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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5580_Библиотеки_им_академика_М_И_Перельмана
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11 Electronic-Structure Informatics for Drug Development 195
https://t.me/med1917
formation of dispersion forces, which are the origin of van der Waals interaction for
intermolecular interaction.
Assuming that B represents a protein and considering that its electronic excited
states are energetically high, Eq. (
11.7) can be simplified by excluding the terms
associated with B1:
Ψ = C00ΨA0Ψ
+ C+−ΨA+Ψ
B0
+ C−+ΨA−Ψ
B−
+ C10ΨA1Ψ
B+
B0
(11.8)
The resulting equation, Eq. (11.8), suggests that the ensuing transition energies
merit consideration as molecular descriptors in a machine learning investigation
of pharmaceutical activity: ionization energy (IE), electron affinity (EA), and spinsinglet excitation energy. It is widely acknowledged that IE is associated with the
energy level of the highest occupied MO (HOMO), while EA is correlated with the
energy level of the lowest unoccupied MO (LUMO). These are two features that are
known to be important in various chemical properties.
Choices of IE and EA as the E-ESI descriptors are meaningful even from the
concepts of the electronegativity and of the hardness/softness parameters suggested
by Pearson [
by χ = (IE + EA)/2.0 [
be defined as η = (IE – EA)/2.0 [
18]. Mulliken proposed that electronegativity of an atom can be defined
19]. Parr et al. indicated that the absolute hardness may
20
]. In quantum chemical analyses, χ and η
have been frequently suggested as important electronic factors determining chemical
reactivities of a variety of molecules.
In the above discussion, the spin-singlet excited state has been shown to be meaningful to describe electronic polarization. In order to include an energy descriptor
of this state, the straightforward way is to directly calculate the spin-singlet (S
excitation energy. It is technically possible, but we herein replace it with the lowest
spin-triplet (T
) excitation energy. This is because these two excitation energies are
1
essentially equivalent, except for the electron exchange energy in the fixed orbital
approximation. Computationally, the calculation of the T
state is less demanding,
1
as it allows for a self-consistent field (SCF) calculation.
)
1
11.5.2 Descriptors for Structural Relaxation
Chemical reactivity and the strength of intermolecular interaction are the elementary
processes pertinent to drug activity. Chemical reaction is one of the intermolecular interaction processes accompanied by the bond formation and bond breaking.
The degree of these intermolecular interactions can be understood by investigating
changes in the system’s PES before and after the interaction.
Suppose that both the initial and final states may be represented by a quadratic
function of a reaction coordinate. The PES for the initial state is displaced through
intermolecular interaction, resulting in another PES for the final state. In this
modeling, a chemical reaction or an intermolecular interaction may be considered
196 M. Sugimoto
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as a curve-crossing problem. The crossing point of the two PES is called the transition state, and the energy level from the energy minimum of the initial state is
called “activation energy” represented by
of the two parabolas should have the same curvature,
ΔG‡. When we assume that the curvature
ΔG‡ can be correlated with
ΔG0 and λ, which are called “reaction energy” (“driving force of the reaction”) and
“reorganization energy”, respectively:
ΔG‡ =
ΔG + λ
(
4λ
2
)
(11.9)
This is the well-known relation that appears in the Marcus equation of electron
transfer rate constant [
can be represented as a parabola with the same curvature as shown in Fig.
and that the free energy
Equation (
11.9) indicates that λ may also be regarded as one of the essential quantities
21]. Note that Eq. (11.9) always holds when the two PES
11.4,
G becomes equal to the electronic total energy E at T = 0.
in the quantitative understanding of chemical reactions and molecular interactions.
Intuitively, the importance of Eq. (
11.9) can be realized by thinking that two reactants
must change their molecular structures. In the case of complex formations like ligandreceptor docking, changes in molecular conformations and in solvation environment
are expected to be critical to enhancing the binding affinity between the ligand and
the receptor.
Because of the importance of the reorganization energy upon transition from the
initial state to the final state in a chemical process, it seems reasonable to include
such a quantity, labeled as λ in Fig.
