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10 Two- and Three-Dimensional Molecular Representations … 185
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Chapter 11
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Electronic-Structure Informatics
for Drug Development
Manabu Sugimoto
11.1 Introduction
Efficacy of drugs for disease treatment is determined by a variety of chemical
processes in the human body. This fact suggests that information at various levels
should be collected for drug candidate screening. In other words, in in silico drug
development, reasonable and ubiquitous description of drug candidates are desired
to achieve accurate prediction of their in vivo activities.
Regarding the description of biochemical phenomena, there have been two major
informatics approaches for drug development: bioinformatics and chemoinformatics.
As shown in Fig.
and can provide predictions in different context. Although the resultant information
would be insightful, the lack of electronic level of information can be a source
of ambiguity in predictions because chemical phenomena occur through various
electronic interactions and electronic-structure changes like complex formation and
bond formation/breaking.
Recently, we have been suggesting “electronic-structure informatics (ESI)” [1]
to reinforce the conventional informatics methodologies. It was motivated by a
simple notion: “Electronic-structure calculations can describe any kinds of chemical
phenomena without using any kinds of chemoinformatics descriptors. This indicates
that appropriate molecular descriptors are hidden in the computational output”. If we
would be able to derive such descriptors from the output of quantum chemical calculations, they would be very reasonable, useful, and powerful in machine learning
studies for drug development.
In this chapter, we will discuss plausible ESI methodologies and suggest potentially applicable ESI descriptors for drug development. The present approach does
11.1, the hierarchy of information in these approaches are different,
M. Sugimoto (B)
Faculty of Advanced Science and Technology, Kumamoto University, 2-39-1 Kurokami,
Chuo-Ku, Kumamoto 860-8555, Japan
e-mail: sugimoto@kumamoto-u.ac.jp
© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024
H. Satoh et al. (eds.), Drug Development Supported by Informatics,
https://doi.org/10.1007/978-981-97-4828-0_11
187
188 M. Sugimoto
https://t.me/med1917
Fig. 11.1 Information hierarchy in drug development and the corresponding research fields
not naturally derive descriptors from theoretical consideration. Rather ESI descriptors herein are suggested on the basis of the author’s previous experiences in applied
quantum chemical studies. Although the suggested descriptors have some theoretical
reasoning, the choice is always arbitrary. In order to demonstrate the applicability of
the suggested descriptor set, we will briefly introduce our previous applications in
supervised machine learning, i.e., regression and classification, for drug development
2–8].
[
11.2 Is Electronic-Structure Level Information Required
for Drug Development?
The response to this question may be “yes” or “no”. Chemists know that molecular characteristics, i.e., molecular structure, properties, and reactivities reflect its
electronic structure as illustrated in Fig.
attribute a patient’s illness to the electronic structures of biomolecules.
This difference on focus between chemists and medical scientists might be due to
the following two reasons: One is that the intricate hierarchy of biological phenomena
obscures the crucial characteristics of the electronic structures. Another reason would
be that, since a biomolecule plays a role in a biochemical network, it is more important
to understand medical phenomena from the viewpoint of the network, not that of the
individual network components.
In many research fields, “what happens?” sometimes overwhelms “why it
happens?”. When we try to predict the efficacy of a drug, the knowledge on the
latter is indispensable. In this sense, it seems quite reasonable to make an effort to
develop informatics at the electron level. An appropriate name for such a research
field would be ESI.
The theories in chemistry and physics have shown that chemical reactivities and
transport phenomena can be predicted through numerical calculations and that the
information on the electronic wavefunction describing the electronic structure is
of essential importance. As our body is composed of molecules, all the biochemical phenomena are essentially chemical processes, so the description for drug
development should start from the information of the electronic-structure level.
11.2. In contrast, medical scientists do not
11 Electronic-Structure Informatics for Drug Development 189
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Fig. 11.2 Role of electronic-structure information in a structure–property relationship study
To make the “electronic-structure level” informatics practical, our challenge
would be to know (i) how we can develop a compact description of the electronic structure of biomolecules for machine learning studies and (ii) how we can
save computational time to obtain such information. To tackle these challenges,
it is strongly desired to develop a theoretical method that can suggest appropriate
ESI descriptors. However, unfortunately, such a method is not available at present.
