\makeatletter
\@ifundefined{HCode}
{\documentclass[screen,CRCHIM,Unicode,published]{cedram} 
\newenvironment{noXML}{}{}
\def\tsup#1{$^{{#1}}$}
\def\tsub#1{$_{{#1}}$}
\def\thead{\noalign{\relax}\hline}
\def\tbody{\noalign{\relax}}
\def\endthead{\noalign{\relax}\hline}
\def\tabnote#1{\vskip4pt\parbox{.95\linewidth}{#1}}
\usepackage[figuresright]{rotating}
\RequirePackage{etoolbox}
\def\jobid{crchim20230809}
\def\inlinefig#1{\includegraphics{#1}}
\newenvironment{xxcenter}{\begin{center}}{\end{center}}
\def\xsection#1{}
%\graphicspath{{/tmp/\jobid_figs/web/}}
\graphicspath{{./figures/}}
\usepackage[T1]{fontenc}
\usepackage{comment}
\newcounter{runlevel}
\usepackage{upgreek}
\let\MakeYrStrItalic\relax
\def\Smallskip{\smallskip}
\csdef{Seqnsplit}{\\}
\def\refinput#1{}
\def\back#1{}
\def\rmPhi{\Phi}
\def\0{\phantom{0}}
\def\hyphen{\mbox{-}}
\newenvironment{inftab}{}{}
\def\xmorerows#1#2{#2}
\usepackage{multirow} 
\def\nrow#1{\@tempcnta #1\relax%
\advance\@tempcnta by 1\relax%
\xdef\lenrow{\the\@tempcnta}}
\def\morerows#1#2{\nrow{#1}\multirow{\lenrow}{*}{#2}}
\def\botline{\\\hline}
\def\Lbreak{\newline}
\def\ubreak{\break}
\def\xvarnothing{\emptyset}
\def\mn{\phantom{$-$}}
\makeatletter
\g@addto@macro{\UrlBreaks}{\UrlOrds}
\gappto{\UrlBreaks}{\UrlOrds}
\makeatother
\DOI{10.5802/crchim.290}
\datereceived{2023-09-15}
\daterevised{2023-11-19}
\datererevised{2023-12-23}
\dateaccepted{2024-01-24}
\ItHasTeXPublished
}{\documentclass[crchim]{article}
\def\CDRsupplementaryTwotypes#1#2{}
\def\CDRdoi{10.5802/crchim.290} 
\newenvironment{sidewaystable}{\begin{table*}}{\end{table*}}
\def\href#1#2{\url{#1}}
\def\xsection#1{}
\newenvironment{xxcenter}{}{}
\def\xmorerows#1#2{\morerows{#1}{#2}}
\def\Smallskip{}
\let\newline\break
\let\ubreak\relax
\let\xvarnothing\emptyset
\makeatletter
}
\makeatother

\usepackage[T1]{fontenc}
\usepackage{upgreek}

\dateposted{2024-06-24}
\begin{document}

\begin{noXML}

\CDRsetmeta{articletype}{research-article}

\title{Structural and in silico studies of 2-pyridyl-decorated 
2-amino-1,3,5-triazine with a potency against SARS-CoV-2 proteins}

\alttitle{\'{E}tudes structurales et \protect\textit{in silico} du
2-amino-1,3,5-triazine d\'{e}cor\'{e} de 2-pyridyles avec une
activit\'{e} contre les prot\'{e}ines du SARS-CoV-2}

\author{\firstname{Damir A.} \lastname{Safin}\CDRorcid{0000-0002-9080-7072}}
\address{University of Tyumen, Volodarskogo Str. 6, 625003 Tyumen,
Russian Federation}
\address{Scientific and Educational and Innovation Center for Chemical
and Pharmaceutical Technologies, Ural Federal University named after
the First President of Russia B.N. Yeltsin, Mira Str. 19, 620002
Ekaterinburg, Russian Federation}
\email{damir.a.safin@gmail.com}

\keywords{\kwd{Triazine}\kwd{Pyridine}\kwd{Computational
study}\kwd{Molecular docking}\kwd{Molecular
dynamics}\kwd{DFT}\kwd{COVID-19}}

\altkeywords{\kwd{Triazine}\kwd{Pyridine}\kwd{\'{E}tude
computationnelle}\kwd{Amarrage mol\'{e}culaire}\kwd{Dynamique
mol\'{e}culaire}\kwd{DFT}\kwd{COVID-19}}

\begin{abstract}
Computational studies of 2-amino-4,6-bis(2-pyridyl)-1,3,5-triazine
(NH\tsub{2}Py\tsub{2}T), which is of interest both as a ligand for
coordination chemistry and as a precursor for further functionalization
due to the presence of the NH\tsub{2} functionality, are reported.
Three isomeric structures were considered. Descriptors and potential
corrosion inhibition properties for a series of metals used in implants
were examined by DFT calculations. ADMET properties were estimated
using a set of online tools. Potential inhibition properties toward a
number of SARS-CoV-2 proteins were investigated using molecular
docking, which showed the best binding score with Nsp3-MES. Stability
of complexes of NH\tsub{2}Py\tsub{2}T with the considered proteins was
also studied using molecular dynamics simulations, which showed that
complex with Mpro is the most stable, while complex with PLpro is
unstable.
\end{abstract}

