example of alchemical path that can be used for the calculations. It
considers only a very small number of windows just for illustration
purposes; in reality many more intermediate states should be used.
At the top of this figure, the ligand is decoupled/annihilated from
the protein environment, while at the bottom it is decoupled/
annihilated from the solution environment. The columns ofλ
values for the restraints, coulombic, and Lennard–Jones interac-
tions define each thermodynamic state, that is, each simulation that
is carried out. For instance, in state F (corresponding to state F in
Fig.1 too) nothing has changed yet, since allλvalues are zero and
the simulation is a standard unbiased protein–ligand simulation.
Then, in the second complex simulation, the restraints have been
turned on partially, while the coulombic and LJ interactions are still
fully on; in the third simulation, the restraints have been turned on
completely (λrestr¼1). Then, the coulombic interactions of the
ligand start being modified, and between the fourth and fifth
simulation of the complex, the ligand charges have been completely
decoupled/annihilated. Finally, in the sixth and seventh simulation,
the Lennard–Jones interactions of the ligand have also now been
decoupled/annihilated, reaching state D where the ligand is fully
decoupled and restrained.SeeNote 1for how to set up such an(F)λrestr
λcoul
λvdw0.0
0.0
0.00.5
0.0
0.01.0
0.0
0.01.0
0.5
0.01.0
1.0
0.01.0
1.0
0.51.0
1.0
1.0λrestr
λcoul
λvdw0.0
0.0
0.00.0
0.5
0.00.0
1.0
0.00.0
1.0
0.50.0
1.0
1.01.0
1.0
1.0ΔGsolvrestr
analytical(E) (D)(A) (B) (C)= = = = = =Fig. 3Simplified example of alchemical path and states controlled by theλparameters. The top row
represents the decoupling and restraining of the ligand from the solvated protein–ligand complex; the bottom
row represents the decoupling of the ligand from solution. The thermodynamic states (A)–(F) match the states
shown in the thermodynamic cycle in Fig.1. An orange color for the ligand indicates the presence of
coulombic interactions with the environment, while a white color their absence; when the vdW surface of
the ligand is shown, it indicates the presence of vdW interactions with the environment, while a stick
representation of the ligand indicates the absence of vdW intermolecular interactions; a paper clip represents
the presence of restraints, with its size proportional to the force constant used. The values ofλrestr,λcoul, and
λvdwdefine the thermodynamic state of the simulation
Absolute Alchemical Free Energy 213