Stochastic modelling of tumorigenesis in p53 deficient mice

Unbalanced replication as a major source of genetic instability in cancer cells

The origin of genetic instability in tumors is a matter of debate: while the prevailing model postulates a mutator phenotype resulting from an alteration in a caretaker gene as a prerequisite for genetic alterations leading to tumor formation, there is evidence against this model in the majority of cancers. A model for chromosomal instability should take into account the role of oncogenes in directly stimulating DNA and cellular component replication, creating aberrant structures when overexpressed. I will distinguish here two distinct mechanisms for the genetic instability of tumors: primary and secondary. Primary genetic instability is dependent on the inactivation of genes involved in maintaining genetic stability (caretaker genes), whereas secondary genetic instability is dependent on genes involved in tumor progression, i.e. oncogenes and tumor suppressor genes of the gatekeeper type. Secondary genetic instability, the most frequent condition, can be explained by the fact that some of the genes involved in tumor progression control replication of cell structures from within, leading to replication unbalance.

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).

Timed somatic deletion of p53 in mice reveals age-associated differences in tumor progression

Inactivating mutations in the p53 tumor suppressor gene occur often in the progression of human cancers. p53 inhibits the outgrowth of nascent cancer cells through anti-proliferative actions (including induction of apoptosis or senescence). To test p53 tumor suppressor functions in a novel experimental context, we somatically deleted both p53 alleles in multiple tissues of mice at various ages. Mice homozygously deleted for p53 at 3 months of age showed a longer tumor latency compared to mice deleted for p53 at 6 and 12 months of age. These results are consistent with a model in which tissues accumulate oncogenically activated cells with age and these are held in check by wildtype p53. We also deleted p53 before, concurrent with, and after treatment of mice with ionizing radiation (IR). The absence or presence of p53 during IR treatment had no effect on radiation-induced lymphoma latency, confirming that the immediate p53 damage response was irrelevant for cancer prevention. Even the presence of wildtype p53 for up to four weeks post-IR provided no protection against early lymphoma incidence, indicating that long term maintenance of functional p53 is critical for preventing the emergence of a cancer. These experiments indicate that sustained p53 anti-oncogenic function acts as a final or near final line of defense preventing progression of oncogenically activated cells to malignant tumors.

Systems biological and mechanistic modelling of radiation-induced cancer

This paper summarises the five presentations at the First International Workshop on Systems Radiation Biology that were concerned with mechanistic models for carcinogenesis. The mathematical description of various hypotheses about the carcinogenic process, and its comparison with available data is an example of systems biology. It promises better understanding of effects at the whole body level based on properties of cells and signalling mechanisms between them. Of these five presentations, three dealt with multistage carcinogenesis within the framework of stochastic multistage clonal expansion models, another presented a deterministic multistage model incorporating chromosomal aberrations and neoplastic transformation, and the last presented a model of DNA double-strand break repair pathways for second breast cancers following radiation therapy.

Modeling Intercellular Interactions during Carcinogenesis

By modulating the microenvironment of malignant or premalignant cells, inhibitory or stimulatory signals from nearby cells can play a key role in carcinogenesis. However, current commonly used quantitative models for induction of cancers by ionizing radiation focus on single cells and their progeny. Intercellular interactions are neglected or assumed to be confined to unidirectional radiation bystander effect signals from cells of the same tissue type. We here formulate a parsimoniously parameterized two-stage logistic (TSL) carcinogenesis model that incorporates some effects of intercellular interactions during the growth of premalignant cells. We show that for baseline tumor rates, involving no radiation apart from background radiation, this TSL model gives acceptable fits to a number of data sets. Specifically, it gives the same baseline hazard function, using the same number of adjustable parameters, as does the commonly used two-stage clonal expansion (TSCE) model, so it is automatically applicable to the many data sets on baseline cancer that have been analyzed using the TSCE model. For perturbations of baseline rates due to radiation, the models differ. We argue from epidemiological and laboratory evidence, especially results for the atomic bomb survivors, that for radiation carcinogenesis the TSL model gives results at least as realistic as the TSCE or similar models, despite involving fewer adjustable parameters in many cases.

A stochastic carcinogenesis model incorporating 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 is developed; the model incorporates progressive genomic instability and an arbitrary number of mutational stages. This model is shown to have the property that, at least in the case when the parameters of the model are eventually constant, the excess relative and absolute cancer rates following changes in any of the parameters will eventually tend to zero. It is also shown that when the parameters governing the processes of cell division, death, or additional mutation (whether of the normal sort or that resulting in genomic destabilization) at the penultimate stage are subject to perturbations, there are relatively large fluctuations in the hazard function for the model, which start almost as soon as the parameters are changed. The model is fitted to US Caucasian colon cancer incidence data. A model with five stages and two levels of genomic destabilization fits the data well. Comparison with patterns of excess risk in the Japanese atomic bomb survivor colon cancer incidence data indicate that radiation might act on early mutation rates in the model; a major role for radiation in initiating genomic destabilization is less likely.

