Meiotic double-strand breaks occur once per pair of
(sister) chromatids and, via Mec1/ATR and Tel1/ATM,
once per quartet of chromatids
Liangran Zhanga, Keun P. Kima,c, Nancy E. Klecknera,1, and Aurora Storlazzia,b,1
aDepartment of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138;bIstituto di Genetica e Biofisica A. Buzzati Traverso, Consiglio
Nazionale delle Ricerche, 80131 Naples, Italy; andcSchool of Biomedical Science, CHA University, Seongnam, Gyeonggi 463-836, South Korea
Contributed by Nancy E. Kleckner, November 2, 2011 (sent for review August 15, 2011)
Meiotic recombination initiates via programmed double-strand
breaks (DSBs). We investigate whether, at a given initiation site,
DSBs occur independently among the four available chromatids.
For a single DSB “hot spot”, the proportions of nuclei exhibiting
zero, one, or two (or more) observable events were defined by
tetrad analysis and compared with those predicted by different
DSB distribution scenarios. Wild-type patterns are incompatible
with independent distribution of DSBs among the four chromatids.
In most or all nuclei, DSBs occur one-per-pair of chromatids, pre-
sumptively sisters. In many nuclei, only one DSB occurs per four
chromatids, confirming the existence of trans inhibition where a
DSB on one chromosome interactively inhibits DSB formation on
the partner chromosome. Several mutants exhibit only a one-per-
pair constraint, a phenotype we propose to imply loss of trans in-
hibition. Signal transduction kinases Mec1 (ATR) and Tel1 (ATM)
exhibit this phenotype and thus could be mediators of this effect.
Spreading trans inhibition can explain even spacing of total recom-
binational interactions and implies that establishment of interho-
molog interactions and DSB formation are homeostatic processes.
The two types of constraints on DSB formation provide two differ-
ent safeguards against recombination failure during meiosis.
strand breaks (DSBs), catalyzed by Spo11 transesterase.
DSBs occur preferentially at “hot spots” (e.g., ref. 1) and are
governed both locally (e.g., by absence of nucleosomes) and
domainally (e.g., by global base composition) (2, 3). DSB for-
mation is also modulated by communication along and between
homologs. In cis, the presence of a strong hot spot at one posi-
tion suppresses DSB formation in the vicinity over a distance of
∼25 kb, by mechanisms unknown (4–7). In trans, two effects
occur: (i) Increased activity of the site on one homolog can
decrease DSB formation on the partner homolog at the same
and nearby positions (“trans inhibition”) [refs. 5 (case C) and 6].
This effect can occur at an artificial hot spot where DSB for-
mation is independent of Spo11 and other factors and thus is
probably a direct effect of DSB formation per se, with a DSB on
one homolog disfavoring DSB formation on its partner. (ii) Al-
ternatively, increased or decreased activity at a site on one ho-
molog can coordinately increase or decrease DSB formation on
the homolog [refs. 4, 5 (case C) 8, and 9]. This effect likely occurs
before DSB formation via trans modulation of chromatin/chro-
A DSB on one chromatid identifies a homologous region,
usually on a (nonsister) chromatid of the homolog, giving rise to
a nascent interhomolog D-loop. These initial interhomolog inter-
actions then undergo regulated differentiation, with a subset
designated for maturation into crossover (CO) recombination
products and the remainder fated for maturation into non-
crossover (NCO) products (10–13). COs are evenly spaced along
homolog pairs. This pattern may reflect the combined effects of
a driving force for CO designation and the fact that CO designa-
tion concomitantly sets up a zone of “interference” that disfavors
eiotic recombination initiates via programmed double-
occurrence of further events nearby (12, 14, 15). DSB-initiated
interhomolog interactions also tend to be evenly spaced along
eachhomologpair (e.g.,ref.16),potentiallyby ananalogouslogic.
When DSBs occur,afterDNA replication, a diploid meiotic cell
contains four versions of each chromosome, two sisters for each of
the two (maternal and paternal) homologs. We investigate here
on the four available chromatids and, if not, what constraints
Theoretically Possible DSB Distributions. For any given DSB site, in
the absence of programmed constraints, breaks would occur in-
constrained to occur once per pair of chromatids, presumptively
once per pair of sisters, or once per four chromatids, i.e., once per
pair of homologs (Fig. 1A, scenarios A–C). These scenarios might
occur singly or in combination. For all cases, the probability that
a meiotic nucleus will acquire zero, one, two, or (for scenario A)
more than two DSBs, at a single given site, can be calculated, as
a function of the population average per-chromatid frequency of
Per-Nucleus Analysis of in Vivo Event Distributions. No available
method can evaluate the number of DSBs occurring at a partic-
ular site on a per-nucleus basis. However, at a strong DSB hot
spot, nearly all recombination events that occur in the immediate
vicinity of that position have been initiated by DSBs at that site.
