KINETICS O F MUTATION INDUCTION BY ULTRAVIOLET LIGHT
IN EXCISION-DEFICIENT YEAST
FRIEDERIKE ECKARDT*
AND
R. H. HAYNES
Department of Biology, York University, Toronto, Canada M3.l l P 3
Manuscript received August 13, 1976
Revised copy received November 5, 1976
ABSTRACT
We have measured the frequency of UV-induced reversions (locus plus suppressor) for the ochre alleles ade2-I and lys2-I and forward mutations ( d e 2
adex double auxotrophs) in an excision-deficient strain of Saccharomyces
cereviyiae (rad2-20). For very low UV doses, both mutational systems exhibit
linear induction kinetics. However, as the dose increases, a strikingly different
response is observed: in the selective reversion system a transition to higher
order induction kinetics occurs near 9 ergs/mm2 (25% survival), whereas in
the nonselective forward system the mutation frequency passes through a maximum near 14 ergs/mm2 (4.4% survival) and then declines. This contrast in
kinetics cannot be explained in any straightforward way by current models of
induced mutagenesis, which have been developed primarily on the basis of bacterial data. The bacterial models are designed to accommodate the quadratic
induction kinetics that are frequently observed in these systems. W e have
derived a mathematical expression for mutation frequency that enables us to
fit both the forward and reversion data on the assumptions that mutagenesis is
basically a “single event” Poisson process, and that mutation and killing are
not necessarily independent of one another. In particular, the dose-response
relations are consistent with the idea that the sensitivity of the revertants is
about 25% less than that of the original cell population, whereas the sensitivity
of the forward mutants is about 29% greater than the population average. W e
argue that this relatively small differential sensitivity of mutant and nonmutant cells is associated with events that take place during mutation expression and clonal growth.
INDUCED mutagenesis in microorganisms is a complex, multi-step process
initiated by physicochemical attack on cells by radiations or chemical mutagens to form various types of stable premutational lesions in DNA. W-induced
pyrimidine dimers are a well-known class of such lesions. Normally a large fraction of these dimers, which are also potentially lethal, are removed soon after
irradiation by some mode of “error-free” DNA repair. Premuta tional lesions
which escape error-free repair may undergo a process of fixation or conversion
to informationally altered DNA base sequences, presumably through some mode
of error-prone repair and/or recombination for which replication or pratein s y n thesis may be required. Expression of the mutant base sequence is initiated by
* Present address Department of Biology, Free University of Berlin, D 1000 Berlin 33, Habelschwerdter Allee 30,
Germany
Genetics 8 5 : 225-247 February, 1977
226
F. ECKARDT A N D
R. H.
HAYNES
the synthesis of mutant gene products which give rise to metabolic alterations and
readjustments in the “first” mutant cell. Biochemical disturbances associated
with establishment of the mutant phenotype presumably are damped out or
adequately compensated during the first few divisions of the cell in which the
mutation is first expressed; further multiplication generates mutant clones whose
altered phenotype allows their detection among the nonmutant survivors.
Depending on the mutational assay system employed, varying degrees of competition between mutants and nonmutants can occur as the cells multiply (for
general reviews see BRIDGES
1969; WITKIN1969a, 1975a; KILBEY1975; AUERBACH 1976).
Mutants occur so rarely that conventional biochemical or macromolecular
techniques cannot be used to study directly the intracellular processes involved
in their formation. Thus, many of our ideas ic this area have had to be inferred
from measurements of the dose-response relations for mutant clone formation in
wild-type and repair-deficient strains of bacteria (HILL1965; WITKIN1966,
1967, 1969b; BRIDGESand MUNSON
1968; KONDO
et al. 1970; KONDO1973) and
yeast (MOUSTACCHI
1969; RESNICK
1969; LEMONTT
1971,1972; LAWRENCE& d.
3 974; ECKARDT,
KOWALSKIand LASKOWSKI
1975; LAWRENCE
and CHRISTENSEN
1976). In most assay systems only the initial mutagen dose and the final number
of mutant and nonmutant cells that form visible clones can be measured. [A
recent technique at least makes possible the detection of mutant cells without
requiring them to multiply and form clones (LEntoNTT 1976a, b)]. The shape
of these dose-response relations may be controlled or modified by a number of
parameters, not the least of which are the many physiological and environmental
factors that can influence the processes of fixation, expression and mutant cell
multiplication. Thus it is not surprising that several different types of doseresponse curves have been observed even in closely related mutational systems.
It is customary to classify mutational dose-response curves on the basis of the
power ( n ) by which mutation frequency (mutants per survivor) increases with
dose; the value of ra can be obtained most readily by inspection of log-log plots
of induced mutant frequency uersus dose. The literature contains examples of at
least four main types of response: linear ( n = 1). quadratic ( n = 2) , multiphasic (e.g., linear-quadratic) , and non-integral ( n some fractional power) ;
values of IZ > 2 have been observed occasionally. I n addition, after an initial
increase, some mutation induction curves saturate or reach a maximum and then
decline at high doses.
Early results, especially with X rays, were consistent with the view that
induced mutagenesis is a single-event Poisson process characterized by linear
induction curves in the biologically accessible dose range (ZIMMER1934, 1966;
and STERN1948;
TIMOF~EFF-RESSOVSKY,
ZIMMERand DELBRUCK
1935;SPENCER
VON BORSTEL
1966). Indeed, for any situation in which the relevant premutational lesions are formed in direct proportion to dose, and the expected number
of “biological hits” is proportional to the number of such lesions formed, one
would expect to observe linear induction curves. UV-induced pyrimidine dimers
are formed in DNA in proportion to dose (UNRAU
et al. 1973; FATHand BRENDEL
KINETICS O F INDUCED MUTAGENESIS
22 7
1975) and linear induction kinetics for UV mutagenesis have been reported in a
number of systems (DEMEREC
1951; NOVICK1955; DRAKE1966; BRIDGES
and
HUCKLE
1970; CLEAVER
1976).
