. This network is modelled using a feed-forward artificial neural network, that takes environmental variables as an input and from these determines the cellular behaviour as the output. The response of the network is determined by connection weights and thresholds in the network, which are subject to mutations when the cells divide. As both available space and nutrients are limited resources for the tumour, this gives rise to clonal evolution where only the fittest cells survive. Using this approach we have investigated the impact of the tissue oxygen concentration on the growth and evolutionary dynamics of the tumour. The results show that the oxygen concentration affects the selection pressure, cell population diversity and morphology of the tumour. A low oxygen concentration in the tissue gives rise to a tumour with a fingered morphology that contains aggressive phenotypes with a small apoptotic potential, while a high oxygen concentration in the tissue gives rise to a tumour with a round morphology containing less evolved phenotypes. The tissue oxygen concentration thus affects the tumour at both the morphological level and on the phenotype level.

Spatial stochastic models for cancer initiation and progression

The multistage carcinogenesis hypothesis has been formulated by a number of authors as a stochastic process. However, most previous models assumed "perfect mixing" in the population of cells, and included no information about spatial locations. In this work, we studied the role of spatial dynamics in carcinogenesis. We formulated a 1D spatial generalization of a constant population (Moran) birth-death process, and described the dynamics analytically. We found that in the spatial model, the probability of fixation of advantageous and disadvantageous mutants is lower, and the rate of generation of double-hit mutants (the so-called tunneling rate) is higher, compared to those for the space-free model. This means that the results previously obtained for space-free models give an underestimation for rates of cancer initiation in the case where the first event is the generation of a double-hit mutant, e.g. the inactivation of a tumor-suppressor gene.

The age incidence of chronic myeloid leukemia can be explained by a one-mutation model

Chronic myeloid leukemia (CML) is associated with the Philadelphia chromosome, which arises by a reciprocal translocation between chromosomes 9 and 22 and harbors the BCR-ABL fusion oncogene. It is unknown whether any other mutations are needed for the chronic phase of the disease. The CML incidence increases as a function of age with an exponent of approximately 3. A slope of 3 could indicate that there are two mutations, in addition to the Philadelphia translocation, that have not yet been discovered. In this work, we explore an alternative hypothesis: We study a model of cancer initiation requiring only a single mutation. A mutated cell has a net reproductive advantage over normal cells and, therefore, might give rise to clonal expansion. The cancer is detected with a probability that is proportional to the size of the mutated cell clone. This model has three waiting times: (i) the time until a mutated cell is produced, (ii) the time of clonal expansion, and (iii) the time until the clone is detected. Surprisingly, this simple process can give rise to cancer incidence curves with exponents up to 3. Therefore, the CML incidence data are consistent with the hypothesis that the Philadelphia translocation alone is sufficient to cause chronic phase CML.

Genetic instability and clonal expansion

Inactivation of tumor suppressor genes can lead to clonal expansion. We study the evolutionary dynamics of this process and calculate the probability that inactivation of a tumor suppressor gene is preceded by mutations in genes that confer genetic instability. Unstable cells might have a slower rate of clonal expansion than stable cells because of an increased probability of generating lethal mutations or inducing apoptosis. We show that the different growth rates of genetically stable and unstable cells during clonal expansion represent, in general, only a small disadvantage for genetic instability. The intuitive reason for this conclusion is that robust clonal expansion, where cellular birth rates are significantly greater than death rates, occurs on a much faster time scale than waiting for those mutations that allow clonal expansion. Moreover, in special cases where clonal expansion is very slow, genetically unstable cells have a higher probability to accumulate additional mutations during clonal expansion that confer a selective advantage. Clonal expansion represents a major disadvantage for genetic instability only when inactivation of the tumor suppressor gene leads to a very small increase of the cellular reproductive rate that is cancelled by the increased mortality of unstable cells.

Crypt dynamics and colorectal cancer: advances in mathematical modelling

Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem-cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem-cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

Molecular biology of squamous cell carcinoma of the anus

BACKGROUND

Squamous cell carcinoma of the anal canal provides a model for studying the contribution of human papillomavirus (HPV) and human immunodeficiency virus (HIV) infection to the development of neoplasia. This paper reviews the existing literature relating to the molecular biology of anal squamous cell carcinoma and proposes a theory of pathogenesis.