At such a locus, the number of recombinational interactions in
a single nucleus, detected after meiosis, can serve as a proxy for
the number of DSBs. In budding yeast, such analysis is possible
by classical tetrad analysis. Given suitable marker differences
between maternal and paternal homologs at the locus of interest,
the number and nature of recombination events occurring in
each individual meiotic cell are manifested in the genotypes of its
four resulting haploid spores. The four haploid spores of each
tetrad are separated, placed on growth medium, and germinated
under fully permissive conditions, and genotypes of the cells in
each spore clone determined by physical and genetic methods.
Frequencies of nuclei exhibiting different numbers of recombi-
national interactions, and thus different numbers of in vivo
DSBs, can, after accommodating certain complexities (below),
be compared with the frequencies predicted by theoretical sce-
narios for DSB distributions among the four chromatids.
This approach is illustrated for the HIS4LEU2 hot spot, where
DSBs occur within a single ∼100-bp region (5, 17). Recombination
events initiated by these DSBs were detected using strains in which
the two parents differ by three markers: a pair of heterozygosities
Author contributions: L.Z., K.P.K., N.E.K., and A.S. designed research, performed research,
analyzed data, and wrote the paper.
The authors declare no conflict of interest.
1To whom correspondence may be addressed. E-mail: email@example.com or
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
| December 13, 2011
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| no. 50www.pnas.org/cgi/doi/10.1073/pnas.1117937108
at nearby flanking positions and a single base pair heterozygosity
within the ∼100-bp DSB site itself (Fig. 1B). Individual chromatid
genotypes were determined (SI Materials and Methods) and tetrads
sorted into categories according to the number of recombination
events detected (full tetrad descriptions in Fig. S2). Tetrads with
zero events exhibit two chromatids of each parental genotype
(type 0; Fig. 1C, Middle Left). Tetrads with one event exhibit either
two nonparental chromatids whose marker arrangements reflect a
single CO or one nonparental chromatid reflecting non-Mende-
lian segregation at the central marker without any evidence of a
CO, i.e., a single “noncrossover” event (non-Mendelian segrega-
tion or “NCO+”) (type 1; Fig. 1C, Middle Right). Tetrads exhib-
iting other marker combinations must have undergone two or
more events, with various combinations of COs and/or NCO+
events possible (type 2; Fig. 1C, Bottom). Analysis of a sufficiently
large number of tetrads yields experimentally derived frequencies
of type 0, type 1, and type 2 tetrads that describe the probabilities
that a nucleus will contain zero, one, or two (or more) experi-
mentally detectable recombinational interactions (T0, T1, and T2;
T0, T1, and T2 were defined at three hot spots in wild-type
(WT) meiosis: HIS4LEU2 (above); a second allele of this same
locus, “HIS4LEU2old”, where DSBs occur at two different sites
separated by ∼2 kb (site I and site II) (5); and an unrelated hot
spot, his4::URA3-arg4, created by molecular insertion of ARG4
sequences at HIS4 (18, 19). T0, T1, and T2 were also defined for
HIS4LEU2 in sevenmutantstrainsknowntoaffectrecombination
without dramatically affecting spore viability (required for this
analysis). Table 1 shows T0, T1, and T2 and the population-av-
Experimental vs. Predicted Event Distributions. T0, T1, and T2
(above) cannot be compared directly with the predicted proba-
bilities of nuclei exhibiting zero, one, two (or more) DSBs given
by binomial distribution analysis, for two reasons:
i) Some DSB-provoked recombinational interactions are “in-
visible” to experimental detection because they do not alter
the array of assayed markers along the chromatids. Such
interactions include (i) recombinations between a DSB and
its sister chromatid and (ii) recombinations between a DSB
and a homolog chromatid that are resolved without yielding
either a CO or non-Mendelian segregation at the central
marker (“NCO−” events). Theoretical equations for scenar-
ios A–C were thus modified to include a parameter, “inv”,
which is the fraction of DSBs that give invisible events (Fig.
S1D). The resulting equations yield the theoretically pre-
dicted probabilities that a nucleus will exhibit zero, one, or
two experimentally observable events (P0, P1, P2), as a func-
tion of both the population average DSB frequency per chro-
matid (X) and inv.
ii) In scenario A (but not scenarios B and C), a nucleus might
acquire three or four DSBs (Fig. 1). Over the range of DSB
levels relevant in vivo (below) the predicted possible fre-
quencies of such nuclei are sufficiently small that they can
be safely ignored. Nonetheless, we assume that such nuclei
survive but exhibit multiple events, thus appearing as type 2
tetrads (Fig. S1B). Indistinguishable results are obtained by
assuming that such nuclei do not yield four viable spores
and are thus not represented in the experimental dataset
(Fig. S1B legend).
