Mutation and Cancer: The Antecedents to Our Studies of Adaptive Mutation
John Cairns

It is clear that the experimental evidence supporting many currently popular hypotheses concerning mutational processes is quite inadequate.

(Drake 1970)

LITTLE excuse is needed for still being interested in mutation. We are here thanks to the germline mutations experienced by our ancestors, and, at least in the developed nations of the world, more of us die from somatic mutations than from any other single cause. For the evolutionary biologist, the process of mutation presents no problems. For anyone attempting an overview of cancer research, however, the process has become increasingly obscure. It was this obscurity that prompted my laboratory in the 1980s to look again at the interplay between mutation and selection.

Germline mutation: To some extent, the particular mutational changes that generated the evolutionary tree can be deduced from comparisons of the differences in sequence that distinguish the different branches of the tree. It is not easy, however, to investigate what were the causes of those changes. Perhaps for that reason, it is customary to think of mutation as being driven by chance events attributable to the natural instability of nucleic acids and the inherent imprecision of polymerases, and these may not in a sense have any identifiable external cause.

What does have a clearly identifiable causal chain, however, is the extent to which each organism is protected against changes in sequence. As Drake (1969) showed, mutation rates (per basepair) go down as complexity increases. The thought is that as organisms increased in complexity and lifespan, they presented an ever larger target for chance events, and their survival required the evolution of a multitude of protective mechanisms — starting with the use of double-stranded nucleic acids and then going on to include proofreading polymerases, the monitoring and repair of DNA, and culminating apparently in some form of large-scale monitoring of the developing embryo. It is not clear, however, whether the degree of protection against errors has evolved to optimize mutation rates (each species tending to retain the level of variability that had allowed it to evolve in response to past changes in the environment) or simply to optimize the return from investing in protective mechanisms (a matter of costs vs. benefits).

Because the germline is physically isolated from the environment, the obvious thought is that in large multicellular organisms, mutation rate may be optimized for the germline, whereas the cost: benefit ratio is optimized in somatic cells, for if the germline is not in contact with the environment, its mutation rate must be largely in the hands of intrinsic determinants. This view is usually attributed to Weismann, even though he himself claimed that “The primary causes of variation is always the effect of external influences. Were it possible for growth to take place under absolutely constant external influences, variation would not occur” (Weismann 1893). Similarly, Darwin believed that the rate of genetic variation was determined by the environment, which is perhaps why the opening chapter of The Origin of Species deals with the apparent increase in rate of variation when species are domesticated. So the party line at the beginning of the 20th century was anything but clear.

The first suggestion that mutation rates could be raised artificially came as a casual aside in a speech by De Vries (1904) when he suggested that the newly discovered Röntgen rays might be mutagenic, but it was some time before suitable systems became available that could be used to demonstrate the mutagenicity of physical and chemical agents.

For practical purposes, however, evolutionary mutation rates were regarded as being constant under normal conditions. If you are considering what kind of selection would have resulted in some particular observed combination of traits coming to the fore, you have to simplify, and the first step is to assume a constant rate of mutation.

Cancer and somatic mutation: The history of ideas about somatic mutation is very different because the subject is of immediate, practical importance. It is the process that underlies (or soon will underlie) roughly half of all human deaths. It is responsible for most forms of cancer and is probably responsible for a large proportion of all deaths from cardiovascular disease. Unlike classical (germline) geneticists, who are more interested in genetic mechanisms and natural selection than in mutagenesis, somatic geneticists tend to be concerned with mutagenesis rather than the selective processes that may operate in somatic tissues.

The early microscopists saw that each cancer appears to be made up of a family of cells that have inherited the same appearance and invasive characteristics. Indeed, the presence of chromosome abnormalities in cancer cells was part of the earliest evidence that genetic traits are carried by chromosomes. So it was a natural thought that cancers were the result of “somatic mutation” (Tyzzer 1916). It was therefore no surprise when X rays were shown to be mutagenic because they had long been known to be carcinogenic. Later, the discovery of X-chromosome mosaicism allowed the demonstration that nearly all cancers were indeed clonal (Fialkow 1974). More surprisingly, this was also true for the clumps of cells that make up atheromatous plaques in the walls of arteries (Benditt and Benditt 1973).

