Stochastic tunneling and metastable states during the somatic evolution of cancer

Tumors initiate when a population of proliferating cells accumulates a certain number and type of genetic and/or epigenetic alterations. The population dynamics of such sequential acquisition of (epi)genetic alterations has been the topic of much investigation. The phenomenon of stochastic tunneling, where an intermediate mutant in a sequence does not reach fixation in a population before generating a double mutant, has been studied using a variety of computational and mathematical methods. However, the field still lacks a comprehensive analytical description since theoretical predictions of fixation times are only available for cases in which the second mutant is advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing the deterministic dynamics of large populations we systematically identify the parameter regimes captured by existing approaches. Our analysis also reveals fitness landscapes and mutation rates for which finite populations are found in long-lived metastable states. These are landscapes in which the final mutant is not the most advantageous in the sequence, and resulting metastable states are a consequence of a mutation-selection balance. The escape from these states is driven by intrinsic noise, and their location affects the probability of tunneling. Existing methods no longer apply. In these regimes it is the escape from the metastable states that is the key bottleneck; fixation is no longer limited by the emergence of a successful mutant lineage. We used the so-called Wentzel-Kramers-Brillouin method to compute fixation times in these parameter regimes, successfully validated by stochastic simulations. Our work fills a gap left by previous approaches and provides a more comprehensive description of the acquisition of multiple mutations in populations of somatic cells.Comment: 33 pages, 7 figure

Patterns of Proliferative Activity in the Colonic Crypt Determine Crypt Stability and Rates of Somatic Evolution

Epithelial cells in the colon are arranged in cylindrical structures called crypts in which cellular proliferation and migration are tightly regulated. We hypothesized that the proliferation patterns of cells may determine the stability of crypts as well as the rates of somatic evolution towards colorectal tumorigenesis. Here, we propose a linear process model of colonic epithelial cells that explicitly takes into account the proliferation kinetics of cells as a function of cell position within the crypt. Our results indicate that proliferation kinetics has significant influence on the speed of cell movement, kinetics of mutation propagation, and sensitivity of the system to selective effects of mutated cells. We found that, of all proliferation curves tested, those with mitotic activities concentrated near the stem cell, including the actual proliferation kinetics determined in in vivo labeling experiments, have a greater ability of delaying the rate of mutation accumulation in colonic stem cells compared to hypothetical proliferation curves with mitotic activities focused near the top of the crypt column. Our model can be used to investigate the dynamics of proliferation and mutation accumulation in spatially arranged tissues

DNA replication timing and higher-order nuclear organization determine single nucleotide substitution patterns in cancer genomes

Single nucleotide substitutions (SNS) are a defining characteristic of cancer genomes. Many SNS in cancer genomes arise due to errors in DNA replication, which is spatio-temporally stratified. Here we propose that DNA replication patterns help shape the mutational landscapes of normal and cancer genomes. Using data on five fully sequenced cancer types and two personal genomes, we determined that the frequency of intergenic SNS is significantly higher in late DNA replication timing regions, even after controlling for a number of genomic features. Furthermore, some substitution signatures are more frequent in certain DNA replication timing zones. Finally, integrating data on higher-order nuclear organization, we found that genomic regions in close spatial proximity to late replicating domains display similar mutation spectra as the late replicating regions themselves. These data suggest that DNA replication timing together with higher-order genomic organization contribute to the patterns of SNS in normal and cancer genomes

A Race between Tumor Immunoescape and Genome Maintenance Selects for Optimum Levels of (epi)genetic Instability

The human immune system functions to provide continuous body-wide surveillance to detect and eliminate foreign agents such as bacteria and viruses as well as the body's own cells that undergo malignant transformation. To counteract this surveillance, tumor cells evolve mechanisms to evade elimination by the immune system; this tumor immunoescape leads to continuous tumor expansion, albeit potentially with a different composition of the tumor cell population (“immunoediting”). Tumor immunoescape and immunoediting are products of an evolutionary process and are hence driven by mutation and selection. Higher mutation rates allow cells to more rapidly acquire new phenotypes that help evade the immune system, but also harbor the risk of an inability to maintain essential genome structure and functions, thereby leading to an error catastrophe. In this paper, we designed a novel mathematical framework, based upon the quasispecies model, to study the effects of tumor immunoediting and the evolution of (epi)genetic instability on the abundance of tumor and immune system cells. We found that there exists an optimum number of tumor variants and an optimum magnitude of mutation rates that maximize tumor progression despite an active immune response. Our findings provide insights into the dynamics of tumorigenesis during immune system attacks and help guide the choice of treatment strategies that best inhibit diverse tumor cell populations

On the Validity of Using Increases in 5-Year Survival Rates to Measure Success in the Fight against Cancer

