Age-specific incidence of inherited versus sporadic cancers: a test of the multistage theory of carcinogenesis

Occam's razor gets a new edge: the use of symmetries in model selection

We demonstrate the power of using symmetries for model selection in the context of mechanistic modelling. We analyse two different models called the power law model (PLM) and the immunological model (IM) describing the increase in cancer risk with age, due to mutation accumulation or immunosenescence, respectively. The IM fits several cancer types better than the PLM implying that it would be selected based on minimizing residuals. However, recently a symmetry-based method for model selection has been developed, which has been successfully used in an in silico setting to find the correct model when traditional model fitting has failed. Here, we apply this method in a real-world setting to investigate the mechanisms of carcinogenesis. First, we derive distinct symmetry transformations of the two models and then we select the model which not only fits the original data but is also invariant under transformations by its symmetry. Contrary to the initial conclusion, we conclude that the PLM realistically describes the mechanism underlying the colon cancer dataset. These conclusions agree with experimental knowledge, and this work demonstrates how a model selection criterion based on biological properties can be implemented using symmetries.

Alzheimer's disease as a multistage process: an analysis from a population-based cohort study

In cancer research, multistage models are used to assess the multistep process that leads to the onset of cancer. In view of biological and clinical similarities between cancer and dementia, we used these models to study Alzheimer’s disease (AD). From the population-based Rotterdam Study, we included 9,362 non-demented participants, of whom 1,124 developed AD during up to 26 years of follow-up. Under a multistage model, we regressed the logarithm of AD incidence rate against the logarithm of five-year age categories. The slope in this model reflects the number of steps (n–1) required for disease onset before the final step leading to disease manifestation. A linear relationship between log incidence rate and log age was observed, with a slope of 12.82 (95% confidence interval: 9.01-16.62), equivalent to 14 steps. We observed fewer steps for those at high genetically determined risk: 12 steps for APOE-ε4 carriers, and 10 steps for those at highest genetic risk based on APOE and a genetic risk score. The pathogenesis of AD complies with a multistage disease-model, requiring 14 steps before disease manifestation. Genetically predisposed individuals require fewer steps indicating that they already inherited multiple of these steps. Unravelling these steps in AD pathogenesis could benefit the development of intervention strategies.

Estimating the number of genetic mutations (hits) required for carcinogenesis based on the distribution of somatic mutations

Individual instances of cancer are primarily a result of a combination of a small number of genetic mutations (hits). Knowing the number of such mutations is a prerequisite for identifying specific combinations of carcinogenic mutations and understanding the etiology of cancer. We present a mathematical model for estimating the number of hits based on the distribution of somatic mutations. The model is fundamentally different from previous approaches, which are based on cancer incidence by age. Our somatic mutation based model is likely to be more robust than age-based models since it does not require knowing or accounting for the highly variable mutation rate, which can vary by over three orders of magnitude. In fact, we find that the number of somatic mutations at diagnosis is weakly correlated with age at cancer diagnosis, most likely due to the extreme variability in mutation rates between individuals. Comparing the distribution of somatic mutations predicted by our model to the actual distribution from 6904 tumor samples we estimate the number of hits required for carcinogenesis for 17 cancer types. We find that different cancer types exhibit distinct somatic mutational profiles corresponding to different numbers of hits. Why might different cancer types require different numbers of hits for carcinogenesis? The answer may provide insight into the unique etiology of different cancer types.

Cancer is primarily a result of genetic mutations. Each individual instance of cancer is initiated by a specific combination of a small number of mutations (hits). In trying to identify these combinations of mutations, it is important to know how many hits to look for. However, there are conflicting estimates for the number of hits. We present a fundamentally different model for estimating the number of hits. We found that the number hits ranges from two-eight depending on cancer type. These findings may provide insight into the unique characteristics of different cancer types.

Accurate prediction of the age incidence of chronic myeloid leukemia with an improved two-mutation mathematical model

Chronic myeloid leukemia (CML) is a malignant clonal disorder whose hallmark is a reciprocal translocation between chromosomes 9 and 22 occurring in 95% of affected patients. This translocation causes the expression of a deregulated BCR/ABL fusion oncogene and, interestingly, is detectable in healthy individuals. Based on this information we assumed that the sole presence of the BCR/ABL transcript represents a necessary but not sufficient event for the clonal expansion of CML precursors. We developed a mathematical model introducing a probability that any normal cell undergoes a first aberration, and a probability that a cell that experienced a first mutation undergoes a second mutation as well. Two variants are proposed and analyzed: in the first the probability of the first mutation is supposed to be age independent and in the second, it depends on the hemopoietic cell turnover and mass. The model parameters have been estimated by regression from the observed CML incidence curves. Our models offer a significantly improved version of existing one-step and two-steps models, as they integrate key clinical and biological data reported in the literature and accurately fit the observed incidence. Our models also estimate the increased radiation-associated mutation rate at a younger age in atomic bomb survivors. Although this work focuses on CML, the modelling approach can be applied to all types of leukemia and lymphoma.

