Mutator mutations enhance tumorigenic efficiency across fitness landscapes

Neutral evolution of rare cancer mutations in the computer and the clinic

A distinct model of neutral evolution of rare cancer mutations is described and contrasted with models relying on the infinite sites approximation (that a specific mutation arises in only one cell at any instant). An explosion of genetic diversity is predicted at clinical cell numbers and may explain the progressive refractoriness of cancers during a clinical course. The widely used infinite sites assumption may not be applicable for clinical cancers.

How Should Cancer Models Be Constructed?

Choosing and optimizing treatment strategies for cancer requires capturing its complex dynamics sufficiently well for understanding but without being overwhelmed. Mathematical models are essential to achieve this understanding, and we discuss the challenge of choosing the right level of complexity to address the full range of tumor complexity from growth, the generation of tumor heterogeneity, and interactions within tumors and with treatments and the tumor microenvironment. We discuss the differences between conceptual and descriptive models, and compare the use of predator-prey models, evolutionary game theory, and dynamic precision medicine approaches in the face of uncertainty about mechanisms and parameter values. Although there is of course no one-size-fits-all approach, we conclude that broad and flexible thinking about cancer, based on combined modeling approaches, will play a key role in finding creative and improved treatments.

Weak mixed phase in the mutator model

We consider the mutator model with unidirected transitions from the wild type to the mutator type, with different fitness functions for the wild types and mutator types. We calculate both the fraction of mutator types in the population and the surpluses, i.e., the mean number of mutations in the regular part of genomes for the wild type and mutator type, which have never been derived exactly. We identify the phase structure. Beside the mixed (ordinary evolution phase with finite fraction of wild types at large genome length) and the mutator phase (the absolute majority is mutators), we find another new phase as well-it has the mean fitness of the mixed phase but an exponentially small (in genome length) fraction of wild types. We identify the phase transition point and discuss its implications.

The evolution of metapopulation dynamics and the number of stem cells in intestinal crypts and other tissue structures in multicellular bodies

Carcinogenesis is a process of somatic evolution. Previous models of stem and transient amplifying cells in epithelial proliferating units like colonic crypts showed that intermediate numbers of stem cells in a crypt should optimally prevent progression to cancer. If a stem cell population is too small, it is easy for a mutator mutation to drift to fixation. If it is too large, it is easy for selection to drive cell fitness enhancing carcinogenic mutations to fixation. Here, we show that a multiscale microsimulation, that captures both within-crypt and between-crypt evolutionary dynamics, leads to a different conclusion. Epithelial tissues are metapopulations of crypts. We measured time to initiation of a neoplasm, implemented as inactivation of both alleles of a tumor suppressor gene. In our model, time to initiation is dependent on the spread of mutator clones in the crypts. The proportion of selectively beneficial and deleterious mutations in somatic cells is unknown and so was explored with a parameter. When the majority of non-neutral mutations are deleterious, the fitness of mutator clones tends to decline. When crypts are maintained by few stem cells, intercrypt competition tends to remove crypts with fixed mutators. When there are many stem cells within a crypt, there is virtually no crypt turnover, but mutator clones are suppressed by within-crypt competition. If the majority of non-neutral mutations are beneficial to the clone, then these results are reversed and intermediate-sized crypts provide the most protection against initiation. These results highlight the need to understand the dynamics of turnover and the mechanisms that control homeostasis, both at the level of stem cells within proliferative units and at the tissue level of competing proliferative units. Determining the distribution of fitness effects of somatic mutations will also be crucial to understanding the dynamics of tumor initiation and progression.

Extensive subclonal mutational diversity in human colorectal cancer and its significance

Human colorectal cancers (CRCs) contain both clonal and subclonal mutations. Clonal driver mutations are positively selected, present in most cells, and drive malignant progression. Subclonal mutations are randomly dispersed throughout the genome, providing a vast reservoir of mutant cells that can expand, repopulate the tumor, and result in the rapid emergence of resistance, as well as being a major contributor to tumor heterogeneity. Here, we apply duplex sequencing (DS) methodology to quantify subclonal mutations in CRC tumor with unprecedented depth (104) and accuracy (<10-7). We measured mutation frequencies in genes encoding replicative DNA polymerases and in genes frequently mutated in CRC, and found an unexpectedly high effective mutation rate, 7.1 × 10-7. The curve of subclonal mutation accumulation as a function of sequencing depth, using DNA obtained from 5 different tumors, is in accord with a neutral model of tumor evolution. We present a theoretical approach to model neutral evolution independent of the infinite-sites assumption (which states that a particular mutation arises only in one tumor cell at any given time). Our analysis indicates that the infinite-sites assumption is not applicable once the number of tumor cells exceeds the reciprocal of the mutation rate, a circumstance relevant to even the smallest clinically diagnosable tumor. Our methods allow accurate estimation of the total mutation burden in clinical cancers. Our results indicate that no DNA locus is wild type in every malignant cell within a tumor at the time of diagnosis (probability of all cells being wild type, 10-308).

