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Vol. 11, Issue 6, 959-980, June 2001 Genome-Wide Epistatic Interaction Analysis Reveals Complex Genetic Determinants of Circadian Behavior in Mice1 Howard Hughes Medical Institute; 2 Department of Neurobiology and Physiology, Northwestern University, Evanston, Illinois 60208-3520, USA; 3 The Jackson Laboratory, Bar Harbor, Maine 04609, USA
Genetic heterogeneity underlies many phenotypic variations observed in circadian rhythmicity. Continuous distributions in measures of circadian behavior observed among multiple inbred strains of mice suggest that the inherent contributions to variability are polygenic in nature. To identify genetic loci that underlie this complex behavior, we have carried out a genome-wide complex trait analysis in 196 (C57BL/6J X BALB/cJ)F2 hybrid mice. We have characterized variation in this panel of F2 mice among five circadian phenotypes: free-running circadian period, phase angle of entrainment, amplitude of the circadian rhythm, circadian activity level, and dissociation of rhythmicity. Our genetic analyses of these phenotypes have led to the identification of 14 loci having significant effects on this behavior, including significant main effect loci that contribute to three of these phenotypic measures: period, phase, and amplitude. We describe an additional locus detection method, genome-wide genetic interaction analysis, developed to identify locus pairs that may interact epistatically to significantly affect phenotype. Using this analysis, we identified two additional pairs of loci that have significant effects on dissociation and activity level; we also detected interaction effects in loci contributing to differences of period, phase, and amplitude. Although single gene mutations can affect circadian rhythms, the analysis of interstrain variants demonstrates that significant genetic complexity underlies this behavior. Importantly, most of the loci that we have detected by these methods map to locations that differ from the nine known clock genes, indicating the presence of additional clock-relevant genes in the mammalian circadian system. These data demonstrate the analytical value of both genome-wide complex trait and epistatic interaction analyses in further understanding complex phenotypes, and point to promising approaches for genetic analysis of such phenotypes in other mammals, including humans.
Circadian rhythms represent a complex set of phenotypes for genetic analysis. Such rhythms, present in a broad array of biological processes and taxa, are endogenously generated. These cycles persist in the absence of exogenous time cues with a period close, but rarely equal to, 24 h. In the presence of a daily light-dark cycle, these circadian rhythms are synchronized (entrained) to a 24-h period. The precise nature of the time-keeping mechanism itself remains unclear, but defining work from the modern field's inception during the mid-twentieth century demonstrated a number of unique characteristics of circadian clocks, including their self-sustaining nature, their ability to be precisely synchronized by the environmental light-dark cycle, and the persistence of similar formal properties among diverse organisms. These initial studies also demonstrated that the clock's action is genetic in origin, not relying on the rhythmic nature of the environment for its daily oscillation. Molecular genetic analysis of circadian rhythms, beginning with the
identification of the period (per) gene in
Drosophila melanogaster (Konopka and Benzer 1971 A mammalian feedback loop model has been developed recently, concurrent
with the rapid identification of at least nine genes proposed to be
involved in mammalian circadian rhythms (Bunger et al. 2000 As more circadian genes have been characterized, and as the model of
the mammalian circadian clock has been elaborated, it has become
evident that multiple functional interactions between molecules are
necessary for the generation and regulation of mammalian circadian
rhythms. Among these include the dimerization and transactivational capabilities of CLOCK and BMAL1 (a positive aspect of the feedback loop) (Gekakis et al. 1998 Such complexity might have been predicted in hindsight. Although a
transcriptional feedback loop with a limited number of components may
be sufficient to generate a rudimentary circadian rhythm (Leloup and
Goldbeter 1998 Furthermore, no comprehensive attempts have yet been made to identify all (or even most) mammalian circadian clock genes (e.g., by a recessive saturation mutagenesis screen). Thus, it is likely that many genes that underlie circadian rhythms remain to be discovered. Unlike the present understanding of the Drosophila circadian clock, in which all of the proposed genetic components have been characterized by mutations bearing effects on circadian behavior, many of the proposed components of the mammalian clock do not have demonstrated effects on circadian behavior. Identifying the nature or source of the genetic variability present within strains of mice provides an alternative means to illuminating underlying genetic contributions to this behavior. In light of the evident polygenic underpinning to mammalian circadian
behavior, and the uncertainty of the contributions of many of the
proposed clock genes to this phenotype, we undertook a genome-wide
quantitative trait mapping strategy using an F2 hybrid
intercross between BALB/cJ and C57BL/6J mice to characterize loci in
the mouse genome that contribute to variability of circadian behavior.
