Biomedical Engineering Reference
In-Depth Information
1.2.2 Coil Library
The
φ
and
ψ
dihedral angles of the backbone of protein structures are often
presented in two-dimensional density plots, called Ramachandran plots. The Ra-
machandran space
180
◦
,
180
◦
)
is divided into several regions,
each one referring to a specific secondary structure. The empty regions refer to
the disfavored conformations which are mainly caused by the steric clash between
neighboring side chains or steric hindrance to the formation of hydrogen bonds be-
tween peptide groups and water molecules (Avbelj et al.,
2006
). Here, these density
plots are used to generate the mean force potentials for local interactions in the
unfolded state. For this purpose, we adopt the Boltzmann inversion method
180
◦
,
180
◦
)
[−
→[−
k
B
T
ln
P
(q)
,
(1.3)
where
q
is any desired degree of freedom, P
(q)
is the probability distribution for
q
,
T
is the temperature and
k
B
is the Boltzmann constant.
In order to obtain meaningful potentials for unfolded proteins, appropriate Ra-
machandran data must be extracted from the protein data bank. The required density
plots should not be biased towards any secondary structure, while long-range effects
(hydrophobic or electrostatic interactions) must be absent or have a negligible im-
pact on the density plots. The data that satisfy these conditions best are for the coil
regions of proteins. The coil regions are those parts of proteins that cannot be clas-
sified in any kind of known secondary structure. This implies that their backbone
conformations are not biased to any regular structure. Also it has been shown that
the intrinsic backbone preferences of di-peptides are strikingly similar to the back-
bone conformations of coil regions of proteins (Avbelj et al.,
2006
), confirming the
assumption that long range hydrophobic or electrostatic interactions are negligible
for this class of residues.
The DASSD library is used to extract Ramachandran plots of the coiled regions
of proteins (Dayalan et al.,
2006
). This database contains dihedral angles of cen-
tral residues of short amino-acid fragments (of length 1, 3 and 5), which gives the
possibility to extract meaningful potentials by considering the effect of neighbor-
ing residues on the obtained potentials. The database is extracted from 5,227 non-
redundant high resolution (less than 2 Å) protein structures and a secondary struc-
ture assignment is carried out using the STRIDE algorithm (Frishman and Argos,
1995
).
U
(q)
=−
1.2.3 Three-Letter Amino Acid Model
The current size of the coil library is not large enough to extract CG bending and
torsion potentials for all 20 amino-acids accounting for all possible neighbors. Since
the Ramachandran plots are the main input for the extraction of the CG potentials,
they provide the best reference to compare different amino-acids and to categorize
them into several sub-groups based on the similarities in their Ramachandran data.
