Too Many Mutants with Multiple Mutations

Abstract

It has recently become clear that the classical notion of the random nature of mutation does not hold for the distribution of mutations among genes: most collections of mutants contain more isolates with two or more mutations than predicted by the mutant frequency on the assumption of a random distribution of mutations. Excesses of multiples are seen in a wide range of organisms, including riboviruses, DNA viruses, prokaryotes, yeasts, and higher eukaryotic cell lines and tissues. In addition, such excesses are produced by DNA polymerases in vitro. These “multiples” appear to be generated by transient, localized hypermutation rather than by heritable mutator mutations. The components of multiples are sometimes scattered at random and sometimes display an excess of smaller distances between mutations. As yet, almost nothing is known about the mechanisms that generate multiples, but such mutations have the capacity to accelerate those evolutionary pathways that require multiple mutations where the individual mutations are neutral or deleterious. Examples that impinge on human health may include carcinogenesis and the adaptation of microbial pathogens as they move between individual hosts.

INTRODUCTION

In 1991, Jacques Ninio argued that microbial populations would contain clones initiated by cells that had experienced some transitory attenuation of replication fidelity and therefore expressed a higher-than-average mutation frequency (Ninio, 1991). At least in bacteria, he reasoned, these accidents would not much affect the average mutation frequency, but they could sharply increase the numbers of mutants bearing two or more mutations. Unlike mutator mutants, which are at a selective disadvantage because their offspring carry an ever increasing load of deleterious mutations, cells exposed to transient phenotypic hypermutation would suffer little disadvantage except from their immediate mutations. This was an unusual paper for Genetics because it was rather speculative and did not rest upon a body of new experimental evidence, but I was the editor handling the paper, and I believed that it made an important case for a new view of the mutation process. The paper was well received in the mutagenesis community but slowly sank into the misty mid-regions of history.

In the early months of the current millennium, while analyzing large numbers of mutants generated in vitro by the DNA polymerase of bacteriophage RB69, I noticed that many contained two or more well separated mutations in the same reporter molecule, each of which would have produced a mutant phenotype as a single mutation. A quick calculation revealed that there were many more such “multiples” than were expected, had all the mutations been distributed at random among reporter molecules. I put the matter aside for a year or so, but the implanted observation made the same phenomenon capture my attention when perusing other mutational spectra, and soon I began to accumulate a considerable list. This story was eventually submitted for publication with the title, “Too many mutants with multiple mutations” and was rejected immediately on the grounds that the editorial board abhorred alliteration in titles (although puns seemed to be acceptable). Accordingly, I retitled the paper “Clusters of mutations from transient hypermutability” (Drake et al., 2005). However, I prefer “multiples” over “clusters” because the latter has a separate meaning in animal genetics, the identical progeny of a single, usually mitotically expanded germ-line mutation.

The phenomenon of “too many multiples” implies that different mutation frequencies exist within different fractions of the subject populations, whether these be organisms, tissues, cells, or polymerase molecules. What processes could fuel such a pattern? In addition to this interesting question, it was also immediately obvious that sufficient frequencies of multiples could drive processes of interest to health professionals. Adaptations requiring more than one new mutation would be accelerated, especially when the single mutations were neutral or deleterious. It is already well known that the adaptation of bacterial pathogens to new hosts can be strongly promoted by heritable mutator mutations and that retroviral infections pass through dramatic mutation-dependent evolutionary phases that recur within serial hosts. It is also clear that carcinogenesis entails a considerable string of mutations, more than would be supported by ordinary rates of single mutations, and might be similarly accelerated not only by mutator mutations (Loeb et al., 2003), but also by transient phenotypic hypermutation (but see the constraint described below in the Separations

CRITERIA

Early in the process of collecting examples of multiples, whether or not in excess of expectations based on randomness, it became clear that one should distinguish, and remove from consideration, certain kinds of multiples that appeared to be, or probably were, the consequence of a single error. One of these involved clusters of adjacent changes (mostly base-substitution doublets) for which it seemed likely that the first error strongly predisposed to the next. Another occurred among closely spaced clusters that could be described as a single templating event involving, for instance, template switching and imperfect palindromes. In addition, deletions so large as to spare little of the mutation-reporter sequence should be removed from consideration.

In a few systems, it is possible to distinguish between mutations that do and do not produce a mutant phenotype in the reporter system, in which case only the mutations detectable as singles should be considered first, with the piggybacking, singly undetectable mutations considered separately as a special class. Often this distinction cannot be made, but because the undetectable mutations are typically only a few-fold more frequent than the detectable mutations, whereas multiples are often in large excess over the expectations of a random distribution, the conclusion of “too many multiples” is not abrogated.