11.5, as one of the E-ESI descriptors. This can
be justified when we think of the substrate oxidation by Cytochrome P450. In this
chemical process, reorganization energies for oxidation (ionization) and reduction
of the ionized species (de-ionization) are expected to play important roles. Based
on this consideration, our E-ESI descriptor set is design to include reorganization
energies for the excitation/de-excitation processes as shown in Table
Fig. 11.4 Free energy
change in chemical
transformation and
intermolecular interaction
11.1.
11 Electronic-Structure Informatics for Drug Development 197
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Fig. 11.5 Plausible energy descriptors, shown in red, in the E-ESI method. λ is a descriptor that
may called reorganization energy. Among the four descriptors,
can be evaluated using the other three factors
ΔE
may be omitted because it
F→I
The reorganization energy can also be a measure of how the equilibrium structures
in different electronic states would be similar. It may also be interpreted as a factor
reflecting the structural softness of the compound. Upon intermolecular interaction
with a protein, a ligand molecule may change its structure to have better fitting with
the receptor as shown in Fig.
11.6. The structural softness would be important to
have a pre-docking pose for stronger binding. If the shape does not fit to the binding
pocket of the receptor, stronger binding cannot be expected.
For the electronic transitions from the spin-singlet neutral ground state to either
of the lowest spin-triplet, cation, or anion states, their corresponding reorganization
energies are defined in Fig.
11.5.
Fig. 11.6 Role of structural
reorganization in molecular
docking
198 M. Sugimoto
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11.5.3 Descriptors for Electronic Responses Properties
There are some important molecular properties which play an important role in
intermolecular interactions. One is the electric dipole moment (μ), which is a measure
of the polarity of a molecule. Another is electric polarizability. This property is
considered an origin of dispersion forces yielding van der Waals complexes. These
properties can be related to electronic energy and can be molecular descriptors.
When a uniform electric field is applied to a molecule, the energy of the whole
system varies. When the field is sufficiently small in magnitude, the perturbed energy
Fi=0
22]:
Fi +
i=x,y,zj=x,y,z
1
2!
∂Fi∂F
2
∂
E
j
FiFj + ···
Fi=Fj=0
(11.10)
can be expressed by a Taylor series [
∂E
∂F
i
E(F) = E(0) +
i=x,y,z
In Eq. 11.10, the first order term for the electric field F =Fx, Fy, F
corresponds
z
to dipole moment, while the second order term refers to electric polarizability. Using
perturbation theory, these terms can be represented as follows: The dipole moment
is the first order perturbation term and is given by
Fi=Fj=0
∂E
∂F
=−
= Ψ0|ˆri|Ψ0⟩. (11.11)
i
Fi=0
is given by
ij
⟨Ψ0|ˆri|ΨI⟩⟨ΨI|ˆrj|Ψ0⟩
EI−E
I
0
. (11.12)
E
(
I−E0
are crucially
)
μi =
In the sum-over-states formula, the electric polarizability α
2
∂
E
∂Fi∂F
j
1
α
=
ij
2!
This formula suggests that the electronic excitation energies
important. Another important factor is the numerator, which corresponds to electric
transition dipole moment
⟨Ψ0|ˆri|ΨI⟩.
As is well known the excitation energies and the transition dipole moments are
reflected in the UV/Vis spectra. Therefore, the van der Waals interaction pertinent to the intermolecular interaction has some quantitative relation with electric
polarizability. This motivates us to include the UV/Vis spectra ρ
as a molecular
UV
descriptor. The energy position and intensity of the UV/Vis spectra can be easily
predicted through electronic-structure calculations using the time-dependent density
]. The direct calculation of electric polariz-
functional theory (TDDFT) method [
24
ability is also possible in modern electronic-structure calculation softwares. Because
of the computational time, and the generality of the perturbation-theory expression,
i.e., the formula is similar even in magnetic perturbation, we decided to include the
excitation spectrum.
