The effect of one additional driver mutation on tumor progression

Waiting times in a branching process model of colorectal cancer initiation

We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.

Computational Analysis Reveals the Temporal Acquisition of Pathway Alterations during the Evolution of Cancer

Cancer metastasis is the lethal developmental step in cancer, responsible for the majority of cancer deaths. To metastasise, cancer cells must acquire the ability to disseminate systemically and to escape an activated immune response. Here, we endeavoured to investigate if metastatic dissemination reflects acquisition of genomic traits that are selected for. We acquired mutation and copy number data from 8332 tumours representing 19 cancer types acquired from The Cancer Genome Atlas and the Hartwig Medical Foundation. A total of 827,344 non-synonymous mutations across 8332 tumour samples representing 19 cancer types were timed as early or late relative to copy number alterations, and potential driver events were annotated. We found that metastatic cancers had a significantly higher proportion of clonal mutations and a general enrichment of early mutations in p53 and RTK/KRAS pathways. However, while individual pathways demonstrated a clear time-separated preference for specific events, the relative timing did not vary between primary and metastatic cancers. These results indicate that the selective pressure that drives cancer development does not change dramatically between primary and metastatic cancer on a genomic level, and is mainly focused on alterations that increase proliferation.

Treatment represents a key driver of metastatic cancer evolution

Metastasis is the main cause of cancer death, yet the evolutionary processes behind it remain largely unknown. Here, through analysis of large panel-based genomic datasets from the AACR GENIE project, including 40,979 primary and metastatic tumors across 25 distinct cancer types, we explore how the evolutionary pressure of cancer metastasis shapes the selection of genomic drivers of cancer. The most commonly affected genes were TP53, MYC, and CDKN2A, with no specific pattern associated with metastatic disease. This suggests that, on a driver mutation level, the selective pressure operating in primary and metastatic tumors is similar. The most highly enriched individual driver mutations in metastatic tumors were mutations known to drive resistance to hormone therapies in breast and prostate cancer (ESR1 and AR), anti-EGFR therapy in non-small cell lung cancer (EGFR T790M), and imatinib in gastrointestinal cancer (KIT V654A). Specific mutational signatures were also associated with treatment in three cancer types, supporting clonal selection following anti-cancer therapy. Overall, this implies that initial acquisition of driver mutations is predominantly shaped by the tissue of origin, where specific mutations define the developing primary tumor and drive growth, immune escape, and tolerance to chromosomal instability. However, acquisition of driver mutations that contribute to metastatic disease is less specific, with the main genomic drivers of metastatic cancer evolution associating with resistance to therapy.

Clonal evolution driven by superdriver mutations

Background

Tumors are widely recognized to progress through clonal evolution by sequentially acquiring selectively advantageous genetic alterations that significantly contribute to tumorigenesis and thus are termned drivers. Some cancer drivers, such as TP53 point mutation or EGFR copy number gain, provide exceptional fitness gains, which, in time, can be sufficient to trigger the onset of cancer with little or no contribution from additional genetic alterations. These key alterations are called superdrivers.

Results

In this study, we employ a Wright-Fisher model to study the interplay between drivers and superdrivers in tumor progression. We demonstrate that the resulting evolutionary dynamics follow global clonal expansions of superdrivers with periodic clonal expansions of drivers. We find that the waiting time to the accumulation of a set of superdrivers and drivers in the tumor cell population can be approximated by the sum of the individual waiting times.

Conclusions

Our results suggest that superdriver dynamics dominate over driver dynamics in tumorigenesis. Furthermore, our model allows studying the interplay between superdriver and driver mutations both empirically and theoretically.

An analysis of genetic heterogeneity in untreated cancers

Genetic intratumoural heterogeneity is a natural consequence of imperfect DNA replication. Any two randomly selected cells, whether normal or cancerous, are therefore genetically different. Here, we review the different forms of genetic heterogeneity in cancer and re-analyse the extent of genetic heterogeneity within seven types of untreated epithelial cancers, with particular regard to its clinical relevance. We find that the homogeneity of predicted functional mutations in driver genes is the rule rather than the exception. In primary tumours with multiple samples, 97% of driver-gene mutations in 38 patients were homogeneous. Moreover, among metastases from the same primary tumour, 100% of the driver mutations in 17 patients were homogeneous. With a single biopsy of a primary tumour in 14 patients, the likelihood of missing a functional driver-gene mutation that was present in all metastases was 2.6%. Furthermore, all functional driver-gene mutations detected in these 14 primary tumours were present among all their metastases. Finally, we found that individual metastatic lesions responded concordantly to targeted therapies in 91% of 44 patients. These analyses indicate that the cells within the primary tumours that gave rise to metastases are genetically homogeneous with respect to functional driver-gene mutations, and we suggest that future efforts to develop combination therapies have the potential to be curative.