\begin{altabstract}
Des \'{e}tudes \textit{in silico} du
2-amino-4,6-bis(2-pyridyl)-1,3,5-triazine (NH2Py2T), qui est
int\'{e}ressant \`{a} la fois comme ligand pour la chimie de
coordination et comme pr\'{e}curseur pour une fonctionnalisation
ult\'{e}rieure en raison de la pr\'{e}sence de la fonction NH2, sont
rapport\'{e}es. Trois structures isom\'{e}riques ont \'{e}t\'{e}
consid\'{e}r\'{e}es. Les descripteurs et les propri\'{e}t\'{e}s
potentielles d'inhibition de la corrosion pour une s\'{e}rie de
m\'{e}taux utilis\'{e}s dans les implants ont \'{e}t\'{e} examin\'{e}s
par des calculs DFT. Les propri\'{e}t\'{e}s ADMET ont \'{e}t\'{e}
estim\'{e}es \`{a} l'aide d'un ensemble d'outils en ligne. Les
propri\'{e}t\'{e}s d'inhibition potentielle \`{a} l'\'{e}gard d'un
certain nombre de prot\'{e}ines du SARS-CoV-2 ont \'{e}t\'{e}
\'{e}tudi\'{e}es par amarrage mol\'{e}culaire, qui a donn\'{e} le
meilleur score de liaison avec la prot\'{e}ine non structurale 3
(Nsp3\_range 207-379-MES). La stabilit\'{e} des complexes de NH2Py2T
avec les prot\'{e}ines concern\'{e}es a \'{e}galement \'{e}t\'{e}
\'{e}tudi\'{e}e \`{a} l'aide de simulations de dynamique
mol\'{e}culaire, qui ont montr\'{e} que le complexe avec Mpro est le
plus stable, tandis que le complexe avec PLpro est instable.
\end{altabstract}

\maketitle

\twocolumngrid

\end{noXML}

\section{Introduction}\label{sec1}

Compounds containing heterocycles are currently among the key
components of drugs. It is known that about 80\% of all main active
components of drugs containing cyclic systems are heterocycles with
nitrogen, oxygen and sulfur~\cite{1,2}. The pyridine- and
triazine-based compounds are of particular interest since they possess
a high structural diversity and are considered as agents for the
treatment of diseases. The presence of various substituents on the
heterocyclic core allows one to efficiently vary their biological,
including antibacterial and antiviral, activities~\cite{3,4,5,6}.
Notably, the triazine-containing derivatives are also used in the
fabrication of antimicrobial films on the surface of various materials,
including implants. Such a coating is possible both due to the
introduction of compounds into the polymerization mixture, as well as
the ability to form their own polymeric structures and covalent
interactions with the functional groups of the surface~\cite{7,8,9,10}.
An additional interest in the pyridine- and triazine-based derivatives
as medications is currently due to potential chemical linkage with
proteins. This allows their use for covalent inhibition of bacterial
and viral proteins. In particular, the pyridine derivatives are known
to be pronounced cysteine protease inhibitors~\cite{11,12}.

The latest research on the antiviral activity of the pyridine- and
triazine-based derivatives is due to the severe acute respiratory
syndrome-related coronavirus 2 (SARS-CoV-2)~\cite{13}. The newest
agents for coronavirus disease 2019 (COVID-19) therapy are also
constructed from the pyridine and/or triazine rings~\cite{14}.
Furthermore, triazine is a precursor of another well-known drug,
remdesivir~\cite{15,16}. Some of its derivatives are also known as
efficient antiviral agents~\cite{17}. At the same time, analysts
predict an intensive growth of the triazine market due to its high
demand for medicine~\cite{18}.

We have also been interested in the chemistry of nitrogen-containing
six-membered rings~\cite{19,20,21,22,23,24,25,26} and in computational
studies of potential biological activity of different
compounds~\cite{27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47}. 
In the present work, I have focused on
2-amino-4,6-bis(2-pyridyl)-1,3,5-triazine (NH\tsub{2}Py\tsub{2}T),
which is constructed from the triazine and two 2-pyridine rings
(Figure~\ref{fig1}). Furthermore, this molecule also contains a
triazine-linked primary amine group, which is of potential interest for
further possible functionalizations of NH\tsub{2}Py\tsub{2}T through,
e.g., reactions of condensation and addition.

\begin{figure*}
\includegraphics{fig01}
\caption{\label{fig1}Diagrams of the three discussed
NH\tsub{2}Py\tsub{2}T isomers together with their corresponding
energies under water solvation and in gas phase.}
\end{figure*}

The Cambridge Structural Database (CSD)~\cite{48} did not contain
crystal structures for NH\tsub{2}Py\tsub{2}T. Notably, although
NH\tsub{2}Py\tsub{2}T is of great interest for the coordination
chemistry due to the 2,2$'$-bipyridine- (bpy) or 2,2$'$;6$'$,2$''$-terpyridine
(terpy)-like coordination pockets, the CSD contains only 19 hits
for crystal structures of complexes with a series of lanthanide(III)
cations~\cite{49}, one crystal structure with Cd\tsup{2+}~\cite{50} and
one with Ru\tsup{2+}~\cite{51}. Interestingly, the CSD also contains a
crystal structure of the dihydrochloride salt of NH\tsub{2}Py\tsub{2}T
with two protonated pyridine rings~\cite{52}. Thus, it becomes
important to study structural features of NH\tsub{2}Py\tsub{2}T. As
such, I have performed density functional theory (DFT)-based
calculations to establish and study the most favourable
NH\tsub{2}Py\tsub{2}T isomers, including its electronic and reactivity
properties. Furthermore, by means of a molecular docking approach, I
have examined the binding of NH\tsub{2}Py\tsub{2}T to a series of
SARS-CoV-2 proteins. Stability of the resulting
protein--NH\tsub{2}Py\tsub{2}T complexes was assessed with
molecular dynamics studies.

\section{Methods}\label{sec2}
\subsection{DFT calculations}\label{ssec21}

The gas phase and aqueous structures of the NH\tsub{2}Py\tsub{2}T
isomers were optimized with GaussView 6.0 molecular
visualization~\cite{53} and Gaussian 09, Revision D.01~\cite{54} using
the DFT/B3LYP/6-311${{+}{+}}$G(d,p) method~\cite{55,56,57}. The calculation
in water were performed using the integral equation formalism
polarizable continuum model (IEFPCM).

