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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5486_Библиотеки_им_академика_М_И_Перельмана
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be challenging for deterministic methods. By employing random movements and en-
ergy-based acceptance criteria, it can efficiently sample d iverse conformations and
identify potential binding modes that might be missed by other search strategies.
The Monte Carlo simulation was initially introduced as the energy minimization
procedure for molecular dynamics and was later accepted for the search algorithms
in molecular docking programs. In this method, initially, a ligand is placed within the
cavity of the receptor having a random conforma tion, and certain parameters, such
as energy, are calculated. Afterward, a random change is made in the conformation
of the ligand and all the previously calculated parameters are recalculated. Whether
to accept or reject the new conformation is decided based on the probability score of
the new conformation that is calculated, based on the following Boltzmann probabil-
ity function.
P = Ae
−E1+E0=KT
(9:1)
where A is a constant, E1 is the energy of the new conformation, E0 is the energy of
the previous conformation, K is the Boltzmann constant, and T is the temperature at
which the calculations are performed.
A certain threshold value of P is decided and the conformations having a value
below this threshold value are rejected and the rest are accepted. MCDOCK, ICM,
DockVision, and Prodock are molecular docking software that use this type of search
algorithm [27].
9.2.1.2.2 Genetic algorithm (GA)-based search
Genetic algorithm (GA), as stochastic search algorithms, are a valuable tool in the con-
formational search process of molecular docking. They leverage principles of evolution
to efficiently explore complex binding landscapes, aiding in the identification of biologi-
cally relevant and energetically favorable binding conformations for drug discovery
and molecular interaction studies. GAs are a class of stochastic or random search algo-
rithms widely applied in the field of conformational search within molecular docking
studies. The conformational search involves exploring the three-dimensional spatial ar-
rangements of molecules to identify energetically favorable binding conformations,
which is crucial for understanding molecular interactions and drug discovery. GAs sim-
ulate the process of natural selection and evolution by maintaining a population of po-
tential solutions, or individuals, each representing a molecular conformation. These
individuals are subjected to genetic operations such as mutation and crossover, mimick-
ing genetic recombination and mutation in biology. Through successive generations,
GAs iteratively improve the population’s fitness, by evaluating how well each conforma-
tion fits the binding site, and its energy score. The stochastic nature of GAs allows them
to explore a vast conformational space efficiently, even in the presence of complex en-
ergy landscapes. They are particularly useful when dealing with flexible molecules and
9.2 Theory of molecular docking 189
large search spaces, as they have the potential to discover diverse and energetically fa-
vorable binding poses.
These algorithms take inspiration from the theory of evolution and natural selec-
tion of the biological system. It was introduced for the first time by John Holland in
1975. In this algorithm, the conformation of a ligand is defined by the combination of
certain set parameters. These parameters are kno wn as “genes” in the genetic algo-
rithm. These genes are then combined to form a chromosome, and a population of chro-
mosomes is generated by the different combinations of genes. From this population, the
most favorable chromosomes (having the least energy) are selected for mimicking an-
other biological process known as “crossover”. By the crossover process, new popula-
tion of the chromosomes (offspring) is generated that possess better properties than the
parent chromosomes. Another phenomenon from the biological system, “mutation”,
does occur in these offspring, which ultimately leads the conformation close to the
global minima. A flow diagram of the steps involved in the GA-based search algorithm
is given in Fig. 9.4. The two most widely accepted molecular docking software world-
wide, GOLD and AUTODOCK, employ this type of search algorithm. Other molecular
docking software based on this algorithm are MolDock, FLIPDock, and EADock [28–30].
Fig. 9.4: Overview of the process of the genetic algorithm of the conformational search of the molecular
docking.
190 Chapter 9 Molecular docking and drug–receptor interactions
9.2.1.2.3 Tabu search (TS) algorithm
Tabu search (TS) algorithm is a prominent stochastic or random search algorithm uti-
lized in the field of molecular docking for conformational search. In this context, TS
serves as a powerful optimization technique to explore the vast conformational space
of molecules and efficiently identify energetically favorable binding configurations.
TS, inspired by the principles of local search and optimization, employs a memory-
based strategy to navigate through the solution space. It maintains a short-term mem-
ory, known as the “Tabu list,” to prevent revisiting previously explored solutions, and
facilitate diversification during the search process. This memory mechanism encour-
ages the algorithm to escape local minima and explore different regions of the confor-
mational landscape. In molecular docking, TS plays a crucia l role in predicting the
binding conformations of ligands with the target proteins. It aims to discover the
most energetically favorable binding pose by iteratively perturbing and refining the
legend’s position and orientation within the protein’s binding site. By efficiently sam-
pling diverse conformational possibilities and avoiding redundant searches, TS con-
tributes to the accurate estimation of binding affinities and enhances the success rate
of drug discovery efforts.
