Biomedical Engineering Reference
In-Depth Information
earlier chapter and also earlier in this chapter. Here, we focus only on the energetic
part.
The bilayer deformation, in general, incurs an energetic cost,
G
def
, that con-
G
I
−
>
II
tributes to the overall free energy difference (
tot
) between two different pro-
tein functional states (conformations), denoted here as I and II, respectively, such
that
G
I
−
>
II
tot
G
I
−
>
II
prot
G
I
−
>
II
def
=
+
,
(5.4)
G
I
−
>
II
where
prot
denotes the energetic cost of the protein conformational change
per
se
(including contributions from interactions with the environment, such as changes
in the protein/solution interface, not considered in the protein-bilayer interactions)
and
G
I
−
>
II
def
, the difference in bilayer deformation energy between protein con-
formations I and II (
G
def
). Consequently, the equilibrium
distribution between the different protein conformations is given by:
G
I
−
>
II
def
G
II
=
def
−
exp
G
I
−
>
II
prot
G
I
−
>
II
def
+
K
II
=
−
,
(5.5)
k
B
T
where
K
II
denotes the equilibrium distribution coefficient between protein states
I and II,
T
stands for the absolute temperature of the bilayer environment and
k
B
is Boltzmann's constant. If
G
def
G
def
|
>
is significant, meaning
|
k
B
T
, then
G
I
−
>
II
def
may be sizable, such that the equilibrium distribution between different
membrane protein conformations—and the kinetics of the conformational changes—
could be modulated by the bilayer in which the proteins are embedded [
3
,
20
,
33
,
76
].
The success of Eq.
5.1
in predicting small molecule permeability coefficients nat-
urally leads to the notion of lipid bilayers being thin sheets of liquid hydrocarbons,
stabilized by the lipid polar head groups, as implied in the original formulation of
the fluid mosaic membrane model [
82
]. If that were the case, one would expect that
|
G
def
|
k
B
T
, in which case membrane protein function would be little affected
by changes in bilayer properties—except in cases where the interfacial surface charge
densities vary [
39
,
59
,
65
]. However, lipid bilayers are not just thin sheets of liquid
hydrocarbon; they are liquid crystals that exhibit both short- and long-range order
[
64
]. By virtue of being liquid crystals, lipid bilayers also have elastic properties
[
27
,
37
], with material properties (average thickness, intrinsic monolayer curvature
and elastic moduli) that can be manipulated by the adsorption of amphipathic com-
pounds [
13
,
28
,
58
,
77
,
80
,
84
,
93
] and other ones. The permeability of small mole-
cules across lipid bilayers given by Eq.
5.5
can, on a broader scale, become highly
regulated by the hydrophobic coupling between the lipid bilayer and the bilayer-
spanning membrane proteins. To address this hydrophobic coupling between the
lipid bilayer and the membrane proteins-induced regulation, we have investigated
here both experimentally and theoretically the energetics of gramicidin A channels
in lipid bilayers with different thickness. To generalize the problem, later in this
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