METHODS

A Medline literature search was performed to identify English articles on the pathogenesis of squamous cell carcinoma of the anus; further articles were obtained from the references quoted in the literature initially reviewed.

RESULTS

HPV infection and subsequent HPV DNA integration are necessary, but not sufficient, to cause cancer progression. Loss of heterozygosity at 11q23 is the most consistent genomic change observed. Loss of heterozygosity at 17p, 18q and 5q is frequently observed in tumours of HIV-negative patients, but not in those of HIV-positive patients. Current data suggest that mutations in p53, DCC and APC tumour suppressor genes contribute to the stepwise progression of anal squamous cell carcinoma in immunocompetent individuals.

CONCLUSION

In comparison with immunocompetent individuals, HIV-positive patients have persistent HPV infection in the anal canal. In this population, microsatellite instability, rather than chromosomal instability, appears to be a preferred pathway for rapid progression towards invasive carcinoma.

Dynamics of metastasis suppressor gene inactivation

For most cancer cell types, the acquisition of metastatic ability leads to clinically incurable disease. Twelve metastasis suppressor genes (MSGs) have been identified that reduce the metastatic propensity of cancer cells. If these genes are inactivated in both alleles, metastatic ability is promoted. Here, we develop a mathematical model of the dynamics of MSG inactivation and calculate the expected number of metastases formed by a tumor. We analyse the effects of increased mutation rates and different fitness values of cells with one or two inactivated alleles on the ability of a tumor to form metastases. We find that mutations that are negatively selected in the main tumor are unlikely to be responsible for the majority of metastases produced by a tumor. Most metastases-causing mutations will be present in all (or most) cells in the main tumor.

Genetic instability in human tumors

Genetic, or genomic, instability refers to a series of observed spontaneous genetic changes occurring at an accelerated rate in cell populations derived from the same ancestral precursor. This is far from a new finding, but is one that has increasingly gained more attention in the last decade due to its plausible role(s) in tumorigenesis. The majority of genetic alterations contributing to the malignant transformation are seen in growth regulatory genes, and in genes involved in cell cycle progression and arrest. Genomic instability may present itself through alterations in the length of short repeat stretches of coding and non-coding DNA, resulting in microsatellite instability. Tumors with such profiles are referred to as exhibiting a mutator phenotype, which is largely a consequence of inactivating mutations in DNA damage repair genes. Genomic instability may also, and most commonly, results from gross chromosomal changes, such as translocations or amplifications, which lead to chromosomal instability. Telomere length and telomerase activity, important in maintaining chromosomal structure and in regulating a normal cell's lifespan, have been shown to have a function in both suppressing and facilitating malignant transformation. In addition to such direct sequence and structural changes, gene silencing through the hypermethylation of promoter regions, or increased gene expression through the hypomethylation of such regions, together, form an alternative, epigenetic mechanism leading to instability. Emerging evidence also suggests that dietary and environmental agents can further modulate the contribution of genetic instability to tumorigenesis. Currently, there is still much debate over the distinct classes of genomic instability and their specific roles in the initiation of tumor formation, as well as in the progressive transition to a cancerous state. This review examines the various molecular mechanisms that result in this genomic instability and the potential contribution of the latter to human carcinogenesis.

Epithelial tissue architecture protects against cancer

We consider the design of colon crypts from the point of view of minimizing the likelihood of generation of cancerous mutations. A stochastic mathematical model (a finite branching process) is developed and fully analyzed. It is found that depending on the mutation rates, different designs are evolutionarily advantageous. If the mutation rates associated with stem cells are a lot higher than the mutation rates of daughter cells, then few stem cells per crypt is the evolutionarily optimal strategy. If the mutation rates of stem cells are of the same order of magnitude or lower than those for daughter cells, then having as many stem cells per crypt as possible is the desirable design. We also found that the optimal evolutionary strategy may work very well to protect the organism from cancer in the young age, but the same strategy becomes detrimental as the organism ages. It pushes the onset of cancer back in time, but it results in an elevated cancer initiation rates as the organism gets older. Our model quantifies the idea that cancer and aging are the two sides of one coin.