Consecutive seeding and transfer of genetic diversity in metastasis

During metastasis, only a fraction of genetic diversity in a primary tumor is passed on to metastases. We calculate this fraction of transferred diversity as a function of the seeding rate between tumors. At one extreme, if a metastasis is seeded by a single cell, then it inherits only the somatic mutations present in the founding cell, so that none of the diversity in the primary tumor is transmitted to the metastasis. In contrast, if a metastasis is seeded by multiple cells, then some genetic diversity in the primary tumor can be transmitted. We study a multitype branching process of metastasis growth that originates from a single cell but over time receives additional cells. We derive a surprisingly simple formula that relates the expected diversity of a metastasis to the diversity in the pool of seeding cells. We calculate the probability that a metastasis is polyclonal. We apply our framework to published datasets for which polyclonality has been previously reported, analyzing 68 ovarian cancer samples, 31 breast cancer samples, and 8 colorectal cancer samples from 15 patients. For these clonally diverse metastases, under typical metastasis growth conditions, we find that 10 to 150 cells seeded each metastasis and left surviving lineages between initial formation and clinical detection.

Computational modelling of resistance and associated treatment response heterogeneity in metastatic cancers

Metastatic cancer patients invariably develop treatment resistance. Different levels of resistance lead to observed heterogeneity in treatment response. The main goal was to evaluate treatment response heterogeneity with a computation model simulating the dynamics of drug-sensitive and drug-resistant cells. Model parameters included proliferation, drug-induced death, transition and proportion of intrinsically resistant cells. The model was benchmarked with imaging metrics extracted from 39 metastatic prostate cancer patients who had ¹⁸F-NaF-PET/CT scans performed at baseline and at three cycles into chemotherapy or hormonal therapy. Two initial model assumptions were evaluated: considering only inter-patient heterogeneity and both inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells. The correlation between the median proportion of intrinsically resistant cells and baseline patient-level imaging metrics was assessed with Spearman's rank correlation coefficient. The impact of model parameters on simulated treatment response was evaluated with a sensitivity study. Treatment response after periods of six, nine, and 12 months was predicted with the model. The median predicted range of response for patients treated with both therapies was compared with a Wilcoxon rank sum test. For each patient, the time was calculated when the proportion of disease with a non-favourable response outperformed a favourable response. By taking into account inter-patient and intra-patient heterogeneity in the proportion of intrinsically resistant cells, the model performed significantly better ([Formula: see text]) than by taking into account only inter-patient heterogeneity ([Formula: see text]). The median proportion of intrinsically resistant cells showed a moderate correlation (ρ  =  0.55) with mean patient-level uptake, and a low correlation (ρ  =  0.36) with the dispersion of mean metastasis-level uptake in a patient. The sensitivity study showed a strong impact of the proportion of intrinsically resistant cells on model behaviour after three cycles of therapy. The difference in the median range of response (MRR) was not significant between cohorts at any time point (p   >  0.15). The median time when the proportion of disease with a non-favourable response outperformed the favourable response was eight months, for both cohorts. The model provides an insight into inter-patient and intra-patient heterogeneity in the evolution of treatment resistance.

