Here, we have examined the evolution of a mutator phenotype during tumour progression from a benign lesion to a cancer. We have determined circumstances when, a mutator phenotype evolves during carcinogenesis, and looked at the effect of an evolving mutator phenotype on the efficiency of tumorigenesis.
Our model predicts that the strength of selection for driver mutations determines whether a cancer is likely to evolve a mutator phenotype: in situations where selection for driver mutations is very weak, or very strong, a mutator phenotype is unlikely to evolve. Previous studies have noted the central role of selection, predominating over the mutation rate, in driving the speed of carcinogenesis (Schollnberger et al. 2010
). Indeed, an agent-based modelling study found that when both neutral and driver mutations were necessary for cancer formation, requiring more driver mutations to form a cancer actually increased the probability of cancer formation, as the rapid clonal expansions induced by the extra driver mutations made it more likely that a neutral mutation would be able to hitchhike to dominance within the neoplasm (Maley and Forrest 2000
). Our study illustrates how the fitness advantage of driver mutations determines whether a mutator phenotype is likely to evolve at all. In the case of strong selection for additional driver mutations, the growth of the most aggressive clone (the clone with the most driver mutations) is very rapid, so that many cells that are ‘susceptible’ to acquiring the next driver mutation are rapidly produced. Mutator mutations are assumed to be selectively neutral in the model; mutator mutations therefore accrue only through genetic drift or by hitchhiking on the most aggressive clones. When two or more mutator mutations are required to generate the mutator phenotype [as would be the case for recessive mismatch repair (MMR) genes (Markowitz and Bertagnolli 2009
)], the rate at which mutator genes drift to dominance within the most aggressive clone is much slower than the rate at which the most aggressive clone acquires the next driver mutation. In this way, mutator mutations are effectively removed from the tumour population as a result of their being outcompeted by the most aggressive clones. When selection for additional driver mutations is moderate, cells carrying mutator gene mutations are not outcompeted so rapidly, and so a mutator phenotype can evolve. A mutator cell then acquires driver mutations faster than its nonmutator counterparts, and so the mutator phenotype indirectly bestows a selective advantage. When selection for additional driver mutations is very weak, intratumour clone dynamics are driven nearly entirely by drift (not clonal selection). In this case, acquiring a mutator phenotype, which still accelerates the rate of driver gene mutation accumulation, does little to accelerate the rate of clone growth, and so selection for mutator cells is weak.
In the light of this result, it is instructive to consider what order of fitness advantage is bestowed by driver mutations within tumours. There is a lack of empirical measurements of the relative fitness of different tumour clones, although modelling efforts have suggested that drivers may cause only slight increases in fitness. Beerenwinkel et al. (2007
), using their mathematical model of clonal evolution, suggested a relative fitness advantage of about 1% per driver mutation (i.e. sd
= 0.01; making cells 1% more likely to have surviving offspring) was sufficient to cause progression of colorectal adenomas to cancers in a reasonable time. Similarly, in their study of subclone expansion, Siegmund et al. (2011
) saw only evidence for weak selection in CRCs. Bozic et al. (2010
) estimated a fitness advantage of only about 0.4% per driver mutation for glioblastoma and pancreatic cancers. These predictions are in the ‘moderate’ range of selective advantages in our model. Furthermore, given the disparity in the number of putative driver mutations found in different types of cancer (Salk et al. 2010
), it is likely that the fitness advantage of driver mutations differs significantly between cancer types. Thus, whether or not genetic instability is a hallmark of a particular cancer type may reflect, to some degree, the strength of selection for new driver mutations in the cancer type. Of course, fitness advantages will also differ between mutations at different loci, even within the same cancer type.
We have assumed that all driver mutations have the same consequence for a cell's fitness. In reality, mutations of different genes will have different consequences for fitness; for example, that distinct mutations of the SETD2
gene are found in different intratumour clones in the same renal carcinoma (Gerlinger et al. 2012
) indicates a strong selective pressure for inactivation of this particular gene. Consequently, the rate of clonal evolution within an individual tumour may change over time, and so the likelihood of evolving a mutator phenotype may change over time. For example, it is likely that the driver mutations with the largest selective effects would expand initially (as they would outcompete the clones with weaker driver mutations), leading to weaker driver mutations later in progression. In this case, genetic instability would be unlikely to evolve at the onset of tumour growth and would likely feature in the later stages of carcinogenesis. Indeed, this appears to be the case in Barrett's oesophagus where the detection of aneuploidy is a strong predictor of cancer development risk (Maley et al. 2004
Unless deleterious mutations were very common, they did little to impede the progression of the most aggressive clones, supporting Beckman and Loeb's previous conclusion (Beckman and Loeb 2005
). In fact, we observed that carcinogenesis could be actually accelerated
by increasing the strength of selection against deleterious mutations, as strong selection against deleterious mutations served to increase the relative fitness of clones without deleterious mutations. This observation highlights how competition within tumours likely influences the pattern of clonal evolution. We had initially hypothesised that the rapid accrual of deleterious mutations would inhibit the growth of mutator clones, as have others previously (Cahill et al. 1999
; Tomlinson and Bodmer 1999
; Komarova and Wodarz 2004
; Komarova et al. 2008
). Whilst this was the case when selection for additional driver mutations was very weak, or if deleterious mutations were very common, moderate to strong selection for driver mutations caused cells that had acquired deleterious mutations to be rapidly outcompeted and removed from the tumour, particularly in the case where driver and housekeeper loci were of equal abundance. Increasing the likelihood of a cell acquiring a deleterious mutation (by increasing the abundance of housekeeper loci in each cell) did slow tumorigenesis, and indeed suppress the evolution of a mutator phenotype, indicating that deleterious mutations can act as a brake on carcinogenesis. However, the strength of selection for driver mutations dominated the dynamics of the time to cancer and the emergence of a mutator phenotype. Our model predicts that deleterious mutations will not accrue within tumours. This hypothesis could be tested by examining ‘cancer genomes’ for evidence of clonal mutations (high frequency within the tumour) that are predicted to impede cell growth or survival, or genetically engineering them into cells.