Herein, we suggest some ESI descriptors on the basis of considerations on chemical
phenomena determining the efficacy of drug molecules in the human body.
It has been well known that, in addition to molecular docking studies, socalled ADMET (absorption/distribution/metabolism/excretion/toxicity) studies are
indispensable [
9]. To go beyond docking studies on protein–ligand complexes, in
silico machine learning models applicable even to, e.g., enzymatic redox reactions
should be developed. In this sense, it is desirable to develop machine learning descriptors applicable to a variety of chemical phenomena. For this purpose, the informatics
at the electronic-structure level is highly demanded.
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11.3 The ESI Methodologies and Their Relation
to Previous Theoretical/Computational Studies
The electronic structure of a molecule refers to characteristics of its electronic wavefunction. The function depends on the coordinates of electrons in the molecule and
can be mathematically very complex. A simpler view can be obtained by mathematically representing the wavefunction using a one-electron wavefunction called
“orbital”. For molecules, they are called molecular orbitals (MOs). In this description, topological characteristics of MOs, their energy levels, and electron occupation
numbers define the electronic structure of a molecule.
The wavefunction Ψ is an eigenfunction of the Schrödinger equation given by
ˆ
H Ψ = EΨ. (11.1)
ˆ
In Eq. (11.1),
is its energy. The information on the electronic structure can be attributed to Ψ
E. In quantum chemistry studies on functional molecules, the main interest is
and
on the calculation of E, and the detailed analyses are made to reveal the important
characteristics of their electronic structure. Theoretically, Ψ can also be a target in
the analysis, but the direct analysis of Ψ is rarely done. It is probably because Ψ is a
function of the coordinates of all electrons, i.e., it is a multi-dimensional function of
electron coordinates. Instead, electron density (diagonal element of the one-particle
reduced density matrix), net charges on each atom, and MOs are analyzed in detail
to reveal the important features determining the change in E, i.e., interaction energy
between molecules.
Historically, quantum chemistry and solid-state physics have been using “model
Hamiltonians”. They were developed to simplify or grasp the physics of the system
of interest. The famous example of the model Hamiltonian is the simple Hückel
Hamiltonian [
11
nian [
12] for modeling electron–phonon interaction and the Hubbard Hamiltonian [13]
[
considering physics with strong electron–electron interaction.
Schrödinger equation, it would be reasonable to suggest three types of ESI
methodologies: the Hamiltonian(
ESI (Ψ-ESI), and energy(E)-based ESI (E-ESI).
theoretical chemistry and physics [
through the experiments are taken into consideration in the description of the model
Hamiltonian, which characterizes the electronic features of the system. In recent
studies on materials informatics, in particular, in metrology informatics (measurement informatics), “Hamiltonian selection” is considered one of the most challenging studies [
] in solid-state physics. The other examples are the Holstein Hamiltonian
By overviewing the historical development of numerical studies on the
The H-ESI approach is to develop a model Hamiltonian as has been done in
H is a Hamiltonian of the system (e.g., a drug molecule) and E
], which is essentially equivalent to the tight-binding Hamilto-
10
ˆ
H
)-based ESI (H-ESI), wavefunction(Ψ)-based
11–13]. Knowledge and information obtained
14
]. In theoretical physics, one of the main concerns to understand
11 Electronic-Structure Informatics for Drug Development 191
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materials-scientific phenomena is to suggest a physical model leading to the accurate reproduction of the experimental observations (measurements) and to reasonable
predictions.
The Ψ-ESI approach focuses on the mathematical form of the wavefunction Ψ.As
is well known, this function determines the equilibrium molecular structure as well as
electric property such as a dipole moment as shown in Fig.
of three-dimensional topological features of Ψ and MOs (one-electron wavefunction)
seem major challenges in this ESI approach. The frontier orbital theory by Fukui [
and the Woodward-Hoffmann rule [
the Ψ-ESI approach since characteristics of MOs are used to describe and understand
chemical reactivities. The concept of isolobal analogy by Hoffmann is nothing but
the “electronic structure” version of similarity principle of molecules. Similar to
structural similarity of molecules, this principle can be a guiding principle for drug
discovery.