Biodiversity in the cyclic competition system of three species according to the emergence of mutant species

Understanding mechanisms which promote or hinder existing ecosystems are important issues in ecological sciences. In addition to fundamental interactions such as competition and migration among native species, existing ecosystems can be easily disturbed by external factors, and the emergence of new species may be an example in such cases. The new species which does not exist in a current ecosystem can be regarded as either alien species entered from outside or mutant species born by mutation in existing normal species. Recently, as existing ecosystems are getting influenced by various physical/chemical external factors, mutation due to anthropogenic and environmental factors can occur more frequently and is thus attracting much attention for the maintenance of ecosystems. In this paper, we consider emergences of mutant species among self-competing three species in the cyclic dominance. By defining mutation as the birth of mutant species, we investigate how mutant species can affect biodiversity in the existing ecosystem. Through microscopic and macroscopic approaches, we have found that the society of existing normal species can be disturbed by mutant species either the society is maintained accompanying with the coexistence of all species or jeopardized by occupying of mutant species. Due to the birth of mutant species, the existing society may be more complex by constituting two different groups of normal and mutant species, and our results can be contributed to analyze complex ecosystems of many species. We hope our findings may propose a new insight on mutation in cyclic competition systems of many species.

Deterministic Evolutionary Trajectories Influence Primary Tumor Growth: TRACERx Renal

The evolutionary features of clear-cell renal cell carcinoma (ccRCC) have not been systematically studied to date. We analyzed 1,206 primary tumor regions from 101 patients recruited into the multi-center prospective study, TRACERx Renal. We observe up to 30 driver events per tumor and show that subclonal diversification is associated with known prognostic parameters. By resolving the patterns of driver event ordering, co-occurrence, and mutual exclusivity at clone level, we show the deterministic nature of clonal evolution. ccRCC can be grouped into seven evolutionary subtypes, ranging from tumors characterized by early fixation of multiple mutational and copy number drivers and rapid metastases to highly branched tumors with >10 subclonal drivers and extensive parallel evolution associated with attenuated progression. We identify genetic diversity and chromosomal complexity as determinants of patient outcome. Our insights reconcile the variable clinical behavior of ccRCC and suggest evolutionary potential as a biomarker for both intervention and surveillance.

Non-cell-autonomous effects yield lower clonal diversity in expanding tumors

Recent cancer research has investigated the possibility that non-cell-autonomous (NCA) driving tumor growth can support clonal diversity (CD). Indeed, mutations can affect the phenotypes not only of their carriers (“cell-autonomous”, CA effects), but also sometimes of other cells (NCA effects). However, models that have investigated this phenomenon have only considered a restricted number of clones. Here, we designed an individual-based model of tumor evolution, where clones grow and mutate to yield new clones, among which a given frequency have NCA effects on other clones’ growth. Unlike previously observed for smaller assemblages, most of our simulations yield lower CD with high frequency of mutations with NCA effects. Owing to NCA effects increasing competition in the tumor, clones being already dominant are more likely to stay dominant, and emergent clones not to thrive. These results may help personalized medicine to predict intratumor heterogeneity across different cancer types for which frequency of NCA effects could be quantified.

Reconstructing metastatic seeding patterns of human cancers

Reconstructing the evolutionary history of metastases is critical for understanding their basic biological principles and has profound clinical implications. Genome-wide sequencing data has enabled modern phylogenomic methods to accurately dissect subclones and their phylogenies from noisy and impure bulk tumour samples at unprecedented depth. However, existing methods are not designed to infer metastatic seeding patterns. Here we develop a tool, called Treeomics, to reconstruct the phylogeny of metastases and map subclones to their anatomic locations. Treeomics infers comprehensive seeding patterns for pancreatic, ovarian, and prostate cancers. Moreover, Treeomics correctly disambiguates true seeding patterns from sequencing artifacts; 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumour heterogeneity among distinct samples. In silico benchmarking on simulated tumour phylogenies across a wide range of sample purities (15–95%) and sequencing depths (25-800 × ) demonstrates the accuracy of Treeomics compared with existing methods.

Tumours frequently metastasize to multiple anatomical sites and understanding how these different metastases evolve may be important for therapy. Here, the authors develop a method—Treeomics—that can construct phylogenies from multiple metastases from next-generation sequencing data.

