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The Journal of Neuroscience, April 15, 2001, 21(8):2610-2621
The Homeostatic Regulation of Sleep Need Is under Genetic
Control
Paul
Franken1, 2,
Didier
Chollet1, and
Mehdi
Tafti1
1 Biochemistry and Neurophysiology Unit, Department of
Psychiatry, University of Geneva, Chêne-Bourg, Switzerland, and
2 Department of Biological Sciences, Stanford University,
Stanford, California 94305-5020
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ABSTRACT |
Delta power, a measure of EEG activity in the 1-4 Hz range, in
slow-wave sleep (SWS) is in a quantitative and predictive relationship with prior wakefulness. Thus, sleep loss evokes a proportional increase
in delta power, and excess sleep a decrease. Therefore, delta power is
thought to reflect SWS need and its underlying homeostatically
regulated recovery process. The neurophysiological substrate of this
process is unknown and forward genetics might help elucidate the nature
of what is depleted during wakefulness and recovered during SWS. We
applied a mathematical method that quantifies the relationship between
the sleep-wake distribution and delta power to sleep data of six
inbred mouse strains. The results demonstrated that the rate at which
SWS need accumulated varied greatly with genotype. This conclusion was
confirmed in a "dose-response" study of sleep loss and changes in
delta power; delta power strongly depended on both the duration of
prior wakefulness and genotype. We followed the segregation of the
rebound of delta power after sleep deprivation in 25 BXD recombinant
inbred strains by quantitative trait loci (QTL) analysis. One
"significant" QTL was identified on chromosome 13 that accounted
for 49% of the genetic variance in this trait. Interestingly, the rate
at which SWS need decreases did not vary with genotype in any of the 31 inbred strains studied. These results demonstrate, for the first time,
that the increase of SWS need is under a strong genetic control, and
they provide a basis for identifying genes underlying SWS homeostasis.
Key words:
EEG delta power; slow-wave activity; sleep deprivation; homeostatic regulation of non-REM sleep; simulation of Process S; BXD
recombinant-inbred mouse strains; QTL; Dps1; Dps2; Dps3;
forward genetics
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INTRODUCTION |
Slow oscillations in the delta
frequency range (1-4 Hz) are characteristic of the EEG during
slow-wave sleep (SWS) (i.e., non-REM sleep in humans). Delta
oscillations reflect synchronized burst-pause firing patterns of
hyperpolarized thalamocortical and corticothalamic neurons (Steriade et
al., 1993 ; McCormick and Bal, 1997; Steriade, 1999). Activity in the
delta frequency range can be quantified as delta power by Fourier
analysis. Delta power is negatively correlated with the response to
arousing stimuli (Neckelmann and Ursin, 1993) and SWS fragmentation
(Franken et al., 1991a) and thus can be seen as a measure of SWS
intensity. Delta power is also in a quantitative and predictive
relationship with prior sleep and wakefulness in mammals, including
humans. Sleep loss evokes an increase in delta power during subsequent SWS that is proportional to the loss (Tobler and Borbély, 1986; Dijk et al., 1987), excess sleep results in an attenuation of delta
power (Werth et al., 1996), and delta power decreases over the course
of a sleep period, independent of the circadian phase at which sleep is
initiated (Dijk and Czeisler, 1995). These and other observations have
been interpreted as evidence that SWS is a restorative and
homeostatically regulated behavior and that delta power reflects the
need for SWS (Borbély, 1982; Daan et al., 1984). The dynamics of
this homeostatically regulated process, referred to as Process S
(Borbély, 1982), have been studied extensively, and mathematical
simulations that quantify the relationship between the sleep-wake
distribution and delta power predicted the time course of delta power
remarkably well (Franken et al., 1991b; Achermann et al., 1993).
However, the neurophysiological substrate of what is restored by SWS
(and what is depleted in its absence) is unknown.
Several features of the normal EEG are among the most heritable traits
in humans (Beijsterveldt and Boomsma, 1994); however, little progress
has been made in identifying the underlying genes. Only for a
low-voltage waking EEG variant has linkage with a discrete region of
chromosome 20 been established (Anokhin et al., 1992). By comparing
several inbred strains of mice, we have identified several EEG features
that are under strong genetic control (Franken et al., 1998). For one
of those, the frequency of the theta rhythm, we established a single
gene mode of inheritance (Tafti et al., 1998) and recently identified
its genomic localization (our unpublished results). We also observed
strain differences in the rebound of delta power after a sleep
deprivation (Franken et al., 1999). Following the segregation of this
trait in recombinant offspring should allow identification of genomic
regions containing genes that modify the accumulation of a need for
SWS. Ultimately, the identification of such genes will yield important
information on the neurophysiological substrate of Process S.
We used a computational method that quantifies the relationship between
the changes observed in delta power and the sleep-wake distribution in
six inbred strains of mice. This method separates the effects of
sleep-wake patterns, which varied greatly between strains, from the
effects of different dynamics of Process S on delta power. The analysis
suggests genetic differences in the rate at which SWS need accumulates.
We verify this empirically in a "dose-response" study in which
mice were subjected to sleep deprivations of varying duration. Finally,
we provide a preliminary mapping of genes that modify this trait in
recombinant offspring.
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MATERIALS AND METHODS |
The methods concerning the recording and analysis of the EEG in
mice have been described in detail elsewhere (Franken et al., 1998,
1999). The experimental protocols were approved by the local veterinary
office (Office Vétérinaire Cantonal de Genève) and the ethical committee of the University of Geneva. Experimental animals
were adult male mice obtained from Jackson Laboratory (Bar Harbor, ME),
with the exception of 129/OLA mice in experiment 1 that were bred
locally. All mice were individually housed in an experimental room
under a 12 hr light/dark cycle (lights on at 8:00 A.M.). Food and water
were available ad libitum. Animals were kept under these
conditions for at least 18 d before the experiment. EEG and
electromyogram (EMG) electrodes were implanted under deep pentobarbital
anesthesia. Mice were allowed 10-14 d of recovery from surgery
and habituation before the experiments.
The EEG and EMG signals were recorded continuously for the entire
duration of the experiments. Both signals were amplified, filtered, and
analog-to-digital converted. The EEG signal was subjected to
Fast-Fourier Transform yielding power spectra between 0 and 25 Hz using
a 4 sec window. The behavior in each of these 4 sec epochs was
classified as SWS, paradoxical sleep (PS), or wakefulness by
visual inspection of the EEG and EMG signals. The present analyses
concern the mean power in the delta band (1-4 Hz), referred to as
delta power, and its relation to the sleep-wake distribution.
Experiment 1: simulation of Process S. Data obtained in six
inbred strains [AKR/J (AK), BALB/cByJ (C), C57BL/6J (B6), C57BR/cdJ (BR), DBA/2J (D2), and 129/Ola (129); n = 7 per
strain] contributed to this analysis. The age at the first recording
day ranged from 71 to 87 d, and body-weight ranged from 24 to 35 gm. EEG and EMG signals were recorded continuously for two consecutive
24 hr periods, starting at lights on (8:00 A.M.). Day one was
considered red baseline (BSL). On day two, starting at lights on, mice
were sleep-deprived (SD) for 6 hr by handling. The remaining 18 hr were
considered recovery (REC). Data on strain differences in the
amount and distribution of the behavioral states and EEG spectra
obtained in these mice have been published elsewhere (Franken et al.,
1998, 1999).