A similar intercross strategy, limited to an analysis of circadian
period, has led to the identification of loci significantly affecting
this circadian behavior in the flowering plant, Arabidopsis thaliana (Swarup et al. 1999 Because of the genetic complexity of the circadian pacemaker, in
particular the multiple molecular interactions required for its proper
function, any analysis limited to treating each locus independently is
not sufficient. In a complex system like this, for which the underlying
genetic contributions are also likely to be complex, it is important to
establish whether and how the loci contributing to phenotype interact.
There are likely to be interactions among specific alleles at different
loci that also contribute to the circadian phenotypes. Such epistatic
interactions have been reported to contribute to the variability of
other complex phenotypes, including diabetes and cancer
susceptibility (Fijneman et al. 1996
Inheritance of Circadian Rhythms in an Intercross between the C57BL/6J and BALB/cJ Inbred Mouse Strains To collect our phenotypic data, we began by examining the
distribution of circadian activity among mice from a two-generation intercross arranged between the C57BL/6J (B6) and BALB/cJ (BALB) strains. We produced a total of 196 F2 progeny for phenotypic and genetic analysis. We used a wheel-running assay of circadian behavior to determine the activity phenotypes of mice from this intercross. Mice exhibit a robust circadian rhythm of wheel running that is under direct control of the circadian pacemaker (Schwartz and
Zimmerman 1990
Mapping Loci Underlying Complex Phenotypes in (C57BL/6J X BALB/cJ) F2 Hybrid Mice In recent years, mapping complex phenotypes by quantitative trait
locus (QTL) analysis has become an increasingly efficient technique for
the genetic dissection of complex traits. Although a number of variants
on the basic protocol that can increase power and reduce material costs
have been proposed and successfully applied, including selective
genotyping strategies (Lander and Botstein 1989
Free-Running Period The period of oscillation is a key factor in describing an observed rhythm. The activity-rest behaviors of mice housed under a 24 h light-dark cycle (LD) entrain to the 24 h period of the lighting regime to which they are exposed. Once released into constant darkness, free of entrainment cues, each mouse will begin to free run with a period that soon reflects not the cycle to which it was formerly entrained, but the innate cycle of its own circadian pacemaker. Previous studies have indicated that B6 mice express circadian periods of activity that can range from 23.2 to 24.1 h (Schwartz and Zimmerman 1990 ). The BALB/c
mouse, on the other hand, is notable for an extremely short period
around a mean of 22.6 h (Possidente and Hegmann 1982). As anticipated from these previous reports, the free-running periods of the BALB parental mice observed in our study (22.88 h ± 0.602) were
significantly shorter than those of the B6 mice (23.61 h ± 0.068,
P<10 6). Figure 2A shows a histogram of this trait
in each generation. Although the B6 population exhibited a distribution
with little variance, we observed considerable variation among BALB
mice. The initial outcross between B6 and BALB mice yielded
F1 progeny with a distribution of periods that closely
resembles that of the B6 parental strain, ranging from 23.2 to 23.7 h,
indicating the presence of B6 alleles that regulate this trait in a
dominant manner. Consistent with the divergent phenotypes of its
founder strains, the F2 generation from this cross expressed
a much wider period distribution, ranging from 22.5 to 24.7 h. We also
observed significant differences (P<0.05) between male and
female mice in the F2 generation (Table 1).
To detect loci with significant main effects, we computed one-way ANOVA
F-statistics (with 2 and n-3 degrees of freedom [df]) at each marker
in a genome-wide scan. Significance thresholds were estimated by the
analysis of 1000 permutations of the original data. We recorded the
maximal F value for each permuted data set and found the critical
values to be 7.80 and 10.52 (for alpha = 0.05 and 0.01, respectively). This genome scan (Fig. 4A)
identified significant associations with markers on chromosomes 4 and
5. Peaks occur at markers D4Mit178 (F = 13.46) and D5Mit30
(F = 9.80). We note that the chromosome 4 peak is sharp whereas the
chromosome 5 peak extends over much of the chromosome. We named these
loci Free-running period (Frp)-1 and
Frp-2. The average free-running period for mice homozygous at
the Frp-1 locus for the B6 allele (B/B) was 23.32 h, versus
23.49 h for heterozygotes (B/C) and 23.68 h for BALB homozygotes (C/C).
Interestingly, the B6 allele at this locus is associated with shorter
period lengths, whereas the BALB allele is associated with longer
period lengths, which is in direct contrast to the period lengths
observed in the parental strains. Effects of Frp-1 appear to
be additive, such that each BALB allele adds about 10 min to the
free-running period. The average free-running period for mice
homozygous for the B6 allele (B/B) at Frp-2 was 23.39 h,
versus 23.44 h for heterozygotes (B/C) and 23.68 h for BALB homozygotes
(C/C), again contrary to strain behavior. The B6 allele appears to be
dominant for period at the Frp-2 locus. Additional peaks are
noted on chromosomes 12 and 18 in this genome scan.