Evolutionary scalpels for dissecting tumor ecosystems

Amidst the growing literature on cancer genomics and intratumor heterogeneity, essential principles in evolutionary biology recur time and time again. Here we use these principles to guide the reader through major advances in cancer research, highlighting issues of "hit hard, hit early" treatment strategies, drug resistance, and metastasis. We distinguish between two frameworks for understanding heterogeneous tumors, both of which can inform treatment strategies: (1) The tumor as diverse ecosystem, a Darwinian population of sometimes-competing, sometimes-cooperating cells; (2) The tumor as tightly integrated, self-regulating organ, which may hijack developmental signals to restore functional heterogeneity after treatment. While the first framework dominates literature on cancer evolution, the second framework enjoys support as well. Throughout this review, we illustrate how mathematical models inform understanding of tumor progression and treatment outcomes. Connecting models to genomic data faces computational and technical hurdles, but high-throughput single-cell technologies show promise to clear these hurdles. This article is part of a Special Issue entitled: Evolutionary principles - heterogeneity in cancer?, edited by Dr. Robert A. Gatenby.

Differential selective pressure alters rate of drug resistance acquisition in heterogeneous tumor populations

Recent drug discovery and development efforts have created a large arsenal of targeted and chemotherapeutic drugs for precision medicine. However, drug resistance remains a major challenge as minor pre-existing resistant subpopulations are often found to be enriched at relapse. Current drug design has been heavily focused on initial efficacy, and we do not fully understand the effects of drug selective pressure on long-term drug resistance potential. Using a minimal two-population model, taking into account subpopulation proportions and growth/kill rates, we modeled long-term drug treatment and performed parameter sweeps to analyze the effects of each parameter on therapeutic efficacy. We found that drugs with the same overall initial kill may exert differential selective pressures, affecting long-term therapeutic outcome. We validated our conclusions experimentally using a preclinical model of Burkitt's lymphoma. Furthermore, we highlighted an intrinsic tradeoff between drug-imposed overall selective pressure and rate of adaptation. A principled approach in understanding the effects of distinct drug selective pressures on short-term and long-term tumor response enables better design of therapeutics that ultimately minimize relapse.

Modeling Tumor Clonal Evolution for Drug Combinations Design

Cancer is a clonal evolutionary process. This presents challenges for effective therapeutic intervention, given the constant selective pressure towards drug resistance. Mathematical modeling from population genetics, evolutionary dynamics, and engineering perspectives are being increasingly employed to study tumor progression, intratumoral heterogeneity, drug resistance, and rational drug scheduling and combinations design. In this review, we discuss promising opportunities these inter-disciplinary approaches hold for advances in cancer biology and treatment. We propose that quantitative modeling perspectives can complement emerging experimental technologies to facilitate enhanced understanding of disease progression and improved capabilities for therapeutic drug regimen designs.

Do cell-autonomous and non-cell-autonomous effects drive the structure of tumor ecosystems?

By definition, a driver mutation confers a growth advantage to the cancer cell in which it occurs, while a passenger mutation does not: the former is usually considered as the engine of cancer progression, while the latter is not. Actually, the effects of a given mutation depend on the genetic background of the cell in which it appears, thus can differ in the subclones that form a tumor. In addition to cell-autonomous effects generated by the mutations, non-cell-autonomous effects shape the phenotype of a cancer cell. Here, we review the evidence that a network of biological interactions between subclones drives cancer cell adaptation and amplifies intra-tumor heterogeneity. Integrating the role of mutations in tumor ecosystems generates innovative strategies targeting the tumor ecosystem's weaknesses to improve cancer treatment.

Quantifying Clonal and Subclonal Passenger Mutations in Cancer Evolution

The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion.

Cancer is the consequence of an evolutionary process, which lasts several decades, is impossible to observe during most of its time, and only becomes apparent in late stages. We use mathematical modeling to shed light on the evolutionary dynamics of cancer by studying the accumulation of passenger mutations. We show that the frequencies obtained by passenger mutations depend strongly on the ratio of death and birth rates of cancer cells. We use genetic data of colorectal cancer to estimate this important quantity in vivo. We estimate the size of the cancer cell population that was present when a specific mutation first emerged. Our theory informs the analysis of cancer sequencing data and the phylogenetic reconstruction of cancer evolution.

