Towards a Coarse-Grained Model for Unfolded Proteins - Computer Models in Biomechanics - page 7

The same methodology is also applied to derive the pseudo-torsion potentials.
The main difference with the bending procedure is that in Eq. ( 1.2 ) two separate
sets of Ramachandran data (e.g., φ i , ψ i , φ i + 1 and ψ i + 1 ) are required to convert the
all-atom dihedral angles φ and ψ to the coarse-grained dihedral angle α . Studying
different levels of accuracy resulted in torsion potentials for all possible double-
combinations of X, P and G amino-acids, giving 9 different torsion potentials. The
reader is referred to (Ghavami et al., 2012 ) for more background information.

1.3 Application to Denatured Proteins

High temperature, pressure or the presence of a chemical denaturing agent can break
down the native structure of folded proteins. As a result, it will turn to a dynamic
set of complex conformations which is called the denatured state of a protein (Rose,
2002 ). The addition of denaturants disrupts the native hydrogen bonds and weakens
the hydrophobic forces in the protein (Das and Mukhopadhyay, 2008 ; Lim et al.,
2009 ; Zangi et al., 2009 ). After denaturation, only local interactions that restrict the
polypeptide backbone to limited regions of the conformational space are retained
(Creamer, 2008 ). Experimental studies have revealed that the ensemble-average ra-
dius of gyration of denatured proteins follows a power-law scaling:
R g = R 0 N ν , (1.4)

where N is the number of residues, R 0 is a constant related to the persistence length
of the polymer and ν is a scaling exponent.
The obtained potentials are used to study the effect of the composition of the
protein sequence on the R g of denatured proteins, with special emphasis on the
role of Proline in enlarging and that of Glycine in reducing the conformational ra-
dius. A survey of protein sequences of folded and unfolded proteins shows that
the amount of Proline and Glycine residues never exceeds 15 percent. In order to
study the effect of sequence and composition on the R g of unfolded proteins, a
series of simulations has been performed on protein chains with different lengths,
containing 15 percent of Glycine and Proline residues randomly distributed along
the chain. As expected, the sequences rich in Proline residues lead to a higher R g
compared to the chains rich in Glycine, producing an upper and lower bound for
the R g of denatured proteins (see Fig. 1.3 ). Any chain with less than 15 percent
Proline or 15 percent Glycine falls within this band. The experimental results of
low-charge crosslink-free chemically unfolded proteins with sizes ranging from 16
to 549 residues, shows that R g can be well fitted by the power-law relationship in
Eq. ( 1.4 ) with R 0 = 0 . 037 (Kohn et al., 2004 ),

which indeed falls in between the computed bounds in Fig. 1.3 .
Recently, many studies have been conducted on poly-Proline proteins showing
that these proteins form elongated left-handed helices with a very stiff backbone
structure (Adzhubei and Sternberg, 1993 ). The current model is able to capture the
helix conformation of poly-Proline proteins with a rise of 2.97 Å per Proline, which

0 . 202 ± 0 . 041 nm and ν = 0 . 588 ±