The Mutator Phenotype: Adapting Microbial Evolution to Cancer Biology

The mutator phenotype hypothesis was postulated almost 40 years ago to reconcile the observation that while cancer cells display widespread mutational burden, acquisition of mutations in non-transformed cells is a rare event. Moreover, it also suggested that cancer evolution could be fostered by increased genome instability. Given the evolutionary conservation throughout the tree of life and the genetic tractability of model organisms, yeast and bacterial species pioneered studies to dissect the functions of genes required for genome maintenance (caretaker genes) or for cell growth control (gatekeeper genes). In this review, we first provide an overview of what we learned from model organisms about the roles of these genes and the genome instability that arises as a consequence of their dysregulation. We then discuss our current understanding of how mutator phenotypes shape the evolution of bacteria and yeast species. We end by bringing clinical evidence that lessons learned from single-cell organisms can be applied to tumor evolution.

Evolutionary dynamics and significance of multiple subclonal mutations in cancer

For the last 40 years the authors have collaborated on trying to understand the complexities of human cancer by formulating testable mathematical models that are based on mutation accumulation in human malignancies. We summarize the concepts encompassed by multiple mutations in human cancers in the context of source, accumulation during carcinogenesis and tumor progression, and therapeutic consequences. We conclude that the efficacious treatment of human cancer by targeted therapy will involve individualized, uniquely directed specific agents singly and in simultaneous combinations, and take into account the importance of targeting resistant subclonal mutations, particularly those subclones with alterations in DNA repair genes, DNA polymerase, and other genes required to maintain genetic stability.

Genomic Instability in Cancer: Teetering on the Limit of Tolerance

Cancer genomic instability contributes to the phenomenon of intratumoral genetic heterogeneity, provides the genetic diversity required for natural selection, and enables the extensive phenotypic diversity that is frequently observed among patients. Genomic instability has previously been associated with poor prognosis. However, we have evidence that for solid tumors of epithelial origin, extreme levels of genomic instability, where more than 75% of the genome is subject to somatic copy number alterations, are associated with a potentially better prognosis compared with intermediate levels under this threshold. This has been observed in clonal subpopulations of larger size, especially when genomic instability is shared among a limited number of clones. We hypothesize that cancers with extreme levels of genomic instability may be teetering on the brink of a threshold where so much of their genome is adversely altered that cells rarely replicate successfully. Another possibility is that tumors with high levels of genomic instability are more immunogenic than other cancers with a less extensive burden of genetic aberrations. Regardless of the exact mechanism, but hinging on our ability to quantify how a tumor's burden of genetic aberrations is distributed among coexisting clones, genomic instability has important therapeutic implications. Herein, we explore the possibility that a high genomic instability could be the basis for a tumor's sensitivity to DNA-damaging therapies. We primarily focus on studies of epithelial-derived solid tumors. Cancer Res; 77(9); 2179-85. ©2017 AACR.

Long range personalized cancer treatment strategies incorporating evolutionary dynamics

Background

Current cancer precision medicine strategies match therapies to static consensus molecular properties of an individual’s cancer, thus determining the next therapeutic maneuver. These strategies typically maintain a constant treatment while the cancer is not worsening. However, cancers feature complicated sub-clonal structure and dynamic evolution. We have recently shown, in a comprehensive simulation of two non-cross resistant therapies across a broad parameter space representing realistic tumors, that substantial improvement in cure rates and median survival can be obtained utilizing dynamic precision medicine strategies. These dynamic strategies explicitly consider intratumoral heterogeneity and evolutionary dynamics, including predicted future drug resistance states, and reevaluate optimal therapy every 45 days. However, the optimization is performed in single 45 day steps (“single-step optimization”).

Results

Herein we evaluate analogous strategies that think multiple therapeutic maneuvers ahead, considering potential outcomes at 5 steps ahead (“multi-step optimization”) or 40 steps ahead (“adaptive long term optimization (ALTO)”) when recommending the optimal therapy in each 45 day block, in simulations involving both 2 and 3 non-cross resistant therapies. We also evaluate an ALTO approach for situations where simultaneous combination therapy is not feasible (“Adaptive long term optimization: serial monotherapy only (ALTO-SMO)”). Simulations utilize populations of 764,000 and 1,700,000 virtual patients for 2 and 3 drug cases, respectively. Each virtual patient represents a unique clinical presentation including sizes of major and minor tumor subclones, growth rates, evolution rates, and drug sensitivities.