The simulation procedure was similar to the approach used previously in
the rat (Franken et al., 1991b, 1993, 1995), with the exception that
for the present analyses, absolute delta power values were simulated
instead of linearly transformed values. This required the estimation of
the asymptotes of the two exponential functions from the data, whereas
in the previous simulations, these asymptotes were arbitrarily set to 0 and 1. Furthermore, in the present approach, the initial value
(S0) was derived from the sleep-wake
distribution and the time constants and thus was no longer a
free-parameter (see below).
Within each animal, on the basis of the sequence of the 4 sec
behavioral state scores that constitute the 48 hr recording, the time
course of Process S was calculated iteratively by assuming that it
increases according to an exponential saturating function (Eq. 1) during epochs scored as wakefulness or PS and decreases according to an exponential function (Eq. 2) during epochs scored as
SWS (see Fig. 1a):
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(1)
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(2)
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St+1 and
St are values
of S for consecutive 4 sec epochs (t = 0-43,200 epochs),  i is the time
constant of the increasing exponential saturating function with an
upper asymptote (UA), d
is the time constant of the decreasing exponential function with a
lower asymptote (LA), and dt is the time step of
the iteration (4 sec). Within each mouse, the two asymptotes were
derived from the distribution of delta power values of all 4 sec epochs
of both recording days scored as either SWS or PS (see Fig.
1b). Because PS is characterized by the absence of
synchronized EEG activity in the delta range, the intersection of the
relative delta power distributions in PS and SWS was chosen as the
LA. The choice of the UA is based on the
assumption that as a response to prolonged wakefulness, the median
power in a given SWS episode cannot exceed the 99% level of the
distribution of 4 sec values. The initial value of S at time
0 (S0 at lights on of baseline) with
which the iteration started was determined by assuming that the
baseline represented a steady state, i.e., the value obtained at the
end of the 24 hr baseline period equals the value reached at the end of
the day preceding baseline. For a given combination of time constants,
the value of S reached after 24 hr is independent of
S0 (see Fig. 1c).
Therefore, the simulation was first started with an arbitrary
S0 value (i.e., the mean SWS delta
power in baseline). The value reached after 24 hr baseline was taken as the "real" value for S0, and the
simulation was then restarted for the entire 48 hr recording period.
Thus, only the two time constants were free parameters, and these were
optimized in the simulation.
The values for Process S obtained by this approach were compared
directly with the delta power values observed in sustained SWS episodes
(>5 min). The median delta power of all 4 sec epochs scored as SWS in
a given SWS episode was taken to best represent delta power reached at
the time of episode midpoint. The number of SWS episodes selected did
not differ among strains [one-way ANOVA factor "strain":
p = 0.2; AK (84 ± 4), C (97 ± 3), B6
(91 ± 6), Br (77 ± 3), D2 (79 ± 5), 129 (81 ± 8); mean ± SEM; n = 7 per strain]. The goodness
of fit between simulated (i.e., the level of Process S reached at each
SWS episode midpoint) and empirical data was assessed by calculating
the mean of the square of the differences and Pearson's correlation
coefficient (r). The fit was optimized by minimizing the
mean square of the differences for a range of
i (1-25 hr, step-size 0.12 hr) and
d (0.1-5 hr, step-size 0.025 hr) values,
i.e., the simulation was run for 40,000 different combinations of time
constants for each mouse. Within these ranges of time constants and the
constraints of the model one unique solution was obtained for each
mouse (see Fig. 1d). The time constants with which the best
fit was obtained were used to assess differences between strains.
Further statistical comparisons were made by comparing simulated and
empirical delta power at specific times of the experiment after both
values were expressed as a percentage of the individual mean delta
power in SWS over the last 4 hr of the baseline light period. This
transformation was conducted to correct for individual differences in
the absolute power. Mean values of S and delta power were
calculated over consecutive 45 min intervals within each individual and
then among the seven individuals of each strain. Intervals in which
fewer than four animals contributed to the mean were omitted from the
figure and the t tests evaluating differences between
empirical and simulated data. To follow Process S through the entire
experiment including the SD, 15 min mean values of S were
calculated regardless of behavioral state.
Experiment 2: a sleep deprivation dose-response curve. The
outcome of experiment 1 was verified by subjecting AK and D2 mice to
SDs of varying length (n = 6 per strain; body weight,
29.3 ± 1.1 gm; range, 23.4-35.4 gm; age, 91 d at recording
day 1). EEG and EMG signals were recorded continuously for nine
consecutive 24 hr periods, starting at lights on (8:00 A.M.). The first
2 d were considered baseline (baselines 1 and 2). On days 3, 4, and 5, starting 7 hr after lights on (3:00 P.M.), mice were sleep deprived by handling for 70, 35, and 140 min, respectively. Day 7 was
again considered baseline (baseline 3). On day 8, mice were sleep
deprived for 9 hr starting at lights on (8:00 A.M.). After noticing
that the first 35 min SD on day 4 actually resulted in 71 min of
wakefulness, we repeated this SD on day 9, the day after the 9 hr SD,
expecting that the residual increased sleep drive from the long SD
would shorten sleep latency. Sleep latency, SD duration, and SWS delta
power were significantly attenuated compared with day 4 (analysis not
shown), and the two SDs were therefore treated as two distinct
"doses."
Including the 6 hr SD of experiment 1, six SD doses were obtained per
strain. The SDs were scheduled to end within the third quarter of the
light period so that the subsequent rebound in delta power was not
confounded by the high and changing values of delta power present in
the initial half of the baseline light period or by possible circadian
factors. We point out here that the 6 hr and 9 hr SDs were initiated at
light onset when Process S (and delta power) was higher (~153%;
i.e., S0 in Table 1) compared with the
shorter SDs (~103%) starting 7 hr later. With the simulation, it can
be estimated that delta power after 6 hr SD would have been 13 and 26%
(for AK and D2, respectively) lower, and after 9 hr SD would have been
6 and 15% lower, if these SDs had been initiated 7 hr later.
Some mice were spontaneously awake before the SD. This time and the
time it took to initiate sleep after the end of the SD (i.e., sleep
latency) were added to the total time awake in the dose-response
curve. Therefore the SD durations deviated from the intended durations.
Nevertheless, for convenience, the duration for which the animals were
handled will be used to indicate SD dose.
The response to the SDs was measured by averaging delta power over the
first 225 4 sec epochs scored as SWS after the onset of recovery sleep.
All values were contrasted to the prevailing level of SWS delta power
in the last 4 hr of the baseline light periods (=100%) within each
individual mouse. For the SDs on days 3, 4, and 5, mean delta power
over the last 4 hr of the light periods of baselines 1 and 2 was used
as a reference; for the SDs on days 8 and 9, that of baseline 3; and
for the 6 hr SD, that of the preceding baseline day.
During the SD, special care was taken to mark all 4 sec epochs with EEG
delta waves even if the EMG did not decrease to the low levels normally
associated with SWS. This was observed especially toward the end of the
two longest SDs. The amount of SWS thus obtained is higher than
in previously published SD studies, but because we assume that cerebral
activity is important in sleep regulation, this might represent a more
reliable estimate of the amount of SWS.
