Biology Reference
In-Depth Information
The key limitations imposed on the SCMF and DEE are (i) the
backbone/template is fixed, and (ii) sequence search is restricted to a
discrete set of rotamers. In their application of the SCMF method,
Koehl and Delarue [28-30] refined iteratively a conformational matrix
whose element
CM
(
i,j
) gives the probability that side chain
i
of a pro-
tein takes on rotamer
j
. Hence
CM
(
i,j
) sums to unity over all possible
rotamers for a given side chain
i
. With an initial guess for the confor-
mational matrix, which is usually based on the assumption that all
rotamers had the same probability, that is, for rotamer
k
of residue
i
:
1
CM i k
(, )
=
(1)
K
i
for
k
=
1, 2,
…
,
K
i
. The mean-field potential
E
(
i,k
) is calculated using [28]:
K
N
j
Ei k
(, )
=
U x
(
)
+
U x
(
,
x
)
+
∑
∑
CM j lU x
( ,) (
,
x
)
(2)
ikC
ikC
0
C
ikC
j
lC
j
=≠
1
,
j
i
l
=
1
where
x
0
C
corresponds to the coordinates of the atoms in the template,
and
x
ikC
corresponds to the coordinates of the atoms of residue
i
whose
conformation is described by rotamer
k
. Lennard-Jones (12-6) potential
can be used for the potential energy
U
[28]. Energies of the
K
i
possible
rotamers of residue
i
can subsequently be converted into probabilities
using the Boltzmann law:
−
Eik
RT
Eil
RT
(, )
e
CM
(, )
i k
=
1
(3)
−
(,)
K
i
e
∑
l
=
1
CM
1
(
i,k
) provides an update on
CM
(
i,k
) which can be used to repeat the
calculation of energies and another update on the conformational
matrix until convergence is attained. The convergence criterion is usu-
ally set as 10
−4
to define self-consistency [28]. In addition, oscillations
during convergence could be removed by updating
CM
1
(
i,k
) with a
“memory” of the previous step [28]:
CM
=
λ
CM
+
(
−
λ
)
CM
(4)
1
where optimal step size l was found to be 0.9 [28]. The main disadvan-
tage of SCMF is that though it is deterministic in nature, it does not
guarantee to yield a global minimum in energy [26].
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