11 Electronic-Structure Informatics for Drug Development 199
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In the ρ
spectrum, information of so-called dark states is lost because of the
UV
selection rule of the off-diagonal matrix elements appearing on the numerator. Since
these states are expected to contribute to other type of perturbations, we decided to
include “density of spin-singlet excited states” ρ
as a molecular descriptor in our
ex
E-ESI approach. This spectral data reflects the number of excited states per excitation
energy unit.
As a similar spectral data, we also decided to include “density of MOs” ρ
orb
as
a descriptor. This spectral data is known as “density of states (DOS)” in solid-state
physics [
23]. It is obtained by calculating the number of MOs per orbital energy in
the ground-state density functional theory (DFT) calculation.
There would be some ways of using these two-dimensional spectral data (ρUV,
, ρ
ρ
) as a molecular descriptor. Machine learnings using both the scalar descrip-
ex
orb
tors and the s pectral data might be called multi-modal machine learning. This is an
interesting approach, but, at the present stage, we are using them in a different way.
From the interest in electronic similarity, we take the spectral overlap as a measure
of electronic similarity, and the scalar variable thus obtained is used as a molecular
descriptor. Mathematically this descriptor is defined by
upper lim
S(ρ
X
∫
=
)
ρ
0
X ,ref
(ε)
ρ
d ε, (11.13)
(ε)
X
where X = UV, ex, or orb defined above, and ε is the energy (excitation energy or
orbital energy). The “upper lim” in the above equation corresponds to the highest
energy level obtained in the TDDFT calculations. The subscript “ref” indicates
a reference molecule. In our regression modeling of drug activity, the reference
molecule is chosen as the most active compounds contained in our list of compounds.
The original spectral data are obtained from the peak spectra predicted by electronic structure calculations where each peak was broadened assuming the Gaussian
band shape. The band width was determined after trial and error in perform similarity
ranking of organic molecules. In the spectral overlap calculation, the areas of ρ
are normalized to unity.
ρ
X,ref
and
X
Because of the definition of this descriptor, a difficulty in machine learning studies
arises: we need to refer to a reference molecule: the calculated descriptor values
are not transferable to different projects focusing on e.g., different inhibitors. To
avoid this issue, we have recently used all the calculated excitation energies obtained
through the TDDFT calculations. In our implementation, we calculate low-lying
30 spin-singlet excited states and the 30 excitation energies are taken as molecular
descriptors. In this approach, transition matrix elements are not referred to. In this
extended descriptor set, which we call the ESI-2 descriptor set, the increase of the
size of the descriptor set is a drawback and would encounter an overfitting problem
when the number of available data would be small.
200 M. Sugimoto
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As is well known, a UV/Vis spectrum reflects the structural features of a molecule.
This is due to the fact that MOs tend to localize onto a particular functional group.
Therefore, ρ
of the UV/Vis spectra, i.e., the S(ρ
provides information similar to molecular fingerprint. The similarity
UV
) descriptor can be a measure of both structural
UV
and electronic similarities.
11.5.4 Descriptors for Vibrational Properties
We include spectral data obtained from vibrational modes through normal mode
analysis after geometry optimization. The information is related to many important chemical properties of molecules: curvatures of PESs contributing to accepting
and promoting modes in chemical interactions, zero-point frequencies, vibrational
entropy, heat capacity, and so on [
As molecular descriptors, we focus on IR spectra (ρIR) and density of vibrational
modes (ρ
). The former directly reflects the existence of the functional groups in
vib
a molecule. Therefore, this descriptor is also expected to play a role of molecular
fingerprint. The latter is the spectrum showing the number of vibrational states per
energy. The inclusion of ρ
vib
not described in the IR spectrum.
In our E-ESI studies, we use, as molecular descriptors, the spectral overlap (represented by either S(ρ
)or S(ρ
IR
can be regarded as a distance from the reference molecule. The choice of the reference molecule is arbitrary. In our implementation, the most active molecule in the
dataset is chosen as a reference molecule.