\subsection{Molecular docking}\label{ssec22}

AutoDock Vina was used for molecular docking simulations (Lamarckian
Genetic Algorithm (LGA) scoring function with GA runs $=$\ 100,
population size $=$\ 500, maximum number of evaluations $=$\
 25000000)~\cite{58,59}. The RCSB Protein Data Bank (RCSB PDB) was
used as a source to download the structures of proteins~\cite{60}, from
which water molecules were removed, and hydrogen atoms and missing
residues and charges were inserted. The grid box (30 ${\times}$ 30
${\times}$ 30~\AA{} with  0.375~\AA{} grid spacing) was defined by
AutoDock Tools (v.~1.5.7). The docking procedure was applied to
flexible ligands and rigid proteins. The conformers of the ligands with
the best binding scores were retrieved from the 10 top-ranked poses.
The results of molecular docking were visualized in BIOVIA Discovery
Studio 2020~\cite{61}.

\subsection{\textit{In silico} drug-likeness analysis}\label{ssec23}

The absorption, distribution, metabolism, excretion and toxicity
(ADMET) properties of NH\tsub{2}Py\tsub{2}T were predicted using the
SwissADME~\cite{62}, which also includes the brain or intestinal
estimated permeation method (BOILED-Egg)~\cite{63}, and
ProTox-II~\cite{64,65} web tools.

\subsection{Molecular dynamics simulation}\label{ssec24}

The WebGRO online service was used for molecular dynamics
simulations~\cite{66}. Parameters such as root mean square deviation
(RMSD), root mean square fluctuation (RMSF), radius of gyration (Rg),
solvent accessible surface area (SASA), and intermolecular hydrogen
bonds were assessed. GROMOS96 54a7 forcefield was applied for
complexes, equilibrated using the isothermal--isobaric (NPT) and
canonical (NVT) ensembles. Topology of the ligand was generated with
the PRODRG tool~\cite{67}. Simple point-charge (SPC) was used as
solvent model (triclinic water box with size 50 ${\times}$ 75
${\times}$ 70 \AA{})~\cite{68}. The steepest-descent algorithm (5000
steps) was applied to minimize the energy of the system. 0.15~M NaCl
was used during the simulation at 310~K and 1.0 bar with 1000 frames
per simulation. Three independent simulation runs with a duration of 
50~ns were performed for each protein--ligand complexes and identical
results were obtained.

\section{Results and discussion}\label{sec3}

The structure of NH\tsub{2}Py\tsub{2}T both in gas phase and in water
was examined using DFT (Table~S1 in the Supplementary Material).
Conformational analysis (Figure~S1 in the Supplementary Material)
showed that three different isomers, depending on the orientation of
the pyridine rings, are the most favorable in both gas phase and water
(Figure~\ref{fig1}). In particular, under water solvation, isomer~1,
namely \textbf{1w}, was found to be the most energetically favorable,
while isomers 2 and 3, namely \textbf{2w} and \textbf{3w},
respectively, were only 0.12 and 0.44 kcal/mol less favorable
(Figure~\ref{fig1}). In gas phase, isomer 2, namely \textbf{2g}, was
the most favorable, while isomers 1 and 3, namely \textbf{1g} and
\textbf{3g}, respectively, were 0.28 and 2.25 kcal/mol less favorable
(Figure~\ref{fig1}). Furthermore, under water solvation conditions the
corresponding isomers were 11.78, 11.38 and 13.31~kcal/mol more
favorable in comparison to gas phase (Figure~\ref{fig1}). Thus, the
formation of all three isomers is almost equally possible, especially
in water. The same conformational analysis results (Figure~S1 in the
Supplementary Material) showed that the energy barriers for conversion
of \textbf{1w} to \textbf{2w}, \textbf{1w} to \textbf{3w} and
\textbf{2w} to \textbf{3w} were 8.87, 9.10 and 17.92~kcal/mol,
respectively. In gas phase, the energy barriers for conversion of 
\textbf{1g} to \textbf{2g}, \textbf{1g} to \textbf{3g} and 
\textbf{2g} to \textbf{3g} were 9.27, 18.76 and 10.65 kcal/mol,
respectively. The computed energy barriers are quite high for both gas
phase and under water solvation. Thus, each isomer in both phases does
not exist in equilibrium with the other two isomers.

The calculated C--C and C--N bond lengths within the aromatic rings are
1.328--1.401 \AA{} (Table S2 in the Supplementary Material). The C1--N6
bond is 1.345 \AA{} in the structures of the isomers obtained under
water solvation. This value is 0.006--0.012 \AA{} longer for the
isomers in gas phase (Table S2 in the Supplementary Material). The C--C
bonds between the triazine and pyridine carbon atoms are about 1.5
\AA{} in all the discussed isomers (Table S2 in the Supplementary
Material). The bond angles formed by the non-hydrogen atoms are about
115--125\textdegree{} (Table S2 in the Supplementary Material). The
structures of \textbf{3w} and \textbf{1g}, followed by \textbf{3g} and
\textbf{1w}, are the most deviated from planarity (Figure~\ref{fig2}),
as evidenced from the corresponding dihedral angles (Table S2 in the
Supplementary Material).

\begin{figure*}
\includegraphics{fig02}
\caption{\label{fig2}The DFT-optimized structures of the
NH\tsub{2}Py\tsub{2}T isomers.}
\end{figure*}

Each isomer forms a pair of weak C--H${\cdots}$N
interactions yielding two five-membered pseudo-aromatic rings
(Figure~\ref{fig2}, Table~\ref{tab1}). These rings are characterized by
a conjugation effect with partial covalency~\cite{69,70}. According to
the Harmonic Oscillator Model for Heterocycles with ${\uppi}$-electrons
and/or $n$-electron delocalization (HOMHED)~\cite{70}, the calculated
aromaticity for these non-covalent rings varies from 0.665 to 0.678,
which is similar to those of (is)oxazoles and furans~\cite{70}. The
same index for the triazine and pyridine rings was found to be
0.994--0.999.

