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© 1999 Macmillan Magazines Ltd
there is a long-period sinusoidally modu-
lated structure like that of erbium.
The value of the exchange stabilization
energy of the helix, J(qm)1J(0), may be
estimated from the peak susceptibility using
x
max4
m
0Nm2/{S2[J(qm)1J(0)]} (ref. 7),
where
m
0is the permeability of free space, m
is the atomic moment of gadolinium,
S47/2, Jis the exchange energy and qmis
the reduced wave vector in the c-direction;
x
max475 gives J(qm)1J(0)40.013 K.
Extrapolating from the heavy rare-earth
metals, where J(qm)1J(0)öqm4, we esti-
mate that qm40.029 Å11; the correspond-
ing wavelength,
l
m, is 70 Å.
Examination of gadolinium close to TC,
using techniques to observe the long-period
modulation directly, may confirm that
gadolinium is not really ferromagnetic.
J. M. D. Coey, V. Skumryev, K. Gallagher
Physics Department, Trinity College,
Dublin 2, Ireland
1. Belov, K. P. & Pedko, A. L. Zh. Eksp. Teor. Fiz. 47, 87 (1962).
(English transl., Sov. Phys. JETP 15, 62–64 (1962).
2. Cable, J. W. & Wollan, E. O. Phys. Rev. 165, 733–734 (1968).
3. Dan’kov, S. Y., Tishin, A. M., Pecharsky, V. K. & Gschneider,
K. A. Jr Phys. Rev. B 57, 3478–3489 (1998).
4. Chen, D.-X. & Sanchez, A. J. Appl. Phys. 70, 5463–5477
(1991).
5. Geldart, D. J. W., Hargraves, P., Fujiki, N. M. & Dunlap, R. A.
Phys. Rev. Lett. 62, 2728–2731 (1989).
6. del Moral, A. & Lee, E. W. J. Phys. F 4, 280–290 (1974).
7. Kitano, Y. & Nagamia, T. Prog. Theor. Phys. 31, 1–37 (1964).
Physiology
Warm feet promote the
rapid onset of sleep
Even healthy people occasionally have diffi-
culty falling asleep. Psychological relaxation
techniques, hot baths, soothing infusions of
plant extracts, melatonin and conventional
hypnotics are all invoked in the search for a
good night’s sleep. Here we show that the
degree of dilation of blood vessels in the skin
of the hands and feet, which increases heat
loss at these extremities, is the best physio-
logical predictor for the rapid onset of sleep.
Our findings provide further insight into
the thermoregulatory cascade of events that
precede the initiation of sleep1.
Our analysis combines data from two
intervention studies designed to induce
phase shifts in the circadian pacemaker2,3.
Healthy young men were given melatonin,
bright light, or both, in the evening (n48),
or a large carbohydrate-rich meal in either
the morning or the evening (n410). These
manipulations had different thermoregula-
tory effects and so gave a broad variance,
enabling us to extract the best predictor
variables for the latency of sleep onset.
Subjects lay in bed under controlled
conditions (lighting less than 8 lux; 22 °C),
taking small snacks of constant caloric value
every hour during wakefulness. The latency
of sleep onset was defined as the time
between lights out (24:00) and the first
occurrence of stage 2 in the sleep EEG
recordings. Heart rate, core body tempera-
ture (rectal) and proximal (combined infra-
clavicular, thigh, stomach, forehead) and
distal (combined hands and feet) skin tem-
peratures were continuously measured4
(and later collapsed into 30-min bins).
Sleepiness was rated2every 30 min and saliva
was collected for melatonin assay5. We cal-
culated the distal–proximal temperature
gradient (DPG), a measure of blood flow in
distal skin regions (efficiently regulated by
artereovenous anastomoses)6that provides
an indirect index of distal heat loss.
By using a multiple regression model for
repeated measures, with the latency of sleep
onset as the dependent variable (n418
subjects, 144 data points; between-subjects
differences taken into account), we found
the highest correlation with the DPG aver-
aged over the three data points between
22:30 and 24:00 (r410.47, P*0.0001).
