Introduction

Inclusion complex is the focus of current host-guest chemistry and supramolecular chemistry [1–5]. Experimental [6–8] and theoretical [9–13] investigations on this topic have been actively pursued for decades. Particularly, studies on searching the desired host molecules dominate the scene. Many examples of host molecules, such as cyclodextrins (CDs) [14–16], macrocyclic antibiotics [17, 18], proteins [19] and chiral micelles [20] are available now. The representative host molecule cyclodextrins (CDs) have received much attention because they can separate many enantiomers by forming inclusion complexes with specific guest molecules [21, 22], this characteristic has been successfully applied to many fields including solubility enhancement, drug delivery, chemical protection, separation technology, and supramolecular chemistry [23, 24]. Another reason of the popularity of CDs is that the high symmetry and rigidity of their structures facilitate the study of inclusion complexes by NMR techniques [25]. However, this lack of conformational flexibility is a limitation regarding efficiency of inclusion complex. It’s difficult for the CDs molecules to adjust their geometries to fit the guest molecules in an optimal interaction mode. Notably, these conformational disadvantages of CDs are just good qualities for cyclic peptides which are polypeptide linked by amino acid residues. In recent years, cyclic peptides have been synthesized and used as anticancer, antimalarial, antibacterial drug carriers and enzyme inhibitors, where they act as host molecules to form inclusion complexes with biological molecules [26–29].

Understanding the structural details of the inclusion complexes of cyclic peptides with guest molecules may help us delineate the features that are responsible for the remarkable potency of cyclic peptides. However, knowledge of the precise interaction mechanism of cyclopeptides with enantiomers of a chiral molecule at the molecular level is still very limited [30]. Especially, conformations and structures of cyclic peptides are not yet clear experimentally. Some theoretical studies on the structures of cyclic peptides have been performed over the past several years [31–34]. Guangju Chen and co-workers have reported the structural characteristics of an important type of cyclopeptides formed by cyclo[(-β3-HGly)4-] based on density function theory (B3LYP) [35]. Their results provide us with new insights into the formation of polypeptide. Inspired by the study of Guangju Chen and co-workers on cyclopeptide, we have performed a density functional theory (DFT) study of the interactions between cyclic peptides and enantiomers, which may have much theoretical and practical importance. In the present work, we focused on the structure of model cyclic peptide derived from glycine. The glycine, as the simplest amino acid, was used to create a cyclopeptide template. Cyclic decapeptide (assigned as CDP) (shown in Chart 1a), constructed with ten identical glycines, is used as a receptor that is capable of including trapping the guest molecules inside the peptide cavity possibly caused by the conformational flexibility and noncovalent interactions.

Chart 1
figure 1

Schematic representation for the conformations of (a) cyclic decapetide (CDP) and (b) 1-phenyl-1-propanol enantiomers (E-PP)

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1-phenyl-1-propanol, a chiral molecule existing in a couple of enantiomers forms (assigned as E-PP, E = R or S, shown in Chart 1b), is a good candidate for constructing a simple model to study chiral discrimination. The separation of the enantiomers of 1-phenyl-1-propanol has already been carried out in the experiment [36]. However, the separation result is not desirable. In this work, CDP and E-PP are selected as host molecule and guest molecules, respectively, to investigate the conformational and structural features of CDP/E-PP and the interaction of CDP with E-PP.

Computational methods

The search of the energy minimum

In this paper, the selected initial structure of CDP is E-type backbone due to the E-type backbone of cyclopeptide is more stable than that of B-type when the number of amino acid residues is equal to or bigger than 10 [37].

The coordinate system used to define the inclusion process of CDP with E-PP is shown in Chart 2, which was adopted from a previous work [38]. Briefly, the CDP ring was positioned symmetrically around the Z-axis, such that all oxygen and nitrogen atoms in the glycine are in the XY plane. The E-PP molecule was docked into the cavity of CDP along with the Z-axis. Multiple initial positions were generated by movement of E-PP along the Z-axis. The relative position between CDP and E-PP was measured by the Z-coordinate of the labeled carbon atom of E-PP (shown in Chart 2). In order to find a more stable structure of CDP/E-PP, we calculated all of the structures of each E-PP molecule by scanning θ, circling around the Z-axis, at 20° intervals from -180° to 180° and scanning the Z-coordinate at 0.3 Å intervals with semi-empirical calculations (PM3), which can be currently applied in biochemical systems with its improved description of the interactions between non-bonded atoms, e.g., hydrogen bond and steric effects [39]. All of local energy minimum structures from potential energy surface (PES) by scan calculations were fully optimized at the B3LYP/3-21G level of theory [40, 41]. Subsequently, CDP/E-PP with the lowest energy obtained by B3LYP/3-21G calculations were fully optimized using the basis set of 6-31 + G(d,p). Additionally, the frequency calculations for CDP/E-PP were also carried out to verify the optimized structures to be energy minima without any imaginary frequency.