Phase Angle of Entrainment The phase angle of entrainment is defined as the phase difference between the onset of the activity rhythm and the light cycle to which the animal is entrained. By convention, the phase angle has a negative value when activity leads the entrainment cue, and a positive value when it lags. In the case of nocturnal animals, onset of activity is compared relative to the onset of darkness. To entrain to a 24 h cycle, mice, whose rhythms are typically shorter than 24 h, need to see light at dusk, which produces phase delays. Measuring this pre-dark arousal is complicated however, because in mice light exposure tends to suppress locomotor activity, thus masking the true timing of circadian arousal. The most reliable way to measure this trait is therefore to transfer an entrained animal into constant darkness and then record the onset of activity (in darkness) and compare this to the expected time of the entrainment cue (DeCoursey 1960). Figure 2B shows phenotype
distribution of this trait in each generation.
We observed significant (P<109) differences
between B6 and BALB mice in the phase angle of entrainment. B6 mice
became active an average of 12 min after the scheduled time of lights
off, whereas activity of BALB mice preceded lights off by an average of
3 h and 36 min. BALB mice show significantly greater variance than B6
mice. The phase angle distributions of both the F1 and
F2 generations were generally continuous but deviated
significantly from normal, skewing towards the B6 parent  once
again reflecting the dominance of B6 alleles. We observed no
significant differences between male and female cohorts in each
generation. The single marker genome scan for phase (Fig.
5A) shows two distinct peaks on chromosome 12 at D12Mit81 (F = 9.22) and at D12Mit7 (F = 10.31) both of which exceed the alpha = 0.01 permutation critical value of 8.62. These loci are named Angle-1 and Angle-2, respectively. The
average phase angle for mice homozygous at Angle-1 locus for
the B6 allele (B/B) was  1.08 h, versus 0.79 h for heterozygotes
(B/C) and 2.10 h for BALB homozygotes (C/C). The average phase angle
for mice homozygous at Angle-2 locus for the B6 allele (B/B)
was 0.27 h, versus 1.48 h for heterozygotes (B/C) and 1.77 h for
BALB homozygotes (C/C). These peaks appear to be distinct from the chromosome 12 locus Frp-3. Additional peaks are noted on
chromosomes 7 and 18 in the main effects genome scan. The pairwise
genetic interaction genome scan (Fig. 5B, Table 3) did not detect any marker pairs that exceeded the critical values 6.48 and 7.24 (for alpha = 0.05 and 0.01). This trait has a very skewed distribution (Fig. 2B), and thus the thresholds were much higher than for other traits. When we first consider loci that meet a less stringent genome-wide significance level (alpha = 0.1) for which the threshold value is 5.31, a consistent picture emerges. Three clusters of marker
pairs with peaks at D7Mit30 and D12Mit81 (corresponding to
Angle-1) (F-all = 5.77), D12Mit81 and D18Mit17
(F-all = 6.21), and D12Mit195 (corresponding to Angle-2, as
with D12Mit7; see above) and D18Mit17 (F-all = 5.47) meet this
criterion. (An additional pair, D7Mit30 and D12Mit195, falls just below
the threshold; F-all = 5.18). We have named these loci on chromosomes
18 and 7 Angle-3 and Angle-4, respectively (Table 3).
There is weak evidence for interaction between Angle-1 and
Angle-3 (F-int = 2.65, P = 0.016). An additional
cluster with peak (F-all = 5.23) at D8Mit13 and D12Mit263 approaches
the significance threshold. There is significant evidence for
interaction between these loci(F-int = 5.89, P = 0.00053).
The chromosome 12 locus D12Mit263 is within the region spanned by
Angle-2. The chromosome 8 locus is named Angle-5. A multiple regression model (Table 4) with all five phase angle loci
(Angle-1, Angle-2, Angle-3,
Angle-4, and Angle-5) and two interaction effects explains
37% of the total variance in the phase angle phenotype. The multiple
regression without Angle-5 and its interaction with
Angle-2 (data not shown) explains only 29% of the variance in
phase angle. Graphical summaries of the two interaction effects are
shown in Figure 5C,D.
Amplitude of Circadian Rhythm The amplitude of a circadian rhythm reflects the strength or robustness of the rhythm, i.e., the extent to which the circadian behavior is separated into distinct active and resting periods within each cycle. In this study, we have estimated the amplitude of the circadian rhythm from the power spectral density of the circadian peak obtained by Fourier analysis (Bracewell 1986). This measure is scored
based on the percentage of activity falling within the circadian peak,
with higher percentage scores reflecting higher amplitude rhythms.