Most of the estimates of expected numbers of multiples that follow are easily made. If mutations are randomly distributed among reporter sequences, then, by the Poisson distribution, the expected number of multiples depends on M, the number of sequenced mutants, and F, the mutant frequency. The average number of mutations per mutant a= −ln(1–F). The expected number of mutants with two mutations (“doubles”) is E₂ = Ma²e^−a/2F. For F ≤ 0.1, this expression is closely approximated by E₂ = MF/2; for instance, for F = 0.1, the longer calculation predicts 0.0996 doubles, the shorter 0.1000. For higher multiples, E₃ = aE₂/3 and E_i+1 = aE_i/(i + 1).

UBIQUITY

Table 1 presents a list of spectra with multiples (Drake et al., 2005) supplemented with a few spectra accidentally encountered since then. Because I anticipated little further gain from an exhaustive search of all published spectra, the list is necessarily somewhat anecdotal, which does not matter in the present context and may provide a pleasing exercise to someone else. Table 1 also lists the spectra in the original collection that lacked examples of multiples, for which display space was previously not adequate. The list is ordered by genomic complexity from riboviruses to humans, with the examples of polymerases examined in vitro directly following the corresponding organism. The current list contains 39 examples of multiples in excess, in a few cases by small factors and in many by large factors. The list also contains 17 examples where no multiples were observed. Finally, the list contains seven examples where multiples were observed but were not in excess of the predictions of randomness; some of these are revealing and will be considered later.

TABLE 1.

