Chemistry Reference
In-Depth Information
optimal (minimum COST) complete matching of the bipartite graph in polynomial [O(N
3
)]
time. Below we briefly describe the implementation of the NOE matching COST function.
The function C(
k
,
q
) defines the edge weight values (Figure 5.2):
C
(
k
,
q
)
i
M
i
(
k
,
q
)
i
=
1,
N
L
(5.1)
where
N
L
is the number of resolved, assigned ligand
1
H groups (e.g.
N
L
=
3 in Figure 5.2).
Equation (5.1) has been modified to ensure that obviously incorrect group-to-group match-
ings (e.g. an aliphatic group to an aromatic group) do not occur. This will be described in
detail elsewhere. Referring to Figure 5.2, the matching cost
M
between an experimental
peak and a predicted peak is defined by the following expressions:
M
i
(
X, X
)
=
0
(
no experimental peak, no predicted peak
)
(5.2)
M
i
(
O, X
)
=
K
1
(
IE
i
)
2
(
experimental peak present, no predicted peak
)
(5.3)
M
i
(
X, O
)
=
K
2
(
IP
i
)
2
(
no experimental peak, predicted peak present
)
(5.4)
M
i
(O
,
O)
:
(
experimental peak present, predicted peak present
)
If IE
i
>
IP
i
M
i
(
O, O
)
=
K
H
[
f (
H
)/σ
H
]
2
+
K
C
[
f
(
C
)/σ
C
]
2
+
K
3
[
f
(
I
)
]
2
Else
f
(
I
)
M
i
(
O, O
)
=
K
H
[
f (
H
)/σ
H
]
2
+
K
C
[
f (
C
)/σ
C
]
2
+
K
4
[
]
2
(5.5)
End If
See ref. 15 for a detailed description of the terms and parameters in Equations (5.2)-(5.5).
Equation (5.5) has been modified to incorporate data from nonuniformly labeled samples.
These modifications will be described elsewhere.
The total cost of a given pose corresponds to an optimal solution of the completematching
problem, which is a permutation
ε
of {1, 2,
...
,
N
} that minimizes
COST
pose
=
C
[
j
,
ε (j)
]
j
=
1,
N
(5.6)
j
5.3 Applications to Lead-like Compounds Bound to Small Proteins
The ability of NOE matching to identify the correct pose from a collection of decoy poses
was demonstrated on three test cases involving lead-like compounds bound to small pro-
teins. One of these test cases involves muscle fatty acid-binding protein (mFABP) and the
other two involve the leukocyte function-associated antigen 1 I-domain (LFA-1). As these
results have been presented in detail elsewhere,
[
15
]
here we only summarize the results
obtained when the BMRB average chemical shifts (diamagnetic protein statistics) were
used for chemical shift predictions. The compounds used for these test cases are shown in
Scheme 5.1 (compound
3
contains a proprietary core, which is represented by an ellipse).