Stochastic modeling reveals an evolutionary mechanism underlying elevated rates of childhood leukemia

Young children have higher rates of leukemia than young adults. This fact represents a fundamental conundrum, because hematopoietic cells in young children should have fewer mutations (including oncogenic ones) than such cells in adults. Here, we present the results of stochastic modeling of hematopoietic stem cell (HSC) clonal dynamics, which demonstrated that early HSC pools were permissive to clonal evolution driven by drift. We show that drift-driven clonal expansions cooperate with faster HSC cycling in young children to produce conditions that are permissive for accumulation of multiple driver mutations in a single cell. Later in life, clonal evolution was suppressed by stabilizing selection in the larger young adult pools, and it was driven by positive selection at advanced ages in the presence of microenvironmental decline. Overall, our results indicate that leukemogenesis is driven by distinct evolutionary forces in children and adults.

Cancer Evolution and the Limits of Predictability in Precision Cancer Medicine

The ability to predict the future behavior of an individual cancer is crucial for precision cancer medicine. The discovery of extensive intratumor heterogeneity and ongoing clonal adaptation in human tumors substantiated the notion of cancer as an evolutionary process. Random events are inherent in evolution and tumor spatial structures hinder the efficacy of selection, which is the only deterministic evolutionary force. This review outlines how the interaction of these stochastic and deterministic processes, which have been extensively studied in evolutionary biology, limits cancer predictability and develops evolutionary strategies to improve predictions. Understanding and advancing the cancer predictability horizon is crucial to improve precision medicine outcomes.

The mini-driver model of polygenic cancer evolution

Much of cancer genetics research has focused on the identification of the most-important somatic mutations ('major drivers') that cause tumour growth. However, many mutations found in cancer might not be major drivers or 'passenger' mutations, but instead might have relatively weak tumour-promoting effects. Our aim is to highlight the existence of these mutations (termed 'mini drivers' herein), as multiple mini-driver mutations might substitute for a major-driver change, especially in the presence of genomic instability or high mutagen exposure. The mini-driver model has clinical implications: for example, the effects of therapeutically targeting such genes may be limited. However, the main importance of the model lies in helping to provide a complete understanding of tumorigenesis, especially as we anticipate that an increasing number of mini-driver mutations will be found by cancer genome sequencing.

Toward an evolutionary model of cancer: Considering the mechanisms that govern the fate of somatic mutations

Our understanding of cancer has greatly advanced since Nordling [Nordling CO (1953) Br J Cancer 7(1):68-72] and Armitage and Doll [Armitage P, Doll R (1954) Br J Cancer 8(1):1-12] put forth the multistage model of carcinogenesis. However, a number of observations remain poorly understood from the standpoint of this paradigm in its contemporary state. These observations include the similar age-dependent exponential rise in incidence of cancers originating from stem/progenitor pools differing drastically in size, age-dependent cell division profiles, and compartmentalization. This common incidence pattern is characteristic of cancers requiring different numbers of oncogenic mutations, and it scales to very divergent life spans of mammalian species. Also, bigger mammals with larger underlying stem cell pools are not proportionally more prone to cancer, an observation known as Peto's paradox. Here, we present a number of factors beyond the occurrence of oncogenic mutations that are unaccounted for in the current model of cancer development but should have significant impacts on cancer incidence. Furthermore, we propose a revision of the current understanding for how oncogenic and other functional somatic mutations affect cellular fitness. We present evidence, substantiated by evolutionary theory, demonstrating that fitness is a dynamic environment-dependent property of a phenotype and that oncogenic mutations should have vastly different fitness effects on somatic cells dependent on the tissue microenvironment in an age-dependent manner. Combined, this evidence provides a firm basis for understanding the age-dependent incidence of cancers as driven by age-altered systemic processes regulated above the cell level.

A spatial model predicts that dispersal and cell turnover limit intratumour heterogeneity

Most cancers in humans are large, measuring centimetres in diameter, and composed of many billions of cells. An equivalent mass of normal cells would be highly heterogeneous as a result of the mutations that occur during each cell division. What is remarkable about cancers is that virtually every neoplastic cell within a large tumour often contains the same core set of genetic alterations, with heterogeneity confined to mutations that emerge late during tumour growth. How such alterations expand within the spatially constrained three-dimensional architecture of a tumour, and come to dominate a large, pre-existing lesion, has been unclear. Here we describe a model for tumour evolution that shows how short-range dispersal and cell turnover can account for rapid cell mixing inside the tumour. We show that even a small selective advantage of a single cell within a large tumour allows the descendants of that cell to replace the precursor mass in a clinically relevant time frame. We also demonstrate that the same mechanisms can be responsible for the rapid onset of resistance to chemotherapy. Our model not only provides insights into spatial and temporal aspects of tumour growth, but also suggests that targeting short-range cellular migratory activity could have marked effects on tumour growth rates.