The possibility of a match between the experimental data for
any given strain and any particular DSB distribution scenario can
be evaluated by comparing T0, T1, and T2 with P0, P1, and P2 for
that scenario over appropriate ranges of total DSB levels and
frequencies of invisible events (X and inv), as illustrated for
HIS4LEU2 in WT meiosis (Fig. 2A). For each scenario (A, B, or
C),predictedprobabilitycurves foreachnucleus type(P0,P1,and
P2 in blue, red, and green, respectively) are shown for values of X
and inv that span experimentally observed values (Table 1). The
three different scenarios give qualitatively different predicted
patterns, all of which are relatively insensitive to variations in inv.
Values of T0, T1, and T2 are shown, relative to predicted pat-
terns, as horizontal lines in Fig. 2A. An individual match (T0/P0,
T1/P1, or T2/P2) occurs when the horizontal line intersects
a predicted curve (Fig. 2A, circles). When a given dataset matches
a given theoretical scenario, (i) matches occur for all three nu-
cleus types, (ii) the three matches all occur at the same single
value of X, and (iii) this common value of X corresponds to the
value of X observed experimentally (Table 1 and Fig. 2, black
triangles). By these criteria, the distributions of nucleus types for
HIS4LEU2 in WT meiosis are not compatible with any of the
three basic scenarios (A–C). The same results are seen more
compactly in Fig. 2 B and C, with matches evaluated at the ex-
perimentally defined value of inv for each strain (Table 1).
Possible distributions of DSBs at a single site among four chromatids. (B) Map
of the HIS4LEU2 locus. (C) Representative examples of nuclei exhibiting zero,
one, or two (or more; text) events (T0, T1, or T2, respectively).
Theory and analysis of DSB distribution among four chromatids. (A)
Table 1. Per-nucleus recombination patterns
Strain T0T1 T2ObservedTotal†
*As in Fig. 1 except data for his4::URA3-arg4 are from ref. 18. Margins of
error at 95% confidence levels are ≤0.06 in all cases (Table S1). Spore viability
frequencies are in Table S1.
†“Total” represents the sum of the frequencies of observed events plus in-
visible events and corresponds to the total population average level of DSBs
per chromatid, defined as parameter “X” in binomial distribution equations
(text and Fig. S1). Total = X = [Obs/(1 − inv)], where inv is the fraction of DSBs
that give an invisible event (text). Values of inv are specified experimentally
for all strains: inv = 0.15 except for sgs1-ΔC795 and mec1Δ sml1Δ, inv = 0.3;
ndj1Δ, inv = 0.2; and HIS4LEU2old, inv = 0.3 (SI Materials and Methods).
‡Adjusted for increase in two-event DSBs (ref. 21 and SI Materials and
§sml1Δ suppresses the inviability of mec1Δ. sml1Δ alone has no detectable
effect on recombination (Table S1 and text).
Zhang et al.PNAS
| December 13, 2011
| vol. 108
| no. 50
Event Distributions in WT Meiosis. If DSBs were distributed in-
dependently among the four chromatids (scenario A; Fig. 2 A and
B, Left), increasing DSB level would be accompanied by a de-
creased probability of nuclei with zero observable events (P0) and
an increased probability of nuclei exhibiting two observable
events (P2). These two effects roughly balance such that the
predicted probability of nuclei exhibiting one observable event
(P1) remains relatively constant.
In WT meiosis, for all three hot spots examined, the observed
probabilities ofnucleus types (T0,T1, andT2) donot match those
predicted by scenario A (P0, P1, and P2) (Fig. 2 A and B). In all
three cases, (i) there is no match between observed and predicted
probabilities of one-event nuclei at any DSB level because the
observed frequency is always significantly higher than the pre-
dicted frequency, and (ii) matches are possible for zero- and two-
event nuclei, but occur at nonoverlapping ranges of DSB levels
that, also, are higher and lower than the experimental value, re-
spectively. Thus, meiotic DSBs at a single hot spot are not dis-
tributed independently among the four chromatids.
At HIS4LEU2, scenario B is excludedby absenceof any possible
match for one-event nuclei and scenario C is excluded because it
implies that every nucleus willget eitherzero orone DSB,whereas
However, scenario B gives a significantly better match than sce-
nario A, with a lesser discrepancy for one-event nuclei (P1 vs. T1)
and matches for both zero- and two-event nuclei (P0 vs. T0 and P2
vs. T2) at intermediate DSB frequencies that are approximately
within the range of experimentally defined values. Thus, imposition
of the one-per-pair constraint significantly improves the match
between observed and predicted distributions of nucleus types
relative to that obtained with scenario A. Moreover, scenarios B
and C are inadequate to explain observed event distributions for
complementary reasons: The observed level of one-event nuclei is
too high for scenario B, but not for scenario C, whereas the ob-
served level of two-event nuclei is too high for scenario C, but not
for scenario B. Thus, the in vivo situation might be explained sat-
isfactorily by a combination of one-per-two and one-per-four con-
straints. Any one-per-four constraint would imply trans inhibition.
