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190 Cell-Penetrating Peptides: Processes and Applications
the bilayer is simulated as a continuous domain. Indeed, this simple bilayer description
is treated as a simple continuous hydrophobic domain, taking into account
charge potential induced by the polar head groups of phospholipids. In this representation,
proteins, peptides, or any amphiphilic molecules entering membrane are
modeled at atomic resolution.
Such approaches have been used with success in the analysis of amphipathic
peptides, 31-33 hydrophobic peptide, 31 tilted peptides, 34 and membrane protein. 35 Modeling
results were similar to the experimental data when the latter were available.
If the approximation of the bilayer as a hydrophobic–hydrophilic continuum is
somewhat simplistic, the existence of such a continuum interface was shown by
x-ray and neutron diffraction studies. 36,37 At 10 to 15 Å, head groups of phospholipids
and water molecules are co-located. This picture is reinforced by several molecular
dynamics (MD) simulations of pure lipid bilayers 32 or peptides in interaction with
lipid bilayers, 38,39 but the later simulations are restricted to a few nanoseconds, which
is insufficient to simulate the transfer of a molecule through the membrane.
This chapter about cell-permeant peptides will focus on modeling techniques
recently developed to describe peptide behavior in context of their interaction with
biological membranes and to provide a predictive method to further design peptide
vectors aimed to address different classes of compounds into cells.
9.2 METHODS
9.2.1 DESCRIPTION OF WATER–BILAYER INTERFACES
We postulate that the properties of membranes are constant in the plane of the bilayer
(x/y plane). Thus, the lipid–water interfaces are described by a function, C (Z), which
varies along the z axis only; z (in angstroms) is perpendicular to the plane of the
membrane and its origin is at the center of the bilayer. C (Z) (Figure 9.1) is an empirical
function varying from 1 (completely hydrophilic) to 0 (completely hydrophobic)
derived from Milik and Skolnick. 40
C
1
= 1−
α(
0 )
1+
e
( z) z−z (9.1)
where α and z 0 are mathematical parameters calculated so that C (⏐Z = 18 Å⏐) = 1 and
C (⏐Z = 13.5 Å⏐) = 0 and so that the function is approximately constant from –∞ to –18 Å
(hydrophilic phase), from –13.5 to 13.5 Å (hydrocarbon core), and from 18 Å to ∞
(hydrophilic phase). Z = 13.5 Å is the distance at which the first polar heads appear, 41
and an interface of 4.5 Å gives the best results for simulations. The same interface
width was used in the Monte Carlo technique developed by Milik and Skolnick. 40
This mathematical form of C (Z) was chosen because it is continuous and can be
rapidly computed.
Because C does not vary into the plane x/y, a molecule is fully described by its
internal geometry: two rotations (around x and y) and one translation (along z). The
main simplification of this approach is that it totally neglects specific interactions
between the molecule and lipids or other molecules buried in the membrane. However,