μ
0
n, S ¼ γ A À A p
À
Á þ
C
A
¼ γA þ
A
C
, where A, A p ,γand C are area of one molecule at
interface, area of polar group (able to be included in bulk term), density of hydrophobic free energy (3.5 Â 10
-20 Jnm
-2 ) and constant of repulsive free energy
(1.15 Â 10
-20 Jnm
2 ). Packing constraint is a crucial factor in assembly of lipid
molecules in aqueous environment. Area of one lipid molecule in thermodynamic
balance is determined as follows. Condition of the minimum interface free energy
∂μ
0
n, S
∂A
¼ 0, i.e.
μ
0
n, S min
ð
Þ ¼ 0
and substituting each value give
A 0 ¼
ffiffi ffi
C
γ
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1:15Â10
À20 Jnm
2
3:5Â10
À20 Jnm -2
q
¼ 0:57nm
2 . One lipid molecule occupies nearly 0.60
nm
2 in lipid bilayer membranes.
2.3 Shape of Lipid Molecule and Structure of Lipid
Assembly
Hydration of polar heads of phospholipid molecules makes the lipid molecules
disperse in water, and the lipid molecules spontaneously assemble. The process of
hydration depends on lipid species. Phosphatidylcholine is easily hydrated, but
phosphatidylethanolamine is hardly hydrated, and the hydrations proceeds with
main phase transition. Shapes of phosphatidylcholine and phosphatidylethanolamine
are cylinder rand inverted cone, respectively. Phosphatidylcholine molecules assemble in planar structure of bilayer, and phosphatidylethanolamine molecules assemble
in hexagonal II structure. Relationship between molecular shape and structure of
lipid assembly is theoretically explained by Jacob N. Israerachvili [1]. Molecular
shape of phospholipid is defined by packing parameter where v, A 0 , l are volume of
hydrocarbon chain, area of cross section on interface of water phase and length of
hydrocarbon chain, respectively.
packing parameter ¼
v
A 0 l
:
Packing parameter <1, packing parameter ¼1 and packing parameter >1 correspond to cone, cylinder and inverted cone, respectively. From these definitions, a
structure of lipid assembly is obtained theoretically by shape of lipid molecule.
Volume of the assembly divided by volume of the lipid molecule gives number of
constituent lipid molecules, the number must be equal to number that area of the
surface divided by area of cross section of lipid in inter phase of water. Using this
condition of constraint,
4
3 R
3 À RÀl
ð
Þ
3
f
g
v
¼
πR
2
A 0
is obtained in a case of outer layer of
22
2 Cells and Biomembranes
0
n, S ¼ γ A À A p
À
Á þ
C
A
¼ γA þ
A
C
, where A, A p ,γand C are area of one molecule at
interface, area of polar group (able to be included in bulk term), density of hydrophobic free energy (3.5 Â 10
-20 Jnm
-2 ) and constant of repulsive free energy
(1.15 Â 10
-20 Jnm
2 ). Packing constraint is a crucial factor in assembly of lipid
molecules in aqueous environment. Area of one lipid molecule in thermodynamic
balance is determined as follows. Condition of the minimum interface free energy
∂μ
0
n, S
∂A
¼ 0, i.e.
μ
0
n, S min
ð
Þ ¼ 0
and substituting each value give
A 0 ¼
ffiffi ffi
C
γ
q
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
1:15Â10
À20 Jnm
2
3:5Â10
À20 Jnm -2
q
¼ 0:57nm
2 . One lipid molecule occupies nearly 0.60
nm
2 in lipid bilayer membranes.
2.3 Shape of Lipid Molecule and Structure of Lipid
Assembly
Hydration of polar heads of phospholipid molecules makes the lipid molecules
disperse in water, and the lipid molecules spontaneously assemble. The process of
hydration depends on lipid species. Phosphatidylcholine is easily hydrated, but
phosphatidylethanolamine is hardly hydrated, and the hydrations proceeds with
main phase transition. Shapes of phosphatidylcholine and phosphatidylethanolamine
are cylinder rand inverted cone, respectively. Phosphatidylcholine molecules assemble in planar structure of bilayer, and phosphatidylethanolamine molecules assemble
in hexagonal II structure. Relationship between molecular shape and structure of
lipid assembly is theoretically explained by Jacob N. Israerachvili [1]. Molecular
shape of phospholipid is defined by packing parameter where v, A 0 , l are volume of
hydrocarbon chain, area of cross section on interface of water phase and length of
hydrocarbon chain, respectively.
packing parameter ¼
v
A 0 l
:
Packing parameter <1, packing parameter ¼1 and packing parameter >1 correspond to cone, cylinder and inverted cone, respectively. From these definitions, a
structure of lipid assembly is obtained theoretically by shape of lipid molecule.
Volume of the assembly divided by volume of the lipid molecule gives number of
constituent lipid molecules, the number must be equal to number that area of the
surface divided by area of cross section of lipid in inter phase of water. Using this
condition of constraint,
4
3 R
3 À RÀl
ð
Þ
3
f
g
v
¼
πR
2
A 0
is obtained in a case of outer layer of
22
2 Cells and Biomembranes