Cancer research has always been quick to apply discoveries in the basic sciences and sometimes has even been in the lead. In the 1930s, much effort had gone into establishing which chemicals were carcinogenic and which were not, and in the early 1940s, two classes of chemical carcinogens were shown to be mutagenic—the nitrogen mustards by Auerbach in England and the nitrosamines by Rapaport in Russia. As soon as DNA was established as the genetic material, these and other chemical carcinogens were quickly tested for their interaction with DNA (Boyland 1952) and their mutagenicity for bacteria (Demerec 1948), and, conversely, chemicals that had been shown to be mutagenic were tested for their carcinogenicity (Boyland and Horning 1949).

It was therefore natural to suppose that most human cancer was caused by either radiation or certain reactive chemicals in our environment. Once ways for assaying mutagenicity using bacteria or yeasts had been developed, a search began for the major mutagens to which we are exposed. This proved to be a popular enterprise because it was initially coupled with the belief that most cancer is the product of modern industry and that it can be prevented by stopping industrialists from contaminating our diet and environment.

There was a branch of cancer research that was giving us direct information about the causes of cancer—the science of epidemiology. However, because it is a somber discipline that is somewhat remote from the day-to-day hurly-burly of clinical medicine and the laboratory sciences, it has not been accorded the respect it deserves. Yet it is a source of precise information about the fate of millions of the very animal in whom we are most interested, and this sets limits on the kind of factors that must be important in determining the incidence of the various kinds of cancer (Doll and Peto 1981).

First and foremost, it is clear that most types of cancer do have external causes. When populations migrate from one country to another, they leave behind the cancers that are typical of their birthplace and then take on the cancers that are typical of their new home. Next, it is clear that modern industry cannot be held responsible for more than a small fraction of all cancers because the spectrum of cancers found in each of the developed nations of the world is not related to the kinds of industries they support; for example, the types of cancers that arise in the United States are not markedly different from those in essentially agrarian countries such as Iceland and New Zealand. Last in this short list of important facts is the observation that carcinogenesis represents an accumulated response to prolonged exposure to causative factors; for example, the risk of lung cancer for old smokers is determined by both the number of cigarettes they currently smoke and the amount they smoked half a century earlier. The same is true for experimental carcinogenesis: a single exposure to a carcinogen given to a young mouse will permanently alter its susceptibility to subsequent exposures.

The list of factors that have been identified by epidemiologists as contributing to the incidence of one or more types of cancer is far more peculiar than most people imagine and not at all what might have been supposed from the work on experimental carcinogenesis. For the industrialized world at the end of the 20th century, the list is headed by tobacco smoke (which is a highly toxic irritant but is not carcinogenic for most experimental animals), various viruses such as hepatitis B and certain papilloma viruses (which are not thought to be mutagenic), infection of the stomach with Helicobacter (which is not likely to be mutagenic), various hormonal factors, too many calories in your diet, and ultraviolet light. Of these, only the last is a conventional mutagen.

It is highly significant, therefore, that skin cancer is the only common cancer that is increased in frequency in people who inherit a defect in nucleotide excision repair (German 1979; Cairns 1981; Kraemeret al. 1994), even though the patients' cells show a greatly raised sensitivity to ultraviolet light and to agents that cause bulky adducts (a category that includes most of the chemical mutagens in our environment). Some people have chosen to argue that the xeroderma pigmentosum patient does not get internal cancers because these take longer to develop than skin cancers, but this argument does not bear scrutiny. Squamous and basal cell carcinomas of the skin, like the common internal cancers, normally tend to occur in old age, and their incidence is a function of lifetime exposure to sunlight. Furthermore, certain other inherited disorders, such as Bloom's syndrome, seem to have no problem in accelerating the development of internal cancers to the point where they appear in young patients. So the least tortuous conclusion is that ultraviolet light may be by far the most important directly acting mutagen that most people encounter. For the other factors listed above, the only thing in common among them is that they are associated with increased cell proliferation (Preston-Martinet al. 1990).

If this argument against the importance of chemical mutagens seems too heretical, consider the following. We can identify members of the population who are awash with chemical mutagens by looking for people who have a high concentration of mutagens in their urine. Three groups stand out: smokers, users of certain semipermanent hair dyes, and patients undergoing cytotoxic chemotherapy. Smokers show only marginally raised rates of nonrespiratory cancers, and no increase in cancer rates has been detected in those who use hair dyes. Also, even though cytotoxic chemotherapy certainly does increase the incidence of other normally rare cancers, this could be because the primary, intended effect of these drugs is to kill cells rather than to cause mutations, so they are strong stimulators of cell proliferation. Most of these points were laid out in great detail 20 years ago (Peto 1977), and they have not lost any persuasiveness since then.