Stochastic modeling indicates that aging and somatic evolution in the hematopoetic system are driven by non-cell-autonomous processes

Age-dependent tissue decline and increased cancer incidence are widely accepted to be rate-limited by the accumulation of somatic mutations over time. Current models of carcinogenesis are dominated by the assumption that oncogenic mutations have defined advantageous fitness effects on recipient stem and progenitor cells, promoting and rate-limiting somatic evolution. However, this assumption is markedly discrepant with evolutionary theory, whereby fitness is a dynamic property of a phenotype imposed upon and widely modulated by environment. We computationally modeled dynamic microenvironment-dependent fitness alterations in hematopoietic stem cells (HSC) within the Sprengel-Liebig system known to govern evolution at the population level. Our model for the first time integrates real data on age-dependent dynamics of HSC division rates, pool size, and accumulation of genetic changes and demonstrates that somatic evolution is not rate-limited by the occurrence of mutations, but instead results from aged microenvironment-driven alterations in the selective/fitness value of previously accumulated genetic changes. Our results are also consistent with evolutionary models of aging and thus oppose both somatic mutation-centric paradigms of carcinogenesis and tissue functional decline. In total, we demonstrate that aging directly promotes HSC fitness decline and somatic evolution via non-cell-autonomous mechanisms.

Dynamics of preventive vs post-diagnostic cancer control using low-impact measures

Cancer poses danger because of its unregulated growth, development of resistance, and metastatic spread to vital organs. We currently lack quantitative theory for how preventive measures and post-diagnostic interventions are predicted to affect risks of a life threatening cancer. Here we evaluate how continuous measures, such as life style changes and traditional treatments, affect both neoplastic growth and the frequency of resistant clones. We then compare and contrast preventive and post-diagnostic interventions assuming that only a single lesion progresses to invasive carcinoma during the life of an individual, and resection either leaves residual cells or metastases are undetected. Whereas prevention generally results in more positive therapeutic outcomes than post-diagnostic interventions, this advantage is substantially lowered should prevention initially fail to arrest tumour growth. We discuss these results and other important mitigating factors that should be taken into consideration in a comparative understanding of preventive and post-diagnostic interventions.

DOI:http://dx.doi.org/10.7554/eLife.06266.001

About one person in every two will get cancer during their lives. Surgery and chemotherapy have long been mainstays of cancer treatment. Both, however, have substantial downsides. Surgery may leave behind undetected cancer cells that can grow into new tumours. Furthermore, in response to chemotherapy drugs, some cancer cells may emerge that resist further treatment. There is therefore interest in whether preventive strategies—including lifestyle changes and medications—could reduce the likelihood of confronting a life-threatening cancer.

Now, Akhmetzhanov and Hochberg have developed a mathematical model to help compare the effectiveness of preventive strategies and traditional cancer treatments. The model—which assumes that a person can only develop a single cancer from a single region of pre-cancerous cells—suggests that long-term cancer prevention strategies reduce the risk of a life-threatening cancer by more than traditional treatment that begins after a tumour is discovered. The preventive measures may be less effective in some cases compared to traditional treatments if they initially fail to stop a tumour growing, although on average they still work better than treating the cancer after detection.

According to Akhmetzhanov and Hochberg's model, surgical removal followed by chemotherapy is less likely to be successful than prevention, and when successful, requires larger impacts on the cancer (and therefore creates more side-effects for the patient) to achieve the same level of control as prevention. The model also suggests that even at very low levels of impact on residual cancer cells, chemotherapies are likely to be counterproductive by boosting the subsequent emergence of treatment-resistant tumours.

Akhmetzhanov and Hochberg's model predicts how effective preventive measures need to be in terms of slowing the growth of cancer cells to result in given reductions in the future risk of a life-threatening cancer. Future work should test this model by measuring the effects on tumour growth of prevention and of traditional therapies.