The effects of spontaneous awakenings of varying duration on subsequent
delta power were analyzed within the last 4 hr of the three baseline
light periods. During these periods, delta power reached lowest values,
and no changes in its overall level were observed. Therefore, the
effects of waking episodes on delta power in subsequent SWS episodes
could be assessed without the confounding effects of the varying
"background" levels of delta power associated with its normal
decline during the initial part of a baseline light period (Franken et
al., 1999) and of potential circadian factors. Waking bouts (range,
3-51 min) were selected that did not contain a single 4 sec epoch of
sleep and were followed by >8 min of sleep. Waking bouts were divided
into three categories according to their duration: <12 min, 12-24
min, and >24 min. The mean number of bouts in each category were for
AK: 4.3, 4.7, and 4.6, respectively; for D2 they were 3.3, 3.0, and 3.0 (n = 6 per category per strain). Delta power in a sleep
bout after a given waking bout was calculated over a minimum of 75 and
a maximum of 225 4 sec epochs scored as SWS. Delta power values were
averaged for the three categories and related to the average time awake
for each category.
Decreased rates for Process S were derived from the observed data by
determining the decrease of delta power over the first 1000 4 sec
epochs (1.1 hr) after recovery onset after the six SDs that contributed
to the dose-response curve and by following the time course of delta
power in the initial 6 hr after the 6 hr SD. In both analyses, the
delta power data represent means over consecutive 225 4 sec epochs (15 min) scored as SWS expressed as a percentage of the same reference
discussed above. For the analyses presented in Figure 5, the delta
power difference between the initial 15 min of SWS of recovery
(d1) at time
t1, and its value
(d2) reached in the last 15 min of SWS
of a 1.1 hr period at t2, was
expressed as a function of d1. Both
t1 and
t2 represent the mean times at which
the 225 SWS epochs that contributed occurred and differed in time by
0.65 ± 0.2 hr (n = 74). The time constant (d) of this exponential function
was calculated according to Equation 3 for each combination of
d1 and
d2 (n = 37 per
strain):
|
(3)
|
Combinations for which either
d2 or
d1 was less than LA were
omitted from the analyses (AK: n = 32; D2:
n = 36). As LA, the level of
d1 at which the delta decrease is 0 according to the linear relationship between
d1 and
(d1 d2) was taken (1O2% for both AK and D2; see Fig. 5).
For the analyses presented in Figure 6, the parameters describing the
exponential decrease in delta power after the 6 hr SD were estimated
with a nonlinear fitting procedure (method, Gauss-Newton; procedure, NLIN; SAS/STAT software, SAS Institute, Cary, NC) according to Equation 4:
|
(4)
|
where S0 is the estimated level
of delta power at recovery sleep onset (t = 0) and
t is the time elapsed.
Experiment 3: Quantitative trait loci (QTL) analysis of delta
power at sleep onset after enforced and spontaneous periods of
wakefulness. Data from 25 BXD/Ty recombinant inbred (RI) strains (n = 114, 4-6 per strain; weight, 25.8 ± 0.3 gm;
range, 18.3-33.7 gm; age, 94 ± 1 d; range, 67-142 d) and
their two progenitor strains B6 and D2 (n = 7 per
strain; same individuals as in experiment 1) contributed to this
analysis. The experimental protocol was identical to that in experiment
1. As in experiment 2, the response to a 6 hr SD was determined by
averaging delta power in the first 225 4 sec epochs scored as SWS after
the onset of recovery sleep.
We also determined delta power in the first 225 4 sec epochs scored as
SWS after the onset of the major sleep period(s) during baseline. Both
the onset and the end of the major sleep periods were individually
determined according to previously published criteria (Franken et al.,
1999). In short, SWS time was determined over 2 hr intervals that were
offset 15 min to produce a running average. This variable was then
expressed as a fraction of the mean amount of SWS over the 24 hr
baseline. Consecutive 15 min intervals in which this value was >1
constituted a sleep period.
QTL analysis was used to identify genomic regions containing genes that
may modulate the delta power rebound after SD and the delta power at
sleep onset in baseline. For this initial mapping, point-wise or
nominal correlations between the strain distribution pattern (SDP) of
the quantitative trait (i.e., delta power) and the genotypic SDPs of
the 788 MIT markers polymorphic between B6 and D2 mice and typed
in the BXD-RI strains (alleles set to 0 and 1 for the B6 and D2
genotypes, respectively) were performed. The BXD MIT marker map was
kindly provided by Dr. Robert W. Williams (Williams et al.,
2001). In testing multiple markers in a genome-wide scan, one
will obtain significant correlations just by chance (type-1 error). To
correct for this, genome-wide probability thresholds can be established
using a permutation algorithm in which trait data are 10,000 times
randomly reassigned among the RI strains (Churchill and Doerge, 1994).
For each permutation, the single best correlation statistic is recorded
generating an empirical probability distribution for the p
values of the correlation between the randomized trait and genotype.
The genome-wide significance thresholds for false positive rates are
set to 0.63, 0.05, and 0.001 for "suggestive," "significant,"
and "highly significant" linkage, respectively, according to Lander
and Kruglyak (1995).
In the three experiments, all main effects of factors "strain,"
"SD dose," "waking-bout duration," and "time-of-experiment" on the various variables were assessed with ANOVA statistics. Whenever
significant (p < 0.05), post hoc
comparisons were performed with t tests or, when more than
two levels per main factor were compared, Tukey's studentized multiple
range tests to control the experiment-wise error rate. Linear and
nonlinear regression analyses were used to quantify relationships
between SD length or wake-bout duration and subsequent SWS delta power
and between time elapsed since recovery sleep onset and delta power.
All statistical analyses were performed using SAS/STAT software.
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RESULTS |
Simulation of Process S
An example of the time course of Process S, derived from the
behavioral state sequence, and of delta power reached in SWS episodes
is depicted in Figure 1e. This
example shows that the model can predict the data with great accuracy
in individual recordings. In addition, it illustrates that the
relationship between wakefulness and delta power in undisturbed
baseline conditions and during recovery from a SD are similar; i.e.,
the spontaneous 6 hr waking bout in baseline results in a level of
delta power in subsequent SWS comparable to that after the 6 hr SD.
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Figure 1.
Illustration of the assumptions and parameter
estimation of the simulation of Process S. a, The time
course of S was calculated iteratively on the basis of the sequence of
the 4 sec scores of the behavioral states wakefulness
(W), slow-wave sleep (SWS),
and paradoxical sleep (PS) and was assumed to increase
during W and PS and to decrease during SWS, according to Equations 1
and 2 (see Materials and Methods), respectively. S varies between an
upper (UA) and lower asymptote (LA;
dashed lines). b, These asymptotes were
derived from the relative frequency distribution of delta power for 4 sec epochs scored as PS or SWS during the 48 hr recording. The 99%
level of the SWS distribution (gray area) was
chosen as the UA; the intercept of the PS and SWS distributions was
chosen as the LA. c, As the initial S value
(S0) at light onset of the baseline day, the value of
S obtained at the end of the baseline dark period
(black horizontal bar on top) was used.
This value was not affected by the values with which the iteration
started, illustrated by starting at either the UA (curve
1) or the LA (curve 2). Curve 3
starts at the S0 used in the final simulation for this mouse.