“Multiples” in mutational spectra

System	Genotype or strain	Reporter gene	F	M	Dexp	Dobs	Tobs	>Tobs	Notes	Reference
Tobacco mosaic virus	WT	MP	4.3 × 10−2	17	0.40	3	3			Malpica et al., 2002
HIV-1 RT in vitro	WT	lacZα	6.4 × 10−2	434	13.9	24			a,b	Bebenek et al., 1989
		lacZα	2.3 × 10−2	99	1.2	2			a,b	Eckert and Kunkel, 1993
			1.3 × 10−1	97	6.2	19	1		a,b	Eckert and Kunkel, 1993
Bacteriophage T4	WT	ac	1.6 × 10−5	68	0.00053	0				Wang and Ripley, 1998
	43tsL141	ac	1.8 × 10−5	170	0.0016	0				Wang and Ripley, 1998
T4 pol gp43 in vitro	Exo−	lacZα	1.1 × 10−2	121	0.65	2			b	Kroutil et al., 1998
Phage T4/RB69	WT	rI	3.1 × 10−5	79	0.0012	0			c	Bebenek et al., 2001
	Exo−	rI	2.0 × 10−2	72	0.72	3			c	Bebenek et al., 2001
	PolY567A/S/T	rI	2.7 × 10−2	147	2.0	3			c	Bebenek et l., 2001
RB69 pol gp43 in vitro	PolY567A	lacZα	2.1 × 10−2	1324	14	151	6		b,d	Drake et al., 2005
		lacZαud	1.9 × 10−1	237	22	23	1		b,e	Drake et al., 2005
Herpes simplex virus	WT	supF	4.9 × 10−4	80	0.020	7	1		f	Drake et al., 2005
			1.3 × 10−4	85	0.0054	0			f	Hwang et al., 2002
		tk	6.0 × 10−5	66	0.0020	1			f	Lu et al., 2002
	PAAr5	supF	1.0 × 10−3	87	0.045	4	2		f	Hwang et al., 1999
	Y7	supF	1.9 × 10−3	53	0.050	0	1		f	Lu et al., 2002
			4.7 × 10−4	92	0.021	0			f	Hwang et al., 2002
		tk	4.0 × 10−2	66	1.3	6			f	Lu et al., 2002
	Y7 Exo−	supF	4.8 × 10−3	249	0.60	11			f	Hwang and Hwang, 2003
	YD12	supF	1.5 × 10−3	77	0.059	2			f	Hwang et al., 1999
Escherichia coli	WT	supF	2.1 × 10−7	38	0.000004	1			f	Akasaka et al., 1992
		lacI	2.0 × 10−6	167	0.00017	0				Schaaper et al., 1986
		lacId	1.3 × 10−7	368	0.00002	2				Oller and Schaaper, 1994
		lacId	1.1 × 10−7	413	0.00002	0				Schaaper and Dunn, 1991
			2.4 × 10−7	269	0.00003	0				Sargentini and Smith, 1994
		egbR	3.0 × 10−8	73	0.000001	1				Hall, 1999
	mutD5	lacId	1.5 × 10−3	498	0.37	4				Schaaper, 1988
	mutL−	lacId	3.5 × 10−5	243	0.0043	2				Schaaper, 1993
		lacId	1.2 × 10−5	196	0.0011	1				Schaaper, 1993
	mutHLS	lacId	2.6 × 10−7	487	0.00063	0				Schaaper and Dunn, 1987
	dnaE911	lacId	0.8 × 10−7	476	0.00002	1				Oller and Schaaper, 1994
	dnaE173	rpsL	9.2 × 10−6	56	0.00026	1	1			Mo et al., 1991
E. coli pol I(K) in vitro	WT	lacZα	4.7 × 10−3	118	0.28	3			b,g	Bell et al., 1997
	Y766A/S	lacZα	3.8 × 10−2	224	4.3	5			b,g	Bell et al., 1997
Sulfolobus acidocaldarius	WT	pyrE	3.4 × 10−7	108	0.00002	0				Grogan et al., 2001
Saccharomyces cerevisiae	WT	SUP4-o	1.9 × 10−6	297	0.00028	2				Kunz et al., 1990
	rad1	SUP4-o	1.3 × 10−5	242	0.0015	1				Kunz et al., 1990
		URA3	2.2 × 10−6	35	0.00004	0				Lee et al., 1988
	WT	CAN1	2.0 × 10−7	21	0.000002	2			h	Venkatesan et al., 2006
	pol3L612F/M/K/G	CAN1	2.0 × 10−6	76	0.000075	3			h	Venkatesan et al., 2006
S. cerevisiae pol δ in vitro	WT	lacZα	3.3 × 10−3	182	0.30	1			b	Nick McElhinny et al., 2007
	L612M	lacZα	2.2 × 10−2	401	4.3	13			b	Nick McElhinny et al., 2007
	D520V	lacZα	2.3 × 10−2	486	5.7	9			b	Nick McElhinny et al., 2007
Rat cell line	WT	cII	1.3 × 10−4	99	0.0064	1			i	Watson et al., 1988
Mouse cell line	WT	gpt	2.0 × 10−5	43	0.00043	0		1(5)	j	Ashman and Davidson, 1987
Chinese hamster cell line	WT	gpt	1.2 × 10−4	18	0.0011	2			k	Romac et al., 1989
			1.3 × 10−5	58	0.00038	0			k	Tindall and Stankowski, 1989
Monkey cell line	WT	supF	8.2 × 10−4	120	0.049	0			f	Cabral-Neto et al., 1993
Human cell lines	WT	HPRT	9.0 × 10−6	200	0.0009	6	1		l	Lichtenauer-Kaligis et al., 1996
			1.8 × 10−5	51	0.00046	0				Ikehata et al., 1989
			3.0 × 10−6	33	0.00005	0				Giver et al., 1993
Mouse tissue	WT	cII	9.5 × 10−5	182	0.0086	1			m	Harbach et al., 1999
		lacI	4.2 × 10−5	348	0.0073	2			n	de Boer et al., 1997
			2.3 × 10−5	435	0.0050	7		1(5)	o	Buettner et al., 2000
Monkey tissue	WT	HPRT	3.0 × 10−6	40	0.00006	0			p	Harbach et al., 1995
Human tissue	WT	HPRT	1.9 × 10−4	82	0.0078	5		1(4)		Colgin et al., 2002
			6.0 × 10−6	31	0.00009	0				Rossi et al., 1990
Rat hepatoma pol β in vitro	WT	lacZα	1.1 × 10−1	296	15.7	≤16			b,q	Kunkel, 1985
Chick embryo pol β in vitro	WT	lacZα	7.3 × 10−2	144	5.2	≤1			b,q	Kunkel, 1985
Rat pol β* in vitro	WT	HSV-tk	1.4 × 10−3	86	0.060	2			r	Opresko et al., 1998
	T79S	HSV-tk	2.7 × 10−3	79	0.11	3	3	6(4–9)	r	Maitra et al., 2002
	Y265C	HSV-tk	4.4 × 10−2	79	1.7	31	8	6(4–5)	r	Maitra et al., 2002

All of the Systems are in vivo except for the several DNA polymerases, which are labeled “in vitro.” The reporter gene is natural unless noted to be a transgene. WT = wild type. F = frequency of spontaneous mutants, adjusted where possible and appropriate for the efficiency of detecting mutants and for mutations that do not produce a phenotype. M = number of mutants sequenced exclusive of large deletions and ignoring insertions of mobile elements. D_exp = number of doubles expected from a random distribution of mutations. D_obs = observed number of mutants with two mutations, T_obs = observed number of mutants with three mutations, > T_o = observed number of mutants with more than three mutations, with numbers of mutations inside (s). Multiple mutations exclude tandem mutations, synonymous mutations, and complex mutations that arise repeatedly and appear to be templated by a specific, imperfect and usually reverse repeat.

