potential associated with changes in intramolecular structure. Usually, such a
potential has terms to describe variation in bond length (bond length potential),
angle (bond angle potential), dihedral angle (improper and proper dihedral angle
potential) (refer to first five terms in Eq. 1). Since the classical force-field cannot
describe the bond-breaking processes, a harmonic potential is in general used to
describe structural changes associated with bond lengths and bond angles.
However, note that the dihedral angle motion is not local and can describe conformational changes in molecules and in case of peptides these contribute to
changes in the secondary structure. The total potential including both intra- and
intermolecular interactions for a biomacromolecule alone or in solution or in
combination with other molecules can be described by the Eq. 1.
The force constants and equilibrium values for bond length and bond angle are
obtained from spectroscopic data and from the structural data, respectively. Also,
electronic structure theory-based calculations can be employed to get these
parameters.
In general, the binding of a ligand to a protein can be described as the equilibrium
between the protein–ligand complex and the protein and the ligand (Eq. 2). The
change in free energy/the binding free energy (DG Bind ) can thus be calculated as the
difference between the free energies of the ligand and protein in free and bound form
(Eq. 3) which is then compared to experimental binding affinity (inhibition constant
or IC 50 ).
P Aq þ L Aq $ PL Aq
ð2Þ
DG Bind ¼ GðPLÞ Aq À GðPÞ Aq À GðLÞ Aq
ð3Þ
All these free energies can be computed using explicit solvent models, namely
SPC, TIP3P, TIP4P, TIP5P, but it is computationally very demanding. Alternatively,
one can use the implicit solvent models, and then the free energies of the three
systems, namely complex, receptor and ligand, can be computed with less computational effort [18]. This involves calculation of solvation free energy of a subsystem
in a solvent media described with a dielectric constant which is a macroscopic
parameter specific to solvent and describes its ability to polarize the solute [18]. The
electrostatic interaction between the solute and the solvent is solved using generalized born (as in the MM-GBSA) or Poisson–Boltzmann (as in the MM-PBSA) to
get the polar part of the solvation free energies [19]. The non-polar part of the
solvation free energies is computed from the solvent-accessible surface area of the
solute. In the implicit solvent model, the only used solvent parameter is dielectric
constant, usually the solvent coordinates are removed from the molecular dynamics
or Monte Carlo trajectories, and only the protein–ligand coordinates are used.
Force-field methods for calculating free energies (e.g. MM-GBSA or
MM-PBSA) with implicit solvent models forsolvation part achieved considerable
success in explaining the drug binding to a number of receptors or biomacromolecular targets [20–22]. In particular, MM-PBSA method was successfully used
to predict the binding affinities of many antibacterial, antiviral benchmark
Recent Advancements in Computing Reliable Binding Free Energies …
227
potential has terms to describe variation in bond length (bond length potential),
angle (bond angle potential), dihedral angle (improper and proper dihedral angle
potential) (refer to first five terms in Eq. 1). Since the classical force-field cannot
describe the bond-breaking processes, a harmonic potential is in general used to
describe structural changes associated with bond lengths and bond angles.
However, note that the dihedral angle motion is not local and can describe conformational changes in molecules and in case of peptides these contribute to
changes in the secondary structure. The total potential including both intra- and
intermolecular interactions for a biomacromolecule alone or in solution or in
combination with other molecules can be described by the Eq. 1.
The force constants and equilibrium values for bond length and bond angle are
obtained from spectroscopic data and from the structural data, respectively. Also,
electronic structure theory-based calculations can be employed to get these
parameters.
In general, the binding of a ligand to a protein can be described as the equilibrium
between the protein–ligand complex and the protein and the ligand (Eq. 2). The
change in free energy/the binding free energy (DG Bind ) can thus be calculated as the
difference between the free energies of the ligand and protein in free and bound form
(Eq. 3) which is then compared to experimental binding affinity (inhibition constant
or IC 50 ).
P Aq þ L Aq $ PL Aq
ð2Þ
DG Bind ¼ GðPLÞ Aq À GðPÞ Aq À GðLÞ Aq
ð3Þ
All these free energies can be computed using explicit solvent models, namely
SPC, TIP3P, TIP4P, TIP5P, but it is computationally very demanding. Alternatively,
one can use the implicit solvent models, and then the free energies of the three
systems, namely complex, receptor and ligand, can be computed with less computational effort [18]. This involves calculation of solvation free energy of a subsystem
in a solvent media described with a dielectric constant which is a macroscopic
parameter specific to solvent and describes its ability to polarize the solute [18]. The
electrostatic interaction between the solute and the solvent is solved using generalized born (as in the MM-GBSA) or Poisson–Boltzmann (as in the MM-PBSA) to
get the polar part of the solvation free energies [19]. The non-polar part of the
solvation free energies is computed from the solvent-accessible surface area of the
solute. In the implicit solvent model, the only used solvent parameter is dielectric
constant, usually the solvent coordinates are removed from the molecular dynamics
or Monte Carlo trajectories, and only the protein–ligand coordinates are used.
Force-field methods for calculating free energies (e.g. MM-GBSA or
MM-PBSA) with implicit solvent models forsolvation part achieved considerable
success in explaining the drug binding to a number of receptors or biomacromolecular targets [20–22]. In particular, MM-PBSA method was successfully used
to predict the binding affinities of many antibacterial, antiviral benchmark
Recent Advancements in Computing Reliable Binding Free Energies …
227