Simulations of Biomolecules Using Molecular Dynamics

2
Free Energy Simulations
Free energy perturbation simulations involve a kind of "computer alchemy". These simulations model processes
that cannot be carried out experimentally. In these simulations, the focus is on the determination of relative free
energy differences of two processes, illustrated in Figure 2 for the binding of two ligands to the same molecular
compound.
ΔG 1
M + L 1 M -L 1
ΔG 2
M + L 2
M -L 2
Figure 2. Free energies for binding of two ligands, L 1 and L 2 , to molecule M.
For the processes shown in Figure 2, the free energies denoted by ΔG 1 and ΔG 2 correspond to the binding of two
different ligands (L 1 and L 2 ) to the same molecule (M) to form complexes (M-L 1 and M-L 2 , respectively). The
relative free energy of binding, Δ(ΔG), is given by the relation
Δ(ΔG) = ΔG 2 – ΔG 1 . (1)
Processes 1 and 2 generally are difficult to simulate using molecular dynamics, so to determine Δ(ΔG)
computationally, an alternative route is used, as illustrated in Figure 3.
ΔG 1
M + L 1 M -L 1
M + L 2
M -L 2
ΔG 2
Figure 3. Free energy cycle for binding of two ligands, L 1 and L 2 , to molecule M.
Processes 3 and 4 mutate ligand 1 into ligand 2 in the unbound and bound states. Since the Gibbs free energy is a
thermodynamic state function, we have the equivalence
Δ(ΔG) = ΔG 2 – ΔG 1 = ΔG 4 – ΔG 3 . (2)
Obviously, processes 3 and 4 cannot be performed experimentally since they generally involve mutation of one atom
into another or one functional group into another. However, computationally, all that the mutations require are
modifications of the force field used to represent the system.
To carry out the simulations, known as free energy perturbation simulations, a perturbation parameter λ is defined
such that λ=0 corresponds to the processes involving ligand 1 and λ=1 corresponds to the processes involving ligand
2. The force field V can then be defined as
V = λ V 2 + (1 – λ) V 1 , (3)