Thus, the greater the distal vasodilation in
the late evening, the shorter was the time
taken to fall asleep. We found that correla-
tions were weaker with subjective sleepiness
ratings (r410.33, P*0.0001), core body
temperature (r40.26, P*0.005), melatonin
(r410.15, n.s.; after excluding the mela-
tonin intervention data), rate of change of
core body temperature (r410.05, n.s.) and
heart rate (r40.05, n.s.).
36 NATURE
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brief communications
Temperature (K)
Temperature (K)
80
70
60
50
40
30
20
10
0
100
80
60
40
20
0
40
20
0
100
270 275 280 285 290 295 300
150 200 250 300
χ'χ', χ''χ', χ''
χ'||
χ'||
χ''||
χ'|
χ'|
χ''|
a
b
Figure 1 Magnetic susceptibility of a gadolinium crystal. a,Real
and imaginary parts of the susceptibility measured with an alter-
nating-current technique on long samples cut from a crystal of
gadolinium with the field applied parallel (ää) and perpendicular
(>) to the
c
-axis. The susceptibility is independent of frequency in
the range 10 Hz to 1 kHz. The horizontal dotted lines indicate the
saturation values expected for a divergent susceptibility, given the
sample shape. b, Internal susceptibility of gadolinium in the vicini-
ty of
T
C, corrected for the demagnetizing effect caused by the
sample shape.
magnetization and His the magnetic field
strength, have been performed on crystals
with a demagnetizing factor, N, of 0.1 to
0.3. The demagnetizing factor depends
only on shape and determines the strength
of the reverse field that appears inside a
sample when it is magnetized;
x
is limited
by the demagnetizing effect to 1/N. We
therefore use long, thin samples with
Nö0.01, and measure
x
in a small alter-
nating-current field of 8 A m11, compen-
sating for the Earth’s field with a pair of
Helmholz coils.
Figure 1a shows that the real compo-
nent
x
8(T) measured perpendicular to the
c-axis has a sharp peak at the magnetic
transition with a maximum value of 4954.
As the temperature decreases further,
x
8
increases to saturate near the demagnetiz-
ing-limited value 1/N477. When the field
is parallel to c, there is only a shoulder in
x
8(T) at TCand the value does not exceed
10.
x
8(T) increases at lower temperature,
reaching the demagnetizing limit 1/N466
at 230 K.
Figure 1b shows the real and imaginary
components,
x
8and
x
9, for the two direc-
tions in the vicinity of TC, after correcting
for the demagnetizing effect4. The
x
>8(T)
peak at the magnetic transition is accompa-
nied by a small peak in the
x
>9(T) compo-
nent, but
x
ää8(T) barely exceeds 10 at TCand
x
ää9(T) is zero within experimental error.
There is no evident divergence at TC. To see
whether the observed non-divergence of the
c-axis susceptibility could be related to pin-
ning of domain walls, we applied a 50-Hz
alternating-current bias field of 80 A m11to
mobilize the walls. The form of
x
8and
x
9
did not change.
The susceptibility of a ferromagnet
normally diverges as ä
e
ä1
g
, where
e
4(T1TC)/TCand the critical exponent
g
is 1.38 for isotropic spins (Heisenberg
model) or 1.24 for extreme uniaxial aniso-
tropy (Ising model). The presence of uniax-
ial dipolar anisotropy5should not prevent
divergence at TC.
