A disequilibrium model for detecting genetic mutations for cancer

It has been recognized that genetic mutations in specific nucleotides may give rise to cancer via the alteration of signaling pathways. Thus, the detection of those cancer-causing mutations has received considerable interest in cancer genetic research. Here, we propose a statistical model for characterizing genes that lead to cancer through point mutations using genome-wide single nucleotide polymorphism (SNP) data. The basic idea of the model is that mutated genes may be in high association with their nearby SNPs because of evolutionary forces. By genotyping SNPs in both normal and cancer cells, we formulate a polynomial likelihood to estimate the population genetic parameters related to cancer, such as allele frequencies of cancer-causing alleles, mutation rates of alleles derived from maternal or paternal parents, and zygotic linkage disequilibria between different loci after the mutation occurs. We implement the EM algorithm to estimate some of these parameters because of the missing information in the likelihood construction. The model allows the elegant tests of the significant associations between mutated cancer genes and genome-wide SNPs, thus providing a way for predicting the occurrence and formation of cancer with genetic information. The model, validated through computer simulation, may help cancer geneticists design efficient experiments and formulate hypotheses for cancer gene identification.     

Genetic progression and the waiting time to cancer

Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers may evolve through mutations in as many as 20 different cancer-associated genes. We use data published by Sjöblom et al. (2006) to develop a new mathematical model for the somatic evolution of colorectal cancers. We employ the Wright-Fisher process for exploring the basic parameters of this evolutionary process and derive an analytical approximation for the expected waiting time to the cancer phenotype. Our results highlight the relative importance of selection over both the size of the cell population at risk and the mutation rate. The model predicts that the observed genetic diversity of cancer genomes can arise under a normal mutation rate if the average selective advantage per mutation is on the order of 1%. Increased mutation rates due to genetic instability would allow even smaller selective advantages during tumorigenesis. The complexity of cancer progression can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth.     

A mathematical model of breast cancer development, local treatment and recurrence

Cancer development is a stepwise process through which normal somatic cells acquire mutations which enable them to escape their normal function in the tissue and become self-sufficient in survival. The number of mutations depends on the patient's age, genetic susceptibility and on the exposure of the patient to carcinogens throughout their life. It is believed that in every malignancy 4-6 crucial similar mutations have to occur on cancer-related genes. These genes are classified as oncogenes and tumour suppressor genes (TSGs) which gain or lose their function respectively, after they have received one mutative hit or both of their alleles have been knocked out. With the acquisition of each of the necessary mutations the transformed cell gains a selective advantage over normal cells, and the mutation will spread throughout the tissue via clonal expansion. We present a simplified model of this mutation and expansion process, in which we assume that the loss of two TSGs is sufficient to give rise to a cancer. Our mathematical model of the stepwise development of breast cancer verifies the idea that the normal mutation rate in genes is only sufficient to give rise to a tumour within a clinically observable time if a high number of breast stem cells and TSGs exist or genetic instability is involved as a driving force of the mutation pathway. Furthermore, our model shows that if a mutation occurred in stem cells pre-puberty, and formed a field of cells with this mutation through clonal formation of the breast, it is most likely that a tumour will arise from within this area. We then apply different treatment strategies, namely surgery and adjuvant external beam radiotherapy and targeted intraoperative radiotherapy (TARGIT) and use the model to identify different sources of local recurrence and analyse their prevention.     

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.     

Cancer stem cells--old concepts, new insights

Cancer has long been viewed as an exclusively genetic disorder. The model of carcinogenesis, postulated by Nowell and Vogelstein, describes the formation of a tumor by the sequential accumulation of mutations in oncogenes and tumor suppressor genes. In this model, tumors are thought to consist of a heterogeneous population of cells that continue to acquire new mutations, resulting in a highly dynamic process, with clones that out compete others due to increased proliferative or survival capacity. However, novel insights in cancer stem cell research suggest another layer of complexity in the process of malignant transformation and preservation. It has been reported that only a small fraction of the cancer cells in a malignancy have the capacity to propagate the tumor upon transplantation into immuno-compromised mice. Those cells are termed 'cancer stem cells' (CSC) and can be selected based on the expression of cell surface markers associated with immature cell types. In this review, we will critically discuss these novel insights in CSC-related research. Where possible we integrate these results within the genetic model of cancer and illustrate that the CSC model can be considered an extension of the classic genetic model rather than a contradictory theory. Finally, we discuss some of the most controversial issues in this field.     

