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Structure Prediction of CPPs and Iterative Development of Novel CPPs 199
of 200,000 × 27 = 5,400,000 cells. In Figure 9.4B, we plotted all values of the total
energetic restraint of a molecule as a function of the position of its mass center
during the simulation.
In order to facilitate the analysis, a subsequent treatment of these huge files is
applied. Since Monte Carlo is a minimization procedure, only the minimum values
of the restraints need to be taken into consideration (gray points, Figure 9.4B); their
extraction is carried out within a range of the mass center penetration (between +30
and –30 Å in this case). Between these two limits, a resolution step (0.5 Å in this
case) is defined and we extract the lowest value of the energetic constraint within
each 0.5 Å step (Figure 9.4C).
The results can also be plotted in three dimensions. In this case, each axis stands
for a parameter of interest. As an example, Figure 9.4D shows evolution of the total
energy restraint as a function of the mass center penetration of a molecule and as a
function of its angle regarding the bilayer normal.
As an alternative we also looked for the envelope minima corresponding to the
energy for the mass center penetration axis (between +30 and –30 Å with a step of
0.5 Å) and for the angle between the molecule and the bilayer normal axis (between
0 and 180° with a step of 3°), defining a two-dimensional mesh (Figure 9.4E).
9.2.8 MOLECULAR HYDROPHOBICITY POTENTIAL (MHP)
MHP is a three-dimensional plot of the potential of hydrophobicity of a molecule
in order to visualize its amphipathy. Molecules and MHPs are drawn with Win-
MGM. 53 The hydrophobicity of a molecule is calculated using its partition coefficient
between water and octanol. In order to visualize the amphipathy, a three-dimensional
molecular plot of hydrophobicity was proposed by Fauchère et al. 47 for small molecules.
The MHP approach was then extended to plot the surface of the isopotential
contours of larger molecules. 35 We postulate that the hydrophobicity induced by an
atom i and measured at a point M of space decreases exponentially with the distance
between this point M and the surface of atom i. The molecular hydrophobicity
potential at a point M in space is thus estimated according to the equation:
N
MHP = ∑ E r −d
exp
M tri i i
i=
1
( )
where N are all the atoms of the molecule, E tri is the transfer energy of the atom i,
r i is the radius of the atom i, and d i is the distance between the atom i and the point
M. E tri is the energy required to transfer an atom i from an hydrophobic to an
hydrophilic medium. Atomic E tri were calculated from the molecular E tr compiled
by Tanford, 54 assuming that molecular E tr are the sum of the atomic E tr. Atomic E tr
values were derived for seven different types of atoms.
The isopotential surfaces of protein hydrophobicity were then calculated by a
cross-sectional computational method. A 1-Å-mesh-grid plane was set to sweep
across the molecule by steps of 1 Å. At each step, the sum of the hydrophobicity