^aHuman immunodeficiency virus reverse transcriptase.

^bAbout 40% of lacZα mutants are lost during the assay, so that F = (observed mutant frequency)/0.6. The system distinguishes between mutations that are detectable or not when present as singles, and only detectable mutations are tabulated.

^cThe RB69 and T4 replicases (gp43) have both polymerase (Pol) and exonuclease proofreading (Exo) sites. The data derive from experiments in which T4 replication was driven by a plasmid-borne RB69 gp43 and the rI reporter gene was in T4. The Pol^Y567A/S/T entry is the sum of three different substitutions at the RB69 gp43 Y567 with very similar mutator properties, F being the combined value for each mutant weighted by its M.

^eThe data derive from the same experiments as above but the mutations were undetectable as singles but were detected as piggybackers on detectable mutations. F = 1.851 × 10⁻¹ was the combined value for each supplement regimen weighted by its M. The expected number of triples was 1.5.

^fsupF is a tRNA transgene from E. coli and of a type that may be generally hypermutable, whereas tk is an endogenous gene and displays an approximately normal mutation rate.

^gK indicates the Klenow fragment of pol I. Y766A/S are mutator mutants.

^hThe data derive from fluctuation tests for which F values were not available, but in such tests, the mutation rate and F are similar, so the former were used. The pol3 data were pooled from four mutator mutants, F being the weighted average of the individual values.

ⁱEmbryonic fibroblast cell line with cII transgene from phage λ.

^jA9 cell line with gpt transgene from E. coli. The 5 mutations were BPSs scattered throughout gpt.

^kOvary cell line with gpt transgene from E. coli. First report also listed one double containing one missense and one synonymous mutation.

^lTK6 lymphoblastoid cell line with a human HPRT cDNA transgene at five different sites. Also two doubles containing one missense or indel and one synonymous mutation.

^mMouse liver, lung and spleen with cII transgene from phage λ.

ⁿMouse liver with lacI transgene from E. coli.

^oNumerous mouse tissues with a lacI transgene from E. coli.

^pHPRT mutations arising in vivo in cynomolgus monkey T-lymphocytes.

^qBecause doubles were combined with duplications and complex mutations, the D values are ≤.

^rRecombinant enzyme made in E. coli and bearing an added Gly-Ser at its 5′ end

Almost all organisms for which mutational spectra are available, and almost all similarly tested DNA polymerases, produce more multiples than predicted from random distributions in at least one spectrum (Drake et al., 2005). Many such spectra contain only one or two multiples. Therefore, many of the spectra displaying no multiples would probably display one or more had many more mutants been examined.

The kinds and relative frequencies of mutations observed in multiples, including base- or base-pair substitutions (BPSs) or indels (insertions or deletions of any size but most commonly single-base deletions and insertions), are usually similar to those observed in mutants with single mutations (data not shown).

TRIVIALITIES

A key step in obtaining the DNA sequences of mutation reporters is often amplification by the polymerase chain reaction, which is usually done with a somewhat error-prone enzyme and is sometimes preceded by much more error-prone reverse transcription. Provided that sufficient RNA or DNA molecules are present at the first step of amplification, the introduced errors will be a small fraction of the final molecules and will not provide false multiples. All of the entries in Table 1meet this criterion.

It is instructive to compare certain parameters of spectra with multiples in excess versus spectra with no multiples at all (Table 2).

TABLE 2.

Spectra with numbers of multiples in excess of expectations from random distributions (+) or with no multiples at all (−) as functions of mutant frequency (F), number of mutants sequenced (M), and year of publication (Y)^*