Black bars at the bottom mark SWS
episodes during which S decreases. d, Contour plot of
the mean square of differences (DIF2) between
simulated and empirical data as a function of the time constants for
the increase (Ti) and the decrease (Td)
of Process S. Numbers that label the contour lines
indicate the number of times the DIF2 was larger
than the least DIF2 (i.e., 44 µV4) obtained at Ti = 6.9 and Td = 1.5 hr.
e, Final simulation of Process S (solid
line) for one individual mouse of the C strain. The estimation
of the parameters for this animal is illustrated in
b-d. Process S was fitted to the
absolute median values of delta power (gray
circles) reached in SWS episodes of >5 min. Dark
horizontal bars on top indicate the 12 hr dark
periods.
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The overall performance of the model was good in that the main features
of the time course of delta power such as the exponential decrease
during the main sleep period and the increase after the 6 hr SD and
subsequent rapid decline were reliably reproduced (Fig.
2). This conclusion was supported by
highly significant correlation coefficients (r) for all
strains (Table 1), which indicates that a
large portion of the variance in delta power (77-85%) can be
explained by the distribution of SWS. The three-way ANOVA with factors
"method"' (simulation vs empirical), "strain," and "time"
indicated that the fit did not vary according to genotype (Table 1) but
that it did interact with time (factor method, p = 0.053; factors strain and time, p < 0.0001;
interactions method × strain, p = 0.60;
method × time, p = 0.027; strain × time,
p < 0.0001). Post hoc analysis within
strains identified only occasional intervals for which Process S and
delta power differed (Fig. 2), but when data from the six strains were
combined, a tendency was observed in both baseline and recovery that
the simulated values were higher than the observed data in the first
half of the dark period. During this period, mice of all strains were
predominantly awake (84% of recording time), and delta power measured
in the little SWS that occurred might not reliably reflect SWS need. Alternatively, the strong circadian drive for wakefulness at this time
might directly modulate delta power expression.
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Figure 2.
Mean time course over 48 hr of empirical and
simulated delta power for six inbred strains of mice in baseline
(BSL) and recovery (REC) from a 6 hr
sleep deprivation (SD). Black dots
indicate mean (±SEM) delta power averaged over 45 min intervals
(n = 4-7 per interval; see Materials and Methods).
Gray areas delimit the mean ± SEM range for the
simulated Process S for consecutive 15 min intervals. Forty-five minute
intervals for which delta power and S significantly differed are
indicated by gray bars underneath the curves of each
strain (paired t tests; p < 0.05).
Black horizontal bars mark the dark periods. Data for
the BSL dark period are plotted twice to illustrate the dark-to-light
transition. Delta power and S values are both expressed as a percentage
of the mean SWS delta power in the last 4 hr of the BSL light
period.
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The most conspicuous outcome of the simulation is the large strain
differences observed for the rate at which SWS need increases (i), with the largest difference between
strains AK and D2 (Table 1). The difference between a time constant of
5.3 hr in AK and 12.6 hr in D2 translates into an initial threefold
larger increase in delta power for AK for a given period of wakefulness
(estimation based on the parameters listed in Table 1). As wakefulness
progresses and delta power further approaches the upper asymptote, this
difference reduces to a 2.3-fold larger increase after 6 hr and,
ultimately, would stabilize to a 1.4-fold increase according to the
upper asymptotes estimated for the two strains. The dynamic range of Process S (i.e., the distance between the two asymptotes) also varied
between strains (Table 1). This can affect the outcome of the analysis
because to maintain a good fit with the data, a decrease of the upper
asymptote will be countered by an increase in the rate of increase
(i.e., shorter i). However, the longest i was obtained in D2, the strain with the
second lowest upper asymptote. Raising the upper asymptote in D2 to the
level determined for AK mice while maintaining a similar good fit with
the data resulted in a further lengthening of
i. In addition, the two strains for which the
upper asymptotes differed the most (AK and C) displayed the shortest
time constants. Having established large differences between increase
rates (and asymptotes), the similarity of the decrease rates between
strains becomes equally striking (Table 1). Finally, the difference in
S0, the value used to initiate the
iteration (Table 1), reflects differences in the sleep-wake distribution in baseline: C mice displayed the lowest value at light
onset because their main sleep episode started ~5 hr earlier (and
thus SWS need had already dissipated), whereas in the remaining strains, the onset of the main sleep episode more or less coincided with the dark-to-light transition (Franken et al., 1999) (Figs. 1e, 2).
A sleep deprivation dose-response curve
The simulation presented in experiment 1 demonstrated that the
time constant for the accumulation of a need for SWS, but not for its
decline during SWS, varied between genotypes. To confirm these
predictions, we designed a dose-response experiment in which sleep was
deprived for varying durations (i.e., dose) to verify that the delta
power increase in subsequent SWS (i.e., response) varies with both
genotype and SD duration. In this study, we compared AK and D2 mice for
which the largest difference in increase rates was predicted (Table
1).
Quantifying the increase rate of Process S during wakefulness
The SD doses did not differ between strains (Table
2). Included in the actual SD duration is
sleep latency, defined as the time between the end of the SD and sleep
onset, which can also be taken as a measure of sleep need. In
accordance with this, sleep latency was inversely related to SD
duration (Table 2). Sleep latency did not differ significantly between
the strains for any of the SDs, although it generally appeared to be
shorter for D2 mice.
The dose-response curve confirmed the outcome of experiment 1. Delta
power increased as a function of SD length in both strains (Fig.
3), with even the shortest SDs evoking a
significant increase in delta power over the control values in
baseline. Most importantly, the results also confirmed that the rate of
increase is faster in AK than in D2 mice; for SDs >100 min, the
increase in delta power was larger for AK mice (Fig. 3). On a smaller
scale, similar observations were made for the relation between waking
duration and subsequent delta power under undisturbed baseline
conditions (Fig. 3). Also here, delta power was higher after longer
waking bouts and, although not significant, seemed to increase at a
faster rate for AK mice.
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Figure 3.
The relationship between waking duration and delta
power. Left panel, The SD dose-response curve. The
response in delta power (mean ± SEM; n = 6 per dose except 6 hr SD; n = 7) varied with SD dose
and genotype [two-way ANOVA factors strain and dose:
p < 0.0001; interaction: p = 0.0004; Tukey's range test: AK: 6 hr >9 hr >140 min >70 min = 35 min (day 4) = 35 min (day 9); D2: 6 hr = 9 hr >140
min = 35 min (day 4) = 70 min = 35 min (day 9);
p < 0.05]. Delta power was higher in AK than in
D2 mice for the 140 min (p = 0. 02) and 6 hr
SD (p = 0.001; indicated by the gray
stars). After the 9 hr SD, values tended to be higher
(p = 0.09, t tests). The
relationship between SD duration and delta power appeared linear for
SDs of <9 hr (thinner lines; linear regression: AK:
delta power = 24.6%/hr · SD duration + 92%; D2: delta
power = 12.6%/hr · SD duration + 106%; p < 0.0001; r2 = 0.94 for both
strains). Right panel, Relationship between the duration
of spontaneous waking bouts and delta power in the last 4 hr of the
three baseline light periods. The duration determines the level of
delta power in subsequent SWS (two-way ANOVA factor strain:
p = 0.7; factor "category":
p < 0.0001; interaction: p = 0.5; Tukey's range test for both AK and D2: <12 min = 12-25
min < 12-25 min = >24 min; p < 0.05, n = 6 per category per strain; see Materials and
Methods for details). This relationship was quantified by linear
regression (AK: delta power = 26.4%/hr · W duration + 93%;
p = 0.003;
r2 = 0.41; D2: delta power = 16.2%/hr · W duration + 95%; p = 0.0009;
r2 = 0.53; n = 6 per category per strain). For both panels the solid black
lines connect mean values for AK mice (black
dots); dashed lines connect values for D2 mice
(gray squares). Values represent the mean delta
power in the first 225 (left panel) or 75-225
(right panel) 4 sec epochs scored as SWS after
the end of wakefulness. Although scaling differed between panels, the
delta power/waking time ratio is preserved, allowing slope
comparisons.