Age-specific acceleration in malignant melanoma

Background: The overall incidence of melanoma has increased steadily for several years. The relative change in incidence at different ages has not been fully described.  Objective: To describe how incidence at different ages has changed over time and to consider what aspects of tumour biology may explain the observed pattern of change in incidence.  Methods: The slope of incidence vs age measures the acceleration of cancer incidence with age. We described the pattern of change over time in the overall incidence of melanoma, as well as in acceleration. We used data for males and females from 3 different countries in the 17 sequential 5-year birth-cohort categories from 1895-99 to 1975-79, from which we derived the incidence patterns.  Results: Over time, there has been a tendency for the overall incidence of melanoma to increase and for the acceleration (slope) of the age-incidence curves to decline. The changing patterns of melanoma incidence and acceleration differ between males and females and between the countries analysed.  Conclusions: The observed pattern in melanoma of rising incidence and declining acceleration occurs in other cancers in response to genetic knockouts of mechanisms that protect against cancer. Perhaps some protective mechanism with respect to melanoma may be less effective now than in the past, possibly because of more intense environmental challenges.

Invariant death

In nematodes, environmental or physiological perturbations alter death’s scaling of time. In human cancer, genetic perturbations alter death’s curvature of time. Those changes in scale and curvature follow the constraining contours of death’s invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death’s scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.

Somatic mosaicism and disease

The large number of cell divisions required to make a human body inevitably leads to the accumulation of somatic mutations. Such mutations cause individuals to be somatic mosaics. Recent advances in genomic technology now allow measurement of somatic diversity. Initial studies confirmed the expected high levels of somatic mutations within individuals. Going forward, the big questions concern the degree to which those somatic mutations influence disease. Theory predicts that the frequency of mutant cells should vary greatly between individuals. Such somatic mutational variability between individuals could explain much of the diversity in the risk of disease. But how variable is mosaicism between individuals in reality? What is the relation between the fraction of cells carrying a predisposing mutation and the risk of disease? What kinds of heritable somatic change lead to disease besides classical DNA mutations? What molecular processes connect a predisposing somatic change to disease? We know that predisposing somatic mutations strongly influence the onset of cancer. Likewise, neurodegenerative diseases may often begin from somatically mutated cells. If so, both neurodegeneration and cancer may be diseases of later life for which much of the risk may be set by early life somatic mutations.

Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases

Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a "wild-type" state to a given "terminally differentiated," "resistant," or "cancerous" state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be "nonlinear" (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times.

Excess congenital non-synonymous variation in leukemia-associated genes in MLL- infant leukemia: a Children's Oncology Group report

Infant leukemia (IL) is a rare sporadic cancer with a grim prognosis. Although most cases are accompanied by MLL rearrangements and harbor very few somatic mutations, less is known about the genetics of the cases without MLL translocations. We performed the largest exome-sequencing study to date on matched non-cancer DNA from pairs of mothers and IL patients to characterize congenital variation that may contribute to early leukemogenesis. Using the COSMIC database to define acute leukemia-associated candidate genes, we find a significant enrichment of rare, potentially functional congenital variation in IL patients compared with randomly selected genes within the same patients and unaffected pediatric controls. IL acute myeloid leukemia (AML) patients had more overall variation than IL acute lymphocytic leukemia (ALL) patients, but less of that variation was inherited from mothers. Of our candidate genes, we found that MLL3 was a compound heterozygote in every infant who developed AML and 50% of infants who developed ALL. These data suggest a model by which known genetic mechanisms for leukemogenesis could be disrupted without an abundance of somatic mutation or chromosomal rearrangements. This model would be consistent with existing models for the establishment of leukemia clones in utero and the high rate of IL concordance in monozygotic twins.

Applying ecological and evolutionary theory to cancer: a long and winding road

Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.