Multiples	F	−log F	M	Y
+	3.0 × 10−8	7.52	73	1999
+	8.0 × 10−8	7.10	476	1994
+	1.3 × 10−7	6.89	368	1994
+	2.0 × 10−7	6.70	21	2006
+	2.1 × 10−7	6.68	38	1992
+	1.9 × 10−6	5.92	297	1990
+	2.0 × 10−6	5.70	76	2006
+	9.0 × 10−6	5.05	200	1996
+	9.2 × 10−6	5.04	56	1991
+	1.2 × 10−5	4.92	196	1993
+	1.3 × 10−5	4.89	242	1990
+	2.0 × 10−5	4.70	43	1987
+	2.3 × 10−5	4.64	435	2000
+	3.5 × 10−5	4.56	243	1993
+	4.2 × 10−5	4.38	348	1997
+	6.0 × 10−5	4.22	66	2002
+	9.5 × 10−5	4.02	182	1999
+	1.2 × 10−4	3.92	18	1989
+	1.3 × 10−4	3.88	99	1988
+	1.9 × 10−4	3.72	82	2002
+	4.9 × 10−4	3.31	80	1999
+	1.0 × 10−3	3.00	87	1999
+	1.4 × 10−3	2.85	86	1998
+	1.5 × 10−3	2.82	77	1999
+	1.5 × 10−3	2.82	498	1988
+	1.9 × 10−3	2.72	53	2002
+	2.7 × 10−3	2.57	79	2002
+	3.3 × 10−3	2.48	182	2007
+	4.7 × 10−3	2.33	118	1997
+	4.8 × 10−3	2.32	249	2003
+	1.1 × 10−2	1.96	121	1998
+	2.0 × 10−2	1.70	72	2001
+	2.1 × 10−2	1.68	1324	2005
+	2.2 × 10−2	1.66	401	2007
+	4.0 × 10−2	1.40	66	2002
+	4.4 × 10−2	1.36	79	2002
+	4.7 × 10−2	1.33	17	2002
+	6.4 × 10−2	1.19	434	1989
+	1.3 × 10−1	0.89	97	1993
−	1.1 × 10−7	6.96	413	1991
−	2.4 × 10−7	6.62	269	1994
−	2.6 × 10−7	6.59	487	1987
−	3.4 × 10−7	6.47	108	2001
−	2.0 × 10−6	5.70	167	1986
−	2.2 × 10−6	5.66	35	1988
−	3.0 × 10−6	5.52	33	1993
−	3.0 × 10−6	5.52	40	1995
−	6.0 × 10−6	5.22	31	1990
−	1.3 × 10−5	4.89	58	1989
−	1.6 × 10−5	4.80	68	1998
−	1.8 × 10−5	4.74	51	1989
−	1.8 × 10−5	4.74	170	1998
−	3.1 × 10−5	4.51	79	2001
−	1.3 × 10−4	3.89	85	2002
−	4.7 × 10−4	3.33	92	2002
−	8.2 × 10−4	3.09	120	1993

^*The table omits seven entries from Table 1 in which multiples were present in nearly the predicted numbers: HIV-1 RT in vitro, second entry; phage T4/RB69 in vitro, third entry; RB69 pol gp43 in vitro, second entry; E. coli pol I(K) in vitro, second entry; S. cerevisiae pol δ in vitro, third entry; and both rat hepatoma and chick embryo pol β in vitro.

One trivial explanation for multiples is that they are sequencing errors (to be considered separately from amplification errors); that is, they do not exist except as a result of the act of measurement (somewhat à la Heisenberg). Sequencing errors presumably do occur. If they were sufficiently frequent to impact the overall pattern, what parameter of Table 2 might reveal this? Taking an analytical hint from microeconomics (Levitt and Dubner, 2006), one may surmise that the frequency of sequencing errors will have decreased during the steady procedural improvements of the past two decades, so that the proportion of spectra with an excess of multiples would decrease over time. However, it does not (Table 3) but instead rises. In addition, the frequency of spectra with multiples does not appear to vary inversely with the quality of the research group data not shown). Thus, sequencing errors are unlikely to create an important fraction of observed multiples.

TABLE 3.

Spectra with multiples in excess (Yes) or absent (No) as a function of year of publication

	Multiples
Year	Yes	No	Fraction with multiples in excess
1986	0	1
1987	1	1
1988	2	1
1989	2	2
1990	2	1
1991	1	1
1992	1	0
1993	3	2
1994	2	1
1995	0	1
1996	1	0
1997	2	0
1998	2	2
1999	5	0
2000	1	0
2001	1	2
2002	7	2
2003	1	0
2004	0	0
2005	1	0
2006	2	0
2007	2	0
86–90	7	6	0.54
91–95	7	5	0.58
96–00	11	2	0.85
01–05	10	4	0.71
86–96	15	11	0.58
97–07	24	6	0.80

Two other parameters of Table 2, M and F, might relate to the frequency with which spectra display multiples. The impacts of these factors are shown in Table 4. First, the more mutants sequenced, the greater should be the chance of encountering an infrequent multiple. The numbers fall in the expected direction but with unconvincing p values, so that, within the range of these examples, M has at most a weak effect on the detection of multiples. Second, because the proportions of expected multiples in a spectrum must increase with F, it will be correspondingly easier to detect an excess of multiples. This appears to be a strong determinant of detection. Note also that there is no obvious a priori reason why the frequency of sequencing errors should vary with the observed mutant frequency.

TABLE 4.

Parameters of mutants with and without excess multiples

Group	No. of spectra	Mean M	Median M	Median −log F	Median F
Excess multiples	39	196.9	97	3.72	1.9 × 10−4
No multiples	17	135.6	85	5.22	6.0 × 10−6
p for difference*		0.31	0.77	0.0015

^*The p values are two-sided, for the mean M by the Mann-Whitney test, and for the medians by the median test.

