A stochastic model for cancer risk

We propose a simple stochastic model based on the two successive mutations hypothesis to compute cancer risks. Assume that only stem cells are susceptible to the first mutation and that there are a total of D stem cell divisions over the lifetime of the tissue with a first mutation probability mu(1) per division. Our model predicts that cancer risk will be low if m = mu(1)D is low even in the case of very advantageous mutations. Moreover, if mu(1)D is low the mutation probability of the second mutation is practically irrelevant to the cancer risk. These results are in contrast with existing models but in agreement with a conjecture of Cairns. In the case where m is large our model predicts that the cancer risk depends crucially on whether the first mutation is advantageous or not. A disadvantageous or neutral mutation makes the risk of cancer drop dramatically.     

Evolution and Phenotypic Selection of Cancer Stem Cells

Cells of different organs at different ages have an intrinsic set of kinetics that dictates their behavior. Transformation into cancer cells will inherit these kinetics that determine initial cell and tumor population progression dynamics. Subject to genetic mutation and epigenetic alterations, cancer cell kinetics can change, and favorable alterations that increase cellular fitness will manifest themselves and accelerate tumor progression. We set out to investigate the emerging intratumoral heterogeneity and to determine the evolutionary trajectories of the combination of cell-intrinsic kinetics that yield aggressive tumor growth. We develop a cellular automaton model that tracks the temporal evolution of the malignant subpopulation of so-called cancer stem cells(CSC), as these cells are exclusively able to initiate and sustain tumors. We explore orthogonal cell traits, including cell migration to facilitate invasion, spontaneous cell death due to genetic drift after accumulation of irreversible deleterious mutations, symmetric cancer stem cell division that increases the cancer stem cell pool, and telomere length and erosion as a mitotic counter for inherited non-stem cancer cell proliferation potential. Our study suggests that cell proliferation potential is the strongest modulator of tumor growth. Early increase in proliferation potential yields larger populations of non-stem cancer cells(CC) that compete with CSC and thus inhibit CSC division while a reduction in proliferation potential loosens such inhibition and facilitates frequent CSC division. The sub-population of cancer stem cells in itself becomes highly heterogeneous dictating population level dynamics that vary from long-term dormancy to aggressive progression. Our study suggests that the clonal diversity that is captured in single tumor biopsy samples represents only a small proportion of the total number of phenotypes.     

Wnt pathway mutations selected by optimal beta-catenin signaling for tumorigenesis

Mutations in components of the Wnt/beta-catenin pathway are observed to be the earliest initiating event for most colorectal tumors. The majority of the mutations occur in the tumor suppressor adenomatous polyposis coli (APC), even though there are other genes that are capable of modulating the pathway activity. Moreover, the specific APC mutations associated in colon cancer indicate the possibility that the tumor selects for certain truncated forms of APC that partially retain its function, namely, inhibition of beta-catenin. We estimated the effects of various mutations in APC and other known mutations using a recent mathematical model of the Wnt pathway that was constructed to represent the conserved core molecular events. We provide evidence that APC mutations are selected not based on the maximal level of beta-catenin but rather based on distinct state of activity that appears to be optimal for the tissue-specific tumorigenesis. This optimal level is determined by balancing beta-catenin signaling and the induction of Axin2 that acts as a potent negative feedback. The predominant pattern of APC mutations may provide synergistic oncogenic effects that promote colorectal tumorigenesis: the optimal signaling for cell survival and renewal, disrupted cell adhesion, chromosomal instability, and altered asymmetric division of stem cells.     

Severely incapacitating mutations in patients with extreme short stature identify RNA-processing endoribonuclease RMRP as an essential cell growth regulator

The growth of an individual is deeply influenced by the regulation of cell growth and division, both of which also contribute to a wide variety of pathological conditions, including cancer, diabetes, and inflammation. To identify a major regulator of human growth, we performed positional cloning in an autosomal recessive type of profound short stature, anauxetic dysplasia. Homozygosity mapping led to the identification of novel mutations in the RMRP gene, which was previously known to cause two milder types of short stature with susceptibility to cancer, cartilage hair hypoplasia, and metaphyseal dysplasia without hypotrichosis. We show that different RMRP gene mutations lead to decreased cell growth by impairing ribosomal assembly and by altering cyclin-dependent cell cycle regulation. Clinical heterogeneity is explained by a correlation between the level and type of functional impairment in vitro and the severity of short stature or predisposition to cancer. Whereas the cartilage hair hypoplasia founder mutation affects both pathways intermediately, anauxetic dysplasia mutations do not affect B-cyclin messenger RNA (mRNA) levels but do severely incapacitate ribosomal assembly via defective endonucleolytic cleavage. Anauxetic dysplasia mutations thus lead to poor processing of ribosomal RNA while allowing normal mRNA processing and, therefore, genetically separate the different functions of RNase MRP.     