TS is an iterative algorithm developed by Glover and designed initially for the op-
timization of complex systems. This program is based on the principle that a certain
amount of change in the conformation of an initial ligand is made, and its RMSD, with
all the conformations available in the Tabu list, is compared. If its RMSD comes more
than the cutoff value with any of the conformation of the Tabu list, then this confor-
mation is rejected; otherwise, it is accepted. Pro-LEADS and PSI-DOCK are two molecu-
lar docking software that implement this search algorithm [31–33].
9.2.1.3 Simulation method-based search algorithms
Simulation method-based search algorithms are integral in the conformational search
process within molecular docking studies. These algorithms play a pivotal role in ex-
ploring the vast conformational space of molecules, particularly when predicting the
binding modes of ligands to target proteins. Rather than exhaustively sampling all
possible conformations, simulation-based approaches efficiently navigate through
this space to identify e nergetically favorable conformations. One prominent tech-
nique is molecular dynamics simulation, which employs Newtonian mechanics to sim-
ulate the motion of atoms and molecules over time. By iteratively adjusting atomic
positions, based on forces and energies, molecular dynamics explores various confor-
mations, allowing researchers to capture dynamic interactions between ligands and
receptors. Incorporating simulation methods into conformational searches enhances
the accuracy and reliability of molecular docking results, providing valuable insights
into the binding mechanisms and energeticall y favorable configurations of drug-like
molecules in complex biological systems.
9.2 Theory of molecular docking 191
These are the most recent search algorithms employed for the search of the prob-
able bioactive conformation of the ligand. The most widely employed technique for
this purpose is the simulated annealing (SA) approach [34].
9.2.1.3.1 Simulated annealing (SA)
SA-based search algorithm is suitable for those ligand molecules that contain multiple
local minima. A major advantage of this type of algorithm is that it can search for the
minima in both uphill and downhill directions. This approach follows a temperature-
dependent molecular dynamics methodology. Initially, a random conformer is placed in-
side the cavity of the receptor and allowed to move inside the cavity as per Newton’s
second law of motion. In the next cycle, the conformer is allowed to move to the lower
temperature. These cycles are repeated until we move to 0 K temperature. As the move-
ment of the molecules is temperature-dependent and it is considered at 0 K, there are
zero velocities in the system. Hence, the conformation obtained at 0 K is considered as
the minima.
Although SA is a very accurate algorithm, it is highly time-consuming if the num-
ber of conformations that go under simulations is large. To overcome this problem,
the SA approach is often coupled with other approaches, such as Monte Carlo, to de-
crease the number of conformations, and ultimately reduce the total time. AutoDock
employs this kind of hybrid Monte Carlo-SA search algorithm [35, 36].
9.2.2 Scoring of the ligand–receptor binding
Scoring of ligand–receptor binding in molecular docking for CADD is a critical process
that evaluates and quantifies the strength of binding interactions between ligands (po-
tential drug molecules) and their target receptors (typically proteins). This scoring is
essential for ranking and selecting the most promising ligand–receptor complexes
from a pool of candidate poses generated during the docking process. SFs aim to esti-
mate the binding affinity or free energy of a given ligand–receptor complex. They
consider various intermolecular forces and interactions, such as van der Waals forces,
electrostatic interactions, hydrogen bonding, and solvation effects. The ultimate goal
is to predict which ligand poses have the highest likelihood of forming stable and bio-
logically relevant complexes.
There are several types of SFs, including empirical, knowledge-based, and physics-
based approaches. Empirical SFs are based on statistical analysis of known ligand–recep-
tor complexes and utilize parameters derived from experimental data. Knowledge-based
scoring relies on databases of known protein–ligand interactions to make predictions.
Physics-based SFs employ molecular mechanics and quantum mechanics principles to
calculate binding energies from first principles. While SFs are crucial for molecular dock-
ing, it is important to acknowledge that accurately predicting binding affinities remains a
192 Chapter 9 Molecular docking and drug–receptor interactions
complex challenge due to the inherent limitations of current computational models. How-
ever, these SFs play a pivotal role in virtual screening and lead optimization, helping re-
searchers identify potential drug candidates and prioritize them for further experimental
validation. Refining and improving SFs continue to be a focus of research in the field of
CADD to enhance the reliability of molecular docking results.