Molecular analysis of the PI3K-AKT pathway in uterine cervical neoplasia: FrequentPIK3CAamplification and AKT phosphorylation

Uterine cervical carcinogenesis is probably dependent on cellular genetic damage in addition to the integration of high-risk HPV DNA in the epithelial cell genome. Gain of chromosome 3q24-29 is commonly observed in cervical neoplasia. The putative oncogene PIK3CA located in this region encodes a phosphatidylinositol 3-kinase (PI3K). In a process reversed by PTEN, PI3K generates inositol phospholipids that trigger AKT phosphorylation, which in turn effects tumor driving signals. We studied 46 specimens of formalin-fixed, paraffin-embedded cervical neoplastic tissue. The activation state of the PI3K-AKT pathway was assessed immunohistochemically using an antibody with specificity towards serine 473-phosphorylated AKT. AKT phosphorylation was found in 39 out of 46 examined specimens. To examine the possible molecular basis for this activation, we searched for PIK3CA amplification using quantitative real-time polymerase chain reaction. PIK3CA gene copy number was estimated to be 3 or more in 28 out of 40 successfully examined cases. Further, a PTEN mutation analysis of all 9 PTEN exons was carried out, but except for 1 metastasis with an exon 9 V369I heterozygosity, all cases showed normal PTEN sequence. Immunohistochemical staining for PTEN was strong in all lesions. In conclusion, an increased activation state of AKT kinase appears to be present in cervical carcinogenesis, and may be accounted for by PIK3CA amplification, whereas PTEN mutation seems to be of little importance.

Negative clonal selection in tumor evolution

Development of cancer requires the acquisition of multiple oncogenic mutations and selection of the malignant clone. Cancer evolves within a finite host lifetime and mechanisms of carcinogenesis that accelerate this process may be more likely to contribute to the development of clinical cancers. Mutator mutations are mutations that affect genome stability and accelerate the acquisition of oncogenic mutations. However, mutator mutations will also accelerate the accumulation of mutations that decrease cell proliferation, increase apoptosis, or affect other key fitness parameters. These "reduced-fitness" mutations may mediate "negative clonal selection," i.e., selective elimination of premalignant mutator clones. Target reduced-fitness loci may be "recessive" (both copies must be mutated to reduce fitness) or "dominant" (single-copy mutation reduces fitness). A direct mathematical analysis is applied to negative clonal selection, leading to the conclusion that negative clonal selection against mutator clones is unlikely to be a significant effect under realistic conditions. In addition, the relative importance of dominant and recessive reduced-fitness mutations is quantitatively defined. The relative predominance of mutator mutations in clinical cancers will depend on several variables, including the tolerance of the genome for reduced-fitness mutations, particularly the number and potency of dominant reduced-fitness loci.

A comprehensive continuous-time model for the appearance of CGH signal due to chromosomal missegregations during mitosis

Aneuploidy, the gain or loss of large regions of the genome, is a common feature in cancer cells. Irregularities in chromosomal copy number caused by missegregations of chromosomes during mitosis can be visualized by cytogenetic techniques including fluorescence in situ hybridization (FISH), spectral karyotyping (SKY) and comparative genomic hybridization (CGH). In the current work, we consider the propagation of irregular copy numbers throughout a cell population as the individual cells progress through ordinary mitotic cell cycles. We use an algebraic model to track the different copy numbers as states in a stochastic process, based on the model of chromosome instability of Gusev, Kagansky, and Dooley, and consider the average copy number of a particular chromosome within a cell population as a function of the cell division rate. We review a number of mathematical models for determining the length of the cell cycle, including the Smith-Martin transition probability model and the 'sloppy size' model of Wheals, Tyson and Diekmann. The program MITOSIM simulates the growth of a population of cells using the aforementioned models of the cell cycle. MITOSIM allows the cell population to grow, with occasional resampling, until the average copy number of a given chromosome in the population reaches a preset threshold signifying a positive copy number alteration in this region. MITOSIM calculates the relationship between the missegregation rate and the growth rate of the cell population. This allows the user to test hypotheses regarding the effect chromosomal aberrations have upon the cell cycle, cell growth rates, and time to population dominance.