I n recent years, however, quadratic (“dose-squared”) induction curves have
been reported frequently for UV mutagenesis in E. coli (BRIDGES,
DENNISand
MUNSON
1967; WITKINand GEORGE
1973; WITKIN1974; DOUBLEDAY,
BRIDGES
and GREEN1975; SKAVRONSKAYA
and SMIRNOV
1975) and yeast (LAWRENCE
et al. 1974). If it is assumed that quadratic kinetics reveal the nature of the initial
steps in the mutational pathway, then at least three ‘Ltwo-event”processes could
be imagined to be at work at the level of premutational-lesion formation and fixation (BRIDGES
1975). First, there are models that postulate the interaction or
cooperation of two lesions (DOUDNEY
and YOUNG1962; BRIDGES
1966; MENNIGMANN 1972; DOUDNEY
1975) or the overlap of two repair events (BRESLER
1975;
BRESLER
et al. 1975; SEDGWICK
1975a) to prcduce the mutant base sequence. The
second postulates an enhanced inhibition of error-free, as compared with errorprone, repair as dose increases, thereby increasing the relative number of premutational lesions available for fixation (BRIDGES
1975). The third postulates a
requirement for two pyrimidine dimers, one to serve as a premutational lesion,
the other to stimulate induction of the error-prone repair system (the ‘Lone
lesion 4-SOS induction” hypothesis) (WITKIN
and GEORGE
1973; RADMAN
1974;
WITKIN1974,1975b). Recently, biochemical experiments have strengthened the
plausibility of the repair-induction hypothesis in E. coli ( GUDASand PARDEE
1975; SEDGWICK
197513, c) and evidence indicating the existence of possibly
1971, 1975) has also appeared; so far
related processes in Ustilago (HOLLIDAY
no direct evidence for UV-induced repair in yeast has been reported.
From a theoretical standpoint the above suggestions are limited by one problem
in common: as presented they account only for quadratic induction curves. Different assumptions must be made to explain the more complex responses that
have also been reported in microorganisms. First, curves which rise with values
of n between one and two have been found (AUERBACH
and RAMSAY
1968;
CHANG,
LENNOX
and TUVESON
1968; DAVIES
and LEVIN1968). Second, biphasic,
linear-quadratic curves have been reported for certain E. coli mutants (WITKIN
and GEORGE
1973; WITKIN1974,1975a) and, in at least one instance, for a wildtype strain (BRIDGES,
MOTTERSHIELD
and COLLELA
1973) ;similar biphasic kinetics have been described in yeast (ECKARDT
1974; ECKARDT
and HAYNES
1976)
and can be read out of data reported for radiation-sensitive diploid strains (LAWRENCE and CHRISTENSEN
1976). Third, biphasic curves which rise linearly to a
maximum and decline at high doses have been found for bacteria (KAPLAN
1956)
and yeast (ABBANDANDOLO
and SIMI 1971; HANNAN,
DUCKand NASIM1976;
1977). Curves of this latter type are particularly difficult
ECKARDT
and HAYNES
to explain on the basis of any of the above-mentioned hypotheses.
We are faced with the question of whether these different kinetic patterns
reflect diff erent molecular mechanisms at the level of premutational lesion
formation and fixation, as seems to be assumed in the models described above;
or whether they might be attributed to various metabolic and other factors which
228
F. ECKARDT A N D R. H. H A Y N E S
come into play during expression and clonal growth, to modify what is basically
a linear induction process. This latter possibility has been raised by SWANSON
(1955) and discussed at length by AUERBACH
and RAMSAY(1968) , AUERBACH
and KILBEY (1971) and AUERBACH
(1976), who cite instances in which the
genetic background of particular strains and the conditions of irradiation and
growth, among other factors, influence the shape of the mutational dose-response
curves. Factors which act on the level of expression and cell multiplication to
influence the probability of mutant clone formation might be expected to lead
to different survival probabilities for mutant and nonmutant cells. On this basis,
mutation and killing cannot be regarded as statistically independent processes,
and any mathematical treatment of mutational dose-response curves should be
general enough to take account of this possibility. In this paper we present such
an analysis for the theoretically simple case of UV-induced mutagenesis in
excision-deficient strains of yeast.
We measured mutation induction frequencies for certain nutritional markers
in a haploid excision-deficient (rad2) strain of Saccharomyces cereuisiae over a
rather wide range of cell survival. We used a selective reversion system in which
we scored locus and suppressor mutants of the ochre alleles ade2-l and lys2-1,
as well as a nonselective forward system in which we scored ade2 adex double
auxotrophs. Two essentially opposite types of induction curves were found in
this one strain: biphasic linear-quadratic curves were obtained with the selective
reversion systems, but linear induction curves rising to a maximum were found
in the nonselective forward system. Qualitatively similar data, to be reported
later, were obtained in RAD wild-type strains. These results led to our derivation
of a general equation for induced mutation frequency as a function of dose based
011 the assumption that mutation and killing need not be independent processes.
The equation provides a good fit for the two types of induction curves found in
our experiments. More particularly. it emphasize; that in addition to modifying
factors which work at the level of mutagenic lesion formation and fixation,
account must be taken of those which act during expression and cell multiplication. We conclude that these latter factors may be more important determinants
of mutation frequencies than has hitherto been realized.
MATERIALS A N D METHODS
Strain: Saccharomyces cereuisiae haploid strain 2105-15, originally constructed by S . KOWAL(1971), was used in all experiments reported here. Its genotype is (a,ade2-2, Zys2-2, hk3,
ural, rad2-20). The reversion experiments were carried out in Berlin (ECKARDT
1974), whereas
the forward mutation experiments were carried out in Toronto in 1976. The UV LD,, exposure dose for this strain as measured in Berlin was 6.2 ergs/mmZ; in Toronto it proved to he
4.0 ergs/mmz (Figure 1). We attribute this difference in UV sensitivity primarily to the different techniques of UV exposure and dosimetry used in the two laboratories, although slight
biological differences among the clones used as stock cultures cannot be excluded.