Chart 2
figure 2

Coordinate systems used to define the inclusion process (H atoms included in CDP are omitted)

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Fig. 1
figure 3

Scan of total energy of the inclusion complex of the E-PP enantiomers into CDP at different positions (z) and orientations (θ): (a) S(-)-1-phenyl-1-propanol (S-PP) and CDP; (b) R(+)-1-phenyl-1-propanol (R-PP) and CDP. The position of the E-PP molecule was determined by the Z-coordinate of the labeled carbon atom (*) in the phenyl group. θ refers to the angle of each guest molecule circling around the Z-axis of the system

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Fig. 2
figure 4

B3LYP/3-21G stabilization energy including BSSE correction of the CDP/E-PP: (a) S-PP and CDP; (b) R-PP and CDP. θ refers the start angle of each guest molecule into CDP circling around the Z-axis of the system

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Definition of the binding energy (BE)

In order to investigate the driving forces leading to CDP/E-PP between CDP and E-PP, the binding energy (BE) upon CDP/E-PP for the minimum energy structure is evaluated from the following equation.

$$ B{\mathbf{E}} = {\mathbf{E}}{\text{[CDP/E - PP}}] - {\mathbf{E}}{\text{[E - PP]}} - {\text{E[CDP]}} $$
(1)

Where, E[CDP/E-PP], E[E-PP] and E[CDP] represent the energies of CDP/E-PP, E-PP and CDP, respectively. The magnitude of BE would be a sign of the driving force toward CDP/E-PP. A negative value of BE means that the corresponding CDP/E-PP is energetically stable; the more negative the BE is, the more stable the complex is.

The deformation energies of CDP and E-PP were calculated by Eq. 2 and 3 [42].

$$ {\mathbf{DE}}{\text{[E - PP]}} = {\mathbf{E}}{\text{[E - PP]}}_{\text{sp}}^{\text{opt}} - {\mathbf{E}}{{\text{[E - PP]}}_{\text{opt}}} $$
(2)
$$ {\mathbf{DE}}{[}{\mathbf{CDP}}{]} = {\mathbf{E}}{[}{\mathbf{CDP}}]_{\text{sp}}^{\text{opt}} - {\mathbf{E}}{{[}{\mathbf{CDP}}{]}_{\text{opt}}}, $$
(3)

where DE[E-PP] and DE[CDP] are the deformation energies of E-PP and CDP respectively; \( {\mathbf{E}}{\text{[E - PP]}}_{\text{sp}}^{\text{opt}} \) and \( {\mathbf{E}}{{\text{[E - PP]}}_{\text{opt}}} \) are the single point energy of E-PP on the configuration taken from the optimized CDP/E-PP and the energy of the optimized geometry of E-PP respectively; \( {\mathbf{E}}{[}{\mathbf{CDP}}]_{\text{sp}}^{\text{opt}} \) and \( {\mathbf{E}}{{[}{\mathbf{CDP}}{]}_{\text{opt}}} \) are the single point energy of CDP on the configuration taken from the optimized CDP/E-PP and the energy of the optimized geometry of CDP respectively.

Thermodynamic analysis for the inclusion process of CDP with E-PP

The geometries of the two inclusion complexes were fully optimized without any geometrical or symmetry constrains using the B3LYP/6-31 + G(d,p) method. The frequencies were performed for the evaluation of the enthalpy changes (ΔΗ) and Gibbs free energy changes (ΔG) of the inclusion process between CDP and E-PP.

Moreover, the electronic properties of CDP/E-PP were studied using the natural bond orbital (NBO) analysis at the B3LYP/6-31 + G(d,p) level of theory [43]. NBO calculations quantify the H-bond interactions between host and guest molecules via the determination of the stabilization energy E(2). The stabilization energy E(2) related to the delocalization trend of electrons from donor to acceptor orbital is calculated via perturbation theory. A large stabilization energy E(2) between a lone pair LP(Y) of an atom Y and an antibonding σ* (X—H) orbital is generally indicative of a strong \( {\rm X} - {\rm H} \cdots {\text{Y}} \) hydrogen bond [44]. Basis set superposition error (BSSE) of binding energies is calculated by using the counterpoise corrections method [45]. All calculations were carried out using the GAUSSIAN 03 program package [46].

Results and discussion

Most stable conformation and binding energy

Two obtained PESs are shown in Fig. 1. It can be seen that the inclusion processes of CDP with E-PP are energetically favorable. Interestingly, most of energy minima structures locate at approximately Z = 0 Å for E-PP approaches. Based on the related scanned energy minima at the level of PM3, B3LYP/3-21G calculations were performed to optimize CDP/E-PP as presented in Fig. 2. Other possible locations and angles of E-PP were examined using the B3LYP method, which were shown to be energetically less favorable and therefore not listed. Based on the B3LYP/3-21G optimized equilibrium geometries of the CDP/E-PP, calculations at the B3LYP/6-31 + G(d,p) level were then performed.