Figure 2C shows the distribution of this trait in each generation. We
observed that amplitudes of circadian activity were significantly
greater (P<109) in B6 mice than in BALB mice, but
that distributions in both strains were not continuous, possibly
reflecting environmental effects and the low numbers of animals
assayed. We observed a significant sex difference in F1
(P<0.05) and F2 (P<0.001) generation, where amplitude was significantly lower in male than female mice; no
such sex differences were detected in B6 and BALB mice. Again in the
F1 generation, we observed a discontinuous distribution that
skewed towards the B6 parentals. Measure of amplitude in the
F2 generation, however, were distributed both normally and continuously.
The single marker genome scan (Fig. 6A)
shows a significant peak at marker D4Mit27 (F = 8.86). We identified
genome-wide thresholds based on 1000 permutation test of 7.50 and 8.90 (for alpha = 0.05 and 0.01, respectively). We named this locus
Amplitude (Amp)-1. The average amplitude
score for mice homozygous at the Amp-1 locus for the B6 allele
(B/B) was 13.99%, versus 12.67% for heterozygotes (B/C) and 9.74%
for BALB homozygotes (C/C). This suggests that the B6 Amp-1
allele acts semidominantly over the BALB allele. The pairwise genome
scan (Fig. 6B, Table 3) shows a single significant pair at D1Mit33 and
D4Mit27 (corresponding toAmp-1) (F = 6.46). The
genome-wide permutation critical values are 5.15 and 5.63 (for
alpha = 0.05 and 0.01). This marker pair shows a significant interaction (F = 6.88, P = 0.000036) which is summarized
in Figure 6D. The locus on chromosome 1 we named Amp-2. High
values of the amplitude score were associated with homozygous B6 at
Amp-1 in combination with homozygous BALB at Amp-2
(Fig. 6D). A multiple regression model was fit to amplitude including
both markers and the interaction. Because gender has a significant
effect on amplitude, we included a term for gender in the joint model;
there was, however, no evidence for interactions between gender and the
QTLs. The regression model explains 26% of the total variance of this
trait in the F2 population (Table 4). Of this, 20% is
attributable to the genetic effects and 5% is attributable to
Amp-1 alone, thus the Amp-1-Amp-2
interaction is the major contributor to genetic variance in this trait.
Activity Level Although the relationship between the level of wheel running activity and circadian rhythmicity is poorly defined, an animal's activity level may reflect broad parameters of the circadian axis, such as the amplitude of the pacemaker's oscillator, the strength of the oscillator's coupling to its output, or the amplitude of the behavioral output. In addition several studies have demonstrated that activity itself can act as an entrainment cue, feeding back to the circadian pacemaker (Edgar and Dement 1991; Edgar et al. 1991a,b;
Mrosovsky 1995).
We determined the level of each animal's daily activity by averaging
the number of daily wheel revolutions over 15 consecutive cycles in
constant darkness. Figure 2D shows phenotype distribution of this trait
in each generation. We observed significantly lower (P<103) daily activity levels in BALB mice than
in B6 parentals. Once again we observed significant sex difference in
F1 (P<0.001) and F2
(P<108) mice, with the activity levels of male
mice significantly lower than female mice.
The single marker genome scan (Fig. 7A) for
this trait shows no significant peaks. However the pairwise genome scan
(Fig. 7B, Table 2) identifies the marker pair D16Mit106 and
DXMit27 (F-all = 5.04), whose significance falls at the
alpha = 0.05 permutation threshold. There is a significant
interaction effect (F = 7.23, P<104) between
these loci. We named the locus on chromosome 16, Activity (Act)-1 and the locus on the X chromosome,
Act-2. It is important to note that X chromosome loci in males
in this F2 population are hemizygous (B or C). In females,
the X chromosome genotypes are either BALB homozygote (C/C) or B6/BALB
heterozygote (B/C) because the F1 generation was produced
using BALB female by B6 male matings, thus females in the F2
generation will have at least one nonrecombinant BALB chromosome X. Therefore we carried out separate analyses of male and female
F2 progeny. There was no evidence for a significant effect of
Act-1, Act-2, or the interaction in males. However
there is a significant effect in females as indicated by the multiple
regression model shown in Table 3. There are no significant main
effects at Act-1 or Act-2 but their interaction is significant. The interaction is summarized
graphically in Figure 7C,D. Heterozygosity at Act-2 increases
activity in females that are homozygous for the B6 allele (B/B) at
Act-1, decreases activity in females that are heterozygous at
Act-1 and has no effect in females that are homozygous for the
BALB allele (C/C) at Act-1. These loci explain
19% of the variation in activity among F2 females
(Table 4).