We certainly cannot, however, discard the idea that cancer is a result of somatic mutation. Thanks to the techniques of modern molecular biology, it has become possible to prepare at least partial inventories of the sequence changes found in cancer cells. And, as has been expected, the cells of each cancer prove to contain sequence changes in several members of that multitudinous cast of genes now known to be involved in the control of cell multiplication and cell-cell interactions. Furthermore, those few varieties of cancers that have been linked to a mutagen (e.g., skin cancers caused by ultraviolet light and liver cancers caused by aflatoxin) show the kind of mutations that are characteristic of the mutagen (Brashet al. 1991; Bressacet al. 1991). So there is no conflict here between the molecular biologist and the epidemiologist.

But what about the vast majority of cancers? They are apparently the result of a stimulation of cell proliferation rather than the result of any obvious exposure to mutagens. What is the relation between excessive cell multiplication and the accumulation of sequence changes in the genes affecting cell behavior?

We know virtually nothing about the rules that govern the growth and turnover of cells in multicellular organisms. More than 90% of all human cancers arise in our epithelia, where the only cells that survive throughout our lifetime (and therefore can accumulate damage) are the stem cells at the base of the epithelium (Cairns 1975). These cells make up only a small minority (Barrandon and Green 1987). Little is known about their behavior and about the rules that limit the opportunities for competition between stem cells (Loeffleret al. 1987), but an argument can be made that the incidence of cancer may depend more on the opportunities for selective competition between stem cells than on their rate of mutation (Cairns 1975; Tomlinsonet al. 1996).

The evidence from epidemiology, experimental carcinogenesis, and molecular biology suggests that a rather large number of genes have to be mutated to convert a normal cell into a fully invasive cancer cell. The human body probably contains ~1010 stem cells. If each of these divides once every other day (the value for mice is once a day), a human lifetime will contain roughly 1014 stem cell divisions. So it is hard to see how any one of these cells can acquire enough mutations to become cancerous, unless some process is raising the mutation rate far above its usual value of ~10−7 mutations per gene per cell division. The problem is made much worse if, as seems likely, the major variables that determine cancer rates are not mutagens. So perhaps we should be looking for some other driving force that can be linked to (or triggered by) cell proliferation.

Two rather similar hypotheses have been proposed. If a single mutation is enough to disrupt the rules of cell replacement so that an expanding group of stem cells is created, this one step would increase the target for the further mutations that are needed to make the cells fully cancerous; this model was originally developed by epidemiologists as one of the ways of explaining the sharp rise in cancer rates that occurs with advancing age (Armitage and Doll 1957; Fisher 1958). Alternatively, the probability of developing cancer would be greatly increased for any cell that acquired a mutator mutation (Nowell 1976; Loeb 1991). There is support for each of these ideas; expanding clones of precancerous cells are indeed found in tissues such as the uterine cervix, which can be monitored over periods of months or years; mutations are often found in genes that are known to be involved in DNA repair and in the control of mutation rates.

The mutator hypothesis is thought to have gained further support with the discovery that roughly half of all human cancers bear mutations in p53 and that the P53 protein (“the guardian of the genome”) is one of the crucial elements that link the checkpoints in the cell cycle to the state of the genome. Against this must be set the awkward fact that although the cells in most cancers contain many point mutations they do not show a raised rate of point mutations when cultivated in vitro (Eshleman and Markowitz 1995; Meuth 1996; Strauss 1997) though they may show great chromosome instability (Lengaueret al. 1997).

One other factor, which I think may be the most important, has to be brought into the analysis of carcinogenesis (Cairns 1975). The cells that make up each multicellular animal do not appear to be in competition with each other. For example, every tissue in a tetraparental animal maintains equal proportions of each of the two kinds of cell unless one of the cells comes of a more aggressive, cancer-prone stock (Tuffrey 1973); an epithelium such as skin maintains its fine X-chromosome mosaicism for the lifetime of mosaic females (Deamant and Iannaconne 1986; Iannaconneet al. 1987);the cells of each intestinal crypt very, very seldom succeed in spreading into neighboring crypts (Liet al. 1994), and so on. It appears that each of us is a fine patchwork of small clones of proliferating cells that are not in competition with each other. In other words, the invention of multicellularity has been accompanied by the development of mechanisms that prohibit natural selection.

