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\begin{document}

\title{Metadynamics Simulations on the Key Factors of Handedness Induction for
the N/C-Terminal Substituted Quinoline Oligoamide Foldamers}



\author[1]{caihua zhou}%
\author[2]{zhiwei liu}%
\author[3]{yannv guo}%
\affil[1]{Xianyang Normal University}%
\affil[2]{University of the Sciences in Philadelphia Department of Chemistry and Biochemistry}%
\affil[3]{Northwest University}%


\vspace{-1em}



  
  \date{May 08, 2024}


\begingroup
\let\center\flushleft
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\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Metadynamics simulation has been used to describe the conformational
energy landscapes of several helical quinoline oligoamides bearing
\selectlanguage{greek}β-\selectlanguage{english}pinene-derived pyridine at either the C or N terminus. Based on the
experimental results, helix-sense preference for four types of foldamers
with the chiral terminal group has been verified. To compare to the key
factors of inducing handedness to helical-sense preference, a terminal
group with three hydrogen bond sites is designed and corresponding
foldamers are built. The calculated results show the delocalization
effect and steric hindrance mainly responsible for a particular
helix-sense preference for the investigated foldamers. The more hydrogen
bonds between the terminal group and oligoamide units are formed, the
more stable foldamers are.%
\end{abstract}%



\sloppy


Metadynamics Simulations on the Key Factors of Handedness Induction for
the N/C-Terminal Substituted Quinoline Oligoamide Foldamers

Caihua Zhou, * \textsuperscript{{[}a{]}} Zhiwei
Liu\textsuperscript{{[}b{]}} Yannv Guo\textsuperscript{{[}c{]}}

\textsuperscript{{[}a{]}}School of Chemistry and Chemical Engineer, Xian
Yang Normal University, Xianyang, Shanxi, 712000,P.R.
China.E-mail:\emph{xbdxzch@}126.com

\textsuperscript{{[}b{]}}Department of Chemistry \&Biochemistry,
University of the Sciences in Philadelphia, Pennsylvania, USA.

\textsuperscript{{[}c{]}} Institute of Physics, Northwest University,
Shanxi, 710000, P.R. China.

\textbf{Keywords:} Metadynamic, Helix, Chirality, Terminal group

Abstract: Metadynamics simulation has been used to describe the
conformational energy landscapes of several helical quinoline
oligoamides bearing \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived pyridine at either the C or
N terminus. Based on the experimental results, helix-sense preference
for four types of foldamers with the chiral terminal group has been
verified. To compare to the key factors of inducing handedness to
helical-sense preference, a terminal group with three hydrogen bond
sites is designed and corresponding foldamers are built. The calculated
results show the delocalization effect and steric hindrance mainly
responsible for a particular helix-sense preference for the investigated
foldamers. The more hydrogen bonds between the terminal group and
oligoamide units are formed, the more stable foldamers are.