Media: The following media were employed: YPD: 1% yeast extract, 2% peptone, 2% dextrose, 2% agar (all Difco); YPD,,: similar to YPD but having 10% rather than 2% dextrose;
MM: a minimal synthetic medium composed of 0.67% yeast nitrogen base without amino acids,
2% agar (all Difco), with the addition of the following substances (given in the final concenSKI
KINETICS O F INDUCED MUTAGENESIS
229
F
2-20
IO
20
30
40
50
U v DOSE (ergs/mm2/
FIGURE
1.-UV survival curve for the haploid rad2-20 strain of S. cerevisiae used i n the forward mutation measurements reported here; the points are average values from four independent
experiments. The LD,, dose for this strain as measured in Toronto is 4 ergs/mm2. Different
samples of the same strain used in the reversion experiments carried out in Berlin had a n LD,,
dose of 6.2 ergd-2.
tration) 10 mg/l adenine, 50 mg/l lysine-HC1, 10 mgJl histidine-HCl, 10 mg/l uracil; omission
media: MM-ade or MM-lys, minimal synthetic medium minus adenine or lysine, respectively
(used in scoring revertants).
Prepmation of cell suspensions: Cells were grown on YPD agar for 4-6 days to stationary
phase; they were then washed off the agar, spun down at 3000 rpm for 3 minutes, and washed
twice by centrifugation at 1000 rpm for 2.5 minutes; the top 3-5 ml of this latter suspension
was retained for experimental use. The cell suspensions always contained fewer than 5% double
cells. In the reversion experiments, the cells were sonicated for 30 seconds with a Branson sonifier
S 75 immediately after being washed off the agar to enhance further the fraction of single cells;
no cell killing or significant change in survival curve shape is caused by this treatment, although
the magnitude of the resistant “tail” is reduced.
Irradiation: In Berlin, a low pressure mercury vapor lamp HNS 12 (Osram) was used; the
dose rate incident o n the cell suspensions was measured as 4.0 ergs/mm2 per second with the
dosimeter constructed by SCHAARSCHMIDT
(1970). In Toronto, a GE 15 watt germicidal lamp
was used; the incident dose rate was adjusted t o either 1.14 or 0.57 ergsJmm2 per second as
measured with a Latarjet dosimeter calibrated in Paris. All experiments were carried out under
yellow light to avoid photoreactivation, and the cell suspensions were agitated during irradiation.
Reversion experiments: The reversion experiments were carried out using the ochre alleles
230
F. ECKARDT A N D R . H. H A Y N E S
ade2-I and Zys2-I. A detailed description of the assay procedures used to measure reversions has
already been published (ECKARDT,
KOWALSKI
and LASKOWSKI
1975), and only the main points
are summarized here. 4-ml suspensions of 108 stationary phase cells per ml were irradiated with
various UV doses. Adenine and lysine revertants were scored on omission media (107 cells per
plate; 5-10 plates per point) whereas survivors, appropriately diluted after irradiation according
to the expected yield of viable clones, were scored on MM medium (3 plates per point). The
plates were incubated for 7 days at 30”. Unlike bacteria, a period of growth on supplemented
medium immediately after irradiation is not found to be necessary in yeast for expression of
UV-induced revertants; the reason for this difference in mutational response is not known.
The effective dose received by cells i n a suspension of 108 per ml is less than the physically
measured dose because of the cell “shading effect” in such moderately concentrated suspensions.
and LASKOWSKI
(1963).
We corrected for the shading effect according to the method of HAEFNER
Under our experimental conditions the effect is negligible for suspensions of 105 cells per ml
or less. Therefore, we measured survival curves for suspensions of l o 5 as well as 108 cells per ml
on MM medium in all experiments. For each level of survival, a dose-modifying factor for the
shading effect was obtained from these two curves and applied to the physically measured dose
corresponding to each reversion frequency. Shading effects can be avoided by the more laborious
procedure of irradiating the cells on plates The validity and accuracy of our shading effect correction was confirmed by measuring a few induction curves on plates.
Forward experiments: The forward-mutation system first established by ROMAN(1956)
makes use of the red pigmentation of ade2 clones and allows scoring of mutations in any one of
the six genes which precede the ade2 gene in the adenine pathway (WOODS
and JACKSON
1973).
The double auxotrophs appear as white clones. Suspensions appropriately diluted to yield 300
clones per plate were irradiated, plated on YPD,, and incubated at 30” for five days. The
maximum titer used was 10s cells per ml for which the dose-modifying factor for shading is only
1.10. The total number of surviving clones for each dose was counted, together with the number
of white mutant colonies (pure plus sectored clones) among the survivors. Since ADE+ prototrophs and ade2 petites also produce white colonies, appropriate scoring procedures were adopted
to eliminate such clones from the count of forward (ade.2adez) white double auxotrophs. A more
1977).
detailed description of these techniques is published elsewhere (ECKARDT
and HAYNES
Calculation of induced mutation frequencies: In order to obtain a correct estimate of the
induced mutation frequency, the contribution of surviving spontaneous mutants from the initially
irradiated suspension must be subtracted from the actual mutant count. Thus, the induced
mutation frequency M for each UV dose z was calculated from the formula,
where N , and N , are, respectively, the number of induced mutants and the number of survivors
for any dose z; N,, is the number of mutant colonies actually counted at dose z;N,, is the number of spontaneous mutants; and N o is the number of viable cells in the initial unirradiated
suspension.
THEORY
Consider a homogeneous suspension of N o single, initially viable cells (or
macrocolony-forming units) per unit volume that is uniformly irradiated with
various incident UV doses, z (ergs/mmz). After each UV dose, every cell in the
irradiated population is scored either as a mutant or a nonmutant, and also as a
survivor or a nonsurvivor. To be detected, a mutant must also be a survivor.