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For both spontaneous and enforced periods of wakefulness (disregarding
the 9 hr SD), the relationship between waking duration and subsequent
delta power appeared linear (Fig. 3) instead of the anticipated
exponential saturating function. Especially for the shorter SDs (<6
hr) in AK, larger increases in delta power were anticipated. Enticed by
these findings, we repeated the simulation of experiment 1 to assess
whether Process S could be described better with a linear function. In
addition, the assumption of a linear function eliminates the necessity
of estimating an upper asymptote, which might have influenced the
values of the time constants. The fit between simulated and empirical
data did not further improve with the use of a linear function (Table
3). However, this analysis again
confirmed that the increase rate varied according to genotype. Given
the different methods by which, and the data sets from which, the
linear increase rates were obtained, they were remarkably similar [AK:
24.6-26.4-27.1%/hr; D2: 12.6-16.2-10.5%/hr for the SDs and
spontaneous waking bouts in experiment 2 (Fig. 3) and the linear
simulation of experiment 1 (Table 3), respectively].
Another unanticipated result was the lower than expected delta power
values obtained after the 9 hr SD. For AK mice, the values obtained
after the 9 hr SD were significantly lower than those obtained after
the 6 hr SD (Fig. 3). Toward the end of the 9 hr SD, it became
increasingly more difficult to keep the animals awake, and attempts to
enter SWS doubled over the last 3 hr, resulting in an additional 30 min
of SWS (Fig. 4). The length of these
short (<10 sec on average) SWS episodes (i.e., the mean reaction time of the experimenters) did not change with time (analysis not shown). One explanation for the lower than expected delta power after the 9 hr
SD is that the numerous short SWS episodes during the SD collectively
are sufficient to counter a further accumulation of SWS need. In
addition, because of the exponential nature of the decrease of Process
S, per unit of SWS time, SWS need is more effectively reduced when the
prevailing need for SWS is high (see below and Fig.
5). To further explore this possibility,
the time course of Process S during the 6 and 9 hr SD were simulated
using the mean strain parameters obtained for the AK and D2 mice in experiment 1 (Table 1). The values of Process S reached at the end of
the SDs were compared with the delta power at sleep onset. Given that
the parameters were obtained in another set of mice and in a different
experiment, the results of the simulation could predict remarkably well
the delta power values reached after the 9 hr SD (Fig. 4). This again
underscores the validity of the model and strongly suggests that
it is indeed the amount of SWS in the last 3 hr of the SD that
precludes a further buildup of delta power. Alternatively, differences
in PS need or pressure accumulated over the SD, and which can affect
the expression of delta power in SWS (Brunner et al., 1990; Endo et
al., 1997), might have contributed to the lower than expected levels of
delta power observed after the 9 hr SD. Inferring from the amount of PS
expressed over the same period that the initial delta power was
calculated, a higher PS pressure was present after the 9 hr SD (PS time
in the first 15 min of SWS after SD; 6 vs 9 hr SD; AK: 1.5 ± 0.4/2.5 ± 0.7 min; D2: 0.3 ± 0.2/1.7 ± 0.5 min;
two-way ANOVA factor strain: p = 0.04; factor dose:
p = 0.02; interaction: p = 0.7).
However, this difference was significant for D2
(p = 0.03), where delta power did not differ for
the two SDs, and not for AK (p = 0.3; t tests), where delta power did significantly decrease.
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Figure 4.
The amount of SWS and time course of Process S
during the SDs. Top panel, Hourly values (mean ± SEM; n = 6 per hour per strain) for the
accumulation of the amount of SWS during the 9 hr SD. Attempts to enter
SWS increase as the SD progresses and result in a doubling in SWS time
in the last 3 hr. SWS did not differ between strains at any of the time
points (two-way ANOVA factor strain: p = 0.6;
factor 1 hr interval: p < 0.0001; interaction:
p = 1.0). Symbols are as in Figure 3. The
six gray diamonds represent mean SWS values for both
strains accumulated over the shorter SDs used in the dose-response
curve. Genotype did not affect these values (two-way ANOVA factor
strain: p = 0.9; factor dose: p < 0.0001; interaction: p = 0.9). Bottom
panel, SWS expressed during the SD can explain the lower delta
power values reached after the 9 hr as compared with the 6 hr SD. With
the assumptions and the parameters of the simulation analyses (Table
1), Process S can be followed through the 6 and 9 hr SDs. Delta
power (filled black symbols:
circles, AK, squares, D2; mean ± SEM) after the 6 (n = 7) and 9 hr
(n = 6) SD can be predicted remarkably well
(simulated values of S: open symbols;
mean ± SEM). Delta power values are indicated at time + 0.1 hr to
avoid overlap of error bars.
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Figure 5.
The decrease in SWS delta power during recovery
depends on its initial level. Left panel, As in Figure 3
but now for each SD, both the mean delta power in the initial 15 min of
SWS (d1) and the last 15 min of SWS
of the first 1.1 hr after the SD
(d2) are plotted (mean ± SEM; n = 6 per strain, except for 6 hr SD;
n = 7). Right panel, Individual
combinations of the delta power decrease
(d1  d2) and initial delta power
(d1). Linear regression analysis
demonstrated that the decrease strongly depended on
d1 for both strains [AK:
(d1 d2) = 0.47 · d1 48;
r2 = 0.89; p < 0.0001; D2: (d1 d2) = 0.49 · d1 50;
r2 = 0.87; p < 0.0001; n = 37 per strain]. These linear
relationships define exponential functions with time constants of
1.3 ± 0.1 hr for AK (n = 32) and 1.1 ± 0.1 hr for D2 (n = 36; p = 0.2;
t test; see Materials and Methods). Symbols are as in
Figure 3.
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Quantifying the decrease rate of Process S during
recovery sleep
According to the outcome of experiment 1, the rate at which
Process S decreases during SWS does not vary with genotype. The exponential nature of the decrease during SWS is best illustrated during recovery sleep from a 6 hr SD during which SWS predominates and
delta power is initially high (Fig. 6).
It has to be kept in mind that the rate of decrease directly estimated
from the data will differ from that determined with the simulation,
because the presence of wakefulness (and PS) during recovery will
counter the decrease, thus resulting in a slower overall decrease rate. On the other hand, for the same reasons, the lower asymptote estimated directly from the data will be higher, which as discussed above for
interdependence between the upper asymptote and
i will in turn yield a faster
d.
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Figure 6.
Decrease in SWS delta power during the first 6 hr
of recovery sleep after a 6 hr SD. Delta power data (mean ± SEM;
n = 7 per strain) are taken from experiment 1. Each
value represents the mean over consecutive 225 4 sec epochs scored as
SWS and is plotted at the mean time after recovery sleep onset.
