dynamics or Monte Carlo simulations due to their inability to sample adequately
from the high-energy regions of the phase space, which also make important
contributions to the free energy. However, the free energy differences (DDG) are
rather simple to compute. The free energy binding for the non-covalent association
of two molecules (protein and ligand in this case) may be written as follows:
DG bind ¼ G complex À G protein þ G ligand
À
Á
ð3Þ
The binding event is an additive interaction of many events [49–52], for example
solvation energy (G sol ), conformational energy (G conf ), energy due to interaction
with residues in the vicinity (G int ), and energy associated with different types of
motions (translational, rotational and vibrational, G motion ). The classical binding
free energy equation now can be rewritten as follows:
DG bind ¼ G sol þ G conf þ G int þ G motion
ð4Þ
Directly computing the free energy from an MD or MC simulation is not trivial;
hence, the following methods have been formulated. Broadly, the methods used for
computing free energy are classified as partitioning-based methods or end-state free
energy methods and non-partitioning-based methods. The partitioning-based
methods partition the binding energy into various components as shown in
Eq. 4; however, this method has been highly criticized [53] stating that it is
physically unreal to partition the free energy into components.
2.3.1 End-State Free Energy Methods or Partitioning-Based Methods
The human body majorly comprises of water; hence, it is imperative to carefully
include the solvation effects while computing the free energy of binding. More
importantly, water plays a crucial role in ligand recognition and in the binding
phenomenon. In computational chemistry, the methods for incorporation of solvent
are divided into three groups: (i) continuum electrostatic methods/implicit solvent,
(ii) explicit solvent models with microscopic detail and (iii) hybrid approaches.
Historically, the continuum electrostatic methods were among the first to consider
the solvent effect, and they still represent very popular approaches to evaluate
solvation free energies, especially in quantum chemistry. Polarizable continuum
model (PCM, [54]), COnductor-like Screening MOdel (COSMO, [55]) and SMD
solvation model [56] are few popular models for treating solvent effects implicitly
in quantum chemistry. Continuum solvation methods are computationally economical; however, the frictional drag of the solvent is highly underestimated and as
a consequence may drive the system to non-physical states. Moreover, solvent–
solvent and solute–solvent interactions are inadequately treated, posing a danger of
underestimating the effects of such interactions. The explicit treatment of solvent
enables one to consider the solvent–solvent and solute–solvent interactions. This
prohibits the systems from visiting non-physical states due to the inclusion of the
8
E. A. F. Martis and E. C. Coutinho
from the high-energy regions of the phase space, which also make important
contributions to the free energy. However, the free energy differences (DDG) are
rather simple to compute. The free energy binding for the non-covalent association
of two molecules (protein and ligand in this case) may be written as follows:
DG bind ¼ G complex À G protein þ G ligand
À
Á
ð3Þ
The binding event is an additive interaction of many events [49–52], for example
solvation energy (G sol ), conformational energy (G conf ), energy due to interaction
with residues in the vicinity (G int ), and energy associated with different types of
motions (translational, rotational and vibrational, G motion ). The classical binding
free energy equation now can be rewritten as follows:
DG bind ¼ G sol þ G conf þ G int þ G motion
ð4Þ
Directly computing the free energy from an MD or MC simulation is not trivial;
hence, the following methods have been formulated. Broadly, the methods used for
computing free energy are classified as partitioning-based methods or end-state free
energy methods and non-partitioning-based methods. The partitioning-based
methods partition the binding energy into various components as shown in
Eq. 4; however, this method has been highly criticized [53] stating that it is
physically unreal to partition the free energy into components.
2.3.1 End-State Free Energy Methods or Partitioning-Based Methods
The human body majorly comprises of water; hence, it is imperative to carefully
include the solvation effects while computing the free energy of binding. More
importantly, water plays a crucial role in ligand recognition and in the binding
phenomenon. In computational chemistry, the methods for incorporation of solvent
are divided into three groups: (i) continuum electrostatic methods/implicit solvent,
(ii) explicit solvent models with microscopic detail and (iii) hybrid approaches.
Historically, the continuum electrostatic methods were among the first to consider
the solvent effect, and they still represent very popular approaches to evaluate
solvation free energies, especially in quantum chemistry. Polarizable continuum
model (PCM, [54]), COnductor-like Screening MOdel (COSMO, [55]) and SMD
solvation model [56] are few popular models for treating solvent effects implicitly
in quantum chemistry. Continuum solvation methods are computationally economical; however, the frictional drag of the solvent is highly underestimated and as
a consequence may drive the system to non-physical states. Moreover, solvent–
solvent and solute–solvent interactions are inadequately treated, posing a danger of
underestimating the effects of such interactions. The explicit treatment of solvent
enables one to consider the solvent–solvent and solute–solvent interactions. This
prohibits the systems from visiting non-physical states due to the inclusion of the
8
E. A. F. Martis and E. C. Coutinho