The E-ESI approach is an informatics approach focusing on electronic energies.
Equilibrium molecular geometries, strength of intermolecular interaction, chemical
reactivity, and electronic properties can be defined and analyzed on the basis of
electronic energies. This approach seems much easier and more straightforward than
the H-ESI and Ψ -ESI approaches in applications to drug discovery. In the subsequent
sections, we will discuss the E-ESI methodology in detail.
16] for chemical reactions can be categorized into
11.2. Description and use
15]
11.4 Applicability of E-ESI to Drug Development: Its
Relationship With Drug Activity Parameters
The initial phase of drug development involves the discovery of a hit (or, ideally, a
lead) compound. An informatics method employed in this context must possess the
capability to predict the pharmaceutical activity of these compounds. To attain this
objective, it becomes imperative to develop and employ molecular descriptors that
have the potential to effectively predict the activity.
In the pursuit of comprehending and enhancing the interpretability of machine
learning, it proves advantageous for the descriptor set to possess theoretical underpinnings in its derivation. While descriptors derived from intuition may offer practical
utility, their definition in this manner is inherently arbitrary. Employing a descriptordesign strategy rooted in theoretical foundations would be imperative to avoid the
pitfalls of arbitrary choices. Adopting such an approach ensures a more principled
and systematic development of the descriptor set, preventing the potential quagmire
of endless refinement.
Typically used measures are either the “half maximal inhibitory concentration”
) or an absolute inhibition constant (Ki). In the context of the Michaelis–Menten
(IC
50
model depicted in Fig.
Prusoff equation [
11.3, these quantities are interconnected through the Cheng-
17
]:
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Fig. 11.3 Reaction scheme in the Michaelis–Menten model. E, S,ES,and P indicate enzyme
(protein), a substrate (ligand molecule), a complex between E and S, and a reaction product, respectively. k
of “catalytic”. In this model, it is assumed that the formation process of P is very slow in comparison
of the formation of ES, i.e., k
(x = –1, 1, cat) is a rate constant of an elementary reaction where “cat” is an abbreviation
x
, k
>> k
+1
–1
cat
IC
1 +
50
[S]
K
m
(11.2)
Ki =
where [S] is the concentration of the substrate. Km is known as the Michaelis constant
given by
+ k
k
−1
Km =
cat
k
+1
(11.3)
Instead of directly using Ki and IC50,the termspKi (–log Ki) and pIC
(–log IC50)
50
may be employed which would be much better in the numerical calculation. Taking
the negative logarithm on both sides of Eq. (
11.2), these terms can be correlated with
each other through the following equation:
pKi = pIC
+ log1 +
50
[S]
K
m
(11.4)
Equation (11.4) suggests that, in cases where [S]/Km is either similar or negligible
across a series of inhibitors under investigation, pK
and pIC
i
there are essentially
50
equivalent.
In the Michaelis–Menten model, it is assumed that k+1, k
ation, the equilibrium constant
KS for dissociation of the ES complex in Fig. 11.3 is
−1
>> k
. In this situ-
cat
given by
KS =
[E][S]
[ES]
=
k
−1
k
1
(11.5)
indicating Km ≈ KS.
The equilibrium constant (K) for an elementary step can be related to a free energy
change (ΔG
)as
0
ΔG0 =−RT ln K (11.6)
11 Electronic-Structure Informatics for Drug Development 193
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Here, R and T represent the gas constant and the temperature, respectively. When K
, ΔG0 effectively characterizes the binding affinity between the inhibitor and
is K
i
the enzyme.
Drawing from the discussions, a key insight emerges: the exploration of the pharmaceutical activity of compounds necessitates the use of descriptors linked to binding
affinity. Consequently, factors influencing the electronic energy changes upon
inhibitor-protein bindings should be incorporated into machine learning approaches
for drug discovery. In this context, the E-ESI approach assumes significance in the
realm of drug molecule development.