Dissociation A clear difference between the locomotor activity of BALB and B6
mice is that the BALB activity rhythm is much more fragmented (dissociated) than B6. B6 mice usually have a major activity onset component followed by a very small offset component. In contrast, BALB
mice typically have multiple activity components, particularly in
constant darkness (DD). In the F1 generation the pattern of activity is similar to B6 in this respect. Some F1 mice
showed no visible activity offset components. The period of each
component was similar in this generation and the parentals. In the
F2 generation, this phenotype was quite variable. Some mice
had activity profiles similar to B6 or BALB. Interestingly, some mice
exhibited patterns that had not been observed in the parental
population. For example, in some mice, two major activity components
are present (onset and offset), which free-run with different periods
and later consolidate. In others, a major activity component is present
with multiple fragmented components, as though discrete aspects of both
the B6 and BALB phenotypes were being expressed simultaneously. This kind of dissociation of activity has been observed in mice and other
rodents. At an extreme, it can lead to a split of the locomotor activity into two components that drift apart and then synchronize at
phases that are 12 h (180°) apart. Such splitting of the locomotor activity in the golden hamster is well documented (Pittendrigh and Daan
1976 We developed a scoring method to characterize this dissociation phenotype in our F2 panel. This is a qualitative trait with rankings from 0 to 5 by the degree of dissociation of activity fragments. We defined d = 0 as an activity rhythm which has a large activity onset component followed by a very small or undetectable activity offset component, both of which have the same or very similar endogenous period. The subsequent scores, d = 1 through d = 5, correspond to activity rhythms that are increasingly disrupted. Figure 3A shows a typical example of each ranked mouse activity record in the F2 population. All B6 mice analyzed were categorized as d = 0. For the BALB strain, only 1 of 17 mice were categorized as d = 0, whereas the rest showed some degree of dissociation. In the F1 generation, 22 of 24 mice were categorized as d = 0, whereas the remaining two were scored as d = 1 and d = 2. The phenotype of the F1 population was close to the B6 parent, once again reflecting the dominance of B6 alleles. The distribution of the F2 generation deviated significantly from normal, skewing toward the B6 phenotype (Fig. 3B). One hundred sixteen out of 196 mice (60%) were categorized as d = 0. There were only four mice categorized as d = 5. This suggests that multiple QTL are involved in this trait and the effect of each alone may be very weak. As we anticipated, the single marker genome scan (Fig.
8A) on the trait dissociation shows no
significant peaks. However the pairwise genome scan (Fig. 8B, Table 2)
identifies the marker pair D12Mit251.1 and D15Mit28
(F-all = 5.90) as being significant at the genome-wide 0.1 level. The
genome-wide critical values are 5.5 and 6.0 for alpha = 0.1 and 0.05, respectively. There is a significant interaction between these loci
(F-int = 8.80, 1.5 × 10
Mapping Candidate Clock Genes To assess whether the loci mapped in this study correspond to known
clock candidate genes, we genetically mapped five of the proposed clock
genes (mPer1, mPer2, mPer3, mCry1,
and mCry2) (Fig. 9). The locations
of the remaining four genes have been reported previously and are shown
in Figure 9 (King et al. 1997
mPer1 We identified linkage between mPer1 and SSLPs on mouse chromosome 11. mPer1 was subsequently mapped to chromosome 11, 1.0 cM (1/103) distal of D11Mit29 and 10.7 cM (11/103) proximal of D11Mit39.mPer2 We identified linkage between mPer2 and SSLPs on mouse chromosome 1, leading to our mapping the gene to mouse chromosome 1, 14 cM (67/482) distal of D1Mit22 and 5.5 cM (26/482) proximal of D1Mit308.mPer3 We identified linkage between mPer3 and SSLPs on the distal end of mouse chromosome 4 resulting in the mapping of mPer3 to the region of D4Mit42 (0/94 recombination events).mCry1 mCry1 was linked strongly to loci on mouse chromosome 10; the mCry1 genetic locus was mapped 8.7 cM (8/92) distal of D10Mit20 and 5.4 cM (5/92) proximal of D10Mit11.mCry2 The mCry2 locus showed a strong linkage to loci on mouse chromosome 2 and mapped 2.1 cM (2/94) distal of D2Mit15 and 4.3 cM (4/94) proximal of D2Mit97.
