the snapshots for the protein, ligand and the complex are extracted by defining
appropriate atom numbers from the parameter and coordinate file. However, in the
multiple trajectory approach, three separate simulations are performed, one each for
the protein, ligand and protein–ligand complex.
DG bind
h
i¼ G complex
À G protein
À G ligand
À
Á
ð6Þ
Furthermore, Eq. 1 is modified to accommodate solvation electrostatics and
hydrophobic terms as shown in Eq. 5. Here, Eqs. 7a–7d give the computation of
the individual terms,
DG bind ¼ DE MM þ DG sol À TDS
ð7aÞ
DG sol ¼ DG solÀelect þ DG nonpolar
ð7bÞ
DE MM ¼ DE int þ DE elect þ DE vdW
ð7cÞ
DE int ¼ DE bond þ DE angle þ DE torsion
ð7dÞ
Here, ΔE MM is computed in the gas phase using classical force fields, ΔG sol is
computed using PBSA or GBSA method, ΔG sol-elect is computed using PB or the
GB method, and the ΔG nonpolar is computed by the solvent accessible surface area
(SA). While employing the single trajectory approach, Eq. 7d generally cancels out
and hence makes negligible contribution to the binding energy.
Linear Interaction Energy (LIE)
Linear interaction energy [77–79] is similar to the MM-PB/GB-SA method with
regard to the partitioning of the electrostatic and van der Waals terms (polar and
non-polar contribution, respectively,); however, the use of the weighting parameter
for electrostatic and van der Waals interactions, is unique to this method. LIE
measures the binding energy by estimating the difference in the interaction energies
of the ligand in the solvent (unbound state) and in the protein environment (bound
state). Hence, to obtain these interactions, two separate MD simulations are performed. In one simulation, only the ligand is placed in the solvent (mostly water) and
in the other, the protein–ligand complex is placed in the solvent. The formulation of
this method is based on deriving the linear response approximation from converged
ensemble interactions, most often extracted from well-equilibrated trajectories from
the MD simulation of the ligand with its surroundings (solvent or protein).
The mathematical formula for computing free energies using LIE method is
given in Eq. 8
DG bind ¼ a E
LÀS
coul
PL
À E
LÀS
coul
L
Â
à þ b E
LÀS
vdW
PL
À E
LÀS
vdW
L
Â
Ã
ð8Þ
10
E. A. F. Martis and E. C. Coutinho
appropriate atom numbers from the parameter and coordinate file. However, in the
multiple trajectory approach, three separate simulations are performed, one each for
the protein, ligand and protein–ligand complex.
DG bind
h
i¼ G complex
À G protein
À G ligand
À
Á
ð6Þ
Furthermore, Eq. 1 is modified to accommodate solvation electrostatics and
hydrophobic terms as shown in Eq. 5. Here, Eqs. 7a–7d give the computation of
the individual terms,
DG bind ¼ DE MM þ DG sol À TDS
ð7aÞ
DG sol ¼ DG solÀelect þ DG nonpolar
ð7bÞ
DE MM ¼ DE int þ DE elect þ DE vdW
ð7cÞ
DE int ¼ DE bond þ DE angle þ DE torsion
ð7dÞ
Here, ΔE MM is computed in the gas phase using classical force fields, ΔG sol is
computed using PBSA or GBSA method, ΔG sol-elect is computed using PB or the
GB method, and the ΔG nonpolar is computed by the solvent accessible surface area
(SA). While employing the single trajectory approach, Eq. 7d generally cancels out
and hence makes negligible contribution to the binding energy.
Linear Interaction Energy (LIE)
Linear interaction energy [77–79] is similar to the MM-PB/GB-SA method with
regard to the partitioning of the electrostatic and van der Waals terms (polar and
non-polar contribution, respectively,); however, the use of the weighting parameter
for electrostatic and van der Waals interactions, is unique to this method. LIE
measures the binding energy by estimating the difference in the interaction energies
of the ligand in the solvent (unbound state) and in the protein environment (bound
state). Hence, to obtain these interactions, two separate MD simulations are performed. In one simulation, only the ligand is placed in the solvent (mostly water) and
in the other, the protein–ligand complex is placed in the solvent. The formulation of
this method is based on deriving the linear response approximation from converged
ensemble interactions, most often extracted from well-equilibrated trajectories from
the MD simulation of the ligand with its surroundings (solvent or protein).
The mathematical formula for computing free energies using LIE method is
given in Eq. 8
DG bind ¼ a E
LÀS
coul
PL
À E
LÀS
coul
L
Â
à þ b E
LÀS
vdW
PL
À E
LÀS
vdW
L
Â
Ã
ð8Þ
10
E. A. F. Martis and E. C. Coutinho