11.5 Molecular Descriptors for E-ESI
In the context of E-ESI, the central parameter is the energy (E) determined by the
Schrödinger equation. This energy acts as a measure for both s tructural stability and
chemical reactivity. Emphasizing E proves advantageous as it enables diverse component analyses, a practice firmly entrenched in various quantum chemistry publications. The resulting insights into interpretation imply the necessity for a range of
molecular descriptors crucial in predicting drug activity through supervised machine
learning.
The delineation of molecular descriptor sets, even within the framework of E-ESI,
can be arbitrary. Leveraging the author’s prior use of electronic-structure calculations,
we propose a set of 21 molecular descriptors, which are shown in Table
Subsequent subsections furnish justifications for these descriptors.
11.1 [1–7].
11.5.1 Descriptors for Electronic Excitations
The potential energy surface (PES), which illustrates energy variation with changes in
nuclear coordinates, offers crucial insights into molecular structures and properties,
encompassing chemical reactivity. The exploration of the topological characteristics
of the PES stands as a central focus in quantum chemistry research.
Given that the PES is a relative energy representation referring to a reference
state, such as the dissociation limit of two interacting chemical species, it inherently
encapsulates their interaction energies. Let us consider our focal system comprising
two molecules denoted as A and B, representing, for instance, a small ligand molecule
and a protein molecule, respectively.
As an approximation, the wavefunction of the interacting system can be expressed
as follows:
Ψ = C00ΨA0Ψ
+C01ΨA0Ψ
+ C+−ΨA+Ψ
B0
+ C10ΨA1Ψ
B1
+ C−+ΨA−Ψ
B−
+ C11ΨA1Ψ
B0
B+
B1
(11.7)
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Table 11.1 Summary of the ESI descriptor set
Descriptor Definition
IE
EA
v
v
Ionization energy upon the vertical transition to the lowest cation state at the
optimized geometry of the S
0
state
Electron affinity upon the vertical transition to the lowest electron-attached state at
the optimized geometry of the S
0
state
ΔST Vertical excitation energy from the S0 state to the T1 state. This energy is expected
to have strong correlation with the S
→ S1 excitation energy where the S1 state is
0
expected to contribute to a chemical reaction
λ
S0→C
λ
C→S0
λ
S0→A
λ
A→S0
λ
S0→T1
λ
T1→S0
Reorganization energy after vertical excitation from the S0 state to the cation state
Reorganization energy after vertical excitation from the cation state to the S0 state
Reorganization energy after vertical excitation from the S0 state to the anion state
Reorganization energy after vertical excitation from the anion state to the S0 state
Reorganization energy after vertical excitation from the S0 state to the T1 state
Reorganization energy after vertical excitation from the T1 state to the cation state
S(ρUV) Similarity of the calculated UV/Vis spectrum of a target molecule to that of a
reference molecule
S(ρex) Similarity of the “density of electronic states” of a target molecule to that of a
reference molecule
S(ρIR) Similarity of the calculated IR spectrum of a target molecule to that of a reference
molecule
S(ρ
) Similarity of the “density of vibrational states” of a target molecule to that of a
vib
reference molecule
S(ρ
) Similarity of the “density of molecular orbital (DOMO)” of a target molecule to
orb
that of a reference molecule. DOMO is called “density of states (DOS)” in
solid-state physics
V
mol
Molecular volume in the S0 state
B1,B2,B3 Lengths of the three edges of a box enclosing a molecule where the isodensity
ΔE
solv
surface is referred to in the definition of its outer surface. In definition, B
B
3
Solvation energy in the S0 state
≥ B2 ≥
1
μ Electric dipole moment in the S0 state
MW Molecular weight (This has no relevance to the electronic structure, but is added
because this quantity is expected important in transport phenomena.)
Here,
C
denotes the coefficient for each term, where S and T take on values of 0, 1,
ST
+ , or –, corresponding to the neutral spin-singlet ground state, the lowest spin-singlet
excited state, the cation state, and the anion state, respectively.
The second and third terms in Eq. (11.7) delineate charge-transfer interactions,
while the fourth, fifth, and sixth terms pertain to intramolecular excitations, which
are required to describe the electronic polarization of the molecules and are induced
by intermolecular interaction. As is well known, electronic polarization results in the
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