%tab1
\begin{table*}
\caption{\label{tab1}Lengths (\AA{}) and angles (\textdegree) of the
C--H${\cdots}$N interactions, and aromaticity indexes
of the triazine, pyridine and five-membered non-covalent rings in the
optimized structures of the NH\tsub{2}Py\tsub{2}T isomers}
\begin{tabular}{ccccccccccc}
\thead
& \xmorerows{1}{C--H${\cdots}$N} & \xmorerows{1}{$d$(C--H)} &
\xmorerows{1}{$d$(H${\cdots}$N)} & \xmorerows{1}{$d$(C${\cdots}$N)}
& \xmorerows{1}{${\angle}$(CHA)}
& \multicolumn{5}{c}{Aromaticity index} \\\cline{7-11}
& & & & & & Triazine & Py$_{\mathrm{N4}}$  &
Py$_{\mathrm{N5}}$ & $R$1 & $R$2 \\
\endthead
\textbf{1w} & C5--H3${\cdots}$N3 & 1.080 & 2.447 & 2.800 & 97.44 & \morerows{1}{0.994}  & \morerows{1}{0.996}  & \morerows{1}{0.996}  & \morerows{1}{0.667}  & \morerows{1}{0.667}  \\
            & C10--H7${\cdots}$N3 & 1.081 & 2.447 & 2.800 & 97.73 &  &  &  &  &  \\ 
\textbf{2w} & C5--H3${\cdots}$N1 & 1.081 & 2.448 & 2.799 & 97.3\0 &  \morerows{1}{0.995}  & \morerows{1}{0.996}  & \morerows{1}{0.996}  & \morerows{1}{0.667}   & \morerows{1}{0.667} \\
            & C10--H7${\cdots}$N3 & 1.080 & 2.442 & 2798 & 97.55 &  &  &  &  &  \\ 
\textbf{3w} & C5--H3${\cdots}$N1 & 1.081 & 2.465 & 2.805 & 96.71 & \morerows{1}{0.997}  & \morerows{1}{0.996}  & \morerows{1}{0.996}  & \morerows{1}{0.666}  & \morerows{1}{0.665}  \\
            & C10--H7${\cdots}$N2 & 1.081 & 2.465 & 2.805 & 96.71 &  &  &  &  &  \\ 
\textbf{1g} & C5--H3${\cdots}$N3 & 1.081 & 2.461 & 2.811 & 97.31 & \morerows{1}{0.995}  & \morerows{1}{0.996}  & \morerows{1}{0.996}  & \morerows{1}{0.672}  & \morerows{1}{0.672}  \\
            & C10--H7${\cdots}$N3 & 1.081 & 2.461 & 2.811 & 97.31 &  &  &  &  &  \\ 
\textbf{2g} & C5--H3${\cdots}$N1 & 1.081 & 2.442 & 2.800 & 97.70 & \morerows{1}{0.997}  & \morerows{1}{0.996}  & \morerows{1}{0.995}  & \morerows{1}{0.672}  & \morerows{1}{0.678}  \\
            & C10--H7${\cdots}$N3 & 1.081 & 2.408 & 2.779 & 98.35 &  &  &  &  &  \\ 
\textbf{3g} & C5--H3${\cdots}$N1 & 1.081 & 2.444 & 2.798 & 97.43 & \morerows{1}{0.999}  & \morerows{1}{0.995}  & \morerows{1}{0.995}  & \morerows{1}{0.672}  & \morerows{1}{0.672}  \\
            & C10--H7${\cdots}$N2 & 1.081 & 2.445 & 2.798 & 97.41 &  &  &  &  &
\botline
\end{tabular}
\end{table*}

According to atomic charges in the discussed NH\tsub{2}Py\tsub{2}T
isomers, all the H atoms carry a positive charge with the highest
values for NH\tsub{2} \mbox{hydrogens} (Figure~S2 in the Supplementary
Material). The C(NH\tsub{2}) carbon atom, and the C6 and C11 carbons
carry the largest and lowest charges, respectively, within the
non-hydrogen atoms (Figure~S2 in the Supplementary Material). The other
positively charged atoms are C5 and C10 carbons, followed by the
pyridine and triazine N3 nitrogen atoms in \textbf{1g--3g} (Figure~S2
in the Supplementary Material). \mbox{The~latter} nitrogen atoms in
\textbf{1w--3w} are either negatively charged or close to zero
(Figure~S2 in the Supplementary Material). The C4 and C9 pyridine
carbon atoms, followed by the amine nitrogen atom, are also among the
most negatively charged atoms in the discussed isomers (Figure~S2 in
the Supplementary Material).

According to vibrational analysis, no negative frequencies were
obtained (Figure~\ref{fig3}, Table S3 in the Supplementary Material),
testifying to correct optimized structures of all the
NH\tsub{2}Py\tsub{2}T isomers. Notably, the calculated spectra are
pairwise very similar for the corresponding isomers under water
solvation and in gas phase (Figure~\ref{fig3}, Table S3 in the
Supplementary Material). However, some discrepancies clearly appear
between spectra for \textbf{1w--3w} and \textbf{1g--3g}. In particular,
bands for the NH groups were found at 3604 and 3733 cm$^{-1}$ in the
water solvation spectra, while the same bands are shifted by about
8--11 and 11--18 cm$^{-1}$ to higher frequencies in the gas phase
spectra (Table S3 in the Supplementary Material). Furthermore, a
similar shift was observed for the band of the H1--N6--H2 bending and
C1--N6 stretching modes from ${\sim}$1640 cm$^{-1}$ to ${\sim}$1628
cm$^{-1}$ (Table S3 in the Supplementary Material).

\begin{figure*}
{\vspace*{-4pt}}
\includegraphics{fig03}
{\vspace*{-4pt}}
\caption{\label{fig3}The calculated IR (black) and Raman (red) spectra
of the NH\tsub{2}Py\tsub{2}T isomers. Intensities of the spectra are
scaled to the same factor.}
{\vspace*{-4pt}}
\end{figure*}

The highest occupied molecular orbital (HOMO) and lowest unoccupied
molecular orbital (LUMO) for all NH\tsub{2}Py\tsub{2}T isomers range
from ${-}$7.242 to ${-}$6.764 and from ${-}$2.483 to ${-}$2.193 eV,
respectively (Table~\ref{tab2}). Notably, the HOMO decreases and the
LUMO increases from \textbf{1w} through \textbf{2w} to \textbf{3w},
while the reverse is observed for the HOMO of \textbf{1g--3g} and the
LUMO is almost the same for the latter isomers (Table~\ref{tab2}). All
this leads to a gradual increase of the HOMO--LUMO energy gap for
\textbf{1w--3w} and to a gradual decrease for \textbf{1g--3g}, with the
highest values obtained for \textbf{3w} and \textbf{1g}
(Table~\ref{tab2}).

