interaction between these two regions or subsystems. If there is no charge transfer
between these two subsystems, then one can add electrostatic and van der Waals
terms to account for such interaction, and in this way the polarization of the
quantum mechanical subsystem due to the system described using force-field is
accounted for. The implementation is straightforward when the ligand alone is
described by quantum mechanics and receptor and solvents are described using the
force-fields. However, when certain residues of the receptors are to be included in
the QM region, then the description of the chemical bonds between the receptor
parts in QM region and MM region is a bit challenging. Methods such as hydrogen
capping are developed to describe such regions, and it has become routine to use
QM/MM methods for computing the protein–ligand interaction energies and free
energies. Another main problem is due to the over-polarization of the terminal
bonds in QM region due to atomic charges in the immediate MM region. Usually,
the properties of certain atoms or groups closer to the interfacial region are moved
further away into MM region so that such over-polarization is not a problem any
more. Other option is to use damping function in the calculation of electrostatic
contribution to deal with such effect in a mathematical way. It is also worth
mentioning that the QM/MM methods in addition to energetics can be used to
model the enzymatic catalytic reaction and can also be used to model the optical
(linear and nonlinear) and magnetic properties of ligands when they are bound to
receptors.
5.3 Fragment Molecular Orbital
A computationally viable strategy to evaluate the energy of an entire protein or
protein–ligand complex is the fragment molecular orbital (FMO) method [44]. In
the FMO method, the entire system is divided into several fragments and their
energy is evaluated in the presence of all other fragments. This is known as the
one-body FMO (FMO1) method. Usually, a single fragment consists of a single
residue. To further enhance the quality of the calculation and include important QM
effects, all pairs of fragments are evaluated in the presence of the rest of the
fragments. This is known as the two-body FMO (FMO2) method. The total energy
for an FMO2 calculation is given as in Eq. 7
E ¼
X N
I
E I þ
X N
I [ J
DE IJ
ð7Þ
DE IJ ¼ E IJ À E I À E J
ð8Þ
where E I is the energy of a monomer in the electrostatic potential (ESP) of all
other monomers. DE IJ is the interaction energy of fragment I and J evaluated as in
Eq. 8.
Recent Advancements in Computing Reliable Binding Free Energies …
233
between these two subsystems, then one can add electrostatic and van der Waals
terms to account for such interaction, and in this way the polarization of the
quantum mechanical subsystem due to the system described using force-field is
accounted for. The implementation is straightforward when the ligand alone is
described by quantum mechanics and receptor and solvents are described using the
force-fields. However, when certain residues of the receptors are to be included in
the QM region, then the description of the chemical bonds between the receptor
parts in QM region and MM region is a bit challenging. Methods such as hydrogen
capping are developed to describe such regions, and it has become routine to use
QM/MM methods for computing the protein–ligand interaction energies and free
energies. Another main problem is due to the over-polarization of the terminal
bonds in QM region due to atomic charges in the immediate MM region. Usually,
the properties of certain atoms or groups closer to the interfacial region are moved
further away into MM region so that such over-polarization is not a problem any
more. Other option is to use damping function in the calculation of electrostatic
contribution to deal with such effect in a mathematical way. It is also worth
mentioning that the QM/MM methods in addition to energetics can be used to
model the enzymatic catalytic reaction and can also be used to model the optical
(linear and nonlinear) and magnetic properties of ligands when they are bound to
receptors.
5.3 Fragment Molecular Orbital
A computationally viable strategy to evaluate the energy of an entire protein or
protein–ligand complex is the fragment molecular orbital (FMO) method [44]. In
the FMO method, the entire system is divided into several fragments and their
energy is evaluated in the presence of all other fragments. This is known as the
one-body FMO (FMO1) method. Usually, a single fragment consists of a single
residue. To further enhance the quality of the calculation and include important QM
effects, all pairs of fragments are evaluated in the presence of the rest of the
fragments. This is known as the two-body FMO (FMO2) method. The total energy
for an FMO2 calculation is given as in Eq. 7
E ¼
X N
I
E I þ
X N
I [ J
DE IJ
ð7Þ
DE IJ ¼ E IJ À E I À E J
ð8Þ
where E I is the energy of a monomer in the electrostatic potential (ESP) of all
other monomers. DE IJ is the interaction energy of fragment I and J evaluated as in
Eq. 8.
Recent Advancements in Computing Reliable Binding Free Energies …
233