In summary, one of the problems for cancer research now is to find someway of relating the molecular biology to the epidemiology. On the one hand, cancer cells contain point mutations in genes that are known to regulate cell behavior. On the other hand, cancer cells usually do not show a raised rate of point mutations when growing in vitro; the known causes of the cancers in developed nations are not mutagens; and certain major kinds of inherited defects in DNA repair have little or no effect on the rate of most types of cancer. None of these findings might be considered sufficient on its own to disturb the conventional view of carcinogenesis. Taken together, however, they strongly suggest that something is missing.

Spontaneous mutation in Escherichia coli: Because the conventional wisdom about the causes of human cancer seemed so uncertain and incomplete (Cairns 1981), we decided in the early 1980s to return to the simplest system for studying the interactions of mutation and selection, namely, the process that produces spontaneous mutations in bacteria. According to the classical experiments of Luria, Delbrück, Newcombe, Cavalli-Sforza, and the Lederbergs, bacterial mutants arise at a steady rate during growth, in advance of whatever selective procedure is used to demonstrate their presence; in other words, they are not a Lamarckian response to need. (The references are too well-known to need repetition here.)

Since that initial stage in the history of bacterial genetics, the picture has become more complicated. Shapiro (1984) pointed out that the classical experiments had not ruled out adaptive mechanisms of mutation because the selective procedure used to determine the number of mutants was lethal for any bacterium that was not already expressing the mutant phenotype. In 1990, R. Owen (personal communication) discovered that Delbrück himself had made the same comment much earlier (Delbrück 1946). We now know that the only mutants that could be picked up by those selection procedures had to have arisen at least five generations earlier, so the old experiments were not a test of the effect of selection on mutation rates.

A second complication was introduced by Ryan, who showed that populations of bacteria would steadily accumulate selectable mutations, even when the cells were not able to divide (Ryanet al. 1963) and when they were apparently not replicating their DNA (Ryanet al. 1961). But for Ryan's untimely death, his group would have gone on to test whether mutation in stationary phase was dependent on selection and whether it was confined to the selected class of mutations (G. W. Grigg, personal communication). (Twenty-five years later, when I was writing what I thought would be our first and last paper on mutation under conditions of selection, I was on a six-month sabbatical in France at the International Agency for Cancer Research, and the only paper by Ryan I had access to was one he published in Nature, and that reference had to suffice as our acknowledgment that he had studied the subject long before we had.)

During the next 25 years, the mechanisms underlying spontaneous mutation ceased to attract much attention. The reason, I think, was largely the triumphant development of molecular biology, which inevitably diverted everyone's attention away from what might be called the natural history of bacteria. It was, however, partly the opportunities for rewarding study of artificial mutagenesis and partly the discovery of DNA repair that gave a totally new insight into how DNA is protected against mutagenesis.

Our worries about the cause of the mutations underlying cancer eventually prompted us in 1981 to consider what factors determine spontaneous mutation rates in bacteria. Because most forms of cancer do not appear to be dependent on exposure to conventional mutagens and are not made more common by defects in the repair of bulky adducts, I had concluded that major rearrangements of DNA had to be the crucial, rate-limiting mutations (Cairns 1981). Shortly after this, human cancer cells were found to contain point mutations in the human counterparts of several viral oncogenes, and I realized that I had made a logical error. The proper conclusions should have been that (1) exposure to point mutagens is not usually the rate-limiting factor and (2) the point mutations found in cancer cells must therefore be the result of some process that, in a sense, occurs spontaneously. Because of my sloppy thinking, however, we started by looking at what determines the rate of spontaneous movement of an insertion sequence. The results, unfortunately, were fickle and unreproducible.

At that point, chance intervened. Stephan Miller was measuring reversion rates of a lacZam mutation by conventional fluctuation tests and observed that in one genetic background, the number of revertants formed the classical Luria-Delbrück distribution, but in another background, it formed a Poisson distribution. This suggested that the pathways leading to mutations during growth in a nonselective medium and to mutations during stationary phase on selective plates were not exactly the same. A similar conclusion could have been drawn from the results of a much earlier study (Geiger and Speyer 1977) that had shown that a mutation in purB greatly reduced the frequency of all those mutations that could arise on selective plates but had no effect on mutations (like those studied by Luria, Delbrück, and Lederberg) that had to have occurred before selection, during the period of previous growth. Inexorably, we were drawn into studying the effects of selection and growth on the spectrum of spontaneous mutation, and the effect of different genetic backgrounds on spontaneous point mutations and on the movement of insertion sequences.