DOI:http://dx.doi.org/10.7554/eLife.06266.002

A new model of time scheme for progression of colorectal cancer

BACKGROUND

tumourigenesis can be regarded as an evolutionary process, in which the transformation of a normal cell into a tumour cell involves a number of limiting genetic and epigenetic events. To study the progression process, time schemes have been proposed for studying the process of colorectal cancer based on extensive clinical investigations. Moreover, a number of mathematical models have been designed to describe this evolutionary process. These models assumed that the mutation rate of genes is constant during different stages. However, it has been pointed that the subsequent driver mutations appear faster than the previous ones and the cumulative time to have more driver mutations grows with the growing number of gene mutations. Thus it is still a challenge to calculate the time when the first mutation occurs and to determine the influence of tumour size on the mutation rate.

RESULTS

In this work we present a general framework to remedy the shortcoming of existing models. Rather than considering the information of gene mutations based on a population of patients, we for the first time determine the values of the selective advantage of cancer cells and initial mutation rate for individual patients. The averaged values of doubling time and selective advantage coefficient determined by our model are consistent with the predictions made by the published models. Our calculation showed that the values of biological parameters, such as the selective advantage coefficient, initial mutation rate and cell doubling time diversely depend on individuals. Our model has successfully predicted the values of several important parameters in cancer progression, such as the selective advantage coefficient, initial mutation rate and cell doubling time. In addition, experimental data validated our predicted initial mutation rate and cell doubling time.

CONCLUSIONS

The introduced new parameter makes our proposed model more flexible to fix various types of information based on different patients in cancer progression.

Modeling TGF-β in early stages of cancer tissue dynamics

Recent works have highlighted a double role for the Transforming Growth Factor (-): it inhibits cancer in healthy cells and potentiates tumor progression during late stage of tumorigenicity, respectively; therefore it has been termed the “Jekyll and Hyde” of cancer or, alternatively, an “excellent servant but a bad master”. It remains unclear how this molecule could have the two opposite behaviours. In this work, we propose a - multi scale mathematical model at molecular, cellular and tissue scales. The multi scalar behaviours of the - are described by three coupled models built up together which can approximatively be related to distinct microscopic, mesoscopic, and macroscopic scales, respectively. We first model the dynamics of - at the single-cell level by taking into account the intracellular and extracellular balance and the autocrine and paracrine behaviour of -. Then we use the average estimates of the - from the first model to understand its dynamics in a model of duct breast tissue. Although the cellular model and the tissue model describe phenomena at different time scales, their cumulative dynamics explain the changes in the role of - in the progression from healthy to pre-tumoral to cancer. We estimate various parameters by using available gene expression datasets. Despite the fact that our model does not describe an explicit tissue geometry, it provides quantitative inference on the stage and progression of breast cancer tissue invasion that could be compared with epidemiological data in literature. Finally in the last model, we investigated the invasion of breast cancer cells in the bone niches and the subsequent disregulation of bone remodeling processes. The bone model provides an effective description of the bone dynamics in healthy and early stages cancer conditions and offers an evolutionary ecological perspective of the dynamics of the competition between cancer and healthy cells.

Evolutionary foundations for cancer biology

New applications of evolutionary biology are transforming our understanding of cancer. The articles in this special issue provide many specific examples, such as microorganisms inducing cancers, the significance of within-tumor heterogeneity, and the possibility that lower dose chemotherapy may sometimes promote longer survival. Underlying these specific advances is a large-scale transformation, as cancer research incorporates evolutionary methods into its toolkit, and asks new evolutionary questions about why we are vulnerable to cancer. Evolution explains why cancer exists at all, how neoplasms grow, why cancer is remarkably rare, and why it occurs despite powerful cancer suppression mechanisms. Cancer exists because of somatic selection; mutations in somatic cells result in some dividing faster than others, in some cases generating neoplasms. Neoplasms grow, or do not, in complex cellular ecosystems. Cancer is relatively rare because of natural selection; our genomes were derived disproportionally from individuals with effective mechanisms for suppressing cancer. Cancer occurs nonetheless for the same six evolutionary reasons that explain why we remain vulnerable to other diseases. These four principles-cancers evolve by somatic selection, neoplasms grow in complex ecosystems, natural selection has shaped powerful cancer defenses, and the limitations of those defenses have evolutionary explanations-provide a foundation for understanding, preventing, and treating cancer.