We have applied novel whole-genome techniques, complex trait (quantitative trait locus), and genetic interaction analyses in a segregating intercross (F2) population, to characterize genetic polymorphisms affecting circadian rhythms in the mouse. Prior to our experiments, two general strategies have been used for clock gene identification investigations in mammals: analysis of single gene mutations, and characterization of genes identified through cross-species homology. These experiments, although they have laid an essential groundwork, do not include a more thorough examination of the breadth and complexity of genetic influences on circadian behavior. Our effort has led to the identification of 14 loci, based on the analysis of five discrete aspects of circadian behavior, that make significant contributions to the variation of this behavior in mice. We have identified several loci that have significant main effects on quantitative circadian behaviors, including free-running period, phase angle of entrainment, and amplitude of the circadian rhythm. Many of these 14 loci, however, were identified primarily, or solely, from strong epistatic interactions detected among specific alleles at different genetic loci. Indeed, a fundamental conclusion to be drawn from these data is that circadian phenotypes can be significantly affected by complex genetic interactions at multiple loci. This introduces a new, previously undescribed, aspect to the analysis of circadian behavior. The genome-wide interaction analysis identified numerous pairs of loci that, in particular allelic combinations, had epistatic effects on circadian behavior much greater than either of the loci alone. (Additional higher order interactions may also be present; however, our current sample size is not large enough to reliably detect these.) This epistasis is most clearly seen in the analysis of the amplitude of the circadian rhythm, in which particular alleles of the loci, Amp-1 and Amp-2, each had relatively little effect on the phenotype individually, but in specific allelic combination produced a very significant effect (Fig. 6). Results such as these underscore the complexity of this behavior and argue against any approach that devotes all analysis of the circadian clock to single gene effects. A better understanding of such epistatic interactions will be essential to fully understanding the complex nature of circadian rhythms, and complex behaviors in general. We have identified five discrete measures from the records of locomotor activity in the pedigree described here. However, these five phenotypes are not likely to be completely independent of each other. For example, extensive consideration has been given to models that integrate the phase angle of entrainment with the endogenous period and to suggestions that period itself can be modified by a feedback effect of prolonged or intense activity. With these types of phenotypic interactions in mind, it is interesting to compare the map positions of the loci we have identified here to see if variation in these five phenotypic measures might arise from polymorphisms in similar loci. Interestingly, in most cases, the loci are not the same; variation in each of the five measures is affected by a unique set of underlying genes (Fig. 9). There are two possible exceptions to the apparent independence of these phenotypic measures. Frp-1 (35.5 cM) and Amp-1 (42.5 cM) map to similar positions on chromosome 4, and Frp-3 (22 cM) and Disso-1 (29 cM) map to similar positions on chromosome 12. The phenotypes that we would have predicted, a priori, to be the result of similar genetic loci, namely period, phase, and activity level, shared no loci in common in this analysis. Similarly, one might ask how these loci compare to the map positions of
the genes proposed to form the core of the mammalian circadian clock.
Again, as with the different loci arising from multiple phenotypic
measures, the map positions of these genes generally differ from the
loci identified here (Fig. 9). A possible exception is CKI An additional comparative mapping question to consider is how our loci
compare to other complex loci determined previously, in both circadian
and potentially related behaviors. There have been attempts made to
identify circadian rhythm QTLs in B6 × DBA recombinant inbred
strains of mice (Hofstetter et al. 1995 If the underlying genes affected by the loci reported here are unlikely
to be among the proposed clock genes (based on map positions), then
what genes might be affected? There are multiple levels at which these
loci may interact with the clock mechanism and its outputs to affect
behavior. For example, although the molecular clock itself is likely to
be cell autonomous, there are important integrations that result from
interactions among such individual `clock cells` within the pacemaker
tissue (in mammals, the hypothalamic SCN) (Liu et al. 1997 Although the power of the genetic analyses described extends beyond
gene discovery, including revealing genetic interactions among
different loci and providing a landscape of the genes underlying a
given complex phenotype, identification of the genes themselves is
still of great interest. Although cloning is difficult when beginning
with quantitative loci such as these, it is not impossible (Nadeau and
Frankel 2000 Strategies for characterizing loci underlying complex or quantitative
phenotypes usually begin with the identification of strains that show
considerable divergence of the phenotype(s) in question. However, an
interesting result that arose from our analysis of these circadian data
is that the relationship between a particular allele and the way it
affects the phenotype can be counterintuitive. By this, we mean that
the phenotypic characteristics associated with the B6 strain were
sometimes found to be linked to BALB alleles in our F2
hybrids, and vice versa. Thus, for example, a high amplitude rhythm was
linked to BALB alleles at Amp-2 and a long free-running period
was linked to BALB alleles at Frp-1. One must conclude that