Analysis of growth kinetics by division tracking

Cell division tracking using fluorescent dyes, such as carboxyfluorescein diacetate succinimidyl ester, provides a unique opportunity for analysis of cell growth kinetics. The present review article presents new methods for enhancing resolution of division tracking data as well as derivation of quantities that characterize growth from time-series data. These include the average time between successive divisions, the proportion of cells that survive and the proliferation per division. The physical significance of these measured quantities is interpreted by formulation of a two-compartment model of cell cycle transit characterized by stochastic and deterministic cell residence times, respectively. The model confirmed that survival is directly related to the proportion of cells that enter the next cell generation. The proportion of time that cells reside in the stochastic compartment is directly related to the proliferation per generation. This form of analysis provides a starting point for more sophisticated physical and biochemical models of cell cycle regulation.     

Dissecting the senescence-like program in tumor cells activated by Ras signaling

Activated Ras signaling can induce a permanent growth arrest in osteosarcoma cells. Here, we report that a senescence-like growth inhibition is also achieved in human carcinoma cells upon the transduction of H-Ras(V12). Ras-induced tumor senescence can be recapitulated by the transduction of activated, but not wild-type, MEK. The ability for H-Ras(V12) to suppress tumor cell growth is drastically compromised in cells that harbor endogenous activating ras mutations. Notably, growth inhibition of tumor cells containing ras mutations can be achieved through the introduction of activated MEK. Tumor senescence induced by Ras signaling can occur in the absence of p16 or Rb and is not interrupted by the inactivation of Rb, p107, or p130 via short hairpin RNA or the transduction with HPV16 E7. In contrast, inactivation of p21 via short hairpin RNA disrupts Ras-induced tumor senescence. In summary, this study uncovers a senescence-like program activated by Ras signaling to inhibit cancer cell growth. This program appears to be intact in cancer cells that do not harbor ras mutations. Moreover, cancer cells that carry ras mutations remain susceptible to tumor senescence induced by activated MEK. These novel findings can potentially lead to the development of innovative cancer intervention.     

Genetic counselling and testing for susceptibility to breast,ovarian and colon cancer: where are we today?

Recent advances in our understanding of the genetic characteristics of cancer will change approaches to genetic screening and counselling. Cancer results from multiple, cumulative mutations in genes that regulate cell replication and differentiation. In familial cancer a germ-line mutation is passed on in an autosomal dominant pattern, but cancer will develop in people who inherit the defect only if other mutations also occur in susceptible somatic cells. The tumour-suppressor gene known as BRCA1 is thought to affect half of those families who have an inherited breast cancer syndrome and most families with a breast and ovarian cancer syndrome. Another gene, BRCA2, is thought to affect most of the remaining families with a breast-cancer-only syndrome. Hereditary nonpolyposis colon cancer (HNPCC) is caused by mutations in surveillance genes that protect DNA from the spontaneous errors that occur during cell division. Because there are no outcome data on which to base practice guidelines for genetic screening or management of asymptomatic carriers in families at risk, testing should be restricted to research settings.     

Estimation of spontaneous mutation rates

Spontaneous or randomly occurring mutations play a key role in cancer progression. Estimation of the mutation rate of cancer cells can provide useful information about the disease. To ascertain these mutation rates, we need mathematical models that describe the distribution of mutant cells. In this investigation, we develop a discrete time stochastic model for a mutational birth process. We assume that mutations occur concurrently with mitosis so that when a nonmutant parent cell splits into two progeny, one of these daughter cells could carry a mutation. We propose an estimator for the mutation rate and investigate its statistical properties via theory and simulations. A salient feature of this estimator is the ease with which it can be computed. The methods developed herein are applied to a human colorectal cancer cell line and compared to existing continuous time models.     