If the mutant frequency is underestimated, then the expected frequency of multiples will be underestimated. Why might F be underestimated? No mutation screen detects all mutations; for instance, most base-substitution mutations produce a phenotype too weak to be detected under all laboratory screens except blind sequencing. However, because the analysis is usually restricted to detectable mutations, the calculations hold; as noted previously, undetectable mutations piggy-backing upon detectables are usually only a few-fold more frequent than multiples composed exclusively of detectable mutations, whereas factors by which multiples are in excess are usually larger.

A more interesting contributor to false excesses might be phenotypic lag, the interval between the creation of a mutation and the time its expression becomes sufficient for phenotypic detection. If the lag lasts for several generations, which is sometimes the case, then both F and thus the predicted number of multiples will be underestimated, and excesses of multiples will be correspondingly overestimated. The effect can be specified. Putting aside for present purposes the stochastic nature of mutation, as a population grows, it begins to mutate as its size approaches the reciprocal of the mutation rate (although the first mutation will usually have arisen at some earlier time). In that “first” mutating generation (g ≡ 1), on average, one mutation occurs, producing one mutant and one nonmutant progeny. (If one mutation produces two mutant progeny [Witkin and Sicurella, 1964; Witkin and Parisi, 1974], the argument must be recast but the overall results will be similar.) The mutant goes on to generate a clone of 2^(g–1) mutants in the succeeding (g–1) generations until the mutants are scored. In the next generation, two mutations occur on average, and each generates a clone of size 2(g–2), thus contributing 2 × 2(g–2) = 2(g–1) mutants to the final population. Thus, assuming that mutant and non-mutant cells grow at the same rate, each mutating generation contributes the same number of mutant cells to the eventual total of g2^(g–1) mutants. If phenotypic lag lasts for p generations, then the total number of detected (= expressed) mutants will be (g–p)2^(g–1). Thus, the efficiency of detection will be the ratio of expressed mutants to total mutants, (g–p)/g, and the effect of phenotypic lag will decrease as g increases. In practice, most mutation-reporter systems have been adopted in part because they express mutations well, which includes having short phenotypic lags (such as a single generation). An interesting exception may be the halophilic archaeon Haloferax volcanii, in which the number of chromosomes per cell appears to be very large so that considerable segregation must occur until a recessive mutation can be expressed (Mackwan et al., 2007).

Multiples can arise simply by sequential accumulations of singles rather than in virtually simultaneous bursts, but if all the genomes share a continuously constant mutation rate, then multiples will not occur in excess.

If most multiples were caused by mutator mutants in the population, then the phenomenon would not be particularly novel. A semiquantitative argument was made previously (Drake et al., 2005) that took into account the frequency of mutators in cultures of laboratory-adapted E. coli and Salmonella typhimurium (lower than expected from mutation pressure, presumably because of the reduced fitness of mutators in the absence of strong selection for new mutations) and the impact of strong bacterial mutators on the average gene. The observed frequency of doubles F_D is the mutant frequency F times the proportion of doubles among mutants (F_D = FD/M). Strong mutator mutations increase the value of F for a gene by at most about 100-fold (stimulating mutation at some sites by much more but at many sites by much less). In laboratory populations, the frequency of mutator mutants is ≤10⁻⁵. Thus, the frequency of doubles due to mutators will be ≤(100F)²(10⁻⁵) = F²/10 and the fraction of doubles caused by mutators will be ≤FM/10D. This fraction is ≤0.1 for all of the entries in Table 1 for which D_obs is substantially greater than D_exp, so that in such bacteria, at least, heritable mutator mutations produce few of the observed doubles.

RATES

Mutation rates are usually estimated from mutant frequencies, population sizes (a measure of the number of generations), and key assumptions about the geometry of replication (such as exponential, linear, or mixed). In most organisms whose genomes are encoded by DNA rather than RNA, replication is exponential and the mutation rate μ is assumed to be the same for all replication events. This cannot apply for transient hypermutation during replication, in which multiples may arise within a single generation but propagate with the standard μ thereafter. However, there are at least two methods to fractionate a population into two or more subpopulations, each with its own fractional composition of the population as a whole and its own mutation frequency. Given sufficient sample sizes, it might then become possible to model the distribution of hypermutagenic events during the growth of the total population, although such modeling will not be presented here.