Event distributions at the two other loci in WT meiosis sup-
port the possibility of a mixed B/C scenario. At HIS4LEU2old,
predicted relationships to scenarios B and C are very closely
similar to those for HIS4LEU2 (Fig. 2B and further discussion in
Fig. S3) and a one-per-four constraint was identified previously
at this locus by physical analysis (5). his4::URA3-arg4 exhibits the
same trends, with a closer match with scenario B (Fig. 2B) spe-
cifically supporting existence of a one-per-two constraint.
Event Distributions in Mutants. For the seven analyzed mutants,
event distributions at HIS4LEU2 are also not explained by in-
dependent distribution of DSBs among four chromatids, for
and sgs1-ΔC795 exhibit event distributions that are not signifi-
cantly different from that of WT (Fig. 2C, class I). sml1Δ lacks a
negative regulator of ribonucleotide reductase and is implicated
in Mec1/ATR-mediated regulation ofDNA replication (20).sgs1-
ΔC795 lacks a helicase that eliminates multichromatid re-
combination intermediates (21). Correspondingly, Sml1 does not
affect recombination and Sgs1 affects recombination at steps well
after DSB formation and establishment of DSB/partner inter-
actions (21). The other five mutants exhibit a significantly dif-
ferent event distribution from WT (P < 0.001 by G-test). Among
these, four mutants exhibit possible matches with scenario B (Fig.
2C, class II), with scenario C excluded by the presence of signif-
icant levels of two-event nuclei. Identification of this pattern in
several mutants strongly supports the existence of a one-per-pair
constraint on DSB distribution. By implication, WT would exhibit
a mixture of scenarios B and C and the mutants would be spe-
cifically defective in the one-per-four constraint. These four
mutants are tel1Δ and mec1Δ sml1Δ (hereafter mec1Δ; Table 1,
footnote §), which, respectively, lack the related chromosome-
based signal transduction molecules corresponding to mamma-
lian ATM and ATR; ndj1Δ, which lacks a telomere-specific
binding protein and exhibits multiple defects, some of which are
indirect consequences ofregulatorysurveillance controls (22–25);
and spo11-HA3His6 (hereafter spo11HA), which is defective in
the efficiency of Spo11-mediated DSB catalysis (15). The final
mutant, dmc1Δ RAD54-OP, exhibits a possible match to scenario
A (independent distribution among four chromatids) (Fig. 2C,
class III).Scenario C and scenario B are both excluded by the too-
low frequency of one-event nuclei and also, for scenario C, by the
presence of two-event nuclei (Fig. 2C). This mutant lacks meiotic
RecA homolog Dmc1 and overexpresses Rad54 helicase, which
substantially suppresses dmc1Δ defects (26).
Scenario D Combines One-per-Two and One-per-Four Constraints.
The above results point strongly to a situation where a one-per-
pair constraint is present in all nuclei of all analyzed strains and
a one-per-quartet constraint (trans inhibition) is also present in
WT and operates with reduced efficiency in certain mutants
compared with WT HIS4LEU2 and in his4::URA3-arg4 com-
pared with the two HIS4LEU2 alleles (Fig. 3A and below).
This combination of constraints, “scenario D”, is again de-
scribable by the binomial distribution (Fig. 3 A and B). Here,
DSBs occur with an intrinsic probability of “M” per pair of
chromatids, irrespective of any trans effect. In addition, some
fraction of the nuclei, “K”, that would otherwise have given rise to
DSBs on both homologs give, instead, a DSB on only one of the
two homologs. M and K thus correspond to “intrinsic DSB
total DSB levels as predicted by scenarios A–C (P0, P1, and P2; curves) (Fig. 1)
are compared with observed frequencies of such tetrads (T0, T1, and T2;
horizontal lines) (Table 1). Black triangles indicate experimentally derived
frequencies of total DSBs (Table 1, “Total”). Possible matches are indicated
by vertical dashed lines. (A) HIS4LEU2 in WT meiosis. Theoretical dis-
tributions are shown for three values of inv. (B and C) Comparisons of in-
dicated strains at appropriate corresponding values of inv (Table 1).