%tab2
\begin{table*}
\caption{\label{tab2}HOMO and LUMO, gap value, descriptors and charge
transfer parameters for the NH\tsub{2}Py\tsub{2}T isomers}
\tabcolsep=2pt
\fontsize{9.5}{12}\selectfont
\begin{tabular}{ccccccc}
\thead
Parameter & \textbf{1w} & \textbf{2w} & \textbf{3w} & \textbf{1g} &
\textbf{2g} & \textbf{3g} \\
\endthead
$E_{\mathrm{HOMO}}$ (eV) & ${-}$7.204 & ${-}$7.230 & ${-}$7.242 & ${-}$6.972 & ${-}$6.878 & ${-}$6.764 \\ 
$E_{\mathrm{LUMO}}$ (eV) & ${-}$2.483 & ${-}$2.474 & ${-}$2.448 & ${-}$2.193 & ${-}$2.206 & ${-}$2.201 \\ 
${\Updelta}E_{\mathrm{LUMO}-\mathrm{HOMO}} = E_{\mathrm{LUMO}}-E_{\mathrm{HOMO}}$ (eV) & \mn4.721 & \mn4.756 & \mn4.795 & \mn4.779 & \mn4.672 & \mn4.563 \\ 
Ionization energy, $I=-E_{\mathrm{HOMO}}$ (eV) & \mn7.204 & \mn7.230 & \mn7.242 & \mn6.972 & \mn6.878 & \mn6.764 \\ 
Electron affinity, $A=-E_{\mathrm{LUMO}}$ (eV) & \mn2.483 & \mn2.474 & \mn2.448 & \mn2.193 & \mn2.206 & \mn2.201 \\ 
Electronegativity, $\chi = (I + A)/2$ (eV) & \mn4.843 & \mn4.852 & \mn4.845 & \mn4.582 & \mn4.542 & \mn4.482 \\ 
Chemical potential, $\mu = -\chi$ (eV) & ${-}$4.843 & ${-}$4.852 & ${-}$4.845 & ${-}$4.582 & ${-}$4.542 & ${-}$4.482 \\ 
Global chemical hardness, $\eta = (I-A)/2$ (eV) & \mn2.361 & \mn2.378 & \mn2.397 & \mn2.389 & \mn2.336 & \mn2.282 \\
Global chemical softness, $S=1/(2{\eta})$ (eV$^{-1}$) & \mn0.212 & \mn0.210 & \mn0.209 & \mn0.209 & \mn0.214 & \mn0.219 \\
Global electrophilicity index, $\omega = \mu^{2}/(2{\eta})$ (eV) & \mn4.969 & \mn4.950 & \mn4.896 & \mn4.394 & \mn4.416 & \mn4.403 \\ 
Maximum additional electric charge, ${\Updelta}N_{\max} = -{\mu}/\eta$ & \mn2.052 & \mn2.040 & \mn2.021 & \mn1.918 & \mn1.944 & \mn1.965 \\ 
\multicolumn{7}{l}{Molecule-to-metal electron charge transfer,
$\Updelta N_{1} = (\Phi - \chi)/\eta$:} \\ 
Ti & ${-}$0.22 & ${-}$0.22 & ${-}$0.21 & ${-}$0.11 & ${-}$0.09 & ${-}$0.07 \\ 
Fe & ${-}$0.15 & ${-}$0.15 & ${-}$0.14 & ${-}$0.03 & ${-}$0.02 & \mn0.01 \\ 
Zr & ${-}$0.34 & ${-}$0.34 & ${-}$0.33 & ${-}$0.22 & ${-}$0.21 & ${-}$0.19 \\ 
Co & \mn0.07 & \mn0.06 & \mn0.06 & \mn0.17 & \mn0.20 & \mn0.23 \\ 
Cu & ${-}$0.08 & ${-}$0.08 & ${-}$0.08 & \mn0.03 & \mn0.05 & \mn0.07 \\ 
Cr & ${-}$0.15 & ${-}$0.15 & ${-}$0.14 & ${-}$0.03 & ${-}$0.02 & \mn0.01 \\ 
Ni & \mn0.13 & \mn0.13 & \mn0.13 & \mn0.24 & \mn0.26 & \mn0.29 \\ 
Mn & ${-}$0.31 & ${-}$0.32 & ${-}$0.31 & ${-}$0.20 & ${-}$0.19 & ${-}$0.17 \\ 
Mo & ${-}$0.10 & ${-}$0.11 & ${-}$0.10 & \mn0.01 & \mn0.02 & \mn0.05 \\ 
Zn & ${-}$0.22 & ${-}$0.22 & ${-}$0.21 & ${-}$0.11 & ${-}$0.09 & ${-}$0.07 \\ 
Al & ${-}$0.24 & ${-}$0.24 & ${-}$0.24 & ${-}$0.13 & ${-}$0.11 & ${-}$0.09 \\ 
W  & ${-}$0.12 & ${-}$0.13 & ${-}$0.12 & ${-}$0.01 & \mn0.00 & \mn0.03 \\ 
Ag & ${-}$0.25 & ${-}$0.25 & ${-}$0.24 & ${-}$0.13 & ${-}$0.12 & ${-}$0.10 \\ 
Au & \mn0.11 & \mn0.10 & \mn0.11 & \mn0.22 & \mn0.24 & \mn0.27 \\ 
Total negative charge, TNC (e) & ${-}$3.36553 & ${-}$3.62912 & ${-}$3.60288 &
${-}$3.62619 & ${-}$3.10979 & ${-}$3.37761
\botline
\end{tabular}
{\vspace*{-2pt}}
\end{table*}