How carcinogens (or telomere dysfunction) induce genetic instability: associated-selection model

Carcinogens induce carcinogen-specific genetic instability (defects in DNA repair). According to the 'direct-selection' model, defects in DNA repair per se provide an immediate growth advantage. According to the 'associated-selection' model, carcinogens merely select for cells with adaptive mutations. Like any mutations, adaptive mutations occur predominantly in genetically unstable cells. The 'associated-selection' model predicts that carcinogen-driven selection minimizes cytotoxic but maximizes mutagenic effects of carcinogens. A purely mutagenic (neither cytotoxic, nor cytostatic) environment will favor effective DNA repair, whereas any growth-limiting conditions (telomerase deficiency, anticancer drugs) will select for genetically unstable cells. Genetic instability is a postmark of selective pressure rather than a hallmark of cancer per se. Once selected, genetic instability facilitates the development of resistance to any other growth-limiting conditions. As an example, a putative link between prior exposure to carcinogens and the ability to develop a telomerase-independent growth is discussed.     

Cancer initiation and progression: involvement of stem cells and the microenvironment

The molecular events that lead to the cancer-initiating cell involve critical mutations in genes regulating normal cell growth and differentiation. Cancer stem cells, or cancer initiating cells have been described in the context of acute myeloid leukemia, breast, brain, bone, lung, melanoma and prostate. These cells have been shown to be critical in tumor development and should harbor the mutations needed to initiate a tumor. The origin of the cancer stem cells is not clear. They may be derived from stem cell pools, progenitor cells or differentiated cells that undergo trans-differentiation processes. It has been suggested that cell fusion and/or horizontal gene transfer events, which may occur in tissue repair processes, also might play an important role in tumor initiation and progression. Fusion between somatic cells that have undergone a set of specific mutations and normal stem cells might explain the extensive chromosomal derangements seen in early tumors. Centrosome deregulation can be an integrating factor in many of the mechanisms involved in tumor development. The regulation of the balance between cell renewal and cell death is critical in cancer. Increased knowledge of developmental aspects in relation to self-renewal and differentiation, both under normal and deregulated conditions, will probably shed more light on the mechanisms that lead to tumor initiation and progression.     

The molecular control of DNA damage-induced cell death

Because of the singular importance of DNA for genetic inheritance, all organisms have evolved mechanisms to recognize and respond to DNA damage. In metazoans, cells can respond to DNA damage either by undergoing cell cycle arrest, to facilitate DNA repair, or by undergoing cell suicide. Cell death can either occur by activation of the apoptotic machinery or simply be a consequence of irreparable damage that prevents further cell division. In germ cells, mechanisms for limiting alterations to the genome are required for faithful propagation of the species whereas in somatic cells, responses to DNA damage prevent the accumulation of mutations that might lead to aberrant cell proliferation or behavior. Several of the genes that regulate cellular responses to DNA damage function as tumor suppressors. The clinical use of DNA damaging agents in the treatment of cancer can activate these tumor suppressors and exploits the cellular suicide and growth arrest mechanisms that they regulate. It appears that in some but not all types of tumors the propensity to undergo apoptosis is a critical determinant of their sensitivity to anti-cancer therapy. This review describes current understanding of the molecular control of DNA damage-induced apoptosis with particular attention to its role in tumor suppression and cancer therapy.     

Mutations and epimutations in the origin of cancer

Cancer is traditionally viewed as a disease of abnormal cell proliferation controlled by a series of mutations. Mutations typically affect oncogenes or tumor suppressor genes thereby conferring growth advantage. Genomic instability facilitates mutation accumulation. Recent findings demonstrate that activation of oncogenes and inactivation of tumor suppressor genes, as well as genomic instability, can be achieved by epigenetic mechanisms as well. Unlike genetic mutations, epimutations do not change the base sequence of DNA and are potentially reversible. Similar to genetic mutations, epimutations are associated with specific patterns of gene expression that are heritable through cell divisions. Knudson's hypothesis postulates that inactivation of tumor suppressor genes requires two hits, with the first hit occurring either in somatic cells (sporadic cancer) or in the germline (hereditary cancer) and the second one always being somatic. Studies on hereditary and sporadic forms of colorectal carcinoma have made it evident that, apart from genetic mutations, epimutations may serve as either hit or both. Furthermore, recent next-generation sequencing studies show that epigenetic genes, such as those encoding histone modifying enzymes and subunits for chromatin remodeling systems, are themselves frequent targets of somatic mutations in cancer and can act like tumor suppressor genes or oncogenes. This review discusses genetic vs. epigenetic origin of cancer, including cancer susceptibility, in light of recent discoveries. Situations in which mutations and epimutations occur to serve analogous purposes are highlighted.     