A set of conformations obtained through the search algorithms of the molecular
docking program are put in for the scoring, based on their binding with the target pro-
tein receptor. Based on this scoring, the best binding conformation is considered as the
bioactive conformation and analyzed further for the type of interactions. Similar to the
search algorithms, the scoring of the ligand–receptor binding is done by the molecular
docking programs by using different algorithms. Scoring of the ligand–receptor binding
is done by calculating the change in Gibb’sFreeenergy(Δ G) using the following
equation:
ΔG = ΔH − TΔS (9:2)
where ΔH is the change in the enthalpy, T is the temperature in kelvin, and ΔS repre-
sents the change in the enthalpy.
This ΔG can also be related to the ligand–receptor binding constant, as given in
the following equation:
ΔG = −RT ln K (9:3)
where R is the ideal gas constant, T is the temperature in kelvin, and K is the binding
constant.
Each scoring algorithm differs from a nother in the calculation of ΔG value. In
other words, it can be said that the SF tells us about the best binding mode of any
drug candidate with a receptor’s cavity.
Previously, SFs of any molecular docking software were classified into force-field-
based, empirical-based, and knowledge-based SFs [37]. However, with the emergence
of more sophisticated methodologies, SFs are nowadays classified into the following
types:
– Physics-based SFs
– Empirical-based SFs
– Knowledge-based SFs
– Machine-learning-based SFs
All these methods have their algorithms for scoring the protein–ligand interactions in
molecular docking.
9.2.2.1 Physics-based scoring functions
The scoring of the protein–ligand binding was started by the force-field-based scoring,
which is also the first physics-based SF. Initial credit for the development of various
9.2 Theory of molecular docking 193
force fields goes to Martin K arplus, who with his coworkers, has done tremendous
work in this field in the 1970s. The Van der Waals interactions and electrostatic inter-
actions were the initial noncovalent interactions that were taken into account for the
initial scoring of the protein–ligand binding by the force fields, and hence the initial
scoring was based on the following equation:
ΔG = ΔE
vdw
+ Δ E
elec
(9:4)
where ΔG is the change in Gibb’sfreeenergy,ΔE
vdw
isthechangeintheVander
Waals interaction energy, and ΔE
elec
represents the change in energy due to the elec-
trostatic interactions.
With the increased understanding of the protein – ligand interaction, it was ob-
served that hydrogen bonding also plays an important role in such interactions; there-
fore, equation (9.4) is further modified to the following equation:
ΔG = ΔE
vdw
+ Δ E
elec
+ ΔE
H-bonding
(9:5)
where ΔE
H-bonding
is a change in the energy due to hydrogen bonding.
DOCK and AUTODOCK software in their initial phases used this kind of scoring,
based on the AMBER force field.
The one major drawback of this kind of scoring is that it does not account for the
effect of the solvent on the protein–ligand docking. This is overcome by adding solva-
tion energy terms in the SF to form the following equation:
ΔG = ΔE
vdw
+ Δ E
elec
+ Δ E
H-bonding
+ Δ G
desolvation
(9:6)
where ΔG
desolvation
is the change in Gibb’s free energy after removing the effect of sol-
vent from the system.
Till now, the scoring of the protein–ligand binding is based on the noncovalent inter-
actions and the effect of the solvent. Incorporating covalent interactions, polarization,
and charge transfer parameters in the SF is not possible by merely using molecular me-
chanics (MM) methods. These new parameters can only be studied by using quantum me-
chanics (QM); however, QM methodology, despite its high accuracy, is a costly and time-
consuming process. To make the balance in scoring the protein–ligand binding in terms
of accuracy, time, and cost, the scientists have introduced a hybrid QM/MM approach,
given by the following equation:
Δ G = ΔE
QM=MM
+ Δ G
desolvation
(9:7)
where ΔE
QM/MM
is the energy change, calculated by using the hybrid method of QM
and MM [38–41].
194 Chapter 9 Molecular docking and drug–receptor interactions
9.2.2.2 Empirical-based scoring function
Empirical-based scoring is another approach for calculating the binding between the
protein and ligand in molecular docking. In this approach, the total binding affinity of
the protein ligand is considered the empirical sum of the individual energy terms. A
generalized equation for calculating the binding energy using empirical scoring is
given in the following equation:
Δ G = ΣwΔG
i
(9:8)
where ΔG is the binding affinity of the protein–ligand, ΔG
i
is the individual energy
terms parameters, such as Van der Waals, electrostatic, and H-bonding, and w is the
coefficient that is the individual weight of that energy term calculated through least-
fit square or multiple linear regression analysis.
