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Structure Prediction of CPPs and Iterative Development of Novel CPPs 197
But
Therefore
The model of the dielectric profile along the bilayer normal, ε (z), used by Flewelling
and Hubbell 50 was adopted:
(9.11)
where ε pho = 2 is the value of the dielectric constant in the hydrophobic core of the
membrane, and ε phi = 78 in bulk water. This function provides a smooth transition
between the two constants in the interfacial region, defined by two parameters d and
h that are the center and width of the transition region, respectively. The extent of
the bilayer is z = ± (d + h/2). Equation 9.8 was solved using a finite difference
algorithm. 51 A boundary condition of zero potential at z = ± 50 Å (relative to the
center of the bilayer at z = 0) was imposed.
Note that the distance a from the plane to the point P does not appear in the
final result. This means that the intensity of the field set up by an infinite plane sheet
of charge is independent of the distance from the charge. In other words, the field
is uniform and normal to the plane of charge.
9.2.5 PROCEDURE
a
sin θ= , r = a + x
r
+∞
∫
2 2 2
dx
Eq k a
ka
a x a
=
=
⎡1
2 δ 2 δ tan
2 2
+ ⎣⎢
– ∞
2πkδ ⇒ Eq
=
ε
ε = ε + ε −ε
( z) pho phi pho
In order to test the three restraints (hydrophobic, lipid perturbation, and charge
simulation), we applied them to small peptides, the configurations of which have
been experimentally determined. The structures of the peptides were helical and
change of internal structure was not allowed. This drastically simplified the problem
as follows:
1. Only three degrees of freedom were considered (two rotations and one
translation) so that the Monte Carlo procedure used is efficient.
2. Since the structures were unchanged, Coulomb, Van Der Waals, hydrogen
bonds, and torsion energies remained constants; thus the three variable
parameters of the simulation are z 0, α, and α lip.
( z)
−1
x ⎤
a ⎦⎥
( ) [ 1+ 10 ] 4
+∞
−∞
−1
( d+ z) /
h