Meanwhile, various unusual forms of spontaneous mutation had been reported. One of these was the excision of an integrated fragment of μ bacteriophage that placed lacZ next to the araB promoter (Shapiro 1984); its spectacular feature was the fact that the event was confined to cells that had been starving for several days and it appeared to depend on selection. The other unusual class of spontaneous mutations were those that allow expression of cryptic genes (Hall 1982), particularly the movement of an insertion sequence that activates a cryptic gene for the fermentation of salicin (Reynoldset al. 1981). These also arise during growth only rarely and are effectively confined to long periods of selection, in some cases (such as cancer, perhaps) because more than one gene has to undergo mutation for the new trait to be expressed.

Our first experiments looked at these various strange classes of spontaneous mutation and the more orthodox reversion of a lacZam mutation. They showed that mutation before selection and mutation during selection are affected differently by changes in medium and by differences of genetic background. Because there were so many experiments waiting to be done and we had only meager resources for doing them, I wrote to Hall in 1986 and suggested that he, too, should look at some of these issues. That led to two papers on “adaptive mutation” (Cairnset al. 1988; Hall 1988).

Adaptive mutation: In the nine years since those two papers were published, a growing number of people have been investigating the interaction between selection and mutation in the life of microorganisms. It would be foolish of me to attempt a general review of the literature because I no longer have it at my fingertips, but I feel that I can safely mention some of the main developments.

The issue that attracted the attention of the neo-Darwinists was, of course, the notion that some types of mutation occur only when they confer an advantage, that is, when they are being selected. The clearest example seemed to be the μ excision that allows transcription of lacZ from a neighboring araB promoter (Shapiro 1984). Everyone agrees that the excision occurs in starved cells and not in growing cells. I originally believed that excision occurred only in the presence of selection. This last conclusion came under attack (Mittler and Lenski 1990), and eventually it became clear that in certain circumstances, excision can occur in starved cells in the absence of selection (Foster and Cairns 1994; Maenhaut-Michel and Shapiro 1994; Sniegowski 1995). Astonishingly, however, it appears that the process of excision may not be completed until after the cell resumes growth because the exact sequence remaining at the site of excision depends on whether growth has resumed either because the cell has excised μ and can now use lactose or simply because its normal source of energy has returned (Maenhaut-Michel and Shapiro 1994). In other words, selection really is determining what happens, so this example has moved from obscurity to clarity and now back to obscurity again.

Point mutations in the normally cryptic ebgA gene of E.coli have been reported to behave rather like the aralac fusion because the exact form of the selection appears to determine which sequence is retained (Hall 1997). Perhaps the most spectacular cryptic genes, at least in terms of their function, are the genes of Pseudomonas putida that code for certain catabolic enzymes. These are also decryptified efficiently under selective conditions, apparently in the absence of growth (Thomaset al. 1992; Kasaket al. 1997).

In an effort to dissect the pathway(s) for stationary phase mutation, we chose the example of reversion of a frameshift in an episomal lacZ (Coulondre and Miller 1977) because it is a point mutation that is largely confined to stationary phase (Cairns and Foster 1991). Some time after we had started this work, Rosenberg acquired our strains and joined in the project. Now, as a result of the work by the two groups, a detailed picture has emerged of the events that create this frameshift and then either preserve it or discard it, but I shall not attempt to review the literature here. To complicate matters, however, it is now clear that different types of mutation must have somewhat different pathways because they do not all have the same time course (Mackayet al. 1994) or the same genetic requirements (Bridges 1994). It seems that when bacteria retire into stationary phase, they face an ever-changing internal environment that may be more varied and challenging than their straightforward existence when growing exponentially.

For want of suitable markers, it has been difficult to determine the rate at which unselected mutations accumulate in stationary phase. This has now seemingly been settled, however, at least for the time being. Certain classes of unselected mutations can be shown to accumulate linearly during the linear accumulation of selected mutations (Foster 1997). It now looks, therefore, as if selection is not necessary for mutation in stationary phase. We should keep in mind, however, the strange case of μ excision mentioned above, where sequencing has shown that the entire process of mutation is not apparently completed until the cell has resumed growth. This would have never have been discovered without sequencing, so we should not assume automatically that the processes leading to the more conventional classes of mutation can be completed in the absence of growth until they have also been checked by sequencing.