Potential roles for prions and protein-only inheritance in cancer

Inherited mutations are known to cause familial cancers. However, the cause of sporadic cancers, which likely represent the majority of cancers, is yet to be elucidated. Sporadic cancers contain somatic mutations (including oncogenic mutations); however, the origin of these mutations is unclear. An intriguing possibility is that a stable alteration occurs in somatic cells prior to oncogenic mutations and promotes the subsequent accumulation of oncogenic mutations. This review explores the possible role of prions and protein-only inheritance in cancer. Genetic studies using lower eukaryotes, primarily yeast, have identified a large number of proteins as prions that confer dominant phenotypes with cytoplasmic (non-Mendelian) inheritance. Many of these have mammalian functional homologs. The human prion protein (PrP) is known to cause neurodegenerative diseases and has now been found to be upregulated in multiple cancers. PrP expression in cancer cells contributes to cancer progression and resistance to various cancer therapies. Epigenetic changes in the gene expression and hyperactivation of MAP kinase signaling, processes that in lower eukaryotes are affected by prions, play important roles in oncogenesis in humans. Prion phenomena in yeast appear to be influenced by stresses, and there is considerable evidence of the association of some amyloids with biologically positive functions. This suggests that if protein-only somatic inheritance exists in mammalian cells, it might contribute to cancer phenotypes. Here, we highlight evidence in the literature for an involvement of prion or prion-like mechanisms in cancer and how they may in the future be viewed as diagnostic markers and potential therapeutic targets.

Malignant transformation and stromal invasion from normal or hyperplastic tissues: true or false?

Carcinogenesis is believed to be a multi-step process, progressing sequentially from normal to hyperplastic, to in situ, and to invasive stages. A number of studies, however, have detected malignancy-associated alterations in normal or hyperplastic tissues. As the molecular profile and clinical features of these tissues have not been defined, the authors invited several well-recognized pathologist, oncologists, biologist, surgeons, and molecular biologist to offer their opinion on: (1) whether these tissues belong to a previously unrevealed malignant entity or focal alterations with no significant consequence? (2) whether these alterations are linked to early onset of cancer or cancer of unknown primary site, and (3) how to further define these lesions?

Stochastic dynamics of cancer initiation

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

Cancer models, genomic instability and somatic cellular Darwinian evolution

The biology of cancer is critically reviewed and evidence adduced that its development can be modelled as a somatic cellular Darwinian evolutionary process. The evidence for involvement of genomic instability (GI) is also reviewed. A variety of quasi-mechanistic models of carcinogenesis are reviewed, all based on this somatic Darwinian evolutionary hypothesis; in particular, the multi-stage model of Armitage and Doll (Br. J. Cancer 1954:8;1-12), the two-mutation model of Moolgavkar, Venzon, and Knudson (MVK) (Math. Biosci. 1979:47;55-77), the generalized MVK model of Little (Biometrics 1995:51;1278-1291) and various generalizations of these incorporating effects of GI (Little and Wright Math. Biosci. 2003:183;111-134; Little et al. J. Theoret. Biol. 2008:254;229-238).

Pancreatic adenocarcinoma in type 2 progressive familial intrahepatic cholestasis

Background

BSEP disease results from mutations in ABCB11, which encodes the bile salt export pump (BSEP). BSEP disease is associated with an increased risk of hepatobiliary cancer.

Case Presentation

A 36 year old woman with BSEP disease developed pancreatic adenocarcinoma at age 36. She had been treated with a biliary diversion at age 18. A 1.7 × 1.3 cm mass was detected in the pancreas on abdominal CT scan. A 2 cm mass lesion was found at the neck and proximal body of the pancreas. Pathology demonstrated a grade 2-3 adenocarcinoma with invasion into the peripancreatic fat.

Conclusions

Clinicians should be aware of the possibility of pancreatic adenocarcinoma in patients with BSEP disease.

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.

Intestinal tumour chemoprevention with the antioxidant lipoic acid stimulates the growth of breast cancer

OBJECTIVE

Breast and intestinal cancers chemoprevention would significantly impact on cancer care. Hence, we assessed the chemopreventive efficacy of the antioxidant lipoic acid (LA) in mice overexpressing a wild-type Her2/neu, as an animal model of breast cancer, and in APCmin mice for intestinal cancer.

METHODS

Mice were randomised at weaning, and were treated with LA for lifetime. Tumour incidence, growth rate and histopathology were analysed on an individual tumour basis.