Probabilities of tetrads with zero, one, or two events as a function of
| www.pnas.org/cgi/doi/10.1073/pnas.1117937108Zhang et al.
efficiency per pair of chromatids” and “strength of trans in-
hibition,” respectively. Predicted probabilities of nuclei exhibiting
zero, one, or two recombination events (P0, P1, and P2) are
a function of these two variables plus inv (defined above).
For any experimental array of nucleus types, at a specified inv,
scenario D defines specific unique values of both M and K at
which T0, T1, and T2 match P0, P1, and P2 (Fig. 3B).
The predicted level of trans inhibition for HIS4LEU2 and
HIS4LEU2old in WT meiosis, and for the two mutants with WT-
like event patterns (class I above; sml1Δ and sgs1-ΔC795), is very
high, K = 0.45–0.65 (Fig. 3B and Fig. S4). That is, in any nucleus
where a first DSB occurs on one homolog, the probability that a
DSB will also occur on the partner chromosome is reduced by
∼50% of what it would have been in the absence of trans in-
hibition. All four of these strains also exhibit very high predicted
intrinsic DSB probabilities, M = 0.6–0.7. That is, a given homolog
(pair of chromatids) has an intrinsic probability of DSBformation
of 60–70% in the absence of trans inhibition. Both parameter
values match other indications that HIS4LEU2 is an unusually
robust and tightly controlled DSB hot spot (e.g., refs. 15 and 27).
distance along the target chromosome in the vicinity of the position
exactly allelic to the site that is the source of the effect (5) (Fig. 3A,
Right). Thus, at any particular assayed position, the amount of trans
inhibition as described by the parameter K of scenario D actually
i.e., inhibition of DSB formation at the assayed site by a DSB at the
exact allelic site on the homolog “donor” chromosome, and (ii)
assayed position is also inhibited by DSBs that occur in the vicinity
of the allelic site on the homolog (DSB donor).
The relative contributions of “allelic” and “spreading” effects
(e.g., at HIS4LEU2) are not known. However, the two effects are
differentiable. A mutation that globally reduces the efficiency of
DSB formation per se, M, will have no effect on allelic trans in-
hibition but will reduce the strength of spreading trans inhibition
because it will reduce the number of (nearby) DSBs that are
contributing to this effect at the assayed locus. Thus, by scenario
D, such a mutation will reduce K as well as M. Correspondingly,
the spo11HA mutation, which is thought to specifically reduce
DSB formation (15), exhibits not only a predicted reduction of
∼35% in the intrinsic probability of DSB formation (M), but also
a reduction of ∼39% in trans inhibition (K) (Fig. 3B).
Interestingly, one assayed mutant, tel1Δ, exhibits no alteration
in the intrinsic efficiency of DSB formation with an essentially
complete absence of trans inhibition (Fig. 3B), implying that
these two features of DSB formation are functionally distinct and
implicatingTel1 as required for trans inhibition per se. Two other
assayed mutants, mec1Δ sml1Δ and ndj1Δ, are similar to spo11HA
in exhibiting reductions in both M and K; however, compared with
spo11HA, both mutants exhibit lesser reductions in DSB efficiency
but greater defects in trans inhibition (Fig. 3B). Thus, in both
mutants, the reduction in DSB efficiency cannot (fully) account
for the defect in trans inhibition. Because sml1Δ exhibits no dif-
ference from WT, the mec1Δ sml1Δ defect is attributable to the
mec1Δ mutation. Correspondingly, Mec1 and Ndj1 are implicated
as being required, separately, for both efficient DSB formation
and efficient trans inhibition. We note that the loss of a one-per-
four constraint in these mutants could alternatively be interpreted
as reflecting a loss of the one-per-pair-of-sisters constraint but
retention of trans inhibition. We cannot exclude this possibility but
consider it to be less obvious.
For the final assayed mutant, dmc1Δ RAD54-OP, scenario D
predicts a value of K much less than zero (K = −1.2). This pre-
diction might mean that occurrence of a DSB on one chromo-
some increases (rather than decreases) the probability of a DSB
on the partner chromosome, e.g., by abrogating the one-per-pair
constraint. Alternatively, promiscuous action of Rad51 in this
mutantmightyielddiscoordination ofthetwo DSBends suchthat
one DSB produces interactions with more than one partner (21).
We also note that because the effect of trans inhibition is to
preclude formation of a subset of DSBs, any mutation that reduces
trans inhibition will tend to increase the population-average levels
of DSBs (and thus DSB-initiated recombinational interactions).
Correspondingly, tel1Δ, which decreases trans inhibition without
affecting DSB efficiency (Fig. 3B), exhibits a higher frequency of
recombination events than WT (Table 1). This increase, not pre-
viously known, is also seen by physical analysis of total levels of
DSBs (Fig. 3C) at HIS4LEU2. Similarly, spo11HA, mec1Δ sml1Δ,
and ndj1Δ mutants, although reduced for the efficiency of DSB
formation, nonetheless exhibit a higher frequency of recombi-
nation events than would be predicted from their DSB efficiencies
alone (Fig. S5). Thus, functions involved in trans inhibition will
appear as negative regulators of DSB formation (Discussion).