Stars at the bottom indicate significant
strain differences in delta power (t tests;
p < 0.05). The two pairs of lines delineate the
average results (±1 SEM) of the individually performed nonlinear
regression analyses assuming an exponential decrease with time in delta
power. The function is determined by the time constant
(d; p = 0.8), the initial
value at recovery sleep onset (S0;
p < 0.0001), and the asymptote (LA;
p = 0.6; t tests AK vs D2;
n = 7 per strain; values in Table 4). Symbols are
as in Figure 3.
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In a first analysis, the delta power decrease over the first recording
hour after the end of the respective SDs of the dose-response curve
was expressed as a function of the delta power reached in the SWS
immediately after the SD (Fig. 5). This decrease in delta power
strongly depended on its initial level. According to the linear
relationship between initial delta power and its subsequent decline,
the hallmark of an exponential decreasing function, 88% of the
variance in the decline could be explained by its initial value. This
linear relationship translated into time constants, d, that did not differ between AK and D2 (Fig.
5). The amount of SWS expressed during the hour over which the decrease
in delta power was calculated varied with dose (data not shown) and
thus could have influenced the outcome of the previous analysis.
However, the amount of SWS did not differ between AK and D2 for any of the SDs and did not vary in a dose-dependent manner.
In a second analysis, d was estimated by a
nonlinear regression analysis on the time course of delta power over
the initial 6 hr after the 6 hr SD. Throughout this 6 hr recovery
period, SWS amount was maintained at a high level in all strains [58% of total recording time (mean over six strains and 6 hr); range, 50%
(C) to 65% (AK)]. The time course of delta power during recovery is
illustrated for AK and D2 mice in Figure 6, and the mean results of the
nonlinear regression analysis for all six inbred strains are shown in
Table 4. Again, the decrease rates did
not differ between genotypes despite marked differences in the
estimated level of Process S at recovery sleep onset. For AK and D2,
surprisingly similar values for d were
obtained in both the dose-response curve analysis (Fig. 5) (AK: 1.3 hr; D2: 1.1 hr) and the present analysis (Fig. 6) (1.2 hr in both).
These two analyses confirm that (1) Process S decreases exponentially,
and (2) the rate of decrease does not significantly vary between the
genotypes.
Experiment 3: QTL analysis of delta power at sleep onset
after enforced and spontaneous periods of wakefulness
Because mice of a particular inbred strain can be
considered genetically identical clones that differ from other inbred
strains, the results of experiments 1 and 2 strongly suggest a genetic basis underlying the accumulation rate for SWS need. The segregation of
this trait in recombinant offspring of strains for which this trait
differed can be used for mapping. Here we present data from RI mice
that were derived from a B6xD2 cross (BXD) and provide a preliminary
mapping of genomic regions associated with the accumulation of SWS need.
QTLs associated with the rebound after 6 hr SD
The wake-dependent increase rates for SWS delta power
(i) between B6 and D2 differed when compared
separately (Table 1) (p = 0.021; t
test; n = 7 per strain). In keeping with this, the level of delta power attained after the 6 hr SD differed between these
two strains (Fig. 7)
(p = 0.016; t tests;
n = 7 per strain). Their RI offspring also varied for
this quantitative trait (Fig. 7) (one-way ANOVA factor strain;
p < 0.0001; Tukey's range test: BXD-5 > BXD-21,
-28, -31, -20, -32; B6 > BXD-14, -12, -29, -30, -2, -21, -28, -31, -20, -32; p < 0.05), with additive genetic factors accounting for 37% of the total variance (i.e., heritability in inbred strains) (Hegmann and Possidente, 1981). Based on these findings, we pursued a QTL analysis by calculating nominal correlations between the SDP of the trait and the SDP of the genotype of each of the
788 MIT markers typed for these RI strains. For the delta power rebound
after the 6 hr SD, the permutation test (see Materials and Methods)
established a suggestive level for LOD scores of >1.77, corresponding
to a p < 0.0043 level for a nominal correlation, and a
significant level for LOD scores of >2.98, corresponding to
p < 0.00021. Using these criteria, two genomic regions
were identified.
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Figure 7.
QTL analysis of the delta power rebound after 6 hr
sleep deprivation in BXD-RI mice. Top panel, SDP of
delta power in the first 15 min of SWS (mean ± SEM;
n = 4-7 per strain) after the sleep deprivation.
Black vertical bars mark progenitor strains B6 and D2.
Zeros above the horizontal axis denote
strains carrying the B6 allele (as opposed to a D2 allele) at the
markers that gave the best LOD score on chromosome 13. Bottom
panel, Point correlations between the SDP of the phenotype
(i.e., delta power) and the genotype of the MIT markers on chromosome
13. p values of the correlations are converted into LOD
scores. The genome-wide suggestive and significant levels are derived
from an empirical probability distribution (see Materials and Methods).
The positions of the markers are given in cM from centromere according
to the MGI database (www.informatics.jax.org). The 38-53 cM range
indicates the interval where the interpolated LOD scores > suggestive, roughly corresponding to a ±2 LOD score confidence
interval.
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A significant QTL was found on chromosome 13 with 37.8-53.4 cM as the
region where LOD scores were above the suggestive threshold [D13Mit231, -254 (39.9/40.0 cM) LOD = 2.36; D13Mit126, -106, -193 (41.0/42.0/43.0 cM) LOD = 3.57; D13Mit107, -147, -145 (48.0/49.0/52.0 cM) LOD = 2.92]. The best LOD score (3.57)
corresponds to a nominal p level of 0.00005 and a
genome-wide p level of 0.01. We termed this QTL
Dps1 (delta power in SWS QTL 1). The LOD scores for all MIT
markers typed in BXD RI strains for chromosome 13 are shown in Figure
7. For only one RI strain (BXD-29), the phenotype clearly did not match
its genotype (Fig. 7). A possible explanation might be the presence of
a double cross-over between two neighboring markers genotyped as B6
alleles. Assuming a D2 genotype for BXD-29 would further increase the
LOD score for Dps1 to 5.04. The only other suggestive QTL
was found on chromosome 2 between 82.3 and 101.6 cM [D2Mit311, -343, -229, -456 (83.1/84.2/85.2/86.3 cM) LOD = 2.13; D2Mit147, -528 (87.0/87.4 cM) LOD = 2.52]. These findings were not related to or
influenced by differences in PS or SWS time expressed during the period
over which delta power was calculated (analyses not shown). The rate at
which delta power decreases during recovery sleep after the SD was
analyzed according to the procedure illustrated in Figure 5. As in the
previous two experiments, no significant differences were present
between strains and no QTLs were identified (analysis not shown).
QTLs associated with delta power at sleep onset in baseline
In an attempt to confirm the QTLs identified for delta power after
enforced wakefulness, the same analysis was performed in undisturbed,
baseline conditions for delta power at the onset of the main sleep
period. However, in 19 of the 25 BXD-RI strains, an additional sleep
period was apparent in the latter half of the dark period, best
illustrated in the progenitor strain B6 (Fig.
8). In 10 of these 19 BXD-RI strains, the
delta power reached at the onset of these additional sleep periods was
higher than at the onset of the main sleep period (Fig. 8). It can be
argued whether this additional sleep period is still part of the active period and thus whether the higher of these two sleep onset values or
the sleep onset value of the main sleep period best reflects the SWS
need accumulated during the active period. Both possibilities were
pursued, and the same four QTLs were detected by either analysis. Only
the results of the latter analysis will be presented below.