each strain includes alleles, or combinations of alleles that are
epistatic to alleles at different loci. In an F2 cross, the
epistatic effects become unlinked and the counterintuitive alleles can
be detected. This result brings into question the general strategy used
when developing mapping crosses to analyze a particular phenotype. If
each of the two strains chosen for analysis harbors alleles that tend
to produce the opposing strain's phenotype, then it becomes difficult
to predict the result of these hybrid matings. Strains that have
similar phenotypes may produce an equally interesting variety of
hybrids because of the expression of otherwise recessive or repressed
alleles; this was seen in an analysis of circadian period in
Arabidopsis (Swarup et al. 1999 This quantitative analysis of circadian rhythms opens a new avenue to
the understanding of this behavior. This analysis, in combination with
a genome-wide interaction analysis, has allowed us to uncover new loci
involved in the genetics of circadian rhythms in the mouse. We have
identified multiple loci affecting several aspects of circadian
behavior, both as main effects and in combination with other loci in
the mouse genome. This approach should provide a window to the analysis
of disorders of such phenotypes in humans. Indeed, a common recognition
emerging from the analysis of multiple human disorders with
hard-to-assess genetic determinants, including heart disease, affective
and neurodegenerative disorders, asthma, diabetes, and hypertension, is
that disease susceptibility is often determined by numerous modest
susceptibility alleles present at multiple loci. These alleles are
likely to have very limited effects in isolation but in combination can
have complicated interactions that produce phenotypic extremes not
predicted by an additive model (Risch 2000 This genetic analysis has revealed previously undetected complexity in the circadian system and points to the presence of many as yet undiscovered genes that contribute to the expression of this behavior in mice. Although severe disruption of circadian rhythms may be caused by mutations in core clock genes, it is possible that the broad variety of circadian behavior observed in mammalian species, including humans, is the result of polymorphisms in multiple, interacting loci such as the ones described here.
Animals (BALB/cJ X C57BL/6J)F2 mice were bred from (BALB/cJ X C57BL/6J)F1 parents that were obtained from the Jackson Laboratory. F1 animals were the result of mating BALB/cJ females with C57BL/6J males. F2 animals were raised in a 12 h light:12 h dark cycle (LD12:12) from birth. After weaning, they were group housed (1-5 mice/cage). At 8-12 wk of age, they were transferred into individual cages equipped with running wheels in LD12:12. After a minimum of 7 d, animals were transferred into DD for three weeks. Wheel-running activity was recorded from a total of 196 F2 generation mice (98 females and 98 males). Analysis of Circadian Behavior Free-Running Period of Activity Rhythm We calculated the free-running period for 15 d (day 1-15 in DD) using a 2 periodogram with 1-min resolution between 20-26
h (The Chronobiology Kit; Stanford Software System).
Phase Angle of Entrainment The phase angle of entrainment is defined as the time difference between activity onset and the predicted time of dark onset, on the first day in constant darkness. The phase angle of entrainment was calculated by extrapolating the estimated activity onset in the last day of the LD cycle and the time of lights off. An activity onset regression line was drawn based on five consecutive activity onsets (day 1-day 5 of constant darkness). When activity starts before the predicted time of lights-off, it is defined as a negative phase angle, whereas a later activity onset is defined as a positive phase angle.Circadian Rhythm Amplitude The amplitude of the Fourier periodogram around 24 h, for 15 d in DD, was used as an indicator of circadian rhythm amplitude (Clock Lab, Actimetrics). Original data were collected at 1-min intervals. To prepare the power spectra, data points were first binned into 6-min intervals, for a total of 3600 bins for the 15-d period to be analyzed. A 4th order Blackman-Har window was then applied to these points prior to calculating the power spectrum using a fast Fourier transform. The spectrum was normalized to an integral of one by dividing each of its elements by the sum of all elements. For each animal the frequency of the spectrum peak is reported, along with the amplitude of the peak, which represents the relative power within a frequency band of 0.0028.Activity Level The total number of running-wheel revolutions was counted from days 1-15 in DD and then averaged to determine the daily activity level.Dissociation The degree of activity rhythm dissociation (splitting) was scored using six different levels (0-5), with 0 corresponding to the most intact rhythms and 5 corresponding to the most dissociated rhythm (see Results and Fig. 3 for additional details). The scoring was performed by two people (K.S. and J.S.T.) independently.Analysis of Genotype Genomic DNA was prepared by phenol-chloroform extraction from tail
biopsies. SSLP markers that were polymorphic for our cross (C57BL/6J x
BALB/cJ) were chosen from the MIT Whitehead Institute database and
purchased from Research Genetics. For each SSLP, one primer was
end-labeled with Single Marker Genome Scans We used the Mapmaker/QTL analysis software for our initial genome scan (Lander et al. 1987). Subsequently, we implemented marker regression-based genome scans in Matlab Software (Mathworks, Inc.). Source code is available from G.A.C. on request. A
single marker genome scan consists of computing the regression one-way
ANOVA F-statistic (which has 2, n-3 df for an F2 population of size n) at each marker in the genotyping array. Statistical significance is assessed by permutation testing (Churchill and Doerge
1994). This approach takes into account the multiple testing implicit
in a genome-wide search.
