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198 Cell-Penetrating Peptides: Processes and Applications
This enabled us to rapidly determine a set of parameters leading to predictions
in agreement with experimental data (see below).
The peptide structures were derived from the 9 ent.pdb. The molecules are fully
described (H included, no heavy atoms) as this has an obvious effect on the accessible
surface used in the calculations. A standard Monte Carlo procedure is then applied
for 2·10 5 steps at 310 K by randomly translating (max. 1 Å) and rotating (max. 5°)
the molecule at each step. Each Monte Carlo was run twice.
9.2.6 MONTE CARLO PROCEDURE
The total constraint E i is calculated at the step i. The molecule undergoes a random
translation and rotation at the step (i+1) where it is submitted to the constraint E i+1.
• If E i+1 < E i
• If E i+1 > E i
the position at the step i+1 of the molecule is conserved
and it undergoes another random movement where it
will be submitted to the constraint Ei+2 and compared
to Ei+1 …
the probability density function
f = e –∆E/kT (0 ≤ f ≤ 1)
where ∆E = E i+1 – E i, k = Boltzman constant, T = temperature
(in K), is compared to a random number Rnd
(0 ≤ Rnd ≤ 1):
• If Rnd < f, the position at point E i+1 is conserved and another random
movement is applied from this position
• If Rnd > f, the position at point E i+1 is rejected and a new random
movement (translation and rotation) is applied to the
molecule at the step i.
The probability for Rnd to be less than f is inversely correlated to ∆E, allowing
the structure to converge towards a global minimum by jumping over the local
minima.
9.2.7 PEX2DSTAT FILES
The results of the Monte Carlo simulations are saved in Pex2Dstat text files 52
(Figure 9.4A). These files consist of one array; each line corresponds to one step of
the simulation. In this study, each Monte Carlo procedure was performed in 200,000
steps. Each column corresponds to a parameter analyzed during the simulation.
Current Pex2Dstat files are made of 27 columns among which the energetic
restraints (col. 1, 2, 4, and 5), the molecule mass center penetration (col. 9), and the
angle of the molecule vs. the bilayer model normal (col. 10) were considered for
the present study.
Because of their size, Pex2Dstat files cannot be easily manipulated in their
current form. Indeed, importing such files in a spreadsheet would give a worksheet