Mathematical model for the cancer stem cell hypothesis

Recent research on the origin of brain cancer has implicated a subpopulation of self-renewing brain cancer stem cells for malignant tumour growth. Various genes that regulate self-renewal in normal stem cells are also found in cancer stem cells. This implies that cancers can occur because of mutations in normal stem cells and early progenitor cells. A predictive mathematical model based on the cell compartment method is presented here to pose and validate non-intuitive scenarios proposed through the neural cancer stem cell hypothesis. The growths of abnormal (stem and early progenitor) cells from their normal counterparts are ascribed with separate mutation probabilities. Stem cell mutations are found to be more significant for the development of cancer than a similar mutation in the early progenitor cells. The model also predicts that, as previously hypothesized, repeated insult to mature cells increases the formation of abnormal progeny, and hence the risk of cancer.     

Single-Cell Genetic Analysis Using Automated Microfluidics to Resolve Somatic Mosaicism

Somatic mosaicism occurs throughout normal development and contributes to numerous disease etiologies, including tumorigenesis and neurological disorders. Intratumor genetic heterogeneity is inherent to many cancers, creating challenges for effective treatments. Unfortunately, analysis of bulk DNA masks subclonal phylogenetic architectures created by the acquisition and distribution of somatic mutations amongst cells. As a result, single-cell genetic analysis is becoming recognized as vital for accurately characterizing cancers. Despite this, methods for single-cell genetics are lacking. Here we present an automated microfluidic workflow enabling efficient cell capture, lysis, and whole genome amplification (WGA). We find that ~90% of the genome is accessible in single cells with improved uniformity relative to current single-cell WGA methods. Allelic dropout (ADO) rates were limited to 13.75% and variant false discovery rates (SNV FDR) were 4.11x10^-6, on average. Application to ER-/PR-/HER2+ breast cancer cells and matched normal controls identified novel mutations that arose in a subpopulation of cells and effectively resolved the segregation of known cancer-related mutations with single-cell resolution. Finally, we demonstrate effective cell classification using mutation profiles with 10X average exome coverage depth per cell. Our data demonstrate an efficient automated microfluidic platform for single-cell WGA that enables the resolution of somatic mutation patterns in single cells.     

How do mutated oncogenes and tumor suppressor genes cause cancer?

In recent decades we have been given insight into the process that transforms a normal cell into a malignant cancer cell. It has been recognised that malignant transformation occurs through successive mutations in specific cellular genes, leading to the activation of oncogenes and inactivation of tumor suppressor genes. The further study of these genes has generated much of its excitement from the convergence of experiments addressing the genetic basis of cancer, together with cellular pathways that normally control important cellular regulatory programmes. In the present review the context in which oncogenes such as proliferation, cell death/apoptosis, differentiation and senescence will be described, as well as how these cellular programmes become deregulated in cancer due to mutations.     

Single-cell mtDNA heteroplasmy in colorectal cancer

Human mitochondria can be genetically distinct within the same individual, a phenomenon known as heteroplasmy. In cancer, this phenomenon seems exacerbated, and most mitochondrial mutations seem to be heteroplasmic. How this genetic variation is arranged within and among normal and tumor cells is not well understood. To address this question, here we sequenced single-cell mitochondrial genomes from multiple normal and tumoral locations in four colorectal cancer patients. Our results suggest that single cells, both normal and tumoral, can carry various mitochondrial haplotypes. Remarkably, this intra-cell heteroplasmy can arise before tumor development and be maintained afterward in specific tumoral cell subpopulations. At least in the colorectal patients studied here, the somatic mutations in the single-cells do not seem to have a prominent role in tumorigenesis.     

Conditional coalescent trees with two mutation rates and their application to genomic instability

Humans have invested several genes in DNA repair and fidelity replication. To account for the disparity between the rarity of mutations in normal cells and the large number of mutations present in cancer, an hypothesis is that cancer cells must exhibit a mutator phenotype (genomic instability) during tumor progression, with the initiation of abnormal mutation rates caused by the loss of mismatch repair. In this study we introduce a stochastic model of mutation in tumor cells with the aim of estimating the amount of genomic instability due to the alteration of DNA repair genes. Our approach took into account the difficulties generated by sampling within tumoral clones and the fact that these clones must be difficult to isolate. We provide corrections to two classical statistics to obtain unbiased estimators of the raised mutation rate, and we show that large statistical errors may be associated with such estimators. The power of these new statistics to reject genomic instability is assessed and proved to increase with the intensity of mutation rates. In addition, we show that genomic instability cannot be detected unless the raised mutation rates exceed the normal rates by a factor of at least 1000.     

Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness: dynamical systems theory of gene expressions under cell-cell interaction explains mutational robustness of differentiated cells and suggests how cancer cells emerge

Here I present and discuss a model that, among other things, appears able to describe the dynamics of cancer cell origin from the perspective of stable and unstable gene expression profiles. In identifying such aberrant gene expression profiles as lying outside the normal stable states attracted through development and normal cell differentiation, the hypothesis explains why cancer cells accumulate mutations, to which they are not robust, and why these mutations create a new stable state far from the normal gene expression profile space. Such cells are in strong contrast with normal cell types that appeared as an attractor state in the gene expression dynamical system under cell-cell interaction and achieved robustness to noise through evolution, which in turn also conferred robustness to mutation. In complex gene regulation networks, other aberrant cellular states lacking such high robustness are expected to remain, which would correspond to cancer cells.     

Conditional neutrality as a method of controlling tumour growth.

Tumours are comprised of populations of mutant cells that are undergoing rapid cell division. The high mutation rate and rapid cell growth results in rapid evolution of the phenotypes required for tumour growth. Short cell cycles, angiogenesis, chemotherapy resistance and metastasis quickly evolve. Here I suggest that the genetic system of cancer cells may be exploited as a potential cancer treatment. If a cancer cell population is supplemented with agents that render some of the genes conditionally neutral, then eventually, through the process of neutral or near neutral evolution and genetic drift, all the cells in the tumour may become dependent on supplementation and the tumour may consequently be controllable through removal of the supplement. I suggest possible methods of suppressing mutations and detail factors that may influence the rate of fixation of the conditionally neutral mutations and the mean time taken for all cells to become dependent on supplementation. In addition I discuss some possible interactions between this method and traditional approaches to cancer therapy.     

Modeling somatic evolution in tumorigenesis

Tumorigenesis in humans is thought to be a multistep process where certain mutations confer a selective advantage, allowing lineages derived from the mutated cell to outcompete other cells. Although molecular cell biology has substantially advanced cancer research, our understanding of the evolutionary dynamics that govern tumorigenesis is limited. This paper analyzes the computational implications of cancer progression presented by Hanahan and Weinberg in The Hallmarks of Cancer. We model the complexities of tumor progression as a small set of underlying rules that govern the transformation of normal cells to tumor cells. The rules are implemented in a stochastic multistep model. The model predicts that (i) early-onset cancers proceed through a different sequence of mutation acquisition than late-onset cancers; (ii) tumor heterogeneity varies with acquisition of genetic instability, mutation pathway, and selective pressures during tumorigenesis; (iii) there exists an optimal initial telomere length which lowers cancer incidence and raises time of cancer onset; and (iv) the ability to initiate angiogenesis is an important stage-setting mutation, which is often exploited by other cells. The model offers insight into how the sequence of acquired mutations affects the timing and cellular makeup of the resulting tumor and how the cellular-level population dynamics drive neoplastic evolution.     

An overview of the mechanisms of mutagenesis and carcinogenesis

Cancer is a genetic disease due to the accumulation of numerous mutations rendering the tumour cell insensitive to control by the local cellular environment and by the whole organism. Analysis of the frequency of appearance of human cancer as a function of age shows that between four and seven mutations in key genes are usually necessary to produce most human cancers. Interesting debates in the literature are concerned with the idea that normal mutation rates followed by selective advantage of mutated clones are enough to produce the numerous mutations found in human cancers. Alternatively, the mutator phenotype hypothesis is based on the idea that the normal mutation rates are insufficient to account for the multiple mutations found in tumours. It is, however, difficult not only to know this exact mutation frequency in cells but also to know the total number of cell divisions giving rise to a cancer. Therefore, during at least one step in the carcinogenic process, a mutator phenotype in target cells may occur due to mutations controlling the fidelity of DNA replication or DNA repair, the apoptosis pathways or the cell cycle checkpoint regulations. Among the multiple mutations found in human cancers such as gene amplification, chromosome alterations and translocations, point mutations are very important and the molecular mechanisms of their production are well documented. I will describe in detail the various mechanisms that a cell can use to produce point mutations due to lower fidelity in the DNA polymerisation step or to inefficient repair pathways. The presence of multiple mutations in human cancer is interesting not only in terms of understanding the carcinogenesis process in humans but also in eventually promoting strategies to decrease the efficiency of this process and to increase cancer therapy regimen.     