1. Introduction

Today, foldamers represent a rapidly growing ensemble of molecules in
terms of diversity and chemical complexity. Foldamers can be as a bridge
between the molecular chirality and recognize of biological molecules.
Many reports have shown that foldamers display biomimetic properties on
reminiscent of allosteric proteins and receptor
molecules\textsuperscript{{[}1-3{]}}. Foldamers can translate chemical
signals into conformation changes, and hence into chemical outputs such
as control of reactivity and selectivity. Recent years, many potential
bioactive foldamers have been discovered, quinoline oligoamides have
been extensively demonstrated to adopt stable helical conformations in
various solvents. Dr. Liu and her group members had reported some
important foldamers with different terminal groups, and they found that
the helix-sense bias of foldamers can really be predicted by analysing
the interactions (hydrogen bond, steric and so
on)\textsuperscript{{[}4-6{]}}, and the chirality of terminal group
influences on the helix-sense of foldamers. A previous report found the
steric and hydrogen bonds have important influences on the helical
handedness of foldamer. So, it is benefit for the biological application
of foldamers by synthesizing new foldamers with bioactive terminal
group.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene is an optically active and racemic molecule, which
presents in turpentine oils. It was demonstrated that when \selectlanguage{greek}β\selectlanguage{english}-\selectlanguage{english}pinene
synergizes with paclitaxel, they can suppress lung carcinoma cells. The
geometrical structure of \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene with chiral atom has big space
steric hindrance, which is benefit for the synthesis of chiral
foldamers. Therefore, a lot of study has been reported on
enantio-selective of\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene derived molecular
\textsuperscript{{[}7,8{]}}. In 2017, the study that \selectlanguage{greek}\emph{β}
\selectlanguage{english}-\selectlanguage{english}pinene-derived pyridyl group can induce the handedness of oligoamide
foldamers has been reported\textsuperscript{{[}9{]}}. Experimental data
has shown that\selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived pyridyl connecting with quinoline
oligoamide behave better selection of handedness at N-terminal than at
C-terminals. They had investigated three types of foldamers, and thought
that hydrogen bond should be an obvious factors of helical handedness.
However, it is reported that hydrogen bonds, steric hindrance and
electrostatics are responsible for the helical handedness either in the
C-terminal or N-terminal in some works \textsuperscript{{[}10,11{]}}. In
order to reveal the intrinsic reason for better selection of helix-sense
at N-terminal than at C-terminal, six experimental synthesized and two
designed oligoamide foldamers substituted by \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene have been
investigated in this paper. Six synthesized oligoamides include four
foldamers containing \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived pyridyl amine at the
C-terminal (\textbf{1a, 1b, 2a,} and \textbf{2b)} , two foldamers
containing \selectlanguage{greek}\emph{β} - \selectlanguage{english}pinene-derived pyridyl carboxylic acid at the
N-terminal (3a and \textbf{3b} ). Two designed oligoamides include two
foldamers containing three-center hydrogen bonds at N-terminal
(\textbf{4a} and \textbf{4b} ). Four types of foldamers (\textbf{1-4} )
have been designed and they have been shown in \textbf{Scheme 1.} In
foldamer \textbf{1--4} , \textbf{na} represents R chirality of\selectlanguage{greek}\emph{β}
-\selectlanguage{english}pinene, \textbf{nb} represents S chirality of \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene. Because
Zheng et al. have found that these foldamers are stable in chloroform
(CDCl\textsubscript{3}), CDCl\textsubscript{3} was selected as the
solvent environment here. Based on the metadynamics simulations, the
helical handedness of four types of foldamers with\selectlanguage{greek}\emph{β}
\selectlanguage{english}-\selectlanguage{english}pinene-derived pyridine has been calculated. From the data of the
dihedral angle, rotation angle, and electronic orbitals constitutions of
foldamers, the key factors of chiral induction to\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene
substituted foldamers have been analyzed and discussed.

\textbf{Scheme 1.} The structures of the foldamer \textbf{1--4}

2. Results and Discussion

To obtain P or M helical bias of foldamers in the solvent, all
investigated foldamers were put into a chloroform box. The metadynamics
method was applied to investigate helical inversion of
pentameric\textbf{1--4} in chloroform, and force field parameters
specifically were optimized for the arylamides containing
quinoline-based. Computations were systematically performed on each
enantiomer to assess their reproducibility.

2.1. Helix handedness of oligomers (1a/1b) substituted by\selectlanguage{greek}\emph{β}
-\selectlanguage{english}pinene-derived pyridyl amine at C-terminal\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

Metadynamics studies of \textbf{1a/1b} (quinoline oligoamide pentamers
substituted by \selectlanguage{greek}β-\selectlanguage{english}pinene-

\textbf{Figure 1.} The free-energy profile of \textbf{1a} \textbf{Figure
2.} The structure of \textbf{1a}