The different effects of apoptosis and DNA repair on tumorigenesis

Complex multicellular organisms have evolved mechanisms to ensure that individual cells follow their proper developmental and somatic programs. Tumorigenesis, or uncontrolled cellular proliferation, is caused by somatic mutations to those genetic constraints that normally operate within a tissue. Genes involved in DNA repair and apoptosis are particularly instrumental in safeguarding cells against tumorigenesis. In this paper, we introduce a stochastic framework to analyse the somatic evolution of cancer initiation. Within this model, we study how apoptosis and DNA repair can maintain the transient stability of somatic cells and delay the onset of cancer. Focusing on individual cell lineages, we calculate the waiting time before tumorigenesis in the presence of varying degrees of apoptosis and DNA repair. We find that the loss of DNA repair or the loss of apoptosis both hasten tumorigenesis, but in characteristically different ways.

The effect of tissue-specific growth patterns of target stem cells on the spectrum of tumours resulting from multistage tumorigenesis

A multistage mathematical model of tumorigenesis has been developed to explore the effects of target cell growth pattern on the proportions of tumours deriving from different tissues (the tumour spectrum). Analytical modelling techniques have shown that the effect of the target cell growth pattern on the tumour spectrum also depends on the number of stages (gene mutations) necessary for malignant change in cells of each tissue type. This suggests the existence of temporal "windows of opportunity" for tumours of different types in relation to stage number and growth kinetics. Models of this kind are applicable to cancer-prone transgenic (e.g. p53 deficient) mice, where homozygotes and heterozygotes differ in one carcinogenic stage, and differ also in the spectrum of tumours observed. Generally, tumours deriving from target stem cells which are developmentally short-lived will arise more frequently in homozygotes than heterozygotes. Such models may also be applicable to human syndromes (e.g. Li-Fraumeni) in which susceptibility to cancer is inherited.

Tamoxifen mutagenesis and carcinogenesis in livers of lambda/lacI transgenic rats: selective influence of phenobarbital promotion

Administration of tamoxifen (TAM) (20 mg/kg per day p.o.) for 6 weeks to female lambda/lacI transgenic rats caused a 4-fold increase in mutation frequency (MF) at the lacI gene locus in the livers of dosed animals compared with controls. After cessation of dosing, the MF showed a further increase with time at 2, 12 and 24 weeks, respectively. Phenobarbital promotion of similarly treated animals resulted in no increase in mutation frequency compared with TAM alone. Treatment with phenobarbital or TAM+phenobarbital resulted in time-dependent increases in liver weight compared with the corresponding controls. There was an increase in cell proliferation in the phenobarbital and TAM+phenobarbital groups, and at 24 weeks in the TAM dosed animals compared with controls. There was also a progressive increase in the number of GST-P expressing foci in the livers of TAM and TAM + phenobarbital rats compared with controls. The induction of cell proliferation and GSTP foci in the rat liver by phenobarbital is consistent with its ability to promote tamoxifen-initiated liver tumours in the rat. If the lacI gene is regarded as being representative of the rat genome in general (albeit that the gene is bacterial) the above observations suggest that promotion by tamoxifen confers selective advantage on mutated genes at loci that contribute to the tumour phenotype and that promotion of rat liver tumours by tamoxifen is not dependent simply upon the enhancement of cellular proliferation.

Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study

The intracellular activity of the p53 tumor suppressor protein is regulated through a feedback loop involving its transcriptional target, mdm2. We present a simple mathematical model suggesting that, under certain circumstances, oscillations in p53 and Mdm2 protein levels can emerge in response to a stress signal. A delay in p53-dependent induction of Mdm2 is predicted to be required, albeit not sufficient, for this oscillatory behavior. In line with the predictions of the model, oscillations of both p53 and Mdm2 indeed occur on exposure of various cell types to ionizing radiation. Such oscillations may allow cells to repair their DNA without risking the irreversible consequences of continuous excessive p53 activation.

Use of transgenic animals for carcinogenicity testing: considerations and implications for risk assessment

Advances in genetic engineering have created opportunities for improved understanding of the molecular basis of carcinogenesis. Through selective introduction, activation, and inactivation of specific genes, investigators can produce mice of unique genotypes and phenotypes that afford insights into the events and mechanisms responsible for tumor formation. It has been suggested that such animals might be used for routine testing of chemicals to determine their carcinogenic potential because the animals may be mechanistically relevant for understanding and predicting the human response to exposure to the chemical being tested. Before transgenic and knockout mice can be used as an adjunct or alternative to the conventional 2-year rodent bioassay, information related to the animal line to be used, study design, and data analysis and interpretation must be carefully considered. Here, we identify and review such information relative to Tg.AC and rasH2 transgenic mice and p53+/- and XPA-/- knockout mice, all of which have been proposed for use in chemical carcinogenicity testing. In addition, the implications of findings of tumors in transgenic and knockout animals when exposed to chemicals is discussed in the context of human health risk assessment.