Biology Reference
In-Depth Information
where
N
water
is the total number of water molecules. Here, the scale factor
K
is calculated from
K
(
r
j
). Thus, the number of electrons
at
r
j
is
qn
j
, where
q
is 10 electrons per water molecule, or for neutron scat-
tering
∆
rS
=
N
water
/
Σ
w
′
1.678 fm (10
−15
m) for 100% H
2
O, 2.486 for 20% D
2
O, 11.856 for
65% D
2
O, and 19.145 for 100% D
2
O. The net number of electrons or
neutron scattering length
N
e
(
r
j
) is, therefore, calculated from
N
e
(
r
j
) =
Σ
−
(
r
j
). Finally, the net electron density or
neutron scattering length density is
D
(
r
j
) =
N
e
(
r
j
)/(
S
Σ
i
n
(
i
,
r
j
)
e
i
N
k
+
qN
water
w
′
(
r
j
)/
Σ
w
′
k
r
).
To obtain the neutron scattering density distribution with comparable
resolution to that of the electron density profile,
D
(
r
j
) is first Fourier trans-
formed and then the structure factor is sampled using a comparable
period. If the continuous function
D
(
r
) is the density of the asymmetric
unit, its Fourier transform is given as
a
(
R
)
∆
ib
(
R
)
,
where
a
and
b
are the
real and imaginary terms. Since the unit density distribution for internodal
myelin is centrosymmetric, the structure factor
F
(
R
) can be written as
F(
R
) = 2
a
(
R
)cos(2
+
uR
), where
u
is the position of the
asymmetric unit from the origin. Here, the value for
u
is chosen such that
Σ
|
b
(
R
)|
π
uR
) - 2
b
(
R
)sin(2
π
2
gives the minimum value. Thus, the density profile at a
resolution of
h
max
/d
is
2
/
Σ
|
a
(
R
)|
h
02
F
()
+
Ê
ˆ
˜
max
Ê
Á
h
d
ˆ
˜
Ê
Á
2
p
rh
d
ˆ
˜
Â
r
¢
()
r
=
F
cos
.
Á
d
d
h
=
1
Model calculation
The chemical composition, i.e.
N
k
and
N
water
for the lipids and water, are
from the published chemical data summarized in Table V of Inouye and
Kirschner (1988). The crystal data for phosphatidylethanolamine
(Elder
et al
., 1977) and cholesteryl dihydrogen phosphate (Pascher,
Sundell, 1982) were used for the myelin phospholipids and cholesterol
in myelin. The atomic coordinates of the phosphate group in choles-
teryl dihydrogen phosphate were excluded. As the hydrogen coordi-
nates in the crystal are not known, they were assigned to the nearest
carbon atoms.
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