derived pyridyl amine at C-terminal) indicated the same helical bias as
the experimental results. \textbf{1a} possesses a (R) --\selectlanguage{greek}\emph{β}
-\selectlanguage{english}pinene-derived pyridyl amine (Figure 1 right), yields a P helix as the
global minimum. From the free-energy profile (FEP) of\textbf{1a} , it
can see that P helix has about 2.3 kcalmol\textsuperscript{-1} minima
free energy. The free-energy of M helix is 3.7
kcalmol\textsuperscript{-1} in \textbf{1a} , the energy gap is 1.4
kcalmol\textsuperscript{-1}, so the helical selectivity of 1\textbf{a}
is not obvious. And \textbf{1b} has the same case\textbf{,}for
\textbf{1b} (enantiomer of \textbf{1a} )\textbf{,} the M helix are more
stable than P helix. \textbf{1b} possesses a (S) --\selectlanguage{greek}\emph{β}
-\selectlanguage{english}pinene-derived pyridyl amine \textsuperscript{(}Supporting Information
S1), yields an M helix as the global minimum, and minimum energy is
about 2.08 kcalmol\textsuperscript{-1}. The free-energy of P helix is
3.5 in \textbf{1b.} Therefore, the helix handedness of\textbf{1a/1b} is
mainly induced by the carbon atomic chirality of\selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived
pyridyl amine. The structural features of the (P)-\textbf{1a}
/(M)-\textbf{1b} were conducted by extracting conformations from the
M-and P-helix using the 400 ns metadynamics trajectories. From the most
stable structure of \textbf{1a} and\textbf{1b} (Supporting Information
S2), it can get following structural parameters. The helical pitch of
\textbf{1a} and \textbf{1b} is 3.5 \selectlanguage{ngerman}Å and 3.6 Å. The terminal group
(\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene-derived pyridyl amine) did not form any hydrogen bonds
with quinoline oligoamide. That is, the hydrogen bond can not affect the
helical handedness in\textbf{1a/1b} . Based on the analysis of the
stable conformations of\textbf{1a/1b} , the two methyl groups of
\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene both rotate to the out of helix, which can decrease the
steric hindrance. Thus, the different between P and M is only from the
angle degree of
[?]N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A} (figure 1
right) and [?]C\textsubscript{Q}-C\textsubscript{Q}-N\textsubscript{A}-C.
The figure 3 shows the structural analysis of \textbf{1a} . From Figure
3, it can see that the angle peaks of
[?]N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A} lie at \selectlanguage{ngerman}±17°
and \selectlanguage{english}[?]C\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-N\textsubscript{A}\selectlanguage{english}-C lies at
+-180deg for \textbf{1a} . The frequency of occurrence of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} is bigger
than that of
\selectlanguage{english}[?]C\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-N\textsubscript{A}\selectlanguage{english}-C, it is
revealed that the
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} obviously
determined the helix bias sense of foldamer. From Figure \textbf{4} , it
can see that the angle

\textbf{Figure 3.} Dihedral angle distributions of \textbf{1a Figure
4.}The frequency of occurrence for

\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} in\textbf{1a
and 1b}

peaks of \selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} are
17deg in P-\textbf{1a} and P-\textbf{1b} , and it is -17deg in
\textbf{M-1a}and \textbf{M-1b.} It
means\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} do
significantly influence the helix handedness of foldamer. Because there
is not formation of hydrogen bond between the terminal group and
quinoline oligoamide, the steric hindrance effect and chiral atom should
be the important factors on the helix handedness of \textbf{1a/1b} .

\textbf{2.2.} \selectlanguage{greek}\textbf{Helix handedness of \emph{β}-pinene-derived
pyridyl amine substituted oligomers 2a/2b at C-terminal}\selectlanguage{english}

To find the proof of hydrogen bonds on the helix-sense bias of foldamer,
Zheng {[}9{]} et al had synthesized the other foldamer \textbf{2} , in
foldamer \textbf{2} , hydrogen bond O--H-N\textsubscript{A} is formed
between terminal group and quinoline-based amine (Figure 5). However,
they found that the hydrogen bond O--H-N\textsubscript{A} cannot enhance
the helix-sense bias of foldamer. So we built foldamer\textbf{2}
according to the experimental data and performed the dynamic
calculation. From the results of metadynamics calculations, it can see
that free-energy of \textbf{2a} (Supporting information S3)
and\textbf{2b} only has little change compared to \textbf{1a}
and\textbf{1b} , \textbf{2b} shows M helix with the global minimum, the
minimum free-energy is about 2.47 kcalmol\textsuperscript{-1} (Figure 6
). And the free-energy gap of \textbf{M} and \textbf{P} is 2.1
kcalmol\textsuperscript{-1}in \textbf{2b} . The structural parameters
of\textbf{2a/2b} are similar to those of \textbf{1a/1b} . The helical
pitch of \textbf{2a} and \textbf{2b} is 3.62 and 3.56\selectlanguage{ngerman}Å, and the R
chirality of\selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene still induces a P helix, and S chirality
induces the M helix in \textbf{2b} (Supporting information S4). Due to
the similar structural parameters and free-energy gap between
\textbf{1a/1b and 2a/2b} , it means that the hydrogen bond
O--H-N\textsubscript{A} does not obviously improve the selection of
foldamer \textbf{2a/2b} .\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image7/image7}

\end{center}
\end{figure}

\textbf{Figure 5.} The structure of foldamer \textbf{2b} \textbf{Figure
6} . Free-energy profile of