The overall distribution of HOMO and LUMO is very similar for all
isomers (Figure~\ref{fig4}). In particular, the LUMO is localized over
the whole molecule except for the CNH\tsub{2}, N3, C8--H6 and C13--H10
fragments (Figure~\ref{fig4}). In isomers 1 and 3, the HOMO is also
localized over almost the whole molecule except for the N4, N5, C6--H4
and C11--H8 fragments in \textbf{1w} and \textbf{1g}, and C6--H4 and
C11--H8 fragments in \textbf{3w} and \textbf{3g}, respectively
(Figure~\ref{fig4}). In isomers 2, the HOMO is located over the whole
triazine--NH\tsub{2} fragment, one of the pyridine rings, and the
C11--H8 group and C4--N4 fragments of the second pyridine ring
(Figure~\ref{fig4}). The density-of-states (DOS) plots of the discussed
NH\tsub{2}Py\tsub{2}T isomers are shown in Figure~S3 in the
Supplementary Material.

\begin{figure*}
\includegraphics{fig04}
\caption{\label{fig4}The HOMO and LUMO of the NH\tsub{2}Py\tsub{2}T
isomers. Results under 0.02 a.u. isovalue.}
\end{figure*}

Corrosion inhibition properties of a compound can be inferred from the
HOMO and LUMO values~\cite{71,72,73,74,75}. Corrosion inhibition is of
importance considering metallic implants~\cite{76,77,78}. In this
regard, we have investigated the ability of the NH\tsub{2}Py\tsub{2}T
isomers to inhibit corrosion in a set of metals, which are actively
used in biomedical implants (Table~\ref{tab2})~\cite{78}, using the
work function ($\rmPhi$)~\cite{79}. Of all the metals studied, it was
established that the isomers are active toward Ni, Au and Co
(Table~\ref{tab2}).

Molecular electrostatic potential (MEP) was calculated for all
NH\tsub{2}Py\tsub{2}T isomers to establish nucleophilic and
electrophilic regions of the molecule. The MEP surface revealed the
triazine and pyridine nitrogen atoms, which form either a bpy- or
terpy-like pocket, as the most pronounced nucleophilic centers, and the
amine hydrogen atoms as the most electrophilic region (Figure~S4 in the
Supplementary Material).

The absorption spectra calculated for the NH\tsub{2}Py\tsub{2}T isomers
each contain bands exclusively in the UV region up to ${\sim}$350 nm
(Figure~\ref{fig5}). In particular, the spectra exhibit an intense
narrow band at ${\sim}$185 nm and a broad band of about half intensity
centered at ${\sim}$250--260 nm (Figure~\ref{fig5}). The main transitions
responsible for the observed bands are given in Table S4 in the
Supplementary Material.

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig05}
{\vspace*{2pt}}
\caption{\label{fig5}The calculated absorption spectra of the
NH\tsub{2}Py\tsub{2}T isomers.}
{\vspace*{2pt}}
\end{figure*}

The values of $I$ and $A$ (Table~\ref{tab2})~\cite{80} for the
NH\tsub{2}Py\tsub{2}T isomers indicate their electron-acceptor nature,
which is also supported by the corresponding chemical potentials
(${\mu}$) (Table~\ref{tab2}). A low $\eta$ value together with a
relatively high $S$ value indicate that the isomers tend to exchange
their electron cloud with the surrounding environment
(Table~\ref{tab2})~\cite{80}. The value of $\omega$ is about 4.90--4.97
eV and 4.39--4.42 eV for \textbf{1w--3w} and \textbf{1g--3g},
respectively (Table~\ref{tab2}), indicating their strong electrophilic
nature~\cite{81}. The $\Updelta N_{\max}$ values show that the isomers
can accept ${\sim}$2 electrons (Table~\ref{tab2}).
\looseness=-1

In the calculated ${}^{1}$H NMR spectra of the reported
NH\tsub{2}Py\tsub{2}T isomers, signals for the amine hydrogen atoms are
observed at 5.36--5.43 ppm for \textbf{1w--3w}, and, as expected,
upfield-shifted up to 4.66--5.01 ppm in the spectra of \textbf{1g--3g}
(Table S5 in the Supplementary Material). The signals for protons H4
and H8, or H5 and H9 are shown at 7.68--8.17 or 7.29--7.84~ppm in the
spectra of \textbf{1w--3w} or \textbf{1g--3g}, respectively \mbox{(Table S5}
in the Supplementary Material). The signals for the remaining protons,
viz. H3, H6, H7, and H10, are significantly downfield-shifted and found
at 8.94--9.55~ppm (Table S5 in the Supplementary Material). For H6 and
H10, this shift is explained by the influence of the neighbouring
electronegative nitrogen atom, thus leading to deshielding, while the
H3 and H7 signals are downfield-shifted due to participation in the
C--H${\cdots}$N hydrogen bonds described above.
Notably, the calculated ${}^{1}$H NMR spectra of \textbf{1w} and
\textbf{3w} are in good agreement with the experimental ${}^{1}$H NMR
spectrum of NH\tsub{2}Py\tsub{2}T recorded in DMSO-$d_{6}$ except for
the signal of the NH\tsub{2} protons~\cite{49}, which is obviously due
to their acidic nature.