Internal checks on the anomalous
behaviour of
x
ää8(T) are provided by the
divergence at lower temperatures in both
directions and by the peak in
x
>(T). The
susceptibility effectively reaches the
demagnetizing-limited values at the spin-
reorientation transition, but not at the
Curie point. The sharp peak observed at TC
when the field is applied in the basal plane
resembles the peak at the Néel point (at
which anti-ferromagnetic materials become
paramagnetic), TN, of 230 K for terbium,
where an in-plane helical structure is estab-
lished6and
x
8reaches a value of 8. When
magnetized in-plane near TC, where mag-
netocrystalline anisotropy is negligible, the
susceptibility of gadolinium resembles that
of a long-period helix rather than a true
ferromagnet. When magnetized along c,
© 1999 Macmillan Magazines Ltd
In a backward stepwise regression analy-
sis among all predictor variables, only DPG
contributed significantly to the model; that
is, vasodilation of distal skin regions was the
best predictor of the body’s readiness for
sleep (Fig. 1). Because interventions such as
light or large carbohydrate-rich meals dif-
ferentially manipulated the independent
variables, the effect on the dependent vari-
able showed that the link between distal
vasodilation and the ability to fall asleep is
functional, not just correlative.
The circadian clock prepares the thermo-
regulatory system for vasodilation to begin
in the early evening as sleepiness increases,
followed by a drop in core body tempera-
ture. Even lying down increases sleepiness
by redistributing heat in the body from the
core to the periphery7. Turning out the light
is a complex cognitive and physiological sig-
nal that also leads to vasodilation4. There is a
tight correlation between the timing of the
endogenous increase in melatonin in the
evening and vasodilation, an effect that is
mimicked by pharmacological doses of
melatonin4,7. Before bedtime, then, many
overlapping events orchestrate the thermo-
regulatory overture.
We would predict that classical hyp-
notics8and other sleep-inducing aids all
cause dilation of distal blood vessels and
heat loss before the onset of sleep. A hot-
water bottle at the feet, while not acting on
mechanisms in the central nervous system
that underly the regulation of sleep, can
rapidly induce vasodilation. The resulting
heat loss is most efficient when the ambient
temperature is cool9. Some sleep disorders
(particularly those associated with ageing
and somatic illness10) may be secondary to
an inability to vasodilate and prepare the
body for sleep.
Kurt Kräuchi, Christian Cajochen,
Esther Werth, Anna Wirz-Justice
Chronobiology and Sleep Laboratory,
Psychiatric University Clinic,
Wilhelm Klein-Strasse 27, 4025 Basel, Switzerland
e-mail: kurt.kraeuchi@pukbasel.ch
1. Campbell, S. S. & Broughton, R. J. Chronobiol. Int. 11, 126–131
(1994).
2. Cajochen, C., Kräuchi, K., Danilenko, K. V. & Wirz-Justice, A.
J. Sleep Res. 7, 145–157 (1998).
3. Wirz-Justice, A. et al. J. Sleep Res. 7(suppl. 2), 308 (1998).
4. Kräuchi, K., Cajochen, C., Möri, D., Hetsch, C. & Wirz-Justice, A.
Am. J. Physiol. 272, R1178–R1188 (1997).
5. Weber, J. M., Unger, I., Wirz-Justice, A. & Schwander, J. C.
J. Sleep Res. 7(suppl. 2),302 (1998).
6. Rubinstein, E. H. & Sessler, D. I. Anesthesiology 73, 541–545 (1990).
7. Kräuchi, K., Cajochen, C. & Wirz-Justice, A. in Circadian Clocks
and Entrainment (eds Honma, K. I. & Honma, S.) 131–146
(Hokkaido Univ. Press, Sapporo, 1998).
8. Gilbert, S. S., van den Heuvel, C. J. & Dawson, D. J. Physiol.
(Lond.) 514, 905–914 (1999).
9. Aschoff, J. Wien. Med. Woch. 19/20, 404–409 (1958).
10.Foley, D. J. et al. Sleep 18, 425–432 (1995).
brief communications
NATURE
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www.nature.com 37
views, there are three connections between
V1and VO, but in the rest either one (33%)
or both (39%) of the peripheral connections
appear to be missing. The three connections
are well separated in the bilobed views (Fig.
1a). In the classes with trilobed views, the
left connection is less well resolved because
it is closer to the central stalk and overlaps
more with V1(Fig. 1b). The two peripheral
connections are each attached to an oval-
shaped area of density on top of V1. In some
other classes (not shown), one of the oval
densities is absent, which correlates with the
loss of a peripheral connection. We con-
clude that the intact V-type ATPase has a
central stalk and two stator connections
(Fig. 1c, d). Likely candidates for the stators
are the bacterial V-type subunits I, E and F,
several copies of which are present.