Cell membranes after malignant transformation. Part I: Dynamic stability at low surface tension

A hydrodynamic cell model is introduced to analyze the dynamic stability of the cell membrane after malignant transformation. The cell membrane is considered as a two-dimensional charged interface between intra- and extra-cellular fluids. Employing a first order stability analysis, conditions are established under which growth of surface fluctuations can occur (leading to microvilli formation or cell division). The system is unstable if the total surface tension, i.e. the pure surface tension plus the free energy of formation of the double layers, is negative. Following that criterion, cell division is promoted in cancer cells; moreover, as cancer cells are more fluid than normal cells, they will divide more rapidly. The model also predicts that microvilli (protrusions of the cell membrane) will have a diameter of the order of the dominant wavelengths of perturbation (0.1 - 1 mu) which supports the view that such protrusions are consequences of amplified cell surface fluctuations.     

A nucleolar isoform of the Fbw7 ubiquitin ligase regulates c-Myc and cell size

The human tumor suppressor Fbw7/hCdc4 functions as a phosphoepitope-specific substrate recognition component of SCF ubiquitin ligases that catalyzes the ubiquitination of cyclin E , Notch , c-Jun and c-Myc . Fbw7 loss in cancer may thus have profound effects on the pathways that govern cell division, differentiation, apoptosis, and cell growth. Fbw7-inactivating mutations occur in human tumor cell lines and primary cancers , and Fbw7 loss in cultured cells causes genetic instability . In mice, deletion of Fbw7 leads to embryonic lethality associated with defective Notch and cyclin E regulation . The human Fbw7 locus encodes three protein isoforms (Fbw7alpha, Fbw7beta, and Fbw7gamma) . We find that these isoforms occupy discrete subcellular compartments and have identified cis-acting localization signals within each isoform. Surprisingly, the Fbw7gamma isoform is nucleolar, colocalizes with c-Myc when the proteasome is inhibited, and regulates nucleolar c-Myc accumulation. Moreover, we find that knockdown of Fbw7 increases cell size consistent with its ability to control c-Myc levels in the nucleolus. We suggest that interactions between c-Myc and Fbw7gamma within the nucleolus regulate c-Myc's growth-promoting function and that c-Myc activation is likely to be an important oncogenic consequence of Fbw7 loss in cancers.     

Cancer stem cell, niche and EGFR decide tumor development and treatment response: A bio-computational simulation study

Recent research in cancer biology has suggested the hypothesis that tumors are initiated and driven by a small group of cancer stem cells (CSCs). Furthermore, cancer stem cell niches have been found to be essential in determining fates of CSCs, and several signaling pathways have been proven to play a crucial role in cellular behavior, which could be two important factors in cancer development. To better understand the progression, heterogeneity and treatment response of breast cancer, especially in the context of CSCs, we propose a mathematical model based on the cell compartment method. In this model, three compartments of cellular subpopulations are constructed: CSCs, progenitor cells (PCs), and terminal differentiated cells (TCs). Moreover, (1) the cancer stem cell niche is, considered by modeling its effect on division patterns (symmetric or asymmetric) of CSCs, and (2) the EGFR signaling pathway is integrated by modeling its role in cell proliferation, apoptosis. Our simulation results indicate that (1) a higher probability for symmetric division of CSC may result in a faster expansion of tumor population, and for a larger number of niches, the tumor grows at a slower rate, but the final tumor volume is larger; (2) higher EGFR expression correlates to tumors with larger volumes while a saturation function is observed, and (3) treatments that inhibit tyrosine kinase activity of EGFR may not only repress the tumor volume, but also decrease the CSCs percentages by shifting CSCs from symmetric divisions to asymmetric divisions. These findings suggest that therapies should be designed to effectively control or eliminate the symmetric division of CSCs and to reduce or destroy the CSC niches.     

Endogenous mutagenesis and cancer

Mutations in DNA accrue relentlessly, largely via stochastic processes. Random changes accumulate, eventually disabling genetic components which result in the formation of the cancer phenotype. Given the infrequency of measured nucleotide changes and the requirement for several mutations to occur in the same cell, it has been postulated that the rate of mutation must become elevated early in the course of evolution of the cancer. Recently, large scale sequencing of tumor DNA has sought to directly measure random mutations. We discuss the implications of these findings and the factors that must be considered in order for fruitful determination of whether a mutator phenotype is a necessary precursor for cancer.     