We have also examined the potential nonlinear optical properties of
\textbf{1w--3w} and \textbf{1g--3g}, (Table S6 in the Supplementary
Material). Regarding the calculated dipole moment (${\upmu}$), the
isomers ranked as follows: $3>1>2$. Notably, for isomers 1 and 3, the 
$\upmu_{y}$ component is the main contributor to the overall dipole
moment, while it is $\upmu_{x}$ for isomers 2 (Table S6 in the
Supplementary Material). Such an increase in dipole moment from isomers
2 through isomers~1 to isomers 3 is due to increasing charge disparity
on the corresponding MEP surfaces (Figure~S4 in the Supplementary
Material). The calculated polarizability (${\upalpha}$) and first-order
hyperpolarizability (${\upbeta}$) for the NH\tsub{2}Py\tsub{2}T isomers
are about 7.9--10.8, except for \textbf{1g} (Table~S6 in the
Supplementary Material). These values are higher to those of urea
(Table S6 in the Supplementary Material), which is a common
reference~\cite{82}. For \textbf{1g}, the first-order
hyperpolarizability parameter is about 10 times lower than that of urea
(Table S6 in the Supplementary Material).

According to ProTox-II~\cite{64,65}, NH\tsub{2}Py\tsub{2}T was
predicted to belong to toxicity class 4 (Figure~\ref{fig6}), and could
target the following classes: kinase, oxidoreductase, family C G
protein-coupled receptor, ligand-gated ion channel, and other cytosolic
protein with probabilities 46.7\%, 33.3\%, 6.7\%, 6.7\% and 6.7\%,
respectively (Figure~\ref{fig6}). NH\tsub{2}Py\tsub{2}T was also
predicted to be hepatotoxic, and active towards Aryl hydrocarbon
Receptor (AhR) and Estrogen Receptor Alpha (ER) (Figure~\ref{fig6}).

\begin{figure*}
\includegraphics{fig06}
\caption{\label{fig6}(Top left and bottom) Toxicity results of
NH\tsub{2}Py\tsub{2}T calculated by ProTox-II. (Top right) Druggability
predictions of NH\tsub{2}Py\tsub{2}T calculated by SwissADME.}
\end{figure*}

The SwissADME bioavailability radar~\cite{62} indicates that
NH\tsub{2}Py\tsub{2}T is favored in five parameters but has a poor
result in the insaturation parameter (Figure~\ref{fig7}), which is
obviously due to the absence of the sp\tsup{3}-hybridized carbons. The
BOILED-Egg method is powerful to predict the human blood--brain barrier
(BBB) penetration and gastrointestinal absorption (GA)~\cite{63}. The
dot position for NH\tsub{2}Py\tsub{2}T \mbox{indicates} a low absorption
probability for BBB and high for GA with blue indicating a possible
substrate of the P-glycoprotein (Figure~\ref{fig7}).

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig07}
{\vspace*{2pt}}
\caption{\label{fig7}(Left) Bioavailability radar for
NH\tsub{2}Py\tsub{2}T (colored zone is the suitable physicochemical
space for oral bioavailability). (Right) BOILED-Egg model of
NH\tsub{2}Py\tsub{2}T.}
{\vspace*{8pt}}
\end{figure*}

We have also studied potential inhibition properties of
NH\tsub{2}Py\tsub{2}T toward a series of SARS-CoV-2 proteins using a
molecular docking approach~\cite{83,84,85}. Notably, the structures
optimized under water solvation (\textbf{1w--3w}) were investigated as
potential inibitors of the herein-selected series of proteins and
similar docking results were obtained. It was found that
NH\tsub{2}Py\tsub{2}T is active against all the tested SARS-CoV-2
proteins and the best binding score was found for Nonstructural protein
3 (Nsp3-MES) (Table~\ref{tab3}). Furthermore, according to our results,
NH\tsub{2}Py\tsub{2}T shows significantly higher absolute values of
binding energy compared to Favipiravir and Aspirin, but inferior to
Remdesivir and all the redocked initial ligands except for the complex
of Nsp3-MES with the corresponding initial ligand 
(Table~\ref{tab3})~\cite{31}. Interactions responsible for the binding
of NH\tsub{2}Py\tsub{2}T with the studied proteins are shown in
Figure~\ref{fig8} and collected in Table S7 in the Supplementary
Material.

%tab3
\begin{table*}
\caption{\label{tab3}The best poses of NH\tsub{2}Py\tsub{2}T inside the
binding sites of the listed proteins}
\tabcolsep=2.5pt
\begin{tabular}{ccccccc}
\thead
Protein & PDB code & Initial ligand$^{\mathrm{a}}$ &
NH\tsub{2}Py\tsub{2}T &  Favipiravir & Aspirin & Remdesivir \\ 
\endthead
Main protease (Mpro) & 6LU7 & ${-}$8.00 & ${-}$6.9(0) & ${-}$4.70 & ${-}$5.40 & ${-}$8.10 \\ 
Papain-like protease (PLpro) & 6WUU & ${-}$9.70 & ${-}$6.8(0) & ${-}$5.30 & ${-}$5.30 & ${-}$8.70 \\ 
Nonstructural protein 3 (Nsp3-AMP) & 6W6Y & ${-}$7.50 & ${-}$6.8(1) & ${-}$4.60 & ${-}$5.60 & ${-}$7.50 \\ 
Nonstructural protein 3 (Nsp3-MES) & 6W6Y & ${-}$5.80 & ${-}$7.4(0) & ${-}$5.60 & ${-}$6.20 & ${-}$8.50
\botline
\end{tabular}                                                                                                             
\tabnote{$^{\mathrm{a}}$(From top to bottom) Initial ligand $=$\ 
$N$-[(5-methylisoxazol-3-yl)carbonyl]alanyl-$L$-valyl-$N
\sim$1${\sim}$-((1$R$,2$Z$)-4-(benzyloxy)-4-oxo-1-\{[(3$
R$)-2-oxopyrrolidin-3-yl]methyl\}but-2-enyl)-$L$-leucinamide, 
methyl\break 4-[2-[[(2${\sim}$\{$S$\})-2-[[(2${\sim}$\{$S
$\})-2-acetamido-4-(1,3-benzothiazol-2-yl)butanoyl]amino]-3-azanyl-propanoyl]{\ubreak}amino]ethanoylamino]butanoate,
[(2$R$,3$S$,4$R$,5$R$)-5-(6-aminopurin-9-yl)-3,4-bis(oxidanyl)oxolan-2-yl]{\ubreak}methyl 
dihydrogen phosphate, 2-morpholin-4-ium-4-ylethanesulfonate.}                                                                                                                         
\end{table*}