\textbf{2b}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image9/image9}

\end{center}
\end{figure}

Of course, the distribution of dihedral angle
[?]N\textsubscript{Q}\textbf{-} C\textsubscript{Q}\textbf{-}
C-N\textsubscript{A}and
[?]C\textsubscript{Q}-C\textsubscript{Q}-N\textsubscript{A}-C can make a
distinction between the chirality of \textbf{2a} and \textbf{2b} . From
Figure 7, it can be seen that the angle peaks of
[?]N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A} at \selectlanguage{ngerman}±10° for
(P)-\textbf{2a} /(M)-\textbf{2b} . The angle peaks of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A}
for\textbf{2a/2b} are less than that in \textbf{1a/1b} , it due to two
three-center hydrogen bonds O--H\selectlanguage{english}-N\textsubscript{A} and
N\textsubscript{Q}--H\selectlanguage{english}-N\textsubscript{A} improve the coplanar of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A}(Figure 8).
Based on above analysis, it shows that atomic chirality is the main
factor on the helical selection of \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived pyridyine

\textbf{Figure} \textbf{7.} The three-center hydrogen bond in
\textbf{2b. Figure 8.} The frequency of occurrence for
N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A} in\textbf{2a}
and \textbf{2b}

substituted foldamer at C-terminal, and hydrogen bond just enhance the
stable of foldamers \textbf{2a/2b} . However, the experimental found
that the N-terminal substituted foldamers have better helical selection
than C-terminal substituted foldamers. What is the intrinsic reason?

\selectlanguage{greek}\textbf{2.3Helix-handedness bias of\emph{β}-pinene-derived pyridyl
carboxylic acid-substituted oligomers 3a/3b at N-terminal}\selectlanguage{english}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image10/image10}

\end{center}
\end{figure}

\textbf{3}is the \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene-derived pyridyl carboxylic acid
substituted quinoline oligoamide foldamer at N-terminal. The
computational results show that the free-energy difference is 4.77
kcalmol\textsuperscript{-1} between P\textbf{-3a} and M-\textbf{3a} .
The R chirality of terminal atom still induces the P helix and S
chirality of terminal atom still induces the M helix(Supporting
information S6).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image11/image11}

\end{center}
\end{figure}

\textbf{Figure 9} . The structure of \textbf{3a Figure 10.} The FEP
graph of \textbf{3a}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image12/image12}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image16/image16}

\end{center}
\end{figure}

Foldamer \textbf{3a} (Figure 9) is consistent with \textbf{1a}
and\textbf{2a} , and the helical pitch is 3.52\selectlanguage{ngerman}Å and 3.74 Å.Two
three-center hydrogen
bonds(N\selectlanguage{english}\textsuperscript{*}--H\selectlanguage{english}-N\textsubscript{A}and
N\textsubscript{A}\selectlanguage{english}-H--N\textsubscript{Q}) were formed between the
terminal \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene-derived pyridyl carboxylic with quinoline
oligoamide, the hydrogen bonds length are 2.28 \selectlanguage{ngerman}Å and 2.09 Å, the bond
angles are 107.9° and 106.8°, respectively. Interestingly, the
distribution of
N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} shows that
angle peaks at +-10deg, which is consistent with \textbf{2} . That is,
three-center hydrogen bonds do improve coplanar of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A}. Next, the
investigation was locked at the character of dihedral angle \selectlanguage{english}[?]N*\selectlanguage{english}-C*\selectlanguage{english}-C=O
in \textbf{3a.} Compare with \selectlanguage{english}[?]N*\selectlanguage{english}-C*\selectlanguage{english}-N\selectlanguage{english}-H dihedral angle in \textbf{1}
and\textbf{2} , rotation of \selectlanguage{english}[?]N*\selectlanguage{english}-C*\selectlanguage{english}-C=O is more difficult than that of
\selectlanguage{english}[?]N*\selectlanguage{english}-C*\selectlanguage{english}-N\selectlanguage{english}-H. In addition, the electronic delocalization effect was found
between bond C=O and pyridine ring of terminal group. The delocalization
can be proved by three bonds length. As Figure 11 shows that
\textbf{3a}and \textbf{1a} has the same bonds
N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}, C\textsubscript{Q}\selectlanguage{english}-C, and
C\selectlanguage{english}-N\textsubscript{A}, but the bonds length of
N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}, C\textsubscript{Q}\selectlanguage{english}-C, and
C\selectlanguage{english}-N\textsubscript{A} are 1.3521 A, 1.4972 A and 1.3720 A in \textbf{3a}
, respectively, which are shorter than those in \textbf{1a} (1.3698,
1.5529, and 1.4330). Furthermore, the orbital properties of the terminal
group also show the delocalization properties of terminal group
in\textbf{3a} . The terminal group has contributions in the HOMO orbital
of\textbf{3a} , but terminal group has no contribution in the HOMO
orbital of \textbf{1a} (Figure 12). It is worthwhile noting that a
metastable state \textbf{EPP} (Q1-Q2 is extended, Q2-Q3 and Q3-Q4 are P
helix) has been found in the FEP of \textbf{3a} (Figure 10), the
free-energy of\textbf{EPP} is about 2.7kcalmol\textsuperscript{-1}. That
is, when the P helix of \textbf{3a} converts to M helix, it needs cross
a metastable state EPP. And the metastable state also results in the big
free-energy gap between P- \textbf{3a} and M-\textbf{3a} , it is the
main reason that\textbf{3a} has better helical selection than
\textbf{1a} . Based on the above discussion, we conclude that the
electronic delocalization effect influences the selection of helical
handedness, and the delivery of chirality in the conjugated chains is
easier than in unconjugated system, which corresponds to some
experimental results \textsuperscript{{[}12-15{]}}.

