Bioorganic Chemistry
27
be used to generate randomized positions
in positional scanning libraries. (This is
because in positional scanning libraries,
there are random positions that occur
af-
ter
the specifc defned positions.) Splitting
and mixing would thereFore lose the inFor-
mation contained in the defned position.
In iterative deconvolution, however, the
terminal position is always the defned
position, so this issue is not relevant.
6
Molecular Modeling
A very useFul tool in the study oF bioor-
ganic chemistry is molecular modeling,
the simulation oF molecules and their in-
teractions. This single designation covers
a vast region oF study including meth-
ods oF molecular mechanics, a range oF
approaches For conFormational sampling,
semiempirical methods,
ab initio
meth-
o
d
sa
sw
e
l
la
sth
ean
a
l
y
s
i
so
Fc
omp
l
e
x
interactions (which may include all oF the
previously named techniques). The over-
all aim oF these methods is to simulate
properties oF molecules, From the small
scale (e.g. dipole moments) to the larger
scale (e.g. thermal stability oF a protein).
All oF these tools have limitations and,
by defnition, approximate the behavior oF
physical systems. At the minimum, it is
suggested that a given computational tech-
nique be validated with a related system For
which experimental evidence can be used
to support the technique’s application. IF
no such external validation is available,
then the results oF a simulation should be
used cautiously.
Molecular mechanics is the computa-
tionally least-intensive method oF estimat-
ing the energy oF a molecule and the
dependency oF this energy on conForma-
tion. The basis oF molecular mechanics is
the
force Feld
, a mathematical representa-
tion oF a molecule’s energy based on an
arithmetic sum oF diFFerent terms. These
terms assess the contributions made by
bond stretching, bond angles, dihedral
rotations, and other movements to the
overall energy oF the molecule. ±igure 21
shows the equation For the AMBER Force
feld. Because the Forces that control these
movements are simulated using very sim-
ple physical models (a stretching spring
to represent a stretching bond, For exam-
ple) the overall energy can be calculated
very rapidly. The challenge is
parameter-
ization,
the determination oF the Factors
Energy =
Σ
K
r
(
r
r
eq
)
2
+ Σ
K
q
(
q
q
eq
)
2
+
Σ
(V
n
/2) [(1
+
cos (
n
∅ −
g
)]
+
Σ
(A
ij
/R
ij
12
B
ij
/R
ij
6
)
+
Σ
q
i
q
j
/eR
ij
Bond
stretching
Bond
angle
Bond dihedral
angle
Van der Waal
interactions
Electrostatic
interactions
Atom 1
Atom 2
r
eq
Fig. 21
Sample force Feld (AMBER). Simple physical model of energy
dependence on atomic position: for example, bond stretching modeled as a
spring stretch with energy required to displace atoms beyond their
equilibrium separation.
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