One method, whose derivation was provided previously (see Supporting Text in Drake et al., 2005), depends on the availability of a spectrum with both doubles (D) and triples (T), and on the condition that most of the multiples were contributed by the minority, high-F subpopulation. Assuming that a population contains two subpopulations, S₁ and S₂ (S₁ >S₂), with respective mutation frequencies F₁ and F₂ (F₁ < F₂), then F₂ = 3 T_obs/D_obs, S₂ = 2FD_obs/MF₂²e^{− F2}, S₁ = 1–S₂, and F₁ = –ln[(1–F–S₂e-F₂)/S₁]. This method is strikingly simple but would be difficult to extend to more than two subpopulations because of the difficulty of untangling multiples produced by more than one hypermutating subpopulation.

Another method is based on the progressive fitting of the four parameters to the data using mixtures of Poisson distributions and an iterative expectation-maximization procedure. This method can be expanded to more than two subpopulations but quickly becomes calculation-intensive with additional subpopulations and/or increasing M.

When these methods were applied to the TMV results summarized in Table 1, they produced similar results (Table 5): most of the population had F ≈ 0.01 (instead of the observed F ≈ 0.04) while 3 to 4% of the population had F = 1 to 3%. Note that the iterative method can be continued until a very large p value is obtained, as here, and can be supplemented by additional subpopulations if desired.

TABLE 5.

Deconstructing a TMV population

Method	S1	F1	S2	F2	p
Algebraic	0.97	0.011	0.03	3.0	0.40
Iterative	0.96	0.013	0.04	1.2	0.98

The TMV population had F = 4.253 × 10⁻², M = 17, D_exp = 0.40, D_obs = 3, T_exp = 0.0058, and T_obs = 3.

In practice, because transient hypermutability can be imagined to occur by diverse mechanisms (as discussed later), it is reasonable to surmise that populations often contain more than two characteristic S_i/F_i fractions. Indeed, a population of molecules produced by the DNA polymerase of phage RB69 simply could not be analyzed by the above methods. However, the methods may be helpful when most of the multiples are produced by only one subpopulation.

SEPARATIONS

Most mutation reporters are 10² to 10³ bases long. Most spectra have too few multiples to discern whether they are clustered or scattered within the reporter sequence. In a few cases, however, the distance distribution between the components of multiples has been determined.

Among mutants of the human HPRT gene in normal primary kidney tubular epithelial cells, multiples were in strong excess (Colgin et al., 2002): F ≈ 2 × 10⁻⁴, M = 82, D_exp ≈ 0.008, D_obs = 5. Ignoring one pair of adjacent mutations, the distances between doubles were 1, 6, 5012, 7023, and 25024 intervening bases. In addition, one quadruple was observed, with distances of 13, 214 and 4895 intervening bases. These distances clearly display strongly nonrandom clustering (p ≈ 0.002), suggesting “a mechanistically linked origin.” In contrast, multiples whose components arose sequentially rather than in a burst had an intervening-base distribution expected for mutations of independent origin (p ≈ 0.8) (Finette et al., 2000).

A nonrandom pattern of clustering was also observed among multiples arising in an E. coli transgenic lacI reporter in the mouse (Hill et al., 2004), where the separations were exponentially distributed with a median separation of 120 bases in a target of about 1.4 kilobases (kb), and were thus described as “chronocoordinate” events. Subsequently, 65 such multiples were subjected to resequencing over about 20 kb outside of the reporter sequence, and ten were found to contain additional mutations (Wang et al., 2007). (When 130 singles were thusly sequenced, only one had a single mutation in the outside regions.) When these additional mutations are considered, the size of the hypermutated region turned out to be ≤30 kb.

Multiples produced in vitro by the DNA polymerase of phage RB69, however, were composed of a random sample of all mutations (Drake et al., 2005). Although the RB69 target was smaller (≈270 bases) than for the mammalian studies performed in vivo (≈1000–25000 bases), the small-distance tail of the mammalian distributions encompassed the RB69 distribution, so the difference is probably real.

These results reveal that the tract of transient hypermutation can extend from a few bases to about 30 kb, and that the shapes of the distribution of intervening bases depends on the system. A further insight can be gained from the TMV results (Malpica et al., 2002). With a reporter sequence of 804 bases, three doubles had separations of 210, 236 and 313 intervening bases and three triples had separations in their component doubles of 21, 279, 286, 336, 336, and 641 intervening bases. Here there is no hint of clustering. However, if the mutation frequency in the reporter sequence applied to the entire 6395-base genome, then these 6 mutants would have had an average of roughly 20 mutations per genome. About two thirds of these mutations would have been indels, and the average base substitution is probably more deleterious in riboviruses than elsewhere, so these genomes would not have survived. Therefore, either transient hypermutation in this system is spatially delimited despite the lack of clustering, or only the tail of a long distribution could be observed among viable multiples whose mutations happened to fall exclusively within the reporter gene.

