Computational Drug Discovery and Design

difference of transitioning between the intermediate states high-

lighted in Fig.1.ΔGsolvelecþvdWis the free energy of decoupling the

ligand from the solution (state A!B), effectively bringing it to gas

phase.ΔGsolvrestris the free energy of restraining the ligand to a certain

portion of phase space while still not interacting with the environ-

ment (state B!C). The free energy of placing the noninteracting

and restrained ligand into the protein binding pocket (state C!D)

is zero, so that it needs not be calculated.ΔG

prot

elecþvdWis then the free

energy of coupling the restrained ligand to the environment again

(state D!E), basically bringing the ligand back into the solution

while being kept into the protein’s binding pocket. Then, finally,

ΔG

prot

restris the free energy of removing the restraints that kept the

ligand in place when not interacting with the environment. Thus,

the binding free energy can be recovered as the sum of these four

major steps, with the addition of a correction for the 1 M standard

state:

ΔGb¼ΔGsolvelecþvdWþΔGsolvrestrþΔG

prot

elecþvdWþΔG

prot

restrkBTln

V

V^0

ð 10 Þ

2.3.1 Restraints The use of restraints is important in the protocol here described as
it prevents the ligand from leaving the protein binding pocket while
it is not interacting with the environment. This is necessary to make
sure that the conformations sampled during the simulations corre-
spond to a well-defined bound state. If the ligand were to leave the
binding pocket in the windows where it is partially or completely
decoupled, and started sampling the whole volume of the box, it
would have a large configurational phase space available, leading to
convergence issues. The use of restraints aids good phase space
overlap between windows and faster convergence [32, 33].
In theory, any type of restraint that keeps the ligand in its
bound pose can be used if its free energy contribution is properly
accounted for. Also note that the use of restraints somewhat com-
plicates the standard state correction, since the volumeVdoes not
correspond anymore to the volume of the whole box [15]. In
practice, we find the set of restraints proposed by Boresch et al.
[32] to be particularly convenient. In summary, this set of restraints
not only allows to keep the ligand in a specific orientation relative to
the binding pocket [33], but also provides an analytical solution for
ΔGsolvrestr, thus reducing the number of simulations to be run. Fur-
thermore, the analytical solution also already includes the standard
state correction. This set of restraints needs to be harmonic and is
comprised by one distance, two angles, and three dihedrals, to be
applied between three atoms of the ligand and three of the protein,
as shown in Fig.2. The authors also showed how the exact value of
the force constant used for the harmonic restraints should not

208 Matteo Aldeghi et al.