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192 Cell-Penetrating Peptides: Processes and Applications
TABLE 9.1
Atomic Surfaces Transfer Energies
for the Seven Atomic Types a
Atomic types
Transfer energies
per accessible surfaces
(kJ/mol Å 2 )
Csp3 –0.0150
Csp2 –0.0134
H (= 0) –0.0397
H(/0) 0.0362
O 0.0403
N 0.1120
S –0.1080
a Csp2, double-bonded and aromatic carbons;
Csp3, single-bonded carbons; H ( = 0), non-charged
hydrogen (bound to C); H (/0), charged hydrogen;
O, oxygen; N, nitrogen; S, sulfur.
where E atr is the atomic transfer energy of one of the N atoms of the molecule
considered. In addition we introduce a correcting factor that takes into account the
fact that solvent interacts only with accessible atoms — known to be essential for
a good description of the hydrophobic effect. 34,46 Our formulation is at least in line
with two experimental facts: the hydrophobic effect is related to the nature and to
the surface of solute in contact with solvent. To calculate the values of E tr, we wrote
an equation system by applying Equation 9.2 to 19 of the 20 natural amino acids
(excluding proline for convenience). We used the experimental transfer energies
measured by Fauchère and Pliska 47 as H values.
Following Brasseur, 45 seven atomic types were considered: double-bonded carbon
(Csp2) (including aromatic cycles carbons), simple-bonded carbon (Csp3),
oxygen (0), sulfur (S), nitrogen (N), uncharged hydrogen bonded to C (H = 0), and
charged hydrogen (H/0). Thus, we can, for example, calculate the transfer energy
of Phe and Asn (with the convention of Figure 9.2) as
H theo (ASN) = E tr (Csp3) (S2+S5) + E tr (Csp2) (S3+S9) + E tr (H=0) (S6+S7+S8+S13+S14)
+ E tr(H/0)S10+ E tr (O) (S4+S12) + E tr (N) (S1+S11)
H theo (PHE) = E tr (Csp3) (S2+S5) + E tr (Csp2) (S3+S9+S11+S13+S15+S17+S19)
+ E tr (H = 0) (S6+S7+S8+S12+S14+S16+S18+S20) + E tr(H/0)S10+ E tr (O) (S4) + E tr (N) (S1)
where S1 to 20 are the accessible surfaces of atoms.
The system written that way consists of more equations than variables (19 vs.
7); hence, a unique solution does not exist and the system must be approximated.
In their original publication, Fauchère and Pliska 47 deduced the measured transfer