Because of the all-or-none character of the end-points scored, single-event Poisson
statistics are applicable to the calculation of both mutation and survival. We
assume that the primary lethal or mutational lesions (e.g., pyrimidine dimers in
KINETICS OF INDUCED MUTAGENESIS
23 1
DNA) accumulate independently and at random in the relevant macromolecular
targets in direct proportion to dose. On this basis we can derive formal mathematical expressions for two related quantities, the induced mutant frequency
(mutants per survivor) and the yield of mutants per cell plated. In this paper we
consider only the case of repair-deficient mutants with essentially exponential
survival curves such as those found for most excision-deficient mutants of S.
cerevisiae. This enables us to introduce the simplifying assumption that the
sensitivity of the cells to killing is a constant independent of dose.
Using the symbols introduced above, the surviving fraction of cells is given by
S(z) = N , / N , , the induced mutant frequency is M ( x ) = N,/N,, and the yield
of induced mutants per cell plated is Y (x)="/No,
where N , is corrected for the
number of surviving spontaneous mutants initially present in the suspension
(equation 1). Note that Y ( x ) = M ( x ) .S(z).
Let k be the sensitivity to killing and m be the sensitivity to UV-induced mutation of the cells; let k, be the sensitivity of those cells that ultimately form
induced mutant clones. For excision-deficient strains with exponential survival
curves, k is a constant independent of dose, and we assume that k, is also a
constant for any given strain, mutational locus and assay procedure. If mutation
and killing are statistically independent processes, then k, = k (ENGELBERG
1962). However, here we wish to consider a more general case in which km is
not necessarily equal to k, that is, the expression and/or detection of mutation
and lethality are allowed to be dependent upon one another. On the basis of these
assumptions we can write the following probabilities:
(i) Probability of survival of a typical non-mutant cell = e-kx
(ii) Probability of mutation = I-e-nzz
(iG) Probability of an induced mutant surviving = e-k.."
The probability of actually detecting a mutant is the joint prolbability of mutation and survival which, from (ii) and (iii) is given by e-k"(l - cmZ).
Thus,
the induced mutation frequency can be written in the form,
The number of mutants is always a small fraction of the number of survivors in
the experimentally accessible dose rsnge, and so no significant error is introduced
by expressing the total number of sur?rivors (nonmutants plus mutants) in the
form N o e*. If we denote the ratio of the mutant to Eonmutant sensitivities to
killing by the parameter 6 = k,/k, then equation (2) can be rewritten in the form
M ( 2 ) = g(l-G)Rz(l-e*s)
(3)
If the mutant and nonmutant sensitivities are identical ( k , = k, or 6 = 1) then
the induced mutation frequency is given simply by
M(s;6=1) = I-eaz
+
= mx - m2z2J2 . . .
(4)
For the very low mutant frequencies that normally occur ( m z < < l ) one would
232
F. ECKARDT A N D R. H. HATNES
not expect to observe any departure from linear induction kinetics because the
quadratic and higher order terms in equation (4)remain vanishingly small at
the highest UV exposures that can be employed experimentally. However,
departures from linearity frequently are observed and such departures can arise
in two, not mutually exclusive, ways: (i) mutant and nonmutant cells might
have different probabilities of survival ( 6 # 1) ;and/or (ii) cell mutability might
be dose-dependent, that is, m may not be a constant. As reported in this paper
and elsewhere, both pmitiue and negatiue departures from linearity are observed.
A positive departure from linearity means that M ( x ) increases at a rate greater
than the first power of dose; a negative departure from linearity means that
M ( x ) changes at a rate less than the first power of dose. From equation ( 3 ) it
can be shown that positive departures arise if 6 < 1 and/or if m increases with
dose; negative departures arise if S > 1 and/or if m decreases with dose.
The way in which the parameters 6 and m can affect the shape of mutation
induction curves may be seen by writing out the first few terms of the power
series expansion of equation (3), viz.,
M ( x ) = [l
+ (1-6)kz + . . .] [mx - m2x2/2+ . . .]
Neglecting cubic and higher order terms we have,
M ( x ) = mx
+ (1-6)
+...
mkx2 - m2x2/2
The third term on the right hand side of equation (6) is small in comparison
with the second since normally mx << 1 and m << k.
On the basis of equation (6) with constant m, mutation induction is linear at
sufficiently low doses, but as dose increases the curves depart either positively or
negatively from linearity accordingly as 6 is less or greater than unity. This
behavior is shown in Figure 2. The curves were calculated from equation ( 3 )
for m = 10+ (ergs/mm2)-l and k = 0.1 (ergs/mm2)-l. Normalization to other
typical m / k ratios does not affect the general shape of these curves. The curve
for 6 = 1 remains sensibly linear on such a log-log plot for all values of M (z)
up to and even beyond frequencies of 10-l. It is important to note that if the
mutants are as little as 10% more or less sensitive than the nonmutants ( 6 = 1.1
or 0.9) ,even this small percentage shift from unity in the value of 6 can produce
dramatic changes in the magnitude and dose-dependence of the induced mutation
frequency.
For the case 6 < 1 it is clear from equation (6) and Figure 2 that the induction
curves first rise linearly with dose, then become quadratic, and ultimately
increase at even greater powers of dose as the cubic and higher order terms containing m and k become significant. An arbitrary but graphically convenient
definition of the transition from linear to quadratic kinetics is the dose, on a plot of
log M uersus log x, at which the extrapolated linear portion of the curve intersects
the line tangent to the curve at the point of slope 2. Determining d M / d x from
equation 3 and solving d(log M)/d(log x ) = ( z / M ) d M / d z = 2 for x (with
approximations suitable to n << 1) yields the dose corresponding to the point
KINETICS O F INDUCED MUTAGENESIS
uv
233
DOSE ( e r g s / m m 2 )
FIGURE
2.-Theoretical induced mutation frequency curves, M (z),calculated from equation
(3) for m = 10-6 and k = 0.1 (ergs/mmZ)-' for various values of 6. The curve for 6 = 1
saturates as M ( z ) + 1. The curves for 6 Ilie below those for 6
1 merely because a single,
fixed value of m was used to calculate all curves.