Evolutionary biology of cancer

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

Can chromosomal instability initiate tumorigenesis?

Cancers result from the accumulation of inherited and somatic mutations in oncogenes and tumor suppressor genes. These genes encode proteins that function in growth regulatory and differentiation pathways. Mutations in those genes increase the net reproductive rate of cells. Chromosomal instability (CIN) is a feature of most human cancers. Mutations in CIN genes increase the rate at which whole chromosomes or large parts of chromosomes are lost or gained during cell division. CIN causes an imbalance in chromosome number (aneuploidy) and an enhanced rate of loss of heterozygosity, which is an important mechanism of inactivating tumor suppressor genes. A crucial question of cancer biology is whether CIN is an early event and thus a driving force of tumorigenesis. Here we discuss mathematical models of situations where inactivation of one or two tumor suppressor genes is required for tumorigenesis. If two tumor suppressor genes have to be inactivated in rate-limiting steps, then CIN is likely to emerge before the inactivation of the first tumor suppressor gene.

Chromosomal instability and human cancer

Genetic instability is a defining feature of human cancer. The main type of genetic instability, chromosomal instability (CIN), enhances the rate of gross chromosomal changes during cell division. CIN is brought about by mutations of CIN genes, i.e. genes that are involved in maintaining the genomic integrity of the cell. A major question in cancer genetics is whether genetic instability is a cause and hence a driving force of tumorigenesis. A mathematical framework for studying the somatic evolution of cancer sheds light onto the causal relations between CIN and human cancer.

Population genetics of tumor suppressor genes

Cancer emerges when a single cell receives multiple mutations. For example, the inactivation of both alleles of a tumor suppressor gene (TSG) can imply a net reproductive advantage of the cell and might lead to clonal expansion. In this paper, we calculate the probability as a function of time that a population of cells has generated at least one cell with two inactivated alleles of a TSG. Different kinetic laws hold for small and large populations. The inactivation of the first allele can either be neutral or lead to a selective advantage or disadvantage. The inactivation of the first and of the second allele can occur at equal or different rates. Our calculations provide insights into basic aspects of population genetics determining cancer initiation and progression.

Loss of expression of the adipocyte-type fatty acid-binding protein (A-FABP) is associated with progression of human urothelial carcinomas

Bladder cancer is the fifth most common malignancy in the world and represents the second most common cause of death among genitourinary tumors. Current prognostic parameters such as grade and stage cannot predict with certainty the long-term outcome of bladder cancer, and as a result there is a pressing need to identify markers that may predict tumor behavior. Earlier we identified the adipocyte fatty acid-binding protein (A-FABP), a small-molecular-mass fatty acid-binding protein that functions by facilitating the intracellular diffusion of fatty acids between cellular compartments as a putative marker of progression based on a limited study of fresh bladder urothelial carcinomas (UCs) (Celis, J. E., Ostergaard, M., Basse, B., Celis, A., Lauridsen, J. B., Ratz, G. P., Andersen, I., Hein, B., Wolf, H., Orntoft, T. F., and Rasmussen, H. H. (1996) Loss of adipocyte-type fatty acid binding protein and other protein biomarkers is associated with progression of human bladder transitional cell carcinomas. Cancer Res.56, 4782-4790). Here we have comprehensively examined the protein expression profiles of a much larger sample set consisting of 153 bladder specimens (46 nonmalignant biopsies, 11 pTa G1, 40 pTa G2, 10 pTa G3, 13 pT1 G3, 23 pT2-4 G3, and 10 pT2-4 G4) by gel-based proteomics in combination with immunohistochemistry (IHC) using a peptide-based rabbit polyclonal antibody that reacts specifically with this protein. Proteomic profiling showed a striking down-regulation of A-FABP in invasive lesions, a fact that correlated well with immunohistochemical analysis of the same samples. The IHC results were confirmed by using a tissue microarray (TMA) containing 2,317 samples derived from 1,849 bladder cancer patients. Moreover, we found that the altered expression of A-FABP in invasive UCs is not due to deregulated expression of peroxisome proliferator-activated receptor gamma (PPARgamma), a trans-activator of A-FABP. Taken together, these results provide evidence that deregulation of A-FABP may play a role in bladder cancer progression and suggest that A-FABP could have a significant prognostic value in combination with other biomarkers.