Pairwise Genome Scans As some loci may affect a phenotype primarily through interaction effects, we have developed an approach and implemented software (Matlab source code available from G.A.C. upon request) to conduct a simultaneous search for pairs of interacting loci. The method of simultaneous search (Dupuis et al. 1995) examines all pairs of
marker loci for association with the trait in a two-dimensional genome
scan. In our procedure, the likelihood under the full regression model
(with two main effects and an interaction) is compared to that under
the null model of no genetic effects. This comparison generates an
F-statistic (with 8 and n-9 d.f.) for every marker pair. We refer to
this statistic as F-all. It is our primary screen for identifying
interesting locus pairs. Significance of F-all is assessed by
permutation analysis, which accounts for the large number of pairs
tested in the genome-wide search. If the F-all statistic for a locus
pair is significant (P< 0.05 genome-wide corrected), we carry
out several additional tests to determine if the pair represents a
genuine interaction, two additive main effects, or is merely an
artifact resulting from a strong association with only one of the two
loci. A second F-statistic (F-int, which has 4 and n-9 d.f.) is
computed to test for interaction effects. F-int compares the full model
(with interaction) to an additive model with two main effects but no
interaction. If this test is significant at a nominal alpha = 0.01
level, we conclude that the two loci interact and stop. If F-int is not
significant, we proceed to the next level of testing. Two additional
F-statistics (F-add1 and F-add2, each with 2 and n-5 d.f.) are computed
to compare each of the single locus models to the two locus additive model. Both of these tests should be significant (at alpha = 0.01 level), to indicate that both loci contribute to the effect. If one of
the loci in the pair fails to achieve significance this suggests that
it may not be contributing to the observed association and simply
carried along by the strong effect of the other locus. Each of these
secondary tests is carried out using nominal P values because
pairs have been selected with a genome-wide criterion using F-all. The
choice of alpha = 0.01 is stringent but somewhat arbitrary.
Multiple Regression Modeling All loci and interactions that are detected by genome scans (single marker and pairwise) are entered into a multiple regression model. Regressions were fit using Minitab software (Minitab, Inc.). The adjusted sums of squares from the mul |
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ABSTRACT
INTRODUCTION
] genes, respectively), by molecular interactions with other clock genes
(the Bmal1 gene), and by homology to clock or photoreceptor genes from other organisms (the mouse Period, Timeless, and Cryptochrome homologs, mPer1, mPer2, mPer3, mTim, mCry1, and
mCry2). Four of these genes, mPer2, mCry1, mCry2, and
Bmal1, have been linked to circadian
function through analysis of gene-targeting mutations.
2.8) (Lander and Kruglyak 1995
-32p-ATP using T4 kinase according to
standard protocols. PCR reaction mixes (5 or 10 µL) contained 12.5 or
25 ng genomic DNA, 16 µM of primers, 0.2 mM each dNTP, 50 mM KCl, 10 mM Tris-HCl (pH 9.0), 0.1% Triton-X, 1mg/mL BSA, 1.25 mM
MgCl2, and 0.025 U Taq polymerase (Perkin Elmer) and
were arrayed in 96- or 192-well plates, overlaid with 10 µL mineral
oil. Thermal cycler conditions, in 96- or 192-well PTC-100
thermocyclers (MJ Research), were 95°C for 4 min followed by 27-35
cycles at 95°C for 15 s, 30 s at 55°C, 15 s at 72°C. After 27-35
cycles, samples were held at 72°C for 5 min and then stored at 4°C
until use. An equal volume of loading buffer (0.25% xylene cyanol and
0.25% bromphenol blue in 50% formamide) was added to the
amplification products, which were denatured for 5 min at 95°C, then
separated on 7% polyacrylamide gels (30 cm × 40 cm) at 100 W for
~2 h. We used 4× combs (Owl Scientific) that allowed us to load 96 lanes per gel. Most of the PCR reactions included two primer pairs in
one reaction (duplex reaction). Typically, two duplex reactions were
loaded onto each lane (double loading) so that we obtained four
genotype scores/lane and a total of 384 genotype scores were generated
from each gel. The duplex primer pairs and combinations of double
loading pairs used for the initial QTL search are listed in Table