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig08}
{\vspace*{2pt}}
\caption{\label{fig8}Views on the interaction of NH\tsub{2}Py\tsub{2}T
with (from left to right) Mpro, PLpro, Nsp3-AMP and Nsp3-MES.}
{\vspace*{2pt}}
\end{figure*}

Using molecular dynamics simulations, we have evaluated interactions in
complexes of NH\tsub{2}Py\tsub{2}T with the tested SARS-CoV-2 proteins.
In particular, complex with Mpro showed an RMSD around 0.3 nm with an
average value of 0.299 nm (Figure~\ref{fig9}). However, complexes of
NH\tsub{2}Py\tsub{2}T with Nsp3-AMP and Nsp3-MES showed a higher RMSD
around 0.4 nm with average values of 0.392 and 0.364 nm, respectively
(Figure~\ref{fig9}). Notably, complex of NH\tsub{2}Py\tsub{2}T with
\mbox{PLpro} showed a much higher RMSD over the simulation time reaching
approximately 2.8 nm with an average value of 1.566 nm
(Figure~\ref{fig9}). Thus, the latter complex is unstable. The RMSF
values for complexes of NH\tsub{2}Py\tsub{2}T with Mpro, Nsp3-AMP and
Nsp3-MES were below 0.511, 0.389 and 0.534 nm, respectively
(Figure~\ref{fig9}). The strongest fluctuations of amino acid residues
for each complex are listed in Table S8 in the Supplementary
Information. Rg values for complexes of NH\tsub{2}Py\tsub{2}T with
Mpro, Nsp3-AMP and Nsp3-MES form relatively stable profiles
(Figure~\ref{fig9}), with values in ranges 2.173--2.287, 2.319--2.475
and 2.317--2.489 nm, respectively. The SASA profiles were obtained to
assess the interaction between complexes and solvents. As a result, the
binding of NH\tsub{2}Py\tsub{2}T to Mpro, Nsp3-AMP and Nsp3-MES did
not impair the stability of the proteins and interaction of the
proteins with the solvent molecule (Figure~\ref{fig9}). The average
SASA was found as 148.44, 163.15 and 163.43 nm\tsup{2} for complexes
of NH\tsub{2}Py\tsub{2}T with Mpro, Nsp3-AMP and Nsp3-MES,
respectively. Complexes of NH\tsub{2}Py\tsub{2}T with Mpro, Nsp3-AMP
and Nsp3-MES, mainly, form one intermolecular hydrogen bond \mbox{during} the
simulation time and two with a much lower frequency
(Figure~\ref{fig9}).

\begin{figure*}
{\vspace*{2pt}}
\includegraphics{fig09}
{\vspace*{2pt}}
\caption{\label{fig9}RMSD, RMSF, Rg, SASA and intermolecular hydrogen
bonds analysis profiles of complexes of NH\tsub{2}Py\tsub{2}T with
Mpro, PLpro, Nsp3-AMP and Nsp3-MES.}
{\vspace*{2pt}}
\end{figure*}

\section{Conclusions}\label{sec4}

In this work, we have performed in silico analyses of
2-amino-4,6-bis(2-pyridyl)-1,3,5-triazine (NH\tsub{2}Py\tsub{2}T) using
DFT. According to the conformational analysis, it was found that three
different isomers, \mbox{depending} on the orientation of the pyridine rings,
are the most favorable in both gas phase and water. Under water
solvation, \textbf{1w} was found to be the most energetically
favorable, while \textbf{2w} and \textbf{3w} are 0.12 and 0.44~kcal/mol
less favorable. In gas phase, \textbf{2g} was found most favorable,
while \textbf{1g} and \textbf{3g} are 0.28 and 2.25~kcal/mol less
favorable. It was also established that under water solvation
conditions the corresponding isomers are about 11--13 kcal/mol more
favorable in comparison to gas phase. The global chemical reactivity
descriptors of the studied NH\tsub{2}Py\tsub{2}T \mbox{isomers} allowed to
assess their electron-accepting and -donating features. The calculated
polarizability and first-order hyperpolarizability parameters of all
the isomers, except for \textbf{1g}, are higher in comparison to those
of urea, which is a commonly used reference.

ADMET properties were predicted using SwissADME, BOILED-Egg and
ProTox-II. It was found that human blood--brain barrier penetration is
unlikely and gastrointestinal absorption likely with
NH\tsub{2}Py\tsub{2}T predicted to be substrate of the P-glycoprotein.
NH\tsub{2}Py\tsub{2}T was predicted to be hepatotoxic and active
towards Aryl hydrocarbon Receptor (AhR) and Estrogen Receptor Alpha
(ER).

According to in silico molecular docking results, NH\tsub{2}Py\tsub{2}T
is active toward all the studied SARS-CoV-2 proteins. The best binding
of NH\tsub{2}Py\tsub{2}T was found with Nsp3-MES. Molecular dynamics
simulation showed that NH\tsub{2}Py\tsub{2}T forms stable complexes
with Mpro, Nsp3-AMP and Nsp3-MES, while its complex with PLpro is
unstable.

\section*{Declaration of interests}

The author does not work for, advise, own shares in, or receives funds
from any organization that could \mbox{benefit} from this article, and has
declared no affiliations other than their research organizations.

\back{}

\section*{Supplementary data}

Supporting information for this article is available on the journal's
website under \printDOI\ or from the author.

\CDRsupplementaryTwotypes{supplementary-material}{\cdrattach{crchim-290-suppl.pdf}}

\bibliographystyle{crchim}
\bibliography{crchim20230809}
\refinput{crchim20230809-reference.tex}

\end{document}
