Biology Reference
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calculated as the average of the area of the simulation box,
XY
, divided by the number
of lipids present in the system,
N
:
X
N
A
¼
However, the presence of other molecules (e.g., proteins) or the heterogeneity of
complex lipid mixtures hampers such calculation. For heterogeneous mixtures, cer-
tain approaches such as employing Voronoi tessellations can help to obtain approx-
imate values of area per lipid for individual species (
Mori, Ogushi, & Sugita, 2012
).
This approach uses certain atoms of each lipid molecule and projects them into a
plane so that we obtain their
x
- and
y
-coordinates. Such layout containing all points
is then tessellated in order to fill the plane with polygons of a certain number of ver-
tices,
V
, where the area of each polygon corresponds to the area of each lipid
molecule:
*
+
2
X
V
1
1
A
polygon
¼
ð
x
i
þ
y
iþ
1
y
i
þ
x
iþ
1
Þ
i¼
0
Various studies (
Pandit et al., 2004; Shushkov, Tzvetanov, Velinova, Ivanova, &
Tadjer, 2010
) have used this approach in an attempt to obtain values of areas per lipid
in ternary or more complex lipid mixtures. Values of areas per lipid obtained thereby
need to be used with caution, as, unfortunately, we still cannot compare these values
with experiments of complex mixtures.
In addition to condensation and thickness, membrane fluidity is one of the key
structural properties one needs to analyze to understand the behavior of lipid mix-
tures. As discussed earlier, the lipid composition has a big impact on membrane flu-
idity and indirectly on the dynamics of membrane proteins. A finer analysis of the
structure of the lipid bilayer requires studying the chain structure of the hydrophobic
tails of membrane phospholipids. Assessing the order of these tails is a way to char-
acterize lipid chain structure as in NMR experiments, where this is habitually mea-
sured through the
S
CD
or deuterium order parameter. This parameter quantifies the
disorder of phospholipid hydrocarbon tails by averaging the angle of each C
d
H
bond,
y
, present in each tail with respect to the bilayer normal (
Vermeer, de
Groot, R
´
at, Milon, & Czaplicki, 2007
).
3 cos
2
y
1
S
CD
¼
2
Highly ordered lipid bilayers show higher values of
S
CD
when compare to more fluid
membranes. This parameter, which is normally in agreement with experiments, is
very useful to understand the structure of our membrane and to study the impact
of different lipid composition on membrane order. In this way, theoretical
S
CD
values
are gradually higher when increasing amounts of cholesterol are added to the mem-
brane system, a rigidifying effect already shown in membrane experiments using this
sterol (
Bartels, Lankalapalli, Bittman, Beyer, & Brown, 2008
). Higher chain order
