Biomedical Engineering Reference
In-Depth Information
1
2
10
150000
10
150000
10
100000
10
100000
10
50000
10
50000
10
0
10
0
1
2
r
Fig. 5.14
Plot of the energy as a function of the reaction coordinate (using Eq.
5.19
here and
hereafter) for gA channels in lipid bilayer energetics at different orders of screening (single- and
double-dashed curves are for the first- and second-order screening, respectively). Only real parts
of the energies have been considered and for simplicity
U
(
r
∗
)
has been used for
U
LJ
(
r
∗
)
here and
other energy plots in all next figures.
q
L
/
q
gA
=
0
.
005,
(
1
/
0
)
q
L
q
gA
≈
1 has been chosen (here
and in Figs.
5.15
and
5.16
) for simplicity,
r
LL
=
0Å has
been excluded to avoid the associated singularity. Numerical integration here (and hereafter) has
been performed using Mathematica 7 within (
7
.
74597 Å. In the plot, the energy at
r
=
−
k
max
2
π/
r
LL
,
k
max
2
π/
r
LL
), where
k
max
=
100 and
the step size for integration
d
r
=
0
.
001 have been taken as judicious choices
bilayer thickness and gA channel lengths. The 'barrel-stave' pore type Alm channels
(see Fig.
5.8
)[
19
,
36
] exist with different sizes, depending on the number of Alm
monomers participating in the pore formation and the pore continuously experiences
structural transitions between different conformations representing different pore
conductance levels (which experimentally manifest themselves as current levels)
following the energetic profile as described in Sect.
5.3.1
. Note that the higher the
cross-sectional area of the pore, the higher the value of the conductance through the
Alm channel.
Figures
5.14
,
5.15
, and
5.16
demonstrate the energetics (in arbitrary units) of a gA
channel in lipid bilayers with different lipid screening orders and lipid dimensions
using the model calculation. In Figs.
5.14
and
5.15
G
I
and
G
II
(
G
I
G
II
) repre-
sent energy levels at conformational states I and II where two gA monomers exist in
free form (no channel formation:
M
I
) and gA dimer form (channels formed:
D
II
),
respectively. Formation of a channel with any level of stability requires an energetic
transition (reduction)
>
G
II
). Although the energy minima appear at
different values of reaction coordinates, we have chosen the transition
G
I
G
I
,
II
(
=
G
I
−
G
II
at a
certain value of reaction coordinate (as shown in Fig.
5.15
) to illustrate how the corre-
sponding back-and-forth conformational changes between gA monomers and dimers
(
M
I
↔
G
I
,
II
, which depends mainly on the
bilayer physical properties for a certain channel type. The binding energy between
two gA monomers alone in a gA channel is many orders of magnitude smaller than
the binding energy of the gA channel with the bilayer at the channel bilayer interface.
⇔
D
II
) may become regulated due to
G
I
,
II
(see Figs.
5.14
and
5.15
) represents the amount of energy gA monomers need
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