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Figure 8.
Distribution of SWS in baseline and the time
course of SWS delta power during the main sleep periods of the 25 BXD-RI strains tested. The SWS distribution (gray
area) represents a 2 hr moving average of percentage recording
time with a 15 min resolution (4-7 per strain). Delta power values
(black dots connected with thick lines)
represent means over consecutive 225 4 sec epochs scored as SWS. Only
delta power values for SWS occurring within the main sleep period(s)
are depicted. One to two major sleep periods were determined per mouse
according to the SWS distribution (see Materials and Methods). The
initial delta power values of these sleep periods were used in the QTL
analysis. The number in the top right-hand corner of
each panel indicates the BXD-RI strain ID. The progenitor strains, B6
and D2, are indicated on the bottom row. Data in the
dark period are displayed twice to visualize the dark-to-light
transition.
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Although the main sleep period was always associated with the light
period, both its onset and end varied with strain (sleep onset:
0.9 ± 0.2 hr; sleep end: 11.5 ± 0.1 hr; mean ± SEM;
n = 128; times relative to lights on; one-way ANOVA
with factor strain: p < 0.0001 for both variables;
n = 4-7 per strain; 27 strains). Delta power at the
onset of the main sleep period differed between the progenitor strains
B6 and D2 (p = 0.051; t test,
n = 7/strain) and varied among the BXD-RI strains (Fig.
8) (one-way ANOVA factor strain: p = 0.0003; Tukey's
range test: B6 > BXD-9, -28, -31; BXD-13 > BXD-31;
BXD-19 > BXD-31; p < 0.05). For this trait, the
permutation test established a suggestive threshold for QTLs with LOD
scores of >1.83, corresponding to a p < 0.0037 level
for a nominal correlation, and a significant level for QTLs with LOD
scores of >3.14 or p < 0.00014. Four QTLs were
identified with these criteria.
First and most important for our purposes is the suggestive QTL found
on chromosome 13 in the range from 34.5 to 41.5 cM [D13Mit13 (35.0 cM)
LOD = 2.30; D13Mit224 (37.5 cM) LOD = 2.44]. This QTL overlaps with the Dps1 QTL. The markers that gave the best
correlation for Dps1 (D13Mit126, -106, -193) now have a LOD
score of 1.61 (i.e., nominal p = 0.0065). This
indicates that the two phenotypes (i.e., delta power after the SD and
after the active period) are genetically correlated, which was
supported by a significant correlation (r = 0.59;
p = 0.0011; n = 27). Another suggestive
QTL was found on chromosome 7 between 21.5 and 28.0 cM [D7Mit229 (23.0 cM) LOD = 2.22; D7Mit145 (26.5 cM) LOD = 2.18]. Two
significant QTLs were found: on chromosome 12 between 52.4 and 58.2 cM
[D12Mit280 (55.0 cM) LOD = 3.30; D12Mit18, -263, -8 (56.0 cM)
LOD = 2.43; D12Nds2 (57.0 cM) LOD = 2.38; D12Mit150 (58.0 cM)
LOD = 1.92] and on chromosome 17 between 16.6 and 22.9 cM
[D17Mit16, -28, -233 (18.15/18.2/20.9 cM) LOD = 3.17; D17Mit11
(22.0 cM) LOD = 2.44]. These two QTL were termed Dps2
and Dps3, respectively.
The QTLs found for SWS delta power at sleep onset in baseline that do
not influence the rebound after sleep deprivation are more likely to be
related to the distribution of SWS (that in turn drives delta power)
rather than directly linked to the increase rate of a need for SWS.
This could be demonstrated for the Dps3 QTL on chromosome
17. The distribution of SWS in BXD-RI mice was highly variable
especially in the 6 hr preceding the main sleep period (Fig. 8).
Changes in this period are likely to affect the expression of delta
power at sleep onset. In an effort to quantify and capture these
changes in one value, the sum of the difference between the maximum
(usually related to the additional sleep period) and the subsequent
minimum amount of SWS and the difference between that minimum and the
subsequent SWS level reached in the main sleep period was calculated
(values not shown). This value was largest for B6 mice because they
exhibited a pronounced peak in the amount of SWS directly followed by
an equally pronounced peak in the amount of wakefulness just before
sleep onset (Fig. 8). Only one suggestive QTL was identified on
chromosome 17 for this trait, which was identical to the
Dps3 QTL. With 1.83 and 3.17 as genome-wide suggestive and
significant levels, this QTL was localized between 15.0 and 24.1 cM
[D17Mit45, -135 (16.4/16.5 cM) LOD = 2.37; D17Mit16, -28, -233 (18.15/18.2/20.9 cM) LOD = 3.04; D17Mit11 (22.0 cM) LOD = 2.49; D17Mit136 (23.0 cM) LOD = 2.44; D17Mit49 (23.2 cM) LOD = 2.67].
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DISCUSSION |
The results of the experiments demonstrate that one of the
parameters of the process underlying the homeostatic regulation of SWS
need, i.e., its rate of increase in the absence of SWS, greatly varies
between genotypes. In contrast, the exponential decrease of SWS need in
the presence of SWS did not seem to vary. Preliminary mapping of this
trait in recombinant inbred strains yielded one significant QTL on
chromosome 13.
The distribution and duration of SWS and Process S
A different time course of delta power can be a consequence of
different dynamics of Process S or a consequence of the distribution and amount of SWS. The simulation, which accounts for differences in
the sleep-wake distribution, provides a tool to distinguish between
these two alternatives. In the present analyses, the remarkable difference in the baseline time course of delta power between C and BR
mice had to be attributed to differences in the SWS distribution because the estimates of the parameters of Process S did not differ. Indeed, the diurnal amplitude of the amount of sleep for C mice is
strongly attenuated as compared with BR (Franken et al., 1999). A
similar observation was made in gene-targeted mice of the 129 strain
that lack albumin D-binding protein (DBP), a circadian transcription
factor (Lopez-Molina et al., 1997; Ripperger et al., 2000). In these
mice, a pronounced reduction of the diurnal amplitude of delta power
was observed (Franken et al., 2000), which also could be attributed to
differences in the distribution of SWS because the time constants
describing Process S were unaffected [i = 9.0 hr; d = 1.7 hr; the 129 mice served as
isogenic controls (Table 1)]. Dbp is localized within the
chromosome 7 QTL, and a functional, different Dbp gene
between B6 and D2 might affect the baseline sleep-wake distribution in
BXD-RI strains and the delta power it drives.
The results of our experiments strongly reemphasize that delta power in
SWS is a marker of a homeostatic sleep regulatory process, i.e.,
Process S in the Two-Process model of sleep regulation (Borbély,
1982; Daan et al., 1984). However, our data also add to the notion that
SWS delta power and SWS duration are regulated differently (Dijk and
Beersma, 1989; Dijk and Kronauer, 1999), which is inconsistent with the
assumptions of the Two-Process model in which Process S, in interaction
with a circadian process, determines sleep duration. In the present
study, large strain differences in sleep duration could be observed
without apparent differences in the dynamics of Process S. Aeschbach et
al. (1996) arrived at the same conclusion when comparing delta power
responses to an SD between human habitual long and short sleepers.