Trans Inhibition at Weaker DSB Sites. By scenario D, the intrinisic
activity of a DSB site and its efficiency in effecting trans inhibition
areunrelated.Thus,DSBsoccurringat a weak DSBsite mightstill
be perfectly efficient at inhibiting DSB formation at the allelic
position on the homolog. Distribution analysis would detect such
a feature if it were possible to specifically identify the events
arising only from one particular weak site. In contrast, physical
analysis of population average DSB levels will detect trans
of chromatids (Left), irrespective of any trans effect. In addition, some frac-
tion of the nuclei, K, that would otherwise have given rise to DSBs on both
homologs give rise, instead, to a DSB on only one of the two homologs
(Right). K reflects trans inhibition in which, at the assayed site, a DSB on one
chromosome is inhibited by a DSB either at the exact allelic site on the ho-
molog (allelic inhibition) or in the vicinity of that allelic site (spreading in-
hibition). M and K are thus “intrinsic DSB efficiency per pair of chromatids”
and “strength of trans inhibition,” respectively. Scenario D is describable by
M2K; F(2) = M2(1 − K). And predicted probabilities of nuclei exhibiting zero,
one, or two recombination events (F0, F1, and F2) can be converted to fre-
quencies of observable events (P0, P1, and P2) as a function of inv (defined as
in scenarios A–C) as for other scenarios (text and Fig. S1 C and D). (B) By
scenario D, each experimental dataset (T0, T1, or T2) is described by unique
values of K and M (symbols; surrounding areas = 95% confidence levels from
Table 1 and Table S1) (text). HIS4LEU2, M = 0.68, K = 0.44; HIS4LEU2 old, M =
0.73, K = 0.65; ndj1Δ, M = 0.53, K = 0.12; mec1Δ, M = 0.56, K = −0.15; tel1Δ, M =
0.67, K= −0.1; sgs1-ΔC795, M =0.72, K= 0.48; and spo11HA, M = 0.46, K= 0.27.
(C) DSB levels in WT and tel1Δ at HIS4LEU2 in a rad50S background over time
in meiosis. (Upper) One-dimensional gels; (Lower) quantification.
Scenario D. (A) DSBs occur with an intrinsic probability of M per pair
Zhang et al.PNAS
| December 13, 2011
| vol. 108
| no. 50
inhibition only at very hot sites. Trans inhibition reduces DSB
formation only the minority subset of nuclei that would otherwise
have undergone two DSBs (one on each homolog), which is
a significant fraction of the total only for the very hottest DSB
sites. This feature explains why, in previous physical analyses of
DSB levels, trans inhibition was detected only for the two hottest
analyzed sites [refs. 5 (case D) and 6]. Even at his4::URA3-arg4,
a stillquite active DSBhotspot,trans inhibition isreadily detected
detected by physical analyses, where presence/absence of in-
hibition is predicted to alter DSB/event levels by only ∼1% (Fig.
S6). This consideration has a further implication: The fact that
another type of trans effect could be detected by physical analysis
even at weaker sites (introductory section at the beginning of this
paper) implies that this second process is affecting many or all
nuclei, not a minority subset, in accord with its occurrence before
DSB formation (introductory section and refs. 5, 8, and 27).
The presented results demonstrate that meiotic DSBs at a single
initiation site are not independently distributed among the four
available chromatids. Logically, DSBs could be constrained to
occur one-per-pair of chromatids and/or one-per-quartet of
chromatids. Experimentally observed patterns of nucleus types in
WT meiosis are not compatible with either of these constraints
alone but are well explained by a combination of the two. It
appears that DSB formation (i) is always constrained to occur
one-per-pair of chromatids, presumptively one-per-pair of sis-
ters, and (ii) is constrained in some nuclei to occur one-per-four
chromatids. The latter constraint implies communication be-
tween homologs in trans. This trans inhibition spreads for some
distance along the target chromosome. Mutant phenotypes raise
the possibility that signal transduction kinases Mec1 (ATR) and
Tel1 (ATM) are potential direct effectors of trans inhibition.
Molecular Basis for Constraints on DSB Distribution Among Chromatids.