RESULTS

LA efficiently chemoprevented tumour appearance in APCmin mice. Strikingly, though, LA doses, that were chemopreventive in APCmin mice (> or = 300 microg/day), increased breast cancer growth in Her2/neu mice. Even in experimental groups, where LA overall reduced tumour risk (80 microg/day), LA consistently stimulated the growth rate of established breast tumours. Breast and colon tumours incidence was unaffected by LA, indicating no significant impact of LA on tumour initiation and no protection from mutations driving tumour progression.

CONCLUSIONS

Stimulation of breast cancer growth and inhibition of intestinal tumours by LA indicate that diverse growth control mechanisms are modulated by LA in different organs. Concern is raised about the use of LA for cancer chemoprevention.

Mutation in aging mice occurs in diverse cell types that proliferate postmutation

To determine the relationship between aging, cell proliferation and mutation in different cell types, hearts, brains and kidneys from G11 PLAP mice between 1 week and 24 months of age were examined. Mutant cells were detected in tissue sections by staining for Placental Alkaline Phosphatase (PLAP) activity, an activity that marks cells that have sustained a frameshift mutation in a mononucleotide tract inserted into the coding region of the human gene encoding PLAP. The number of PLAP(+) cells increased with age in all three tissues. The types of cells exhibiting a mutant phenotype included cells that are proliferative, such as kidney epithelial cells, and cells that do not frequently replicate, such as cardiac muscle cells and neurons. In the brain, PLAP(+) cells appeared in various locations and occurred at similar frequencies in different regions. Within the cerebellum, PLAP(+) Purkinje cell neurons appeared at a rate similar to that seen in the brain as a whole. PLAP(+) cells were observed in kidney-specific cell types such as those in glomeruli and collecting tubules, as well as in connective tissue and blood vessels. In the heart, PLAP(+) cells appeared to be cardiac muscle cells. Regardless of tissue and cell type, PLAP(+) cells occurred as singletons and in clusters, both of which increased in frequency with age. These data show that age-associated accumulation of mutant cells occurs in diverse cell types and is due to both new mutation and proliferation of mutant cells, even in cell types that tend to not proliferate.

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.

What can we learn from the population incidence of cancer? Armitage and Doll revisited

Most cancers occur with the same characteristic pattern of incidence. The simplicity of this pattern is in contrast to the perceived complexity of carcinogenesis. Therefore, age-onset statistics represent a tempting set of data and have provoked many bold but often misguided conclusions concerning the physiopathological mechanisms of cancer. Half a century has passed since the original multistage theory of Armitage and Doll. Although their basic notion of a healthy cell becoming malignant in several rate-limiting steps is still accepted, prevailing wisdom about the nature and number of these steps has never settled into a consensus. Why have we been unable to elucidate the quantitative dependence of cancer incidence on the molecular processes that feature in its aetiology? In this review we aim to provide answers for this question.

Treatment of invasive retinoblastoma in a murine model using an oncolytic picornavirus

Retinoblastoma, the most common intraocular malignancy of childhood, metastasizes by initial invasion of the choroid and the optic nerve. There is no effective treatment for metastatic retinoblastoma, especially when the central nervous system (CNS) is involved, and prevention of this complication is a treatment priority. Seneca Valley Virus (SVV-001) is a conditionally replication-competent picornavirus that is not pathogenic to normal human cells but can kill human retinoblastoma cells in vitro with an IC(50) of <1 viral particle (vp) per cell. A xenograft murine model of metastatic retinoblastoma was used to examine the therapeutic potential of SVV-001. Histopathologic analysis of ocular and brain tissues after a single tail vein injection of SVV-001 (1 x 10(13) vp/kg) showed effective treatment of choroid and ocular nerve tumor invasion (1 of 20 animals with invasive disease in the treated group versus 7 of 20 animals with invasive disease in the control group; P = 0.017) and prevention of CNS metastasis (0 of 20 animals with CNS metastatic disease in the treated group versus 4 of 20 animals with CNS disease in the control group; P = 0.036). There were no observed adverse events due to the virus in any of the treated animals. SVV-001 may be effective as a treatment of locally invasive and metastatic retinoblastoma.