Other support comes from observations in rats and mice in which during the course of recovery from SD, delta power can reach values below baseline (i.e., "negative rebound"), whereas the duration of SWS remains well above baseline (Franken et al., 1991a, 1999; Rechtschaffen et al., 1999). This negative rebound was shown to result from the SD-induced increase in SWS time (Franken et al., 1991b). Thus, although delta power in SWS is "driven" by the previous sleep-wake history, it does not seem to drive SWS duration.
This is the first study to demonstrate that the increase in SWS need,
quantified in baseline and recovery from SD, varies within individuals
of one species. One could argue that the strain differences in delta
power do not relate to differences in the dynamics of Process S that it
is thought to reflect but that the expression of delta power is merely
affected. However, in all strains, regardless of differences in time
constants, delta power did reliably reflect prior sleep duration.
Furthermore, several non-EEG measures are also indicative of
differences in SWS need. Thus, an increased SWS need in AK mice is also
evidenced by a larger SWS amount (during baseline 2.8 hr more than in
D2 mice) and their inability to maintain long waking bouts (Franken et al., 1999). Conversely, although D2 mice display the largest amount of
wakefulness in the dark period, SWS fragmentation, a measure negatively
correlated with SWS need (Franken et al., 1991a), was higher in
subsequent sleep compared with other inbred strains (Franken et al.,
1999).
The dynamics of Process S during wakefulness
The results of experiment 2 suggest that the relationships between
spontaneous and enforced bouts of wakefulness and subsequent delta
power do not differ. This illustrates that nonspecific factors that
inevitably accompany the SD (e.g., increased stress and activity) do
not seem to be a major contributor to the subsequent delta power
rebound; if anything, the increase rate in delta power is higher for
spontaneous waking bouts, possibly related to the absence of SWS during
these bouts (see below).
The relationship between the time spent awake and EEG delta power seems
linear. Performance, a non-EEG measure inversely related to SWS need,
also changes linearly as a function of time spent awake (Kuo et al.,
1998). Recovery of performance during sleep, on the other hand, shows
an exponential saturating function with a time constant comparable to
that of delta power (Jewett et al., 1999). The impression of an
exponential saturating function for the increase of SWS need might
result from the intrusion of short SWS episodes during longer SDs. In
addition, as in rats and humans (Franken et al., 1991a, 1993;
Aeschbach et al., 1999; Cajochen et al., 1999), delta power within
wakefulness increased over the SDs in the six inbred strains of mice
(data not shown). This might not only reflect an increased need for
SWS, but at the same time might result in a slower buildup rate of
Process S. The SWS during the SD, possibly in conjunction with a
slowing of the increase rate, can readily account for a lack of a
further increase or even a decrease in delta power observed after the 9 hr SD in the present study and after longer than 24 hr SDs in the rat
(Rechtschaffen et al., 1999).
Our interpretation that SWS need increases at different rates might be
related to strain differences in the "quality" of wakefulness. Differences in locomotor activity, metabolic rate, brain temperature, the response to the environment, and vigilance, among others, might
affect subsequent sleep (Horne, 1988). For some of those variables, an
effect on delta power has been suggested, but for the few variables
that were compared between D2 and AK mice, no obvious differences seem
present [Trullas and Skolnick, 1993; the Mouse Genome
Informatics (MGI) database (www.informatics.jax.org)]. From the higher
relative contribution of delta power to the waking EEG (Franken et al.,
1998), one could infer that D2 mice in baseline spent a larger portion
of their waking time in a more quiet or "drowsy" state.
Implications of the expression of delta power during wakefulness on
Process S remain to be established. Compared with wakefulness, SWS
clearly represents the more homogeneous behavioral state. The
similarity between strains of the decrease rate of SWS need during SWS
might reflect this.
The genetics of Process S
Two genomic regions were identified that might contain genes that
modify the rate at which SWS need accumulates. To propose candidate
genes at this point is premature because these regions contain several
hundreds of genes. Nevertheless, according to their position listed in
the MGI database, several genes directly associated with the expression
of delta power or mentioned in relation to a possible function of SWS
are worth pointing out. The chromosome 2 QTL contains the gene encoding
brain-glycogen phosphorylase, an enzyme that converts glycogen into
glucose-1-phosphate during metabolic demand. Possibly, SWS serves to
replenish glycogen stores that become depleted during wakefulness
(Benington and Heller, 1995; Holden et al., 2000). Two other
genes encode enzymes that regulate adenosine levels:
S-adenosyl-homocysteine hydroxylase and adenosine deaminase.
Adenosine has been implicated in mediating the EEG manifestation of SWS
need; i.e., delta power (Benington and Heller, 1995;
Porkka-Heiskanen et al., 2000). The genes for growth hormone releasing
hormone (GHRH) and the somatostatin receptor are also localized in this
region. GHRH and somatostatin regulate the pituitary release of growth
hormone. All three hormones have been implicated in the regulation of
SWS and the expression of delta power (Krueger and Obál, 1997;
Van Cauter et al., 1998). Furthermore, the chromosome 2 QTL is homolog
to the human chromosome 20q13.2 region that contains a gene that
mediates a low-voltage EEG trait (Anokhin et al., 1992). The
Dps1 QTL on chromosome 13 encompasses the gene encoding the
neurotrophic tyrosine kinase-2 receptor on which brain-derived
neurotrophic factor (BDNF) acts. BDNF mRNA expression parallels the
expression of delta power and was found to increase with prolonged
wakefulness and to decrease with recovery sleep (Peyron et al.,
1998).
The basic assumption underlying the QTL analysis is that the QTLs that
were found contain functionally polymorphic genes that affect the
phenotype in the progenitor strains (Lander and Botstein, 1989; Lander
and Schork, 1994). Because most quantitative traits are determined by
several genes, any one of them is likely to explain only a certain
percentage of the trait variance. The Dps1 QTL explained a
large portion (49%) of the genetic variance in the rebound in delta
power, suggesting the presence a major gene. We are currently refining
and confirming the mapping of these QTLs in B6xD2 and AKxD2 intercross
and backcross panels. Ultimately, this might lead to a resolution high
enough to warrant either a candidate gene approach (if present) or,
alternatively, positional cloning.
The efficiency of the QTL approach in identifying genes is being
questioned, and, currently, forward genetics by mutagenesis is being
favored (Nadeau and Frankel, 2000). Nevertheless, especially because
the complete genomes of the B6 and D2 strains (and thus their
polymorphisms) will be available soon (Marshall, 2000), QTL
analysis will prove to be a powerful tool in identifying genes underlying complex traits such as sleep and its homeostatic regulation (Tafti et al., 1999) that do not easily lend themselves to the high-throughput screening necessary for mutagenesis.
| |
FOOTNOTES |
Received Nov. 8, 2000; revised Jan. 25, 2001; accepted Jan. 30, 2001.
This study was supported by the Swiss National Science Foundation
(Grants 31.45751.95 and 3100-056000), the National Institutes of Health
(Grant HL64148), and a Roche Research Foundation Fellowship. We thank
Dr. Nihal Okaya for help with mathematical issues and Drs. Bruce
O'Hara and Derk-Jan Dijk for helpful discussions and comments on this manuscript.
Correspondence should be addressed to Dr. Paul Franken,
Department of Biological Sciences, Stanford University, Stanford, CA
94305-5020. E-mail: pfranken{at}stanford.edu.
| |
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TOP
ABSTRACT
INTRODUCTION