While multi-step optimization and ALTO provide no significant average survival benefit, cure rates are significantly increased by ALTO. Furthermore, in the subset of individual virtual patients demonstrating clinically significant difference in outcome between approaches, by far the majority show an advantage of multi-step or ALTO over single-step optimization. ALTO-SMO delivers cure rates superior or equal to those of single- or multi-step optimization, in 2 and 3 drug cases respectively.

Conclusion

In selected virtual patients incurable by dynamic precision medicine using single-step optimization, analogous strategies that “think ahead” can deliver long-term survival and cure without any disadvantage for non-responders. When therapies require dose reduction in combination (due to toxicity), optimal strategies feature complex patterns involving rapidly interleaved pulses of combinations and high dose monotherapy.

Reviewers

This article was reviewed by Wendy Cornell, Marek Kimmel, and Andrzej Swierniak. Wendy Cornell and Andrzej Swierniak are external reviewers (not members of the Biology Direct editorial board). Andrzej Swierniak was nominated by Marek Kimmel.

Electronic supplementary material

The online version of this article (doi:10.1186/s13062-016-0153-2) contains supplementary material, which is available to authorized users.

The rich phase structure of a mutator model

We propose a modification of the Crow-Kimura and Eigen models of biological molecular evolution to include a mutator gene that causes both an increase in the mutation rate and a change in the fitness landscape. This mutator effect relates to a wide range of biomedical problems. There are three possible phases: mutator phase, mixed phase and non-selective phase. We calculate the phase structure, the mean fitness and the fraction of the mutator allele in the population, which can be applied to describe cancer development and RNA viruses. We find that depending on the genome length, either the normal or the mutator allele dominates in the mixed phase. We analytically solve the model for a general fitness function. We conclude that the random fitness landscape is an appropriate choice for describing the observed mutator phenomenon in the case of a small fraction of mutators. It is shown that the increase in the mutation rates in the regular and the mutator parts of the genome should be set independently; only some combinations of these increases can push the complex biomedical system to the non-selective phase, potentially related to the eradication of tumors.

Translating predictive biomarkers within oncology clinical development programs

Predictive biomarkers provide essential information to enable personalized medicine, and hold the promise for enhancing the effectiveness and value of cancer therapies. However, they do not always work. This review provides a framework for managing the risk of predictive biomarkers and maximally harvesting their benefit. Methods are provided which permit data-driven, adaptive decision making about the use of predictive biomarkers during clinical development, applying them to the extent they are validated by the clinical data. Techniques for optimizing overall development efficiency, measured as the number of successful drug indications approved per patient utilized, are also presented.

Can a minimal replicating construct be identified as the embodiment of cancer?

Genomic instability is a hallmark of cancer. Cancer cells that exhibit abnormal chromosomes are characteristic of most advanced tumours, despite the potential threat represented by accumulated genetic damage. Carcinogenesis involves a loss of key components of the genetic and signalling molecular networks; hence some authors have suggested that this is part of a trend of cancer cells to behave as simple, minimal replicators. In this study, we explore this conjecture and suggest that, in the case of cancer, genomic instability has an upper limit that is associated with a minimal cancer cell network. Such a network would include (for a given microenvironment) the basic molecular components that allow cells to replicate and respond to selective pressures. However, it would also exhibit internal fragilities that could be exploited by appropriate therapies targeting the DNA repair machinery. The implications of this hypothesis are discussed.

Nonstandard personalized medicine strategies for cancer may lead to improved patient outcomes

Cancer is an evolutionary process that is driven by mutation and selection. Tumors are genetically unstable, and research has shown that this is the most efficient way for cancers to evolve. Genetic instability leads to genetic heterogeneity and dynamic change within a single individual's tumor, in turn leading to therapeutic resistance. Cancer treatment has also evolved from an empirical science of killing dividing cells to the current era of 'personalized medicine', exquisitely targeting the molecular features of individual cancers. However, current personalized medicine regards a single individual's cancer as largely uniform and static. Moreover, from a strategic perspective, current personalized medicine thinks primarily of the immediate therapy selection. Ongoing research suggests that new, nonstandard personalized treatment strategies that plan further ahead and consider intratumoral heterogeneity and the evolving nature of cancer (due to genetic instability) may lead to the next level of therapeutic benefit beyond current personalized medicine.