>
<
on the curve of slope 2, namely r= 1/(1- 6 ) k . I t is then simple to determine
that the two straight lines intersect at log xt = -log( 1 - 6) ke, so that
xt ==
Mt
1
k(l-S)e
= mxtQ/e
0.53 m
___-
(1.-S) k
where xt is the 'transition-point' dose and M t is the induced mutant frequency
a t this dose. (&It is determined from equation 3, not equation 6; see Appendix
for further details.) For sufficiently small values of 6 the position of the transition point could be low enough for the linear region to escape detection
experimentally.
For the case -6 > 1, induction also begins linearly but reaches a maximum
which can be determined from equation 3 to be
M,,,
=: mx,,,
t
+
=
m
k(6-1)e
234
F. ECKARDT A N D R . H. H A Y N E S
These formulae allow rough estimates of the values of m and 6 to be made if k
and the position of M,,, are known.
If 6 = 1, departures from linearity could be associated with dose-dependent
changes in m. Indeed, curves identical to those shown in Figure 2 can be generated by assuming that m increases exponentially with dose for positive departures from linearity or that m decreases exponentially with dose for negative
departures from linearity.
If mutation induction is, for whatever reason, a ‘two-event’process and 6 = 1,
then induction curves should have no linear region, even at the lowest UV doses,
and they should depart (negatively) from a quadratic dose dependence near the
Poissonian asymptote as M ( z ) 3 1; under these circumstances, additional
assumptions would be required to account for induction curves with maxima
such as those associated with values of 6 > 1.
RESULTS
Log-log plots of our measurements of UV-induced reversion (locus plus suppressor) frequencies f o r the ochre alleles ade2-I and Zys2-I are shown in Figure
3a, b; a similar plot of the total forward (pure plus sectored clones) frequency of
ade2-1 adex double auxotrophs is shown in Figure 4. For very low doses, mutation induction frequencies in all three systems increase linearly with dose.
Beyond this initial region, the reversion frequencies rise more rapidly than the
first power of dose, and for the highest doses measured n attains approximate
values of 3.5 and 2.9 for the adenine and lysine revertants, respectively. The forward mutation results reveal an essentially opposite type of response: after the
initial linear increase the curve approaches a maximum, and finally declines at
high doses.
The curves drawn in Figures 3 and 4 were calculated from equation (3) ;the
values of the parameters (m,k and 6) used to fit the mutant frequency data are
given in Table 1 together with the coordinates of the ‘transition point’ (equation
7) and the point at which the forward frequency reaches a maximum (equation 8). The surviving fraction of cells at xt and x,,, are also shown in the table.
The value of k is determined from the LD,, dose read off from the UV survival
curves of the cells; the value of m is determined directly from the initial linear
part of the frequency curves. Thus, 6 is the only truly adjustable parameter used
in fitting the data to equation 3, and even here there are constraints on the range
of values that could be considered plausible. It should be noted that 8 does not
appear alone, but is part of the exponential coefficient ( 1 - 6) k in equation (3) ;
the empirical value of this coefficientis determined by the nonlinear part of the
induction curve. On general radiobiological grounds the value of 8 should not
differ too much from unity. The fact that values of 8, obtained from the coefficient ( 1 - 8) k and the measured values of k, are close to unity therefore lends a
degree of internal credibility to our analysis. Thus equation (3) provides a useful empirical representation for two very different categories of mutational
response, even if the biological interpretation we attach to the parameters m and
8 is misconstrued.
Io-'
/*-6,
d
/
0
I
IO
U V DOSE (ergs/mmZI
I00
FIGURE
3a (left) and 3b (right) .-Induced reversion frequencies for the ochre alleles ade2-I
and lys2-I in an excision-deficient strain (rad2-20) of S. cereuisiae; each point represents a
single measurement. In both cases the mutation frequency initially rises linearly with dose; a
transition to quadratic kinetics occurs near 9 ergs/mm2, and at higher doses the curves rise even
more rapidly and attain v a d e s of n = 3.5 and n = 2.9, respectively, at the highest doses
measured. The locus and suppressor mutants independently follow similar kinetics.
UV DOSE (ergs/mm2)
8a
ode 2-1- ADE 2
(locus + suppressor)
r a d 2- 20
I
3
236
to-2L
I
2
3
0
k.
?
62 10-3 -
ode2-t--rode 2-t ode X
lpures c sectors)
rod 2 - 2 0
?t
2
5
3
Q
5
I
I
I
I
I I I I I
I
uv-
I
I
I 1 1 1 1 1
to
10
I
I
I
I I I l l
to 0
DOSE l e r g s / m m Z I
FIGURE
4.-Forward mutation frequencies for induction of the double auxotroph ade2 adez
in an excision-deficient strain (rad2-20) of S. cereuisiate; the points are averaged from three
independent experiments, and the average probable error per point is zk 10%. The curve begins
linearly and goes through a maximum near 14 ergs/mm2. For the point at 16 ergs/mm2, only
the contribution of pure mutant clones (1.55 ~ 1 0 - 3 )was measured; the contribution of sectors
(1.1 x 10-3) had to be interpolated hom measurements at neighboring doses. Pure mutant clones
and sectors independently follow similar kinetics.
It is instructive to emphasize the following points in connection with these
results. First, the reversion system is necessarily selective and the prototrophic
revertants are scored amongst IO7 auxotrophs plated on omission medium,
whereas in the survival assay the cells are plated at a variable density chosen to
allow growth of approximately 200 viable clones on supplemented minimal
medium after irradiation. Therefore, in this, as in most reversion assay systems,
mutants and survivors are grown and scored under significantly different biological conditions. On the other hand, the forward ade2 adex system is nonselective
and both mutants and survivors are scored on the same plates under identical
growth conditions; precautions were taken to ensure that all white clones scored
as mutants were authentic ade2 adex double auxotrophs (ECKARDT
and HAYNES
1977).