The discovery of the second stator raises
several points. First, although it has been
suggested that there may be two stators9,
this feature has not been observed before.
This could be because the intact structure is
easily damaged on preparation, which can
be detected only by classifying large sets of
projections. The two stators may be unique
for V-type ATPases because, in the stalk
region of F-type ATPases, only the b subunit
is present in two copies, as a dimer10, partici-
pating in one stator. It is harder to visualize
the stator(s) in F-type ATPase by electron
microscopy because the stalk region is much
shorter than in V-type ATPase8.
Second, there could be more than two
stators: three would match the three-fold
symmetrical ring of the six large subunits
-3
-2
-1
0
Distal-proximal skin temperature
gradient (change in °C)
14 16 18 20 22 24 02 04
06
Time of day (h)
∆
Sleep onset latency (min)
*
30
25
20
15
10
5
0
Figure 1 Time course of the distal–proximal skin-temperature gra-
dient (DPG). The gradient is shown from 14:00 to 7:30 for obser-
vations with the most negative DPG values between 22:30 and
24:00 (large vasoconstriction before lights out at 24:00; pink
symbols), compared with the time course of the most positive
DPG values (large vasodilation before lights out; green symbols)
(mean5s.e.m.,
n
418; asterisk indicates significant differences
between data points;
P
*0.05, Bonferroni-adjusted least signifi-
cant differences). The shaded area indicates the lights-out period.
These two extreme patterns were selected after the mean of the
three DPG values between 22:30 and lights out at 24:00 had
been rank ordered out of 8 observations for each subject. Sleep
onset latency (inset) is significantly shorter when subjects were
most vasodilated (green bar) before lights out (triangle indicates
significant differences; paired
t
-test,
P
*0.001).
Figure 1 Electron microscopy images of V1V0in side view. a, b,
Views obtained by classification: a, bilobed view3; b, trilobed view.
c, d, Model of the arrangement of the stator moiety (green) and
its attachment to the V1headpiece (yellow) by the two oval densi-
ties (red). The view in dshows a larger additional density (dark
blue) of VOon the right side than that in c. The stator moiety is
attached to this additional density, which represents the static part
of VO. The view in dis obtained by rotating cabout 30° back-
wards on the left. Scale bar, 100 Å.
Biological motors
Connecting stalks in
V-type ATPase
In all organisms, adenosine triphosphate
(ATP) provides metabolic energy for driv-
ing energy-dependent processes. It is syn-
thesized and/or utilized by enzymes known
as F-type and V-type ATPases, which are
small rotary motors1,2. Both types consist of
a headpiece, F1or V1, respectively, which is
connected by a stalk region to the mem-
brane-bound part, FOor VO. Electron
microscopic analysis of negatively stained
particles has revealed a peripheral stalk, or
stator, between V1and VOof the V-type
(Na&)ATPase of the thermophilic bacteri-
um Clostridium fervidus3,4, like that in F-
type ATPases5,6. We have analysed many
more particles and now present a more
complete structure of the V-type ATPase
stator moiety.
A central stalk in the ATPase rotates
within a ring of three a- and three b-
subunits in F1(refs 7, 8), or three A and
three B subunits in V1, in discrete steps of
120°. At the FO/VOend, the central stalk is
connected to a ring of c subunits in the
membrane. These subunits rotate against
other subunits of FOand VO, allowing ion
translocation at the interface2. A stator
structure in the form of additional connec-
tions between F1/V1and FO/VOmust pre-
sumably be present to prevent futile
rotation of the a3b3 and A3B3 headpiece2.
We classified a set of 7,500 molecular
projections of detergent-solubilized, nega-
tively stained V1VO, and found a few prefer-
ential orientations in which V1has either
two or three lobes. In about 28% of all