PLP, ChemScore, GlideScore, X-score, LudiScore, and LigScorearesomeofthe
popular SFs that use empirical scoring in calculating the binding affinity of the pro-
tein and the ligand.
Let us understand the empirical SFs with arguably one of the most sophisticated
SF, the GlideScore:
GScore = 0.05 vdwðÞ+ 0.15 CoulðÞ+ Lipo + H bond + Metal + Rewards + RotB + Site (9:9)
where vdW is the Van der Waals energy term, Coul represents the Coulomb’s electro-
static energy terms, lipo is the lipophilic energy term that assigns certain value for
favorable hydrophobic interactions, H bond represents the hydrogen-bonding terms,
metal is the metal binding term that comes into play when there is any metal present
in the receptor protein, Rewards represents other values that are not included above,
RotB is the penalty imposed for freezing the rotatable bonds, and Site is the value
given to the polar interactions inside the active site of the target protein [42–45].
9.2.2.3 Knowledge-based scoring function
The biggest advantage of the knowledge-based SF is its high accuracy and less time
consumption, when compared to the previously described methods. In this type of SF,
binding affinity is calculated in terms of energy potential, als o known as statistical
potential. The name of this SF comes from the fact that the knowledge for the calcula-
tion of binding affinity is based on the already reported protein–ligand complexes in
the protein data bank. In other words, this database of protein–ligand complexes ob-
tained from the protein data bank is used for the calculation of the pairwise potentials
between the atom pairs using the inverse Boltzmann equation. Suppose there is a pair
of atoms x–y, then their distance-dependent potential, based on the inverse Boltz-
mann equation, will be given by the following equation:
w
xy
rðÞ=−k
b
T ln g
xy
rðÞ
(9:10)
9.2 Theory of molecular docking 195
The value of g
xy
(r) can be calculated from the following equation.
g
xy
rðÞ=
ρ rðÞ
ρ
× rðÞ (9:11)
where w
xy
(r) is the distance potential at distance r, k
b
is the Boltzmann constant, T is
the absolute temperature, ρ(r) is the numeric density of the atom pair at distance r,
and ρ
✶
(r) is the numeric density for the same at reference state where inter atomic
interactions are zero. The overall binding affinity (W) can be calculated as the sum of
all of these calculated pairwise potentials using the following equation:
W = Σw
xy
rðÞ (9:12)
IT-Score, DrugScore, BLEEP, PMF, and KScore are a few of the knowledge-based SFs
[46, 47].
9.2.2.4 Machine learning scoring functions
This is the most recent type of SF used extensively, in which QSAR knowledge is
used for assessing the protein–ligand binding. These functions utilize data-driven
algorithms, often based on neural networks or random forests, to predict binding
affinities between ligands and receptors. By leveraging extensive training datasets
of experimentally measured binding data, they capture complex, nonlinear relation-
ships between molecular features and binding energies. Machine learning SFs enhance
the accuracy of ligand–receptor binding predictions, enabling the prioritization of po-
tential drug candidates. Their ability to account for intricate interactions and diverse
molecular structures makes them valuable in rational drug design, expediting the dis-
covery of novel therapeutics. As discussed in previous chapters, QSAR is a tool in which
biological activity is statistically correlated with certain properties of ligands. Likewise,
in machine learning SFs, protein–ligand interactions are first measured in some numer-
ical terms and are then statistically correlated with the binding affinity. These entire
machine learning SFs differ from each other in the use of different methods for the de-
velopment of these QSAR models for assessing the protein–ligand binding. The most
common machine-learning approaches for this purpose include:
– Support vector machine
– Random forest
– Artificial neural network
– Deep learning
A workflow for the machine learning-based SFs is given in Fig. 9.5. RI-Score, RF-Score,
DLSCORE, NNScore, SFScore, and so on are the popular machine learning-based SFs
for molecular docking [48–51].
196 Chapter 9 Molecular docking and drug–receptor interactions
Fig. 9.5: A complete overview of the machine learning (ML) algorithms for calculating the scoring functions of the ligand–receptor docking.
9.2 Theory of molecular docking 197
9.3 Classification of molecular docking techniques
With the emergence of molecular docking in the early 1980s, it has shown tremendous
development in its methodologies. In the current scenario, molecular docking algo-
rithms are classified by using two types of classification systems (Fig. 9.6):
– Classification is based on the flexibility of the molecules
– Classification based on types of molecules used for molecular docking
Fig. 9.6: Different approaches for the classification of molecular docking algorithms.
198 Chapter 9 Molecular docking and drug–receptor interactions
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