\textbf{Figure 11} . The structure of
N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q} \selectlanguage{english}-C
\selectlanguage{english}-N\textsubscript{A}.\textbf{Figure 12} The HOMO orbital distribution.

\selectlanguage{greek}\textbf{2.4 Helix-handedness bias of \emph{β}-pinene-derived pyridyl
carboxylic acid-substituted oligomers 4a/4b at N-terminal}\selectlanguage{english}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image17/image17}

\end{center}
\end{figure}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image18/image18}

\end{center}
\end{figure}

From investigation of foldamer \textbf{1, 2} and \textbf{3,} it is found
that the three-center hydrogen bonds between the terminal group and
oligomers are found both in \textbf{2} and \textbf{3,} but the helical
selection is Figure 13. The FEP of \textbf{4a} Figure 14. The structure
of \textbf{4a}

better in \textbf{3} than in \textbf{2} . To further investigates the
relation between hydrogen bonds and helical

handedness of foldamers. We designed a -NH\textsubscript{2} connected
with pyridine ring of the terminal group (Scheme 1), and
-NH\textsubscript{2} formed another hydrogen bond (N-H--O) with
quinoline amide. When this modified\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene-derived pyridine
connects with N-terminal quinoline oligoamide, the foldamer
\textbf{4}were designed, and \textbf{4a/4b} represents P-helix/M-helix.
Based on the metadynamic calculation, the FEP of \textbf{4a} and
\textbf{4b} were get. The results show that R chirality of\selectlanguage{greek}\emph{β}
\selectlanguage{english}-\selectlanguage{english}pinene still induced the P helix, S chirality still induced M helix.
FEP shows that the difference between the free-energy P-\textbf{4a} and
M-\textbf{4a} is 6.7 kalmol\textsuperscript{-1}, there is the bigger
free-energy gap for\textbf{4} than for \textbf{3} (Figure 13). When the
R-chiral atom induces the P type structure, the new hydrogen bond N-H--O
is formed. The bond length of N-H--O is 1.96 \selectlanguage{ngerman}Å with bond angle of 150°.
Thus, together with two inherent three-center hydrogen bonds
(N\textsubscript{Q}--H\selectlanguage{english}-N\textsubscript{A} and
N\selectlanguage{english}\textsuperscript{*}--H\selectlanguage{english}-N\textsubscript{A}), there are three hydrogen
bonds in \textbf{4a} (Figure 14). When the angle
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} is rotated,
which needs overcome a big free-energy barrier due to three hydrogen
bonds are destroyed. It is proved the more hydrogen bonds of the
terminal group, the more stability of foldamer \textbf{4} . In another
hand, the rotation of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A}can induce
another hydrogen bond N--H\selectlanguage{english}-N\textsubscript{A}, the hydrogen bond length
is 1.789 A, the bond angle is 109deg. So there should have a stable
conformer\textbf{4c} (Supporting information S7). The distributions of
dihedral angle show the angle peaks of
\selectlanguage{english}[?]N\textsubscript{Q}\selectlanguage{english}-C\textsubscript{Q}\selectlanguage{english}-C\selectlanguage{english}-N\textsubscript{A} at +-10degfor
(P)-4a/(M)-4b. And a metastable state \textbf{EPP} also is found in FEP
of \textbf{4a} , the minimum free-energy of \textbf{EPP} is
4.3kcalmol\textsuperscript{-1}, and it is similar to foldamer \textbf{3}
. From the calculated data, it can see that the chiral\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene
connect with oligomers at N-terminal has the better selection of helix
than at the C-terminal. The reason mainly comes from two aspects, one
reason is that delocalization effect is found between\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene
derivatives with quinoline oligomers at N-terminal (foldamer \textbf{3}
and \textbf{4)} , and the delocalization effect improves the delivery of
chirality, resulting in the better helical selection of \textbf{3} and
\textbf{4} than \textbf{1} and\textbf{2} (\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene substituted
at C-terminal). Another reason is that \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene has big steric
hindrance, it is difficult to rotate between different helical
handedness once there are more hydrogen bonds. For foldamer \textbf{3a}
, the delocalized bond improved the selection of chirality,
delocalization effect is the key factors. The free-energy gap of
\textbf{4a} became the bigger than that of \textbf{3a} , which is due to
the more hydrogen bond to strengthen the helical stability of