Because the several mutations required for carcinogenesis must hit genes widely scattered in the human genome, the limit of about 30 kb over which multiples were scattered in the above two mammalian examples somewhat decreases the chance that transient phenotypic hypermutation could promote cancer. Alternatively, in the singles and in multiples that showed no outside mutations, a different pattern might lurk, one that scattered multiples far more widely. An entirely new kind of search is needed to address this possibility.

ORIGINS

The causes of transient hypermutation remain obscure. Ninio (1991) pointed out that it could result when errors of transcription or translation produced mutagenic proteins, and mutator DNA polymerases come immediately to mind. Random DNA damage seems to activate SOS systems in a small fraction of bacteria per generation, increasing the mutation rate for perhaps an hour (e.g., Little, 1991; McCool et al., 2004). DNA resynthesis following DNA mismatch repair might produce clusters within roughly a kilobase if the new DNA strand was not itself subject to mismatch repair, a matter that remains open (Ninio, 2000), and similar clustering might be produced by certain types of gene-conversion events (Ninio, 1996). An error-prone component in the repair of DNA double-strand breaks might also produce clustered multiples (Ponder et al., 2005). When a protein crucial for fidelity is present in small numbers per cell, random asymmetries in its segregation at cell division could yield a transiently hypermutating progeny cell, an example being the MutL and/or MutS components of DNA mismatch repair (Feng et al., 1996). Random physiological states that reduce fidelity are also candidates. Protein mis-folding is a common anomaly that might contribute to replication errors. Perhaps occasional mutagenic tracts are initiated by an incorrectly positioned or composed replication complex that persists for a while. There is a considerable literature demonstrating that nutrient-deprived stationary-phase cells tend to enter a phenotypically mutable condition, sometimes with a hypermutating subpopulation (Bull et al., 2000; Foster, 2004; Ponder et al., 2005). Altogether, there is an impressive number of ways in which the best-evolved fidelity schemes gang aft agley (Burns, 1786).

There are obvious strategies to explore some of these possibilities. Errors of translation are sometimes mutagenic and can be reduced by specific chemical or genetic interventions. SOS systems can be repressed mutationally. Chaperones assist protein folding and can be overexpressed, and some proteins can be unfolded and refolded in vitro with recovery of function. Cell size can be enhanced, perhaps ameliorating asymmetries of protein segregation. Note that only changes that reduce mutagenesis, rather than enhancing it, are truly informative in such a situation. A manipulation that enhances the frequency of multiples in a particular system may or may not be enhancing a particular mechanism already generating multiples, whereas a manipulation that decreases the frequency of multiples must necessarily inhibit the mechanism that already generates them.

A paradox lurks among the entries of Table 1 for DNA polymerases acting in vitro. In order to observe too many multiples, hypermutable synthesis must occur in tracts. However, two of the polymerases that produce excess multiples have limited processivity, substantially shorter than the gaps used as mutation reporters. The processivity of the RB69 polymerase is only about 10¹ to 10² consecutive insertions before the enzyme dissociates from its substrate, so that a single molecule will infrequently traverse a 266-base lacZα gap, whereas the number of intervening bases between the components of the numerous observed doubles was not biased toward closeness. Nevertheless, multiples were observed in excess (expected doubles = 14, observed doubles = 151, and 6 triples) (Table 1), and the presence or absence of accessory proteins had little or no effect on the frequencies of multiples (Drake et al., 2005). The processivity of pol β is ≈ 1, so no excess of multiples should be observed. That may have been the case for native rat pol β purified in the early 1980s (expected doubles ≈ 16, observed doubles ≤ 16) (Kunkel, 1985), but multiples were in excess with the same but now aged enzyme preparation in 2006 (expected ≈ 9, observed = 18 and three triples) (L. García-Villada and J. W. Drake, unpublished results). With recombinant rat pol β in the late 1990s, two groups reported excess doubles, 0.06 expected versus 2 observed (Opresko et al., 1998) and 1.3 expected versus 7 observed (Osheroff et al., 1999), although somewhat fewer were detected in yet another test, 3.6 expected versus 6 observed (L. García-Villada and J. W. Drake, unpublished results). With recombinant human pol β, excess doubles were also observed, 1.2 expected versus 6 observed (Osheroff et al., 1999). The possibility of a contaminating polymerase in the recombinant rat enzyme seems to be reduced by the observation that a version of the enzyme with its polymerase activity obliterated mutationally failed either to increase the background mutant frequency of the test system significantly or to introduce any multiples (L. García-Villada and J. W. Drake, unpublished results). A resolution of the apparent paradox of multiples without processivity is likely to be informative.