Breast cancer intratumor genetic heterogeneity: causes and implications

There is burgeoning evidence to suggest that tumor evolution follows the laws of Darwinian evolution, whereby individual tumor cell clones harbor private genetic aberrations in addition to the founder mutations, and that these distinct populations of cancer cells interact in competitive and mutualistic manners. The combined effect of genetic and epigenetic instability, and differential selective pressures according to the microenvironment and therapeutic interventions, create many different evolutionary routes such that intratumor heterogeneity is inevitable. Numerous cytogenetic, comparative genomic hybridization and, more recently, massively parallel sequencing studies have generated indisputable evidence of this phenomenon. The impact of intratumor heterogeneity on response and resistance to therapy is beginning to be understood; this information may prove crucial for the potentials of personalized medicine to be realized. In this review, the evidence of intratumor heterogeneity in breast cancer, its potential causes and implications for the clinical management of breast cancer patients are discussed.

Modelling the evolution of genetic instability during tumour progression

The role of genetic instability in driving carcinogenesis remains controversial. Genetic instability should accelerate carcinogenesis by increasing the rate of advantageous driver mutations; however, genetic instability can also potentially retard tumour growth by increasing the rate of deleterious mutation. As such, it is unclear whether genetically unstable clones would tend to be more selectively advantageous than their genetically stable counterparts within a growing tumour. Here, we show the circumstances where genetic instability evolves during tumour progression towards cancer. We employ a Wright-Fisher type model that describes the evolution of tumour subclones. Clones can acquire both advantageous and deleterious mutations, and mutator mutations that increase a cell's intrinsic mutation rate. Within the model, cancers evolve with a mutator phenotype when driver mutations bestow only moderate increases in fitness: very strong or weak selection for driver mutations suppresses the evolution of a mutator phenotype. Genetic instability occurs secondarily to selectively advantageous driver mutations. Deleterious mutations have relatively little effect on the evolution of genetic instability unless selection for additional driver mutations is very weak or if deleterious mutations are very common. Our model provides a framework for studying the evolution of genetic instability in tumour progression. Our analysis highlights the central role of selection in shaping patterns of mutation in carcinogenesis.

The effect of one additional driver mutation on tumor progression

Tumor growth is caused by the acquisition of driver mutations, which enhance the net reproductive rate of cells. Driver mutations may increase cell division, reduce cell death, or allow cells to overcome density-limiting effects. We study the dynamics of tumor growth as one additional driver mutation is acquired. Our models are based on two-type branching processes that terminate in either tumor disappearance or tumor detection. In our first model, both cell types grow exponentially, with a faster rate for cells carrying the additional driver. We find that the additional driver mutation does not affect the survival probability of the lesion, but can substantially reduce the time to reach the detectable size if the lesion is slow growing. In our second model, cells lacking the additional driver cannot exceed a fixed carrying capacity, due to density limitations. In this case, the time to detection depends strongly on this carrying capacity. Our model provides a quantitative framework for studying tumor dynamics during different stages of progression. We observe that early, small lesions need additional drivers, while late stage metastases are only marginally affected by them. These results help to explain why additional driver mutations are typically not detected in fast-growing metastases.

Impact of genetic dynamics and single-cell heterogeneity on development of nonstandard personalized medicine strategies for cancer

Cancers are heterogeneous and genetically unstable. Current practice of personalized medicine tailors therapy to heterogeneity between cancers of the same organ type. However, it does not yet systematically address heterogeneity at the single-cell level within a single individual's cancer or the dynamic nature of cancer due to genetic and epigenetic change as well as transient functional changes. We have developed a mathematical model of personalized cancer therapy incorporating genetic evolutionary dynamics and single-cell heterogeneity, and have examined simulated clinical outcomes. Analyses of an illustrative case and a virtual clinical trial of over 3 million evaluable "patients" demonstrate that augmented (and sometimes counterintuitive) nonstandard personalized medicine strategies may lead to superior patient outcomes compared with the current personalized medicine approach. Current personalized medicine matches therapy to a tumor molecular profile at diagnosis and at tumor relapse or progression, generally focusing on the average, static, and current properties of the sample. Nonstandard strategies also consider minor subclones, dynamics, and predicted future tumor states. Our methods allow systematic study and evaluation of nonstandard personalized medicine strategies. These findings may, in turn, suggest global adjustments and enhancements to translational oncology research paradigms.