Second, in Figure 3 total reversion frequencies (locus plus suppressor) are
given. Preliminary experiments have shown that both locus and suppressor
reversions are induced according to biphasic kinetics that are initially linear, but
then rise as the square and even higher powers of dose in the high-dose range
(ECKARDT
1974). I n Figure 4, the total mutation frequency (pure clones plus
sectors) is plotted. Again, other experiments have shown that both pure clones
and sectors independently follow linear induction curves which rise to a maxiand HAYNES
1977). The simimum and then decline at high doses (ECKARDT
larity of induction kinetics for locus and suppressor revertants on the one hand,
1.6
6.0
LYS revertants
ade2 adex forwards
x
x
x
10-4
10-6
10-6
4.0
6.2
6.2
1.29
0.752
0.750
Zt
%ax
-__
__
-
13.7
0.044
-
10-5
x
2.1
-
S(5”
--
( ergs/mm2)
8.1 X 10-6
Mt
0.25
0.25
S(r,)
9.2
9.1
(erp/mm2)
Curve iharacteristics
f%”
3.0 x 10-3
_-
maximum.
and M,,
denote the surviving fraction of cells and the induced forward mutation frequency for the dose at which the forward frequency attains its
* S(xt) and M , denote the surviving fraction of cells and the induced reversion frequencies for the transition point dose xt;S(x,,)
0.62
ADE revertants
Mutants x ~ l e d
Curve fitting parameters
m
1/k
6
(ergs/mm?)-’
(ergs/”?)
Parameiers of mutant frequency curves*
TABLE 1
3
v)
zY
0
M
3>
E
U
M
2
2
r
0
t:
E2
238
F. ECKARDT A N D R. H. H A Y N E S
and for pure and sectored forward mutations on the other, ensures that it is
appropriate to use equation (3) in fitting total frequency data for both mutational systems.
Third, the spontaneous mutation rate for the add-I allele, as determined
in a fluctuation test proved to be (2.3f0.2) x lo-? per cell (calculated according
to KONDO1972). This rate is substantially lower than the lowest measured
induced frequency for this allele. The spontaneous background was found to vary
in different cell populations; the experiments retained for analysis always were
those in which the spontaneous background was low and an absolute increase was
observed in the number of mutants after small doses of radiation. Since stationary
phase cells are plated on unsupplemented omission medium, it is unlikely that
new spontaneous mutants appear during the plating assay.
Finally, it should be pointed out that the apparently more sensitive cells used
in the forward mutation studies in Toronto showed essentially the same biphasic
dose-response curve in a reversion experiment as did the original cells used in the
Berlin experiments. Thus, we can rule out the possibility that the apparent
change in sensitivity of the strain as measured in the two laboratories had any
influence on the two types of mutation induction kinetics observed.
DISCUSSION
In this paper we report two essentially opposite types of mutational doseresponse curves found in one and the Same excision-deficient strain of S. cereuisiae
(rad2-20). We measured induced mutant frequencies over the same dose and
survival range (1 to 60 ergs/mm2; minimum survival 0.1 %) for both revertants
and forward mutations. In the selective reversion system we obtained biphasic
induction kinetics which are linear in the low dose range, gradually become
quadratic, and, in the lowest survival range measured, increase with even higher
powers of dose ( n = 3.5 and n = 2.9 for the adenine and lysiEe revertants, respectively). On the other hand, in the nonselective forward system we found linear
induction curves at low doses which rise to a maximum and then decline at high
doses.
Both types of response can be described by an equation based on Poisson statistics and the assumption that mutation and killing are not necessarily statistically
independent processes (equation 3). The equation is derived here for the case
of mutants which exhibit exponential UV survival curves. The existence of a
resistant “tail” on the particular rad2 strain used in the experiments has no
theoretically significant effect on our analysis or conclusions. I n deriving equation (3) we assume that sensitivity to mutation is given by a constant m, and
sensitivity to killing by a constant k. Statistical dependence of mutation and killing is then introduced by assigning a sensitivity k, to the mutant cells; the ratio
of mutant to nonmutant sensitivity, kJk, is denoted by the parameter S. Equation (3) can be used to fit equally well both the reversion and forward data under
two, not mutally exclusive, conditions: first 6 # 1 and m is constant €or any given
strain, locus or allele; second, 8 = 1 and m is not constant as initially assumed but
KINETICS O F INDUCED MUTAGENESIS
239
rather is considered to be some appropriate function of dose, m (2). W e discuss
both possibilities independently and make comparisons with the various ‘two-hit’
and ‘heterogeneous population’ models which have been used to interpret mutation kinetics.
Models which postulate some necessary interaction, cooperation or overlap of
neighboring lesions (BRIDGES
1966; BRESLER
1975, SEDGWICK
1975a) are hard
to reconcile with linear kinetics. Also, a rough estimate indicates our reversion
frequencies in the nonlinear region are 1O-fold higher than expected statistically
for two-bit kinetics. [This estimate assumes an average yield of 23 dimers/erg/
mm2 in a haploid genome composed of 1.4 X IO‘ base pairs (UNRAU
et al. 1973;
FATH and BRENDEL1975) and an interaction distance of up to IO3 base pairs
between dimers.] Other models, which assume a more indirect interaction of
premutational lesions (MENNIGMANN
1972, DOUDNEY
1975, WITKIN1975c),
could be invoked to explain the reversion data, but they fail to account for the
forward mutation kinetics which do not have any positive quadratic component.
Mutational dose-response curves which go through a maximum are sometimes
takefi as evidence that the treated population is heterogenous with respect to
mutability, that is, with increasing dose a population more resistant to mutation
is assumed to be selected (KAPLAN1956). If the problem of demonstrating the
existence of the required population heterogeneity is overlooked, such a model
could explain the decreasing mutation frequency in the forward data, but it could
not simultaneously explain the increasing frequency of reversions in the same
dose range, unless the mutabilities of the assumed subpopulations are arbitrarily
reversed from one system to the other.
