Biomedical Engineering Reference
In-Depth Information
therefore even longer simulations are required in order to obtain statistically-
meaningful results. The necessity to achieve biologically interesting time and length
scales, have drawn the interest of researchers towards the development of coarse-
grained (CG) models.
There is a limited set of available CG models that account for the disordered state
of proteins. Simple models such as the elastic network and Go-models (Tirion,
1996
)
have been developed but their force fields are completely biased to a unique refer-
ence structure. In the more complex CG models like the MARTINI model (Monti-
celli et al.,
2008
), the Head-Gordon model (Yap et al.,
2007
) and the model devel-
oped by Korkut and Hendrickson (
2009
), a priori knowledge of the local secondary
structure of the protein is required to perform the simulations. The CG models with
more predictive power (Tozzini et al.,
2006
,
2007
; Bereau and Deserno,
2009
)are
parametrized using databases of folded protein structures and therefore cannot be
expected to reproduce the correct conformational dynamics of unfolded proteins.
In the present work, a one bead per amino-acid, implicit solvent model for un-
folded proteins is proposed. Local interaction potentials are obtained by converting
experimentally-obtained Ramachandran plots for the coil regions of proteins into
distributions of pseudo-bond and pseudo-dihedral angles between neighboring
α
-
carbons in the CG chain. These distributions are used to derive bending and torsion
potentials, which are residue- and sequence-specific. As an example, the model is
used to study the ensemble average gyration radius of denatured proteins as a func-
tion of the amino acid sequence.
1.2 Extraction Method to Obtain Coarse-Grained Potentials
In the following sections, the general methodology for extracting the CG potential
functions from the Ramachandran data of coiled regions of proteins is summarized;
more details can be found in (Ghavami et al.,
2012
).
1.2.1 Mapping Backbone Internal Degrees of Freedom (φ,ψ)to
Pseudo Bending and Torsion Angles (θ,α)
A geometrical representation of the coarse-grained polypeptide chain together with
the CG degrees of freedom are shown in Fig.
1.1
. In the all-atom representation
of the backbone (Fig.
1.1
(a)), the bond lengths and bond angles display only a
small variation from their average value so they are assumed to remain fixed in the
present work (Finkelstein and Ptitsyn,
2002
). The average bond lengths of C
α
-N,
C
α
-C and C-N are 0
.
145 nm, 0
.
152 nm, 0.133 nm, respectively, with the average
bond angles C
α
-C-N
116
◦
, C-N-C
α
=
122
◦
and N-C
α
-C
111
◦
. A Trans-
=
=
τ
=
180
◦
) and the rare possibility
of Cis-conformation is neglected. With the stated assumptions, it could be implied
conformation is presumed for the peptide bond (
ω
=