Adaptive Evolution That Requires Multiple Spontaneous Mutations. I. Mutations Involving an Insertion Sequence

Escherichia coli K12 strain chi 342LD requires two mutations in the bgl (beta-glucosidase) operon, bglR0----bglR+ and excision of IS103 from within bglF, in order to utilize salicin. In growing cells the two mutations occur at rates of 4 x 10(-8) per cell division and less than 2 x 10(-12) per cell division, respectively. In 2-3-week-old colonies on MacConkey salicin plates the double mutants occur at frequencies of 10(-8) per cell, yet the rate of an unselected mutation, resistance to valine, is unaffected. The two mutations occur sequentially. Colonies that are 8-12 days old contain from 1% to about 10% IS103 excision mutants, from which the Sal+ secondary bglR0----bglR+ mutants arise. It is shown that the excision mutants are not advantageous within colonies; thus, they must result from a burst of independent excisions late in the life of the colony. Excision of IS103 occurs only on medium containing salicin, despite the fact that the excision itself confers no detectable selective advantage and serves only to create the potential for a secondary selectively advantageous mutation.     

Dynamics between Cancer Cell Subpopulations Reveals a Model Coordinating with Both Hierarchical and Stochastic Concepts

Tumors are often heterogeneous in which tumor cells of different phenotypes have distinct properties. For scientific and clinical interests, it is of fundamental importance to understand their properties and the dynamic variations among different phenotypes, specifically under radio- and/or chemo-therapy. Currently there are two controversial models describing tumor heterogeneity, the cancer stem cell (CSC) model and the stochastic model. To clarify the controversy, we measured probabilities of different division types and transitions of cells via in situ immunofluorescence. Based on the experiment data, we constructed a model that combines the CSC with the stochastic concepts, showing the existence of both distinctive CSC subpopulations and the stochastic transitions from NSCCs to CSCs. The results showed that the dynamic variations between CSCs and non-stem cancer cells (NSCCs) can be simulated with the model. Further studies also showed that the model can be used to describe the dynamics of the two subpopulations after radiation treatment. More importantly, analysis demonstrated that the experimental detectable equilibrium CSC proportion can be achieved only when the stochastic transitions from NSCCs to CSCs occur, indicating that tumor heterogeneity may exist in a model coordinating with both the CSC and the stochastic concepts. The mathematic model based on experimental parameters may contribute to a better understanding of the tumor heterogeneity, and provide references on the dynamics of CSC subpopulation during radiotherapy.     

A stochastic model of cell replicative senescence based on telomere shortening, oxidative stress, and somatic mutations in nuclear and mitochondrial DNA.

Human diploid fibroblast cells can divide for only a limited number of times in vitro, a phenomenon known as replicative senescence or the Hayflick limit. Variability in doubling potential is observed within a clone of cells, and between two sister cells arising from a single mitotic division. This strongly suggests that the process by which cells become senescent is intrinsically stochastic. Among the various biochemical mechanisms that have been proposed to explain replicative senescence, particular interest has been focussed on the role of telomere reduction. In the absence of telomerase--an enzyme switched off in normal diploid fibro-blasts-cells lose telomeric DNA at each cell division. According to the telomere hypothesis of cell senescence, cells eventually reach a critically short telomere length and cell cycle arrest follows. In support of this concept, forced expression of telomerase in normal fibroblasts appears to prevent cell senescence. Nevertheless, the telomere hypothesis in its basic form has some difficulty in explaining the marked stochastic variations seen in the replicative lifespans of individual cells within a culture, and there is strong empirical and theoretical support for the concept that other kinds of damage may contribute to cellular ageing. We describe a stochastic network model of cell senescence in which a primary role is played by telomere reduction but in which other mechanisms (oxidative stress linked particularly to mitochondrial damage, and nuclear somatic mutations) also contribute. The model gives simulation results that are in good agreement with published data on intra-clonal variability in cell doubling potential and permits an analysis of how the various elements of the stochastic network interact. Such integrative models may aid in developing new experimental approaches aimed at unravelling the intrinsic complexity of the mechanisms contributing to human cell ageing.     

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.