Background: The 5-year survival rate of cancer patients is the most commonly used statistic to reflect improvements in the war against cancer. This idea, however, was refuted based on an analysis showing that changes in 5-year survival over time bear no relationship with changes in cancer mortality. Methods: Here we show that progress in the fight against cancer can be evaluated by analyzing the association between 5-year survival rates and mortality rates normalized by the incidence (mortality over incidence, MOI). Changes in mortality rates are caused by improved clinical management as well as changing incidence rates, and since the latter can mask the effects of the former, it can also mask the correlation between survival and mortality rates. However, MOI is a more robust quantity and reflects improvements in cancer outcomes by overcoming the masking effect of changing incidence rates. Using population-based statistics for the US and the European Nordic countries, we determined the association of changes in 5-year survival rates and MOI. Results: We observed a strong correlation between changes in 5-year survival rates of cancer patients and changes in the MOI for all the countries tested. This finding demonstrates that there is no reason to assume that the improvements in 5-year survival rates are artificial. We obtained consistent results when examining the subset of cancer types whose incidence did not increase, suggesting that over-diagnosis does not obscure the results. Conclusions: We have demonstrated, via the negative correlation between changes in 5-year survival rates and changes in MOI, that increases in 5-year survival rates reflect real improvements over time made in the clinical management of cancer. Furthermore, we found that increases in 5-year survival rates are not predominantly artificial byproducts of lead-time bias, as implied in the literature. The survival measure alone can therefore be used for a rough approximation of the amount of progress in the clinical management of cancer, but should ideally be used with other measures

Histone Modifications Are Associated with Transcript Isoform Diversity in Normal and Cancer Cells

Mechanisms that generate transcript diversity are of fundamental importance in eukaryotes. Although a large fraction of human protein-coding genes and lincRNAs produce more than one mRNA isoform each, the regulation of this phenomenon is still incompletely understood. Much progress has been made in deciphering the role of sequence-specific features as well as DNA-and RNA-binding proteins in alternative splicing. Recently, however, several experimental studies of individual genes have revealed a direct involvement of epigenetic factors in alternative splicing and transcription initiation. While histone modifications are generally correlated with overall gene expression levels, it remains unclear how histone modification enrichment affects relative isoform abundance. Therefore, we sought to investigate the associations between histone modifications and transcript diversity levels measured by the rates of transcription start-site switching and alternative splicing on a genome-wide scale across protein-coding genes and lincRNAs. We found that the relationship between enrichment levels of epigenetic marks and transcription start-site switching is similar for protein-coding genes and lincRNAs. Furthermore, we found associations between splicing rates and enrichment levels of H2az, H3K4me1, H3K4me2, H3K4me3, H3K9ac, H3K9me3, H3K27ac, H3K27me3, H3K36me3, H3K79me2, and H4K20me, marks traditionally associated with enhancers, transcription initiation, transcriptional repression, and others. These patterns were observed in both normal and cancer cell lines. Additionally, we developed a novel computational method that identified 840 epigenetically regulated candidate genes and predicted transcription start-site switching and alternative exon splicing with up to 92% accuracy based on epigenetic patterning alone. Our results suggest that the epigenetic regulation of transcript isoform diversity may be a relatively common genome-wide phenomenon representing an avenue of deregulation in tumor development

(A)Symmetric Stem Cell Replication and Cancer

Most tissues in metazoans undergo continuous turnover due to cell death or epithelial shedding. Since cellular replication is associated with an inherent risk of mutagenesis, tissues are maintained by a small group of stem cells (SCs) that replicate slowly to maintain their own population and that give rise to differentiated cells. There is increasing evidence that many tumors are also maintained by a small population of cancer stem cells that may arise by mutations from normal SCs. SC replication can be either symmetric or asymmetric. The former can lead to expansion of the SC pool. We describe a simple model to evaluate the impact of (a)symmetric SC replication on the expansion of mutant SCs and to show that mutations that increase the probability of asymmetric replication can lead to rapid mutant SC expansion in the absence of a selective fitness advantage. Mutations in several genes can lead to this process and may be at the root of the carcinogenic process

Stochastic Tunneling of Two Mutations in a Population of Cancer Cells

Cancer initiation, progression, and the emergence of drug resistance are driven by specific genetic and/or epigenetic alterations such as point mutations, structural alterations, DNA methylation and histone modification changes. These alterations may confer advantageous, deleterious or neutral effects to mutated cells. Previous studies showed that cells harboring two particular alterations may arise in a fixed-size population even in the absence of an intermediate state in which cells harboring only the first alteration take over the population; this phenomenon is called stochastic tunneling. Here, we investigated a stochastic Moran model in which two alterations emerge in a cell population of fixed size. We developed a novel approach to comprehensively describe the evolutionary dynamics of stochastic tunneling of two mutations. We considered the scenarios of large mutation rates and various fitness values and validated the accuracy of the mathematical predictions with exact stochastic computer simulations. Our theory is applicable to situations in which two alterations are accumulated in a fixed-size population of binary dividing cells