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.

Cancer genes and the pathways they control

The revolution in cancer research can be summed up in a single sentence: cancer is, in essence, a genetic disease. In the last decade, many important genes responsible for the genesis of various cancers have been discovered, their mutations precisely identified, and the pathways through which they act characterized. The purposes of this review are to highlight examples of progress in these areas, indicate where knowledge is scarce and point out fertile grounds for future investigation.

Evolutionary dynamics of tumor suppressor gene inactivation

Tumor suppressor genes (TSGs) are important gatekeepers that protect against somatic evolution of cancer. Losing both alleles of a TSG in a single cell represents a step toward cancer. We study how the kinetics of TSG inactivation depends on the population size of cells and the mutation rates for the first and second hit. We calculate the probability as function of time that at least one cell has been generated with two inactivated alleles of a TSG. We find three different kinetic laws: in small, intermediate, and large populations, it takes, respectively, two, one, and zero rate-limiting steps to inactivate a TSG. We also study the effect of chromosomal and other genetic instabilities. Small lesions without genetic instability can take a very long time to inactivate the next TSG, whereas the same lesions with genetic instability pose a much greater risk for cancer progression.

Somatic selection for and against cancer

In multicellular organisms, cells cooperate within a well-defined developmental program. Cancer is a breakdown of such cooperation: cells mutate to phenotypes of uncoordinated proliferation. We study basic principles of the architecture of solid tissues that influence the rate of cancer initiation. In particular, we explore how somatic selection acts to prevent or to promote cancer. Cells with mutations in oncogenes or tumor suppressor genes often have increased proliferation rates. Somatic selection increases their abundance and thus enhances the risk of cancer. Many potentially harmful mutations, however, increase the probability of triggering apoptosis and, hence, initially lead to cells with reduced net proliferation rates. Such cells are eliminated by somatic selection, which therefore also works to reduce the risk of cancer. We show that a tissue organization into small compartments avoids the rapid spread of mutations in oncogenes and tumor suppressor genes, but promotes genetic instability. In small compartments, genetic instability, which confers a selective disadvantage for the cell, can spread by random drift. If both deleterious and advantageous mutations participate in tumor initiation, then we find an intermediate optimum for the compartment size.

Evolutionary dynamics of invasion and escape

Whenever life wants to invade a new habitat or escape from a lethal selection pressure, some mutations may be necessary to yield sustainable replication. We imagine situations like (i) a parasite infecting a new host, (ii) a species trying to invade a new ecological niche, (iii) cancer cells escaping from chemotherapy, (iv) viruses or microbes evading anti-microbial therapy, and also (v) the repeated attempts of combinatorial chemistry in the very beginning of life to produce self-replicating molecules. All such seemingly unrelated situations have a common structure in terms of Darwinian dynamics: a replicator with a basic reproductive ratio less than one attempts to find some mutations that allow indefinite survival. We develop a general theory, based on multitype branching processes, to describe the evolutionary dynamics of invasion and escape.

The significance of unstable chromosomes in colorectal cancer

A very large fraction of cancers have an abnormal genetic content, called aneuploidy, which is characterized by changes in chromosome structure and number. One explanation for this aneuploidy is chromosomal instability, in which cancer cells gain or lose whole chromosomes or large fractions of chromosomes at a greatly increased rate compared with normal cells. Here, we explore experimental and theoretical evidence for the initiation of chromosomal instability in very early colorectal cancers, and reflect on the role that chromosomal instability could have in colorectal tumorigenesis.