If it is assumed that 6 = 1, m can be calculated from equation (3) for each
point on the dose-response curves shown in Figures 3 and 4. The data indicate
that m ( z ) would have to be either a positive or negative exponential function.
Over the dose range from 1 to 60 ergs/mm2. m ( z ) increases by a factor 10 (positive exponential) for the reversion data, but decreases by a factor 60 (negative
exponential) for the forward data. On the basis of current thinking, an increase
of m with dose could indicate induction (or activation) of some error-prone
repair system; a decrease in m could be interpreted as inactivation or destruction
of gene products involved in error-prone repair. But again, if our reversion and
forward data are interpreted in these two distinct ways, one still has the problem
that a model which explains one type of kinetics must be turned about to explain
the other; and simultaneous induction and destruction of gene products involved
in mutagenesis seems unlikely to occur at the same time in the same cell, depending on the type of mutation chosen for assay.
The possibility that mutant and nonmutant cells in the same population
have different probabilities o’f clone formation has been examined experimentally
in different organisms and with various mutagenic agents (GRIGG1952; KAPLAN
1959; HAEFNER
and LASKOWSKI
1963; AUERBACH
and RAMSAY
1968). The general conclusion is quite clear; mutants and nonmutants can have different probabilities of survival but such differences arise in a variety of ways. First, a mutant
can be either inhibited or supported in growth, depending on the genetic back-
240
F. ECKARDT A N D
R.
H. HAYNES
ground and physiology of the nonmutant cells (GRIGG1952; KAPLAN1959). It
should be noted that revertants to wild type (GRIGG1952) as well as mutations
to auxotrophy (KAUDEWITZ,
MOEBUS
and KNESER1963; SCHIMMER
and LOPPES
1975) can be influenced by surrounding parental cells. The reasons for such
effects are not clear. Second, whether mutant cell growth is supported or inhibited
can depend on the density at which treated cells are plated. If the same titre of
cells is plated for the various doses used, a different number of viable, and possibly competing, cells grow on the plates along with the mutants (e.g. BRIDGES,
MOTTERSHIELD
and COLLELA
1973; SIMMONS
1974; SCHIMMER
and LOPPES
1975;
VAN ZEELAND
and SIMONS1976). Third, the composition of the plating medium
can influence the yield of mutants (DEMEREC
and LATARJET
1946; HAEFNER
and
LASKOWSKI
1963; SIMONS1974; DOUBLEDAY,
BRIDGES
and GREEN1975; VAN
ZEELAND
and SIMMONS
1976) and such conditions also would beexpected to affect
induction kinetics. Mutation frequency decline in bacteria, that is, the rapid
‘loss’ of certain mutants if cells are plated under nongrowing conditions (WITKIN
1966),is thought to arise from the elimination of premutational lesions by errorfree repair (WITKIN 1966; SETLOW1966; GEORGE
and WITKIN 1975) ; this
process cannot take place, or is much less efficient, under conditions which allow
immediate protein synthesis. Also, it has been found that medium conditions
which affect the number of detected mutants do not change the number of premutational lesions formed, but rather influence the mutational process at the
level of expression and cell multiplication (DOUBLEDAY,
BRIDGESand GREEN
1975). Finally, studies on nitrite mutagenesis in E. coli have shown that cells
from auxotrophic clones compete with wild-type cells during growth, but that
freshly induced auxotrophs are at a disadvantage (KAUDEWITZ
1960; KAUDEWITZ,
MOEBUSand KNESER1963). This indicates that reconstruction experiments
which normally are carried out to check the possibility of differential survival
do not always reflect accurately the conditions of the assay procedure.
The results cited above lend credibility to the notion that the differential sensitivity of mutant and nonmutant cells, which we describe mathematically by the
parameter 6, can play a decisive role in determining the shape of mutational doseresponse curves. Further plausibility is lent to this idea when one comiders that
in the mutational systems used here, the reversions and forward mutations are
scored under very different qrowth conditions, but the values of 6 required to
account for the two essentially opposite types of dose-response relation are close
to unity.
It remains to ask why 6 is greater than one in some cases but less than one in
others. We also need more information that would reveal at what level in the
mutational pathway the factors that cause 6 to differ from unity are most likely
to act. Unfortunately, we cannot provide clear answers at present, but we feel
that further study of the many factors capable oi modifying expression and clonal
growth will shed light on both questions. In particular, it would be helpful to
develop a nonselective system for scoring reversions, as it is by no means clear
whether the 6 < 1 kinetics are associated with reversion per se or merely with
the fact that the assay systems are selective (and vice versa for the forward sys-
KINETICS O F INDUCED MUTAGENESIS
241
tem) . It should be possible to distinguish between factors that act during expression, as compared with those acting during clonal growth, by exploiting systems
of the type recently developed by LEMONTT
(1976a, b). However, it must be
emphasized that a value of 8 different from unity and a dose-dependent mutability are not mutually exclusive a priori. Thus, it remains possible that in yeast,
the effect of some mode of induced error-prone repair could be masked by differential survival of mutant and nonmutant cells in different assay systems.
The mathematical acalvsis developed here can be extended in various ways.
Fjrqt, we have found that repair-proficient RAD wild-type strains exhibit mutation induction kinetics qualitatively similar to those of the rad2 strain in equivalent assay systems. The mathematical analysis of these data is more complicated,
1975;
since dose-dependent renair functions must be taken into account (HAYNES
WHEATCROFT,
Cox and HAWNES
1975) ; this work will be reported subsequently.
