Biology Reference
In-Depth Information
perturbation (FEP) method.
23
The first applications of this formalism
to biological problems came in the early 1980s with the work of Tembe
and McCammon on protein-ligand binding,
24
followed by Peter
Kollman and coworkers with the first alchemical simulations (see section
below) to estimate the binding free energy difference between a wild-
type and a point-mutated protein.
25
Since these early days, free energy
simulation techniques have been the subject of intense research efforts.
Only recently have these methods become reliable due, on the one hand,
to the better sampling provided by the more powerful computers avail-
able today, but, more importantly, to improved theoretical approaches
with better convergence properties. In this section, we will review some
of the basic methods used in the field as well as the most recent theoret-
ical developments. This survey is not exhaustive, but is centered on the
techniques that are most often used by the Molecular Modeling Group
to address the biological problems encountered in the development of
new cancer therapeutic agents.
Consider a well-defined state
A
described by the potential energy
function
V
A
(
r
) and the corresponding Hamiltonian
H
A
(
r
,
p
). For a given
number
N
of particles at constant volume and temperature
T
, state
A
is
described by the partition function
1
-
b
Hrp
A
(, )
Ú
Z
=
hN
e
dd
r
p
,
A
3
N
!
where
K
B
T
. The normalization constant contains Plank's constant
h
,
a measure of the elementary volume in phase space, and the factor
N
!,
which should be present only when the particles are indistinguishable.
The statistical mechanics definition of the free energy of a system in a
given state
A
is
β =
.
Gk TZ
=-
B
l
n
A
A
In complex systems, however, such absolute free energies are intrinsically
impossible to compute because the partition function is essentially a measure
of the full configuration space accessible to the system. In experiments