A one-per-pair constraint on DSB formation presumptively
reflects a situation in which a DSB can occur on only one of the
twosister chromatids. This constraint, not previously appreciated,
could reflect features built into pre-DSB recombination com-
plexes, which contain both sisters (11, 17, 28), via core recombi-
nosome features and/or surrounding chromosome structural
determinants (13, 17, 28). A one-per-four constraint was pre-
viously implied by physical analysis of DSBs. That analysis also
suggested that this trans inhibition effect is directly mediated by
DSBs, with occurrence of a DSB on one chromosome actively
disfavoring formation of a DSB on the homolog partner, and
showed that this effect spreads some distance away (5, 6). The
present study confirms and extends these conclusions.
By the analysis presented, several mutants exhibit only a one-
per-pair constraint. Scenario D analysis envisions that this phe-
notype implies loss of trans inhibition. Mutants lacking Mec1 or
Tel1, related chromosome-based signal transduction kinases ho-
mologous to ATR and ATM, respectively, are two such mutants.
Direct involvement of these particular molecules in this process
would be attractive, given their diverse central roles in complex
global and local regulation of chromosomal processes in normal
cellular programs, including CO interference during meiosis in
Drosophila, which is also a “spreading trans inhibition effect” (29–
31). Also, a recent mouse study identified ATM as a negative
regulator of DSB formation, with an increase in DSB levels rel-
ative to WT, analogous to the findings reported here (32). Thus,
abrogation of trans inhibition could explain all or part of ATM’s
role in that organism. This analysis further suggests that Mec1/
ATR (but not Tel1/ATM) is also required for efficient DSB
formation per se, irrespective of its role in trans inhibition, im-
plying two mechanistically distinct functions for this molecule
duringearly meiotic prophase. Absence of Ndj1 confers defects in
both DSB formation and trans inhibition similar to those con-
ferred by absence of Mec1/ATR. Because Ndj1 appears to
localize specifically at telomeres (24, 25), its roles may be indirect,
e.g., via triggering of regulatory effects that alter Mec1 activity.
DSB studies have also revealed that an increase in DSB activity
at one position tends to inhibit DSBs in the vicinity in cis (In-
troduction). This effect, not visible in the present analysis, could
potentially operate by a common mechanism to trans inhibition.
Alternatively, cis and trans inhibition might be distinct, occurring
by differentiable mechanisms, e.g., on the donor and “recipient”
homologs and/or before and after DSB formation, respectively.
Implications for Patterning of DSBs/Interhomolog Interactions. In any
given nucleus, DSBs occur at a subset of all available possible
positions, differently in different nuclei. When a DSB contacts its
homolog partner and sets up an interhomolog interaction, it
concomitantly sets up trans inhibition of DSB formation on the
homolog. This effect necessarily also sets up trans inhibition of
additional interhomolog interactions. Such inhibition occurs not
onlyat theallelic position onthe targetchromosome butalso over
some distance in the vicinity of that position along the target
chromosome, thus disfavoring formation of interhomolog inter-
actions nearby. The existence of spreading trans inhibition will
confer two important effects on spatial patterning of DSBs and,
most critically, interhomolog interactions (Fig. 4 A and B).
Even spacing. Occurrence of a DSB and ensuing interhomolog
interaction at one position disfavors subsequent occurrence of
other such events in the immediate vicinity of that first in-
teraction. Then, as the DSB/interhomolog interaction process
continues, subsequent events will tend to fill in the holes between
previous events. As a result DSB/interhomolog interactions will
tend to be evenly spaced along the chromosome (Fig. 4A) (ref.
12 and discussion in ref. 16), thus explaining the experimentally
observed pattern (Introduction).
Homeostasis. When the intrinsic probability of DSB formation at
a particular locus decreases, the level of spreading trans in-
hibition emanation from that position will also decrease, thus
resulting in an increase in the overall probability of DSBs (on the
of DSBs and resultant interhomolog interactions. (A) Starting with a random
array ofpre-DSB recombination complexes (1, gray boxes), sequential DSBsand
interhomolog interactions will tendtofillin the holes between prior events(2),
conferring a tendency for even spacing (3). In 2, pre-DSB recombinosomes un-
affected by trans inhibition could be inactivated by cis inhibition (text). (B)
(Upper) Given an array of pre-DSB recombination complexes (colored boxes),
formation of DSBs and interhomolog interactions at any particular assayed lo-
cus (black box) will be inhibited by spreading trans inhibition emanating from
DSBs at nearby loci on the homolog (colored lines). (Lower) Given a global
decrease in the intrinsic probability of DSB formation throughout the genome,
e.g., by a defect in Spo11-mediated catalysis (and thus a reduced probability of
be inhibited by spreading trans inhibition (seen for a given assayed locus by
fewer colored lines). Thus, at all loci throughout the genome, the effect of re-
duced catalysis efficiency will be partially compensated for by the reduction in
spreading trans inhibition, resulting in “homeostasis” for both DSBs and, more
importantly, interhomolog interactions.
| www.pnas.org/cgi/doi/10.1073/pnas.1117937108Zhang et al.
homolog) and interhomolog interactions in the vicinity (Fig. 4B).