Early onset pancreatic cancer: evidence of a major role for smoking and genetic factors

Pancreatic cancer ranks 4th as a cause of cancer mortality and in approximately 5% to 10% of patients, this lethal tumor develops before age 50. We used age-, sex-, and country-specific cancer incidence and mortality data to describe the burden of early onset pancreatic cancer (EOPC) worldwide. We also reviewed the current published evidence on smoking and genetic factors associated with EOPC. We found an excess of EOPC resulting in a substantial number of years-of-life-lost in countries from Central and Eastern Europe. Worldwide, the proportion of EOPC is strongly correlated with lung cancer mortality (R(2) = 0.53), suggesting that approximately half of the variation in the proportion of EOPC could be explained by smoking. The unusual pattern of the incidence of pancreatic cancer by gender and race supports the primary role of smoking in the etiology of EOPC: the excess male-to-female rate ratio, attributable mainly to smoking, gradually approaches unity with increasing age. Moreover, male-to-female rate ratios are greater in blacks than in whites only in younger patients. Published studies also identified genetic alterations involved either alone or in association with smoking in the development of EOPC. In conclusion, EOPC constitutes only 1% to 5% of the total deaths from pancreatic cancer worldwide, but is responsible for 20% to 30% of the total number of years-of-life-lost caused by the disease. Smoking and genetic mutations are the major identified risk factors and seem to be even more important for EOPC than for PC in older age groups.

Darwinian medicine: a case for cancer

Epidemiological, genetic and molecular biological studies have collectively provided us with a rich source of data that underpins our current understanding of the aetiology and molecular pathogenesis of cancer. But this perspective focuses on proximate mechanisms, and does not provide an adequate explanation for the prevalence of tumours and cancer in animal species or what seems to be the striking vulnerability of Homo sapiens. The central precept of Darwinian medicine is that vulnerability to cancer, and other major diseases, arises at least in part as a consequence of the 'design' limitations, compromises and trade-offs that characterize evolutionary processes.

Does the evidence matter in medicine? The retinoblastoma paradigm

Retinoblastoma (Rb) is the most common intraocular malignant tumour in childhood, with an incidence of 1 in 15,000 live births. Complete information on this rare tumour can be easily accessed through the internet, although many aspect concerning the aetiology and pathogenesis of the disease, are still controversial. The "two hit" theory, formulated in 1971 to explain the variegated clinical expression of the disease, is based on the idea that single gene mutation may determine the development of cancer. However, this view does not take into account the most recent evidences showing the role of aneuploidy and chromosome instability in cancer. Also, a number of other genes and epigenetic mechanisms are involved in the genesis of retinoblastoma. More importantly, the "two hit" theory makes predictions, concerning the age distribution of the tumour, its mode of "transmission" (hereditary retinoblastoma), and its pathogenesis, which are not fulfilled by the clinical reality. Overall, the "two hit" theory represents a rather simplistic and outdated model to explain tumour development and clinical evolution of retinoblastoma.

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 biological sense of cancer: a hypothesis

BACKGROUND

Most theories about cancer proposed during the last century share a common denominator: cancer is believed to be a biological nonsense for the organism in which it originates, since cancer cells are believed to be ones evading the rules that control normal cell proliferation and differentiation. In this essay, we have challenged this interpretation on the basis that, throughout the animal kingdom, cancer seems to arise only in injured organs and tissues that display lost or diminished regenerative ability.

HYPOTHESIS

According to our hypothesis, a tumor cell would be the only one able to respond to the demand to proliferate in the organ of origin. It would be surrounded by "normal" aged cells that cannot respond to that signal. According to this interpretation, cancer would have a profound biological sense: it would be the ultimate way to attempt to restore organ functions and structures that have been lost or altered by aging or noxious environmental agents. In this way, the features commonly associated with tumor cells could be reinterpreted as progressively acquired adaptations for responding to a permanent regenerative signal in the context of tissue injury. Analogously, several embryo developmental stages could be dependent on cellular damage and death, which together disrupt the field topography. However, unlike normal structures, cancer would have no physiological value, because the usually poor or non-functional nature of its cells would make their reparative task unattainable.

CONCLUSION

The hypothesis advanced in this essay might have significant practical implications. All conventional therapies against cancer attempt to kill all cancer cells. However, according to our hypothesis, the problem might not be solved even if all the tumor cells were eradicated. In effect, if the organ failure remained, new tumor cells would emerge and the tumor would reinitiate its progressive growth in response to the permanent regenerative signal of the non-restored organ. Therefore, efficient anti-cancer therapy should combine an attack against the tumor cells themselves with the correction of the organ failure, which, according to this hypothesis, is fundamental to the origin of the cancer.

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.

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.