Tumours that developed a mutator phenotype, when more than one mutator mutation was required to switch to a mutator phenotype, tended to develop it after the tumour had acquired a significant driver mutation burden, which was typically late in tumour progression. This time-delay was due to the time taken for mutator mutations to accrue by drift, or by hitchhiking, in the most aggressive subclones. Therefore, our model predicts that if tumour growth is initiated without an increased mutation rate (Bodmer et al. 2008
), then a mutator phenotype is likely to feature only later in progression, which is again consistent with the data from Barrett's oesophagus (Maley et al. 2004
When only a single mutator mutation is required to switch to a mutator phenotype (case M
= 1), cancers always evolved with a mutator phenotype and carcinogenesis was universally faster. Thus, our model predicts that mutator phenotypes drive efficient carcinogenesis and that mutator mutations should be selected in tumours. This supports the conclusion of Beckman and Loeb (Beckman and Loeb 2006
). The case M
= 1 represents the scenario when mutator genes have a dominant effect; that is, mutating a single copy of the mutator gene causes a switch to a mutator phenotype. However, whether or not mutator genes act dominantly in cancers is uncertain. The mismatch repair genes operate in a recessive fashion (Markowitz and Bertagnolli 2009
) and the genetic basis of other mutator phenotypes seen in cancer is uncertain. It is noteworthy that in model systems, there are examples of dominant negative mutations in TP53
that are associated with genetic instability (Song et al. 2007
The level of genetic diversity within a tumour was related to both the selective advantage attributable to driver mutations and the basal mutation rate. Thus, our model predicts that genetic diversity within a tumour is a proxy measure of both the mutation rate and strength of clonal selection. Similarly, the model of Durrett et al. (2011
) predicted that the degree of genetic diversity within a tumour was largely determined by the age of the tumour, and the stepwise fitness gain of each additional driver mutation. These data illustrate that genetic diversity within a tumour population is not necessarily indicative of an elevated mutation rate, but instead may signify that tumour clones are experiencing only weak selection.
We note that our model makes a number of gross oversimplifications in describing carcinogenesis that could potentially impact the model dynamics. First, driver genes in our model represented only proto-oncogenes or haploinsufficient tumour suppressor genes, that is, a cell acquiring a mutation to a single driver gene locus gained an increase in fitness. In reality, many driver genes are recessive tumour suppressor genes, and so no increase in fitness is caused until both a selectively neutral first hit, and a second hit are acquired at the tumour suppressor locus. In this regard, a mutator phenotype might cause particularly efficient tumorigenesis if many selectively neutral first hits are required for cancer production. Second, we assumed that mutations accrue in a monotonic stepwise fashion. The mutator phenotype CIN is a hallmark of many cancer types (Rajagopalan et al. 2003
): CIN tumours frequently show whole- or part-chromosome arm aberrations, wherein many genes located on a particular chromosome have been ‘mutated’ in a single mutational event. Also, copy number gains are frequently observed in CIN; genetic gains are potentially reversible events, as additional genic copies may later be lost. Thus, CIN cancers are unlikely to accrue mutations in the monotonic stepwise fashion we have described in our model, and so, the dynamics of the evolution of CIN may differ from our model's predictions. Third, we have assumed that mutator genes are themselves selectively neutral, that is, that mutations of mutator genes do not cause an increase in fitness. Some driver genes may double as mutator genes; for example, mutation of the intestinal tumour suppressor gene APC
is sufficient for tumorigenesis (Lamlum et al. 2000
), but may also instigate CIN (Fodde et al. 2001
); similarly mutations to the TP53
tumour suppressor are usually considered driver mutations and are associated with genetic instability (Song et al. 2007
). Selection dominates evolution in our model, and so direct selection for mutator genes would likely alter the dynamics. Fourth, we have assumed that all driver genes have equivalent effects on fitness when mutated and, similarly, that all genes are equally likely to be mutated. The patterns of mutation and selection would likely alter if this unrealistic assumption were relaxed. Fifth, we have neglected to describe spatial heterogeneity within a tumour. Clonal interference, whereby two spatially adjacent clones with similar fitness impede each other's growth, slows the rate of tumour evolution (Martens et al. 2011
). Such spatial considerations may also affect the evolution of mutator clones. Relatedly, we have assumed that the fitness of cells within the tumour is strictly relative; this leads to the least fit cells being rapidly outcompeted by fitter cells, and so clones carrying deleterious housekeeper mutations are rapidly driven to extinction. Relaxing this assumption, for instance by competing cells only with their ‘neighbours’, may alter the clonal dynamics (and indeed overall tumour dynamics), particularly for clones bearing deleterious mutations.
In summary, we have constructed a model of the evolution of genetic instability during tumour progression. Our model incorporates clonal expansions and deleterious mutations and allows the mutation rate to evolve, whereas previous models have considered only some of these issues. Our model predicts that the strength of selection for additional driver mutations determines whether or not a cancer is likely to evolve a mutator phenotype and suggests that future efforts should be devoted to measuring the degree of fitness effects of mutations in carcinogenesis.