Second, it should be pointed out that a similar type of analysis could be develoDed
for different genetic endpoints, as wcll as for different mutagenic agents. For
example, it might be noted that in diploid strains of S. cerevisiae, non-selectively
scored intergenic recombinants exhibit induction kinetics smilar to those found
for the forward system examined here; whe-eas selectively scored intraeenic
recombinants show the kinetics of the reversion type (KOWALSKI
and LASKOWSKI
1975). It would be desirable also to analyse chromosomal events, since the traditioval hypothesis that deletions and certah other types of chromosomal aberrations are caused by two-hit processes is not as clearly established as one might
and KILBEY1971).
wjsh (WOLFF1967; BREWENand BROCK1968; AUERBACH
A variety of dose-responserelations are found also for X-ray mutagenesis. Linear
kinetics have been reported frequently (e.g..OLIVER1932; SPENCER
and STERN
and DE SERRES1965; MORTIMER.
BRUSTAD
and CORMACK
1965;
1948; WEBBER
CLEAVER
Z 976; CONKLING,
GRUNAUand DRAKE1976) ; however. in Neurospora
quadratic curves have been found f o r induction of deletions at high dose rates
(1000 rads/min) (WEBBERand DE SERRES
1965) although at low dose rates (IO
rads/min) the induction curve does possess a linear component at low doses
(DE SERRES,
MALLING
and WEBBER
1967). Most data on chromosomal mutations
of higher orgapisms can be fit best with a biphasic linear-quadratic equation
and PRESTON
1974) ; the transition points occur
(BREWENet al. 1973; BREWEN
at low doses, but exceptions exist (SWANSON
1942; BREWENand BROCK1968;
BREWENand PRESTON
1974). Still more complex patterns have been found for
mutation induction in stamen hairs of Tradescantia; here a linear increase in
mutation frequency is observed at low doses, but this is followed in some cases by
a quadratic region, as the curves approach a maximum, and finally by a decrease
(SPARROW,
UNDERBRINK
and ROW 1972; SPARROW,
SCHATER
and VILLALOBOSPIETRINI
1974; NAUMANN,
UNDERBRINK
and SPARROW
1975).
Finally, it is possible to use equatioll (3) as a basis for the mathematical definition of coefficients of mutability, which should be of practical use in grading the
mutagenicity of various agents for a given locus, or the relative mutability o f '
different loci (in the same organism) for the same agent.
242
F. ECKARDT A N D R. H. H A Y N E S
The reversion studies reported here were carried out as part of a Ph.D. thesis in the Freie
Universitat Berlin. We wish to thank M s . M. BROSEfor technical assistance and Ms. SOO-JEET
TEHfor her careful measurements of the forward mutation frequencies. DR. JOHNW. DRAKE
worked well beyond the normal call of duty as editor in helping us to clarify some of the more
esoteric bits of mathematics in this paper. The research was supported by grants from the
Deutsche Forschungsgemeinschaft (to F.E.) and the National Research Council of Canada.
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Corresponding editor: J. W. DRAKE
10-3
I
IO0
FIGURE
5.-Determination
I
IO/
I02
U V DOSE (ergs / m m 2 )
IO
of the transition point B for mutation frequency curves with
(3)
for m = 10-6, k = 0.1 and 8 = 0.75. The lines CDL and DQ are respectively the linear and
quadratic components of M ( z ) ; the line CA is the tangent to log M ( z ) with slope 2.
6
< 1. The M ( z ) curve passing through the points A and B was calculated from equation
247
KINETICS OF INDUCED MUTAGENESIS
APPENDIX
Definition and Calculation of Transition Point Coordinates
<
For cases in which -6
1 , the mutation frequency M ( r ) as given by equation (3) is a monotonically increasing function that initially rises as the first, and then higher, powers of dose
..IS z increases (Figures 2 and 5). Because these M ( x ) curves bend smoothly upward, the definition of a ‘transition point’ from linear to quadratic kinetics involves an essentially arbitrary
choice of some point where the slope of the log M versus log z curves lies between 1 and 2. The
abscissa of such a point, that in practice can be determined easily and unambiguously, is given by
the intersection of the extrapolated linear component of log M ( z ) and the tangent to the log
M ( x ) curve whose slope is 2 ; these are the lines CDL and CA respectively in Figure 5 and they
intersect at the point C. The transition point defined in this way is at B, and its abscissa may be
calculated by solving simultaneously the equations for the lines CDL and CA. Since the slopes
of CDL and CA are 1 and 2 respectively, we need o n l y determine the coordinates of a point on
each of these lines in order to write down their equations; two such points whose coordinates are
easy to find are D and A, and we proceed with the calculation as follows:
The value of z at which the slope of the tangent to the log M ( z ) curve is 2 is given by
d (IogM)
-----=2
d (logz)
- z dM
M dx
Differentiating equation (3) to obtain dM/& and making appropriate substitutions and approximations in the above equation, we find that the abscissa of the points A and D is given
approximately by 1/(1-8)k, which we denote by zq; the ordinate of A is therefore M ( x , )
nre./(l-S)k. Since the point D lies on the extrapolated linear component of M, it is obvious
from the first term of equation (6) that its ordinate is m / ( l - S ) k . Having thus obtained the
coordinates of A and D and denoting the coordinates of C by (log xt, y ) , we can write the
equations of the lines CA and CDL in appropriate log-log form, viz.,
CA: y
me
- log -__-
( 1 - 4 )k
Eliminating y and solving for log xt, we find that log zt = -log (1-8) ke from which the
coordinates of B as given by equations (7) in the text above are derived immediately.
I t should be noted that zo.is also the abscissa of the point at which the linear and quadratic
components of M ( z ) are equal (the line DQ is a plot of the quadratic component of M , the
second term of equation 6), and that for z zq.M ( z ) rises at powers greater than the square
of the dose.
Two interesting properties of the transition point B are that, first, the ratio of the quadratic
to linear components of M at zt is l / e . Secondly, a t zt the power of dose with which M increases
( i s . , the slope of the log M versus log z curve at z t ) is approximately 1 l/e; more generally,
the value of z at which M increases with power n is given by (n-l)/(l--a)k
for m
k.
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