By extension, if there is a global decrease in the probability of
DSB formation throughout the genome, every locus will be
similarly affected. As a result, throughout the genome, the levels
of both DSBs and interhomolog interactions will be decreased
less than they would otherwise have been. Put another way, be-
cause of spreading trans inhibition, both DSB formation and
establishment of interhomolog interactions are homeostatic
processes: A local or global reduction is partially compensated by
a concomitant reduction in resulting spreading inhibition.
General Implications for Spatial Patterning. The logic described
above for DSB formation and establishment of interhomolog
interactions is the same as that previously proposed for CO pat-
terning, with a driving force for CO designation, and each CO
designation event nucleates a spreading zone of inhibition that
disfavors further CO designation events nearby (CO interference).
As more and more events occur, they will fill in the holes between
prior events, yielding a tendency for even spacing of COs along
a chromosome (12, 14). Additionally, CO designation has been
shown to exhibit homeostasis (15, 33). We therefore propose that
meiotic recombination-mediated interhomolog interactions are
spatially patterned by (at least) two successive rounds of patterning
that involve precisely the same logic, first for DSBs and then for
COs. The basic featuresofevenspacingand homeostasis willapply
to any spatial patterning process that involves the basic logic of
a “driving force” for occurrence of an event plus coupling of event
occurrence to spreading inhibition and to any specific mechanism
that operates by imposition and relief of mechanical stress (12).
Biological Significance(s) of One-per-Two and One-per-Four Constraints
sisters ensures that, if ensuing interhomolog recombination goes
awry, the sister chromatid will always be present as an intact
template for repair of the DSB. Constraining DSB formation to
in establishment of an interhomolog interaction will tend not to
occur twice at the same (allelic) chromosomal position or, given
spreading of trans inhibition, at two nearby chromosomal posi-
tions. Given that interhomolog recombinational interactions ulti-
mately develop into discrete physical linkages between the
structural axes of homologs (e.g., ref. 16), it may be particularly
important not to try to have two such linkages in close proximity
because attempted formation of two interaxis “bridges” at the
same or nearby positions is likely to be deleterious. Because DSB-
mediated interhomolog interactions mediate whole-chromosome
juxtaposition (“pairing”) of homologs, even spacing will be ad-
vantageous in ensuring that this process occurs regularly along the
entire length of a chromosome. Homeostasis should also be ad-
vantageous because, as pointed out previously for CO homeostasis
(15), it provides a buffering system that protects meiotic chromo-
some dynamics from local, regional, and/or global defects in DSB
Materials and Methods
Strains are derived from SK1 (Table S2). Tetrad asci were dissected onto YPD
plates. Spore phenotypes were determined by replica plating and colony
PCR or Southern blot (SI Materials and Methods). The theoretical DSBs dis-
tributions at a single DSB site were described by a set of binomial equations
(Fig. S1) and the level of invisible events (inv) was specified for each strain as
described in SI Materials and Methods.
ACKNOWLEDGMENTS. We thank S. Keeney, N. Hunter, and D. Bishop for
strains/plasmids. Support (for L.Z.) and partial support (for A.S. and K.P.K.)
for this research were provided by National Institutes of Health Grant
GM044794 (to N.E.K.). A.S. was also supported by Consiglio Nazionale delle
Ricerche and by Italian Ministry of Foreign Affairs (2011 Grant “Con il con-
tributo del Ministero degli Affari Esteri, Direzione Generale per la Promo-
zione del Sistema Paese”). K.P.K. was also supported by a National Research
Foundation of Korea grant funded by the government of the Republic of
Korea (Ministry of Education, Science and Technology, no. 20110029504).
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| December 13, 2011
| vol. 108
| no. 50
Correction for “Meiotic double-strand breaks occur once per pair
quartet of chromatids,” by Liangran Zhang, Nancy E. Kleckner,
Aurora Storlazzi, and Keun P. Kim, which appeared in issue 50,
December 13, 2011, of Proc Natl Acad Sci USA (108:20036–20041;
first published November 28, 2011; 10.1073/pnas.1117937108).
The author line should appear as “Liangran Zhang, Keun P.
Kim, Nancy E. Kleckner, and Aurora Storlazzi.”
Additionally, the authors note that Aurora Storlazzi should be
listed as an additional corresponding author. The corrected author
line and correspondence footnote appear below. The online ver-
sion has been corrected.
Liangran Zhang, Keun P. Kim, Nancy E. Kleckner1,
and Aurora Storlazzi1
1To whom correspondence may addressed. E-mail: firstname.lastname@example.org or aurora.
| January 24, 2012
| vol. 109
| no. 4