Just in the last year, the analysis of mutation in stationary phase has acquired a further, fascinating complication. Some time ago, two instances had been recorded where mutants that arose on selective plates appeared to have a raised frequency of mutations in other genes (Boe 1990; Hall 1990). Three groups have now shown that the frequency of unselected mutations is far higher in cells that bear a selected change than in the rest of the population (Foster 1997; Torkelsonet al. 1997; K. B. Low, A. Zysman and F. Hutchinson, personal communication). In other words, most mutations that arise during stationary phase seem to occur in a subpopulation of cells that undergo a much higher mutation rate than the rest. The idea that adaptive mutation might be confined to a hypermutating minority was first suggested many years ago by Hall (1990).

Cells in stationary phase that have acquired a selected mutation are ~50 times more likely to bear an unselected mutation than the cells that make up the rest of the population. A little simple algebra (see appendix) shows that to achieve this, the hypermutating minority must comprise less than 2% of the population and must have a mutation rate that is at least 200 times higher than the rate for the rest of the population. This raises the interesting possibility that the bulk of the population may not be undergoing any mutations at all.

Although some of the mutating minority will be stable hypermutators as the result of a mutator mutation (Maoet al. 1997), most of them are apparently only transient mutators because their descendants do not show araised mutation rate. Such a temporarily unstable minority could be the result of transcriptional or translational errors that affect the genes involved in limiting the rate of spontaneous mutation (Ninio 1991; Boe 1992). Ninio has calculated the likely frequency of such “translational” hypermutators, but he had to combine several estimated rates, not one of which is known much better than to within a factor of 10, and that could easily account for the small discrepancy between his estimate and the actual observations (see appendix).

We should, however, consider a possible minor addition to Ninio's hypothesis. Many of the proteins involved in the maintenance of the correct base sequence are normally present in fairly high numbers; although a defective protein may make (or fail to repair) a changed base, its nondefective counterparts can then undo the damage. It may be only when growth becomes impossible and the concentration of these proteins decreases that individual defective proteins are able to cause changes in sequence. We may find that transient mutators are confined to the terminal stages of growth and to stationary phase. If so, the concentration of polymerases and other repair proteins in starved cells may have been influenced by the evolutionary opportunities that arise when nongrowing populations contain an unstable minority. When growth ceases, there is presumably no way for a cell to determine whether or not it requires a mutation to start growing again. What more natural than to hedge your bets? If the environment has undergone a major change and mutation is required for the resumption of growth, the mutants will be there. If two mutations are needed (as is the case for the activation of certain cryptic genes), the frequency of such double events will be much higher than would be expected for strictly independent events. If, however, growth has stopped because it is autumn and the environmental change is simply the usual temporary retreat from mellow fruitfulness, the majority of the population will wake up in spring, unburdened by needless mutations.

In summary, a significant proportion of the mutations that arise “spontaneously” in bacteria are apparently the result of changes in DNA that accumulate in stationary phase. One of the first steps when growth resumes is presumably the repair of these accumulated changes, which makes unusually large demands on the systems for repair, so this is the moment when mistakes are most likely to occur. Because a small minority of the cells in stationary phase are transient mutators, the frequency of multiple mutations in the cells that come out of stationary phase is much higher when resumption of growth has required a mutation. In other words, populations of cells that have just undergone selection for some novel trait show a much higher frequency of unselected mutations than populations that have not been subject to such selection, even though their subsequent mutation rate may be perfectly normal.

Carcinogenesis: These recent discoveries show that the response of bacteria to selection is more complicated than anyone could have guessed 50 years ago. Many classes of mutation seem to be less a matter of exposure to mutagens and errors made during replication, and more a matter of failure to rectify damage accumulated during prolonged periods when metabolism and repair have to be held to a minimum.