25].
is to use information of the vibrational modes that are
)) with that of a reference molecule. This quantity
vib
11.5.5 Descriptors for Host–Guest Interactions
So far, we have discussed the description of electronic features in chemical transformation and intermolecular interaction from the viewpoint of energetics, electronic
responses, and vibrational modes reflecting the topology of the PES. Regarding the
PES, there is another characteristic to be described in addition to these energy-related
features: it is the location of energy minima along the reaction coordinate.
Figure 11.7 shows a typical potential energy curve. In addition to the depth of the
energy minimum, the location of energy minimum depicted as R
a very important feature of the curve. This geometric feature is essentially correlated
with the size of the molecule in molecular docking and membrane permeation.
Based on this consideration, we include quantities representing the topography
of a molecule. A typical one is the molecular volume (V
program [
26], which the author’s group is using, the volume is calculated with the
Monte Carlo method. In our implementation, we repeat the calculation ten times,
and take their average to evaluate it.
in Fig. 11.7 is also
eq
). In the Gaussian 16
mol
11 Electronic-Structure Informatics for Drug Development 201
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Fig. 11.7 A potential energy
curve and the definition of
the equilibrium structure
(R
) and binding energy
eq
(BE)
Although V
is a reasonable characteristic as a molecular descriptor representing
mol
the topology of PES, it is not sufficient to describe that in molecular recognition:
the anisotropy of a molecular shape cannot be well described. N order to partially
overcome this deficiency, we evaluate the size of a rectangular box that encloses
the target molecule. This fitting can be done using a function “BoundingRegion”
implemented in Mathematica [
27].
11.5.6 Descriptors for Changes of Chemical Environment
Since the human body is chemically heterogeneous, i.e., a drug molecule may exist
in a variety of chemical environments, energy changes for environmental changes
are expected to be essential to describe the properties of molecules. In the E-ESI
approach, we suggest the incorporation of descriptors for this purpose.
For drug development, there are two elementary processes to focus on: One is the
migration process of a drug molecule from the aqueous phase to the cell membrane.
The latter is a lipid phase. In this process, water molecules surrounding the drug
molecule must be eliminated upon penetrating the other phase, as shown in Fig.
Another process is the binding of a drug molecule with a protein. In forming hydrogen
bonds with protein, water molecules surrounding the drug molecule should be, at
least, partially removed, as illustrated in Fig.
11.8b.
For the description of such environmental changes, we include three descriptors:
electric dipole moment (μ), the solvation free energy (ΔG
), and molecular weight.
solv
As is well known, μ is a property critical to the electrostatic interaction with the
surrounding medium.
For calculating of the energy change upon the solvation/de-solvation process, we
need to evaluate the free energy change before/after solvation/de-solvation represented by ΔG
. The accurate calculation of ΔG
solv
requires molecular dynamics
solv
simulations and is computationally demanding. In the present E-ESI approach, we
28
apply the polarizable continuum model (PCM) [
ΔG
molecules (ΔE
as an energy difference with/without electrostatic effect due to the water
solv
).
solv
] and alternatively approximate
11.8a.
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Fig. 11.8 Two possible changes of the chemical environment of a ligand molecule (shown in red):
(a) the molecule migrates from e.g., the aqueous phase (Phase 1) to the different (e.g., lipid) phase
(Phase 2), and (b) partial de-solvation occurs in the molecular docking process
The third descriptor in this category is “molecular weight (MW)”. Although this
is not related t o the electronic structure of a molecule, we include it here because
there are no alternatives to it in the output of the quantum chemical calculations,
and because it is considered important as a key measure of the mass flow rate. This
descriptor is featured in the well-known chemoinformatics descriptors like RDKit
29], Mordred [30], and alvaDesc [31]. It is also known to be a key parameter for
[
druglikeness known as the Lipinski’s rule of five [
32].
11.6 Practical Implementation of the E-ESI Descriptor
Calculation
The computational scheme to evaluate the 21 E-ESI descriptors is outlined in
11.9. The successive steps initiate with the generation of three-dimensional
Fig.
atomic coordinates. In scenarios where the number of target molecules is constrained,
we use a graphical user interface (GUI) for the generation of molecular input. In our
], the GUI for the Gaussian 16 software, has been applied.
research, GaussView [
When the number of target molecules are so many, we make a list of SMILES representation of molecules, and generate their three-dimensional coordinates using the
RDKit tool or the OpenBabel software [
33
34
].