\textbf{4a.}

\textbf{3. Conclusion}

In conclusion, using the metadynamic methods, we prove an experiment
results that the \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene connects with quinoline oligomers at
N-terminal has the better helical induction than at C-terminal. However,
the intrinsic reason is rather electronic delocalization and steric
effect than hydrogen-bond effect. Especially, \selectlanguage{greek}\emph{β} -\selectlanguage{english}pinene is chiral
group of huge steric hindrance, which can induce the helix preference of
foldamer, but the chiral delivery of chiral atom is affected by steric
hindrance and delocalized effect. When the \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene connects
with oligomer units at the C-terminal, the dihedral angle
[?]N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A} is far away
from chiral carbon of pinene, which cannot effectively induce the helix
bias of foldamer. Even an additional hydrogen bond is added at
C-terminal, which still no obviously improve the helical selection. That
is, for foldamer \textbf{1} and \textbf{2} with \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene
derivative at C-terminal, the hydrogen bonds rarely affect the helical
selection of foldamer. When the \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene connects with it at
N-terminal, chiral carbon of \selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene can form the conjugated
bond with
N\textsubscript{Q}-C\textsubscript{Q}-C-N\textsubscript{A}bond, it is
benefit for the delivery of chirality. The chiral\selectlanguage{greek}\emph{β} \selectlanguage{english}-\selectlanguage{english}pinene forms
the more hydrogen bonds with quinoline oligoamide, the foldamers are
more stable. Therefore, the free-energy profiles (FEPs) of \textbf{1--4}
show that there is a small free energy barrier between P and M for
foldamers \textbf{1} and \textbf{2} , but in FEPs of\textbf{3} and
\textbf{4,} free-energy has large difference between P and M, the
foldamer \textbf{4a} with more hydrogen bond has the bigger free-energy
gap between P helix and M than \textbf{3a} has.

\textbf{4. Experimental Section}

We carried out all-atom molecular dynamic simulations (300--500 ns) in
chloroform. Combined with the metadynamics free-energy method, force
field parameters specifically optimized for the quinoline-based
arylamides was calculated by our method \textsuperscript{{[}16,17{]}}.
This method accelerates the simulation by adding small repulsive
potentials (``hills'') to the underlying free energy landscape, thus
gradually biasing the system to escape energy minima and explore the
wide conformational space. From metadynamics simulations, we determined
the free energy of the oligomers with respect to two Control Variables
(CVs) to generate two-dimensional free free-energy profiles (FEPs). At
least one CV in each metadynamics simulation is chosen to be a pitch
dihedral angle. This angle defined by the centers of masses of four
consecutive quinoline rings (``Q'') (Scheme 1). Identify the handedness
of the helix: a positive dihedral angle for right-handed (P) and a
negative angle for left-handed (M) helices. The metadynamics
computational methods had been successfully used to predict and explain
helix handedness bias in the context of helically folded aromatic
oligoamides in previous reports. All simulations were carried out using
the AMBER-18 package \textsuperscript{{[}18{]}}.

\textbf{Acknowledge}

This project was supported by the Shaan'xi Provincial Education
Department Project (No. 18JK0836), Undergraduate Training Programs for
Innovation (No. 201828004) and the Teaching Reform Project (No.
2017Y007).

Received: ((will be filled in by the editorial staff)) Revised: ((will
be filled in by the editorial staff)) Published online: ((will be filled
in by the editorial staff))

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