This fits nicely with what is known about the epidemiology of human cancer. Stem cells in G-zero can be compared to a population of nongrowing bacteria. When undisturbed, their multiplication is strictly controlled; there is no competition between neighboring stem cells and no selection pressure, and, therefore, they will only slowly accumulate mutations. On the other hand, if growth is stimulated so that the stem cell population has to increase temporarily, this will provide the opportunity for selection (and perhaps allow less time to be set aside for correcting the accumulated changes in their DNA) and could, therefore, cause a sharp increase in the frequency of cells with multiple mutations. Indeed, the importance of mutational events in nongrowing cells has been reinforced by the recent demonstration that certain tumor cell lines, which are deficient in mismatch repair, have normal mutation rates during growth but raised rates when they are not growing (Richardset al. 1997).

Taken collectively, these results may explain why the accumulation of cancer cells bearing multiple sequence changes seems to be driven more by agents that stimulate cell proliferation than by the rather low levels of mutagens found in our environment. It was with thoughts such as these that we began our study of spontaneous mutation almost 20 years ago.

Acknowledgments

First and foremost I want to acknowledge Pat Foster's continuing contributions to the study of adaptive mutation. In my enforced absence, she has delineated the subject by means of an exemplary combination of careful experiments and impartial analysis. I would like to thank David Dressler, Monica Hollstein, Frank Stahl, and an anonymous reviewer for help with this manuscript. Last but not least, I am also pleased to have this opportunity to thank Jan Drake, who has come to my aid in one way or another on many occasions during the past 40 years.

APPENDIX: THE ARITHMETIC OF MUTATOR MINORITIES

For the sake of simplicity, I shall assume that the population contains a small proportion (p) of high mutators, all of which have a mutation rate that is M-fold higher than the rate for the majority of the population (the low mutators).

Two mutations (or classes of mutations) are measured: A-mutations and B-mutations. In the low mutators, they occur at frequencies a and b; in the high mutators, they occur at frequencies of aM and bM.

The overall frequency of A-mutations is a[pM+(1p)]. (1) The proportion of As that are in high mutators is pM[pM+(1p)]. (2) The proportion of As that are in low mutators is (1p)[pM+(1p)].

Therefore, the overall frequency of B mutations among the A mutants will equal bM{pM[pM+(1p)]}+b{(1p)[pM+(1p)]}=b{[pM2+(1p)][pM+(1p)] (3)

The absolute rate of mutation, even in the high mutators, is much less than unity. Therefore, the population that has not acquired the A mutation will not be significantly depleted of high mutators; like the starting population, it will contain p high mutators and (1 − p) low mutators.

Therefore, the frequency of B mutations among the non-As is b[pM+(1p)] (4)

The ratio (frequency of Bs among the As)/(frequency of Bs among the non-As) is R=Equation3Equation4=[pM2+(1p)][pM+(1p)]2~[pM2+1][pM+1]2. (5) If all mutations are caused by the high mutators, R=bMpbM=1p. (6)

Three measurements have been made: the frequency of A mutations, the frequency of B mutations among the A mutants, and the frequency of B mutations in the rest of the population. There are, however, four independent variables (a, b, p, and M), so it is not possible from these three measurements to determine the absolute values of the four variables.

Ninio (1991), however, has suggested that the high mutators arise as the result of replicational and translational errors made during the synthesis of DNA, RNA, and the various polymerases and repair enzymes that are concerned with preservation of the genome, and he has calculated that the frequency of such high mutators (p in the present symbolism) should be ~5 × 10−4 (by their very nature, his calculations are not very precise, so we should not attach too much weight to the exact value of his estimate).

Interestingly, Boe (1992) has observed that an increase in the fidelity of translation (as the result of a change in certain ribosomal proteins) roughly halves the rate of spontaneous mutation, which suggests that at least half of all mutations are arising in the high mutating minority. From Equation (1), we see that for this to be true, (M + 1) must be ≤1/p. So if Ninio's estimate of p is correct, M would have to be ≤1999. From Equation 5, it follows that R should be ≤500. In fact, the values of R observed by Foster (1997), Torkelson et al. (1997), and K. B. Low, A. Zysman and F. Hutchinson (personal communication) are closer to 50 than to 500. Ninio may have therefore underestimated the proportion of cells that are hypermutators.

This leads to an interesting thought. It is easily conceivable that Ninio's estimate of p is too low by a factor of 10. If so, the real value of 1/p could be equal to the observed value of R. As Equation 6 shows, this is the case when all mutations are caused by the high mutator minority and most of the population are not accumulating any mutations. Under these special conditions, any third class of mutation will, of course, be no more common in double mutants than in single mutants, and that is a testable prediction.

LITERATURE CITED