Computational Drug Discovery and Design

affect the result, as the effects of different restraint strengths cancels

out betweenΔGsolvrestrandΔGprotrestrþΔGprotelecþvdW.

ΔG

prot

restrneeds to be estimated via simulations, running multiple

intermediate states where the force constants of the six harmonic

restraints are interpolated between their chosen value and zero. On

the other hand, ΔGsolvrestr can be calculated analytically using the

following formula (Eq. 32 in Boresch et al. [32]), which also

includes the standard state correction:

ΔGsolvrestrkBTln

V

V



¼kBTln

8 π^2 V



r^2 aA∙sinθa∙sinθA

kraAkθakθAkφbakφaAkφAB

 1 = 2

ðÞ 2 πkBT^2

"#ð 11 Þ

whereVis the standard volume of 1660 A ̊^3 ,raAis the reference

value chosen for the distance restraint,θaandθAare the reference

values of the two angle restraints, andkare the force constants of

the harmonic restraints for the one distance (raA), two angle (θa

andθA), and three dihedral (φba,φaA,andφAB) restraints. Later in

the text, we will refer to Eq.11 simply asΔGsolvrestr, while implicitly

assuming it also contains a correction for the standard state.

3 Materials

In this section, we summarize the information and tools that are

needed before one can obtain binding free energy predictions as

described in this chapter.

a

b

c

A

B

C

raA

a

ba

A

aA

AB

r = distance a-A

a= angle b-a-A

A= angle a-A-B

ba = dihedral c-b-a-A

aA = dihedral b-a-A-B

AB = dihedral a-A-B-C

Ligand Protein

Fig. 2Set of restraints proposed by Boresch et al. [32] for use in free energy calculations. The atoms and
terms involved in this set of restraints are shown. Atoms “a,” “b,” and “c” belong to the ligand (on the left),
while atoms “A,” “B,” and “C” belong to the protein (on the right)

Absolute Alchemical Free Energy 209