11 Electronic-Structure Informatics for Drug Development 203
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Fig. 11.9 The scheme to evaluate the E-ESI descriptors
The electronic-structure calculations are conducted employing DFT. In our implementation, we employ the M06-2X functional [
extending even to coordination compounds. Regarding the basis set, while highly
accurate basis sets are preferred for precise quantum chemistry computations, our
ESI studies adopt the 6-31G(d,p) basis set. This choice was made from the consideration that the shell-structure-type basis set approximately satisfies both the hypervirial
theorem [
of a target molecule in the spin-singlet ground (S
gence, pertinent information such as total energy, orbital energy spectrum, and dipole
moment are extracted from the output. Subsequently, at the optimized geometry, we
perform additional calculations for normal mode analysis, excited state calculations
with the TDDFT method, molecular volume computation, and solvation energy determination with PCM. Molecular size anisotropy is assessed using the Mathematica
software. This is done using the preinstalled function “BoundingRegion”, giving
the box (cuboid) size enclosing the outer surface of the molecule defined using the
isodensity surface [
36] and the Hellmann–Feynman theorem [37].
Initiating the electronic-structure calculations involves the geometry optimization
].
27
35], chosen for its broad applicability,
) state. Upon achieving conver-
0
11.7 Applications
11.7.1 Prediction of Activity of Inhibitors
Sugimoto et al. utilized the ESI descriptor set in regression modeling to predict the
activity of FAS (fatty acid synthase) inhibitors [
regression model study employing the same descriptor set, focusing on the inhibition
of the growth of E. coli [
the ESI-2 set in regression modeling, which incorporates excitation energies. Across
]. Similarly, Ideo et al. conducted a
2
3
]. Tateishi et al. [4] extended this approach by employing
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these studies, the ESI descriptor sets have been proven practical and reasonable in
regression modeling, showcasing their utility in understanding and predicting various
molecular activities.
11.7.2 Prediction of Toxicity to Tetrahymena Pyriformis
and Classification of Its “Mode of Action”
Mangarra et al. [5, 6] employed the original ESI descriptor set, shown in Table 11.1,
to construct a regression model of the toxic effects of phenol derivatives, particularly
those impeding the growth of Tetrahymena pyriformis. Additionally, they endeavored
to categorize the “mode of action” (MOA) underlying the toxicity by employing the
XGBoost classifier with the E-ESI descriptor set [
the available classification data collected from the literature, an oversampling method
known as the SMOTE (synthetic minority oversampling technique) algorithm [
was applied.
7]. To overcome the imbalance in
38]
11.7.3 In Silico Screening Using ESI
Ideo et al. [3
sized in-house database. In a similar vein, Tateishi et al. [
silico screening of α-glucosidase inhibitors, utilizing the KampoDB natural product
database developed by Yamanishi et al. [
docking simulations with the AutoDock Vina software [
affinity of the screened compounds to the target protein. In our preliminary work,
the chemical space of the KampDB compounds is covered by the screening using
the ESI descriptor set more widely than the RDKit and ECFP4 [
] undertook in silico screening of antibacterial reagents utilizing a small-
4] recently conducted in
39]. Their methodology involved employing
] to assess the binding
40
41] descriptor sets.
11.8 Summary
In this chapter, ESI, proposed by the present author, has been introduced. ESI may
be classified as a distinct informatics discipline. The differentiating factor lies in
the focus of ESI, which centers on physicochemical information acquired from the
electronic-structure level of molecules, diverging from the emphasis on geometricstructure level information focused in chemoinformatics and bioinformatics.
Based on the Schrödinger equation, we have pointed out that three distinct categories of ESI can be developed: Hamiltonian-based ESI (H-ESI), wavefunctionbased ESI (Ψ-ESI), and energy-based ESI (E -ESI). In this chapter, we have focused
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