Biology Reference
In-Depth Information
Ligand-receptor docking [8] is another case where molecular mod-
eling is used to determine the lowest energy conformation of a system;
in this case, one is interested in discovering the lowest energy confor-
mation for a ligand-receptor complex. Various poses of the ligand and
receptor are generated, and their energies evaluated. The calculation
is repeated hundreds of thousands of times for each ligand in a
compound library, allowing the ligands in the library to be ranked
by their binding energy. This ranking can then be used to prioritize
experimental binding assays.
A second type of information that can be obtained from models
relates to the thermodynamics. To model thermodynamics one uses
a technique meant to mimic a particular set of thermodynamic
conditions, such as a specification of the temperature and density,
or temperature and pressure, of the system. These techniques include
molecular dynamics (MD) and several variants, as well as Monte Carlo
(MC). Traditional MD involves computing a sequence of coordinates
for the molecular system that represent its temporal evolution accord-
ing to the laws of classical mechanics (see box on page 72). This is done
by repeatedly updating the atomic positions and velocities in a way
that reflects the positions, velocities, and forces a short time earlier. Of
course, this technique can be used to simulate the kinetics of a system,
The Metropolis Monte Carlo Algorithm
Start with a “state,” a set of coordinates for all the atoms of the system, and the
potential energy of that state:
S
k
={
r
1
,
r
2
, . . .};
U
k
=
U
(
S
k
)
Apply a suitable random process to generate a trial state and evaluate the
potential energy of the trial state:
S
T
={
r
T
,
r
T
, . . .};
U
T
=
U
(
S
T
)
Accept the trial state with a probability of
P
accept
=min(1,e
−
(U
T
−
U
k
)/kT
)
If the trial state is accepted, the next state of the chain is the trial state:
S
k+
1
=
S
T
;
U
k+
1
=
U
T
Otherwise, the original state is repeated in the chain:
S
k+
1
=
S
k
;
U
k+
1
=
U
k
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