The evolution of two mutations during clonal expansion

Knudson's two-hit hypothesis proposes that two genetic changes in the RB1 gene are the rate-limiting steps of retinoblastoma. In the inherited form of this childhood eye cancer, only one mutation emerges during somatic cell divisions while in sporadic cases, both alleles of RB1 are inactivated in the growing retina. Sporadic retinoblastoma serves as an example of a situation in which two mutations are accumulated during clonal expansion of a cell population. Other examples include evolution of resistance against anticancer combination therapy and inactivation of both alleles of a metastasis-suppressor gene during tumor growth. In this article, we consider an exponentially growing population of cells that must evolve two mutations to (i) evade treatment, (ii) make a step toward (invasive) cancer, or (iii) display a disease phenotype. We calculate the probability that the population has evolved both mutations before it reaches a certain size. This probability depends on the rates at which the two mutations arise; the growth and death rates of cells carrying none, one, or both mutations; and the size the cell population reaches. Further, we develop a formula for the expected number of cells carrying both mutations when the final population size is reached. Our theory establishes an understanding of the dynamics of two mutations during clonal expansion.     

Tumour-host interactions: implications for developing anti-cancer therapies

Cancers are a complex set of proliferative diseases that arise in most cases through multi-step pathways involving an accumulation of genetic and epigenetic changes. These steps include inactivation of tumour suppressor genes and activation of oncogenes. However, in addition to genetic mutations in the tumour cells themselves, the local host environment can act as a critical modulator of cancer progression, having either tumour-suppressive or tumour-promoting effects depending on the stage and site of cancer development. Because stromal cells can have these opposing functions during cancer development and progression, a recurring theme throughout this review will be that of balance: maintaining the normal functions of these co-opted cells, yet selectively inhibiting their pro-tumourigenic functions. To achieve this equilibrium, we need to understand the molecular mechanisms by which normal cells become modified by cancer cells before we can hope to target these functions selectively. Here, we will discuss recent efforts to address these key challenges and offer perspectives on the translation of discoveries made in model systems to the clinic.     

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.     

MicroRNA-133a Suppresses Multiple Oncogenic Membrane Receptors and Cell Invasion in Non-Small Cell Lung Carcinoma

Non-small cell lung cancers (NSCLCs) cause high mortality worldwide, and the cancer progression can be activated by several genetic events causing receptor dysregulation, including mutation or amplification. MicroRNAs are a group of small non-coding RNA molecules that function in gene silencing and have emerged as the fine-tuning regulators during cancer progression. MiR-133a is known as a key regulator in skeletal and cardiac myogenesis, and it acts as a tumor suppressor in various cancers. This study demonstrates that miR-133a expression negatively correlates with cell invasiveness in both transformed normal bronchial epithelial cells and lung cancer cell lines. The oncogenic receptors in lung cancer cells, including insulin-like growth factor 1 receptor (IGF-1R), TGF-beta receptor type-1 (TGFBR1), and epidermal growth factor receptor (EGFR), are direct targets of miR-133a. MiR-133a can inhibit cell invasiveness and cell growth through suppressing the expressions of IGF-1R, TGFBR1 and EGFR, which then influences the downstream signaling in lung cancer cell lines. The cell invasive ability is suppressed in IGF-1R- and TGFBR1-repressed cells and this phenomenon is mediated through AKT signaling in highly invasive cell lines. In addition, by using the in vivo animal model, we find that ectopically-expressing miR-133a dramatically suppresses the metastatic ability of lung cancer cells. Accordingly, patients with NSCLCs who have higher expression levels of miR-133a have longer survival rates compared with those who have lower miR-133a expression levels. In summary, we identified the tumor suppressor role of miR-133a in lung cancer outcome prognosis, and we demonstrated that it targets several membrane receptors, which generally produce an activating signaling network during the progression of lung cancer.     

Susceptibility to cell death induced by blockade of MAPK pathway in human colorectal cancer cells carrying Ras mutations is dependent on p53 status

Constitutive activation of mitogen-activated protein kinase (MAPK) pathway is implicated in a variety of human malignancies especially those that carry Ras mutations and is currently exploited as a cancer therapeutic target. The variability of response by cancer cells to the inhibition of the Ras/MAPK pathway both in vivo and in vitro, however, suggests that the genetic background of the tumor cell may modulate the effectiveness of this directed therapeutic. In a panel of colorectal cancer cell lines that carry Ras mutations and have constitutively active MEK/MAPK, we found that inhibition of the MAPK upstream kinase MEK by the small molecular MEK inhibitor U0126 induced cell death only in p53 wild-type cells. By contrast, p53-deficient cells were not affected by blocking the MEK/MAPK pathway. Using isogenic colon cancer cell lines and RNA interference, we show that loss of p53 significantly reduces MAPK phosphorylation and renders cells resistant to U0126 treatment. These findings reveal a critical role for p53 in MAPK-driven cell survival and place p53 upstream in the control cascade of MAPK activity. The therapeutic implication of these observations is that MAPK inhibitors will be most beneficial as a therapeutic agent in p53 normal colon cancers where constitutively active MAPK resulting from a Ras mutation is required for cell survival.