The mutator phenotype in cancer: molecular mechanisms and targeting strategies

Normal human cells replicate their DNA with exceptional accuracy. It has been estimated that approximately one error occurs during DNA replication for each 10(9) to 10(10) nucleotides polymerized. In contrast, malignant cells exhibit multiple chromosomal abnormalities and contain tens of thousands of alterations in the nucleotide sequence of nuclear DNA. To account for the disparity between the rarity of mutations in normal cells and the large numbers of mutations present in cancer, we have hypothesized that during tumor development, cancer cells exhibit a mutator phenotype. As a defining feature of cancer, the mutator phenotype remains an as-yet unexplored therapeutic target: by reducing the rate at which mutations accumulate it may be possible to significantly delay tumor development; conversely, the large number of mutations in cancer may make cancer cells more sensitive to cell killing by increasing the mutation rate. Here we summarize the evidence for the mutator phenotype hypothesis in cancer and explore how the increased frequency of random mutations during the evolution of human tumors provides new approaches for the design of cancer chemotherapy.

The origins of cancer robustness and evolvability

Unless diagnosed early, many adult cancers remain incurable diseases. This is despite an intense global research effort to develop effective anticancer therapies, calling into question the use of rational drug design strategies in targeting complex disease states such as cancer. A fundamental challenge facing researchers and clinicians is that cancers are inherently robust biological systems, able to survive, adapt and proliferate despite the perturbations resulting from anticancer drugs. It is essential that the mechanisms underlying tumor robustness be formally studied and characterized, as without a thorough understanding of the principles of tumor robustness, strategies to overcome therapy resistance are unlikely to be found. Degeneracy describes the ability of structurally distinct system components (e.g. proteins, pathways, cells, organisms) to be conditionally interchangeable in their contribution to system traits and it has been broadly implicated in the robustness and evolvability of complex biological systems. Here we focus on one of the most important mechanisms underpinning tumor robustness and degeneracy, the cellular heterogeneity that is the hallmark of most solid tumors. Based on a combination of computational, experimental and clinical studies we argue that stochastic noise is an underlying cause of tumor heterogeneity and particularly degeneracy. Drawing from a number of recent data sets, we propose an integrative model for the evolution of therapy resistance, and discuss recent computational studies that propose new therapeutic strategies aimed at defeating the adaptable cancer phenotype.

Efficiency of carcinogenesis: is the mutator phenotype inevitable?

Cancer development requires multiple oncogenic mutations. Pathogenic mechanisms which accelerate this process may be favored carcinogenic pathways. Mutator mutations are mutations in genetic stability genes, and increase the mutation rate, speeding up the accumulation of oncogenic mutations. The mutator hypothesis states that mutator mutations play a critical role in carcinogenesis. Alternatively, tumors might arise by mutations occurring at the normal rate followed by selection and expansion of various premalignant lineages on the path to cancer. This alternative pathway is a significant argument against the mutator hypothesis. Mutator mutations may also lead to accumulation of deleterious mutations, which could lead to extinction of premalignant lineages before they become cancerous, another argument against the mutator hypothesis. Finally, the need for acquisition of a mutator mutation imposes an additional step on the carcinogenic process. Accordingly, the mutator hypothesis has been a seminal but controversial idea for several decades despite considerable experimental and theoretical work. To resolve this debate, the concept of efficiency has been introduced as a metric for comparing carcinogenic mechanisms, and a new theoretical approach of focused quantitative modeling has been applied. The results demonstrate that, given what is already known, the predominance of mutator mechanisms is likely inevitable, as they overwhelm less efficient non-mutator pathways to cancer.

Aberrant expression of alternative DNA polymerases: a source of mutator phenotype as well as replicative stress in cancer

The cell life span depends on a subtle equilibrium between the accurate duplication of the genomic DNA and less stringent DNA transactions which allow cells to tolerate mutations associated with DNA damage. The physiological role of the alternative, specialized or TLS (translesion synthesis) DNA polymerases could be to favor the necessary "flexibility" of the replication machinery, by allowing DNA replication to occur even in the presence of blocking DNA damage. As these alternative DNA polymerases are inaccurate when replicating undamaged DNA, the regulation of their expression needs to be carefully controlled. Evidence in the literature supports that dysregulation of these error-prone enzymes contributes to the acquisition of a mutator phenotype that, along with defective cell cycle control or other genome stability pathways, could be a motor for accelerated tumor progression.

Mutational heterogeneity in human cancers: origin and consequences

Cancer recapitulates Darwinian evolution. Mutations acquired during life that provide cells with a growth or survival advantage will preferentially multiply to form a tumor. As a result of The Cancer Genome Atlas Project, we have gathered detailed information on the nucleotide sequence changes in a number of human cancers. The sources of mutations in cancer are diverse, and the complexity of those found to be clonally present in tumors has increasingly made it difficult to identify key rate-limiting genes for tumor growth that could serve as potential targets for directed therapies. The impact of DNA sequencing on future cancer research and personalized therapy is likely to be profound and merits critical evaluation.