dampening effect shown by the solvent atoms. The principal drawback of explicit
solvent models is the number of atoms to be considered in the system leading to
increased computational cost. However, with the help of GPU-based acceleration,
this drawback, now, is hardly any cause for worry.
The end-state free energy methods use the conformations extracted from an MD
or MC simulation, wherein the system is simulated by explicitly defining the solvent. However, while solving the GB or PB equation, the solvent is implicitly
treated by defining the external dielectric constant for water (for most drug design
cases) and a suitable internal dielectric constant [57–61].
Molecular Mechanics-Poisson Boltzmann/Generalized Born Surface Area
(MM-PB/GB-SA)
The MM-GBSA [62–65] approach employs molecular mechanics-based energy
calculations and the generalized Born model to account for the solvation effects in
the calculation of the free energy. Similarly, the MM-PBSA [66–68] approach
solves the linear or nonlinear Poisson–Boltzmann equation [69–71], to account for
the solvation electrostatics, whereas the MM part is calculated as in MM-GBSA
from the derivative of the force field equations. Both these approaches are
parameterized such that they partition the energy components into various terms,
and the net free energy change is the sum of these individual terms (Coulomb, vdW,
solvation, etc.). MM-PBSA has gained considerable attention for estimating the
binding free energies of molecular complexes due to its exhaustive nature of
computing the solvation electrostatics by iteratively solving the PB equation,
whereas the GB method does not involve any rigorous and iterative procedure and
hence is faster. However, this does not necessarily guarantee that the MM-PBSA
method always outperforms MM-GBSA method. In MM-PB(GB)SA methods,
MD- or MC-derived conformational ensembles are used to compute the “average”
free energy of a state and this is approximated as follows:
G
h i ¼ E MM
h
iþ G PBSA=GBSA
À T S MM
h
i
ð5Þ
where the angular bracket <> indicates average over the MD/MC conformations,
E MM is the molecular mechanics energy that typically includes bond, angle, torsion,
van der Waals, and electrostatic terms (see Eqs. 7c and 7d) and is evaluated with no
or extremely large (virtually infinite) non-bonded cut-off limit. The second term is
solved as mentioned in the preceding stanza and it forms the crux of this method.
The last term T, is the solute entropy, which is estimated by quasi-harmonic
analysis [72, 73] of the trajectory or by normal mode analysis [74–76].
The following equation (Eq. 6) shows how the binding free energy is computed
from the energies of the ligand, protein, and its complex over all the MD or MC
snapshots. However, the snapshots can be obtained in two possible ways—one is
called the single trajectory approach and other is the multiple trajectory approach.
In the single trajectory approach, only the protein–ligand complex is simulated, and
Free Energy-Based Methods to Understand Drug Resistance Mutations
9
solvent models is the number of atoms to be considered in the system leading to
increased computational cost. However, with the help of GPU-based acceleration,
this drawback, now, is hardly any cause for worry.
The end-state free energy methods use the conformations extracted from an MD
or MC simulation, wherein the system is simulated by explicitly defining the solvent. However, while solving the GB or PB equation, the solvent is implicitly
treated by defining the external dielectric constant for water (for most drug design
cases) and a suitable internal dielectric constant [57–61].
Molecular Mechanics-Poisson Boltzmann/Generalized Born Surface Area
(MM-PB/GB-SA)
The MM-GBSA [62–65] approach employs molecular mechanics-based energy
calculations and the generalized Born model to account for the solvation effects in
the calculation of the free energy. Similarly, the MM-PBSA [66–68] approach
solves the linear or nonlinear Poisson–Boltzmann equation [69–71], to account for
the solvation electrostatics, whereas the MM part is calculated as in MM-GBSA
from the derivative of the force field equations. Both these approaches are
parameterized such that they partition the energy components into various terms,
and the net free energy change is the sum of these individual terms (Coulomb, vdW,
solvation, etc.). MM-PBSA has gained considerable attention for estimating the
binding free energies of molecular complexes due to its exhaustive nature of
computing the solvation electrostatics by iteratively solving the PB equation,
whereas the GB method does not involve any rigorous and iterative procedure and
hence is faster. However, this does not necessarily guarantee that the MM-PBSA
method always outperforms MM-GBSA method. In MM-PB(GB)SA methods,
MD- or MC-derived conformational ensembles are used to compute the “average”
free energy of a state and this is approximated as follows:
G
h i ¼ E MM
h
iþ G PBSA=GBSA
À T S MM
h
i
ð5Þ
where the angular bracket <> indicates average over the MD/MC conformations,
E MM is the molecular mechanics energy that typically includes bond, angle, torsion,
van der Waals, and electrostatic terms (see Eqs. 7c and 7d) and is evaluated with no
or extremely large (virtually infinite) non-bonded cut-off limit. The second term is
solved as mentioned in the preceding stanza and it forms the crux of this method.
The last term T
analysis [72, 73] of the trajectory or by normal mode analysis [74–76].
The following equation (Eq. 6) shows how the binding free energy is computed
from the energies of the ligand, protein, and its complex over all the MD or MC
snapshots. However, the snapshots can be obtained in two possible ways—one is
called the single trajectory approach and other is the multiple trajectory approach.
In the single trajectory approach, only the protein–ligand complex is simulated, and
Free Energy-Based Methods to Understand Drug Resistance Mutations
9