The BE values including BSSE corrections for most stable inclusion configurations are listed in Table 1. The BE values for CDP/S-PP and CDP/R-PP are -19.94 and -10.54 kJ mol-1, respectively, which demonstrate that CDP can form stable complexes with E-PP. The CDP/S-PP was more favorable than CDP/R-PP by an energy difference of 9.40 kJ mol-1, suggesting that S-PP is bound more firmly by CDP.

Table 1 The binding energies and thermodynamic parameters upon the inclusion complexes of CDP/S-PP and CDP/R-PP at the B3LYP/6-31 + G(d,p) level of theory
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Energies of the inclusion complexes

To investigate the thermodynamics of the inclusion process, the statistical thermodynamic calculations were performed at the B3LYP/6-31 + G(d,p) level of theory. The calculated results are listed in Table 1. It is obvious that the inclusion process of CDP with E-PP are exothermic judged from the negative enthalpy changes. The negative enthalpy changes also suggest that both the inclusion processes are enthalpically favorable. On the other hand, the enthalpy change of CDP/S-PP (-20.93 kJ mol-1) is about 8.30 kJ mol-1 lower than that of CDP/R-PP (-12.63 kJ mol-1). The thermodynamic results indicate that the S-PP structure is preferred to form inclusion complex with CDP based on enthalpy grounds.

One interesting feature of the guest is its conformational flexibility. A better guest conformational flexibility is favorable to the host–guest interactions, it makes it possible for the guest molecule to modify its conformation to ensure a better penetration [47]. Investigation of the deformation energy of the chosen guest E-PP at the B3LYP/6-31 + G(d,p) level of theory (as shown in Table 1) demonstrated that the deformation of S-PP requires slightly more energy to adapt conformation to fit the cavity of CDP than that of R-PP as indicated by the DE[E-PP] data of about 2.29 and 0.93 kJ mol-1 respectively. On the other hand, there are some distortion of CDP in the inclusion process as well. CDP needs 3.68 kJ mol-1 to adapt conformational adaptation for CDP/S-PP and 1.48 kJ mol-1 for CDP/R-PP, indicating that the deformation of CDP is advantageous for the inclusion complex formation.

Conformational characteristics of CDP/E-PP

The favorable structures of CDP/E-PP optimized at the B3LYP/6-31 + G(d,p) level are graphically presented in Fig. 3. Figure 3a shows that for CDP/S-PP, the phenyl of S-PP is almost totally encapsulated in the cyclic decapeptide cavity. While the OH group remains on the rim of the CDP, which is in favor of formation of H-bond with some groups of CDP. The optimized geometries reveal that there are two hydrogen bond interactions between CDP and S-PP. Figure 3b shows clearly that for the CDP/R-PP, the phenyl of R-PP are partially included in CDP and the orientation of OH group directed toward the inside of the CDP cavity, allowing the lone pair of the oxygen atom to act as an H-bond acceptor thus stabilizing the CDP/R-PP.

Fig. 3
figure 5

Energy-minimized structure obtained by B3LYP/ 6-31 + G(d,p) calculations for CDP/E-PP: (a) side view (left) and top view (right) for CDP/S-PP and (b) side view (left) and top view (right) for CDP/R-PP

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Hydrogen bond analysis and NBO analysis

To investigate the reason why geometries of CDP/E-PP are different, the hydrogen bond and NBO analyses are further performed at the B3LYP/6-31 + G(d,p) level of theory. The detailed information of intermolecular hydrogen bond interactions for CDP/E-PP are listed in Table 2 and shown in Fig. 4. It can be seen from Table 2 that the distinct differences for hydrogen bond interactions occur in the different inclusion complexes. In the CDP/S-PP structure, there are two hydrogen bond interactions. One occurs between O1 of CDP and O11 of S-PP, a strong hydrogen bond \( {\rm O}11 - {\text{H11}} \cdots {\text{O1}} \) (\( {{\text{d}}_{\text{H}}}{ \ldots_{\text{O}}} = 1.93 \)Å). The other occurs between the O11 of S-PP and C10 of CDP, a weak hydrogen bond \( {\text{C10}} - {\text{H10}} \cdots {\text{O11}} \) (\( {{\text{d}}_{\text{H}}}{ \ldots_{\text{O}}} = 2.48 \)Å). In the CDP/R-PP structure, only one weak hydrogen bond is formed. Namely, the O5 atom of CDP donates a hydrogen bond (\( {{\text{d}}_{\text{H}}}{ \ldots_{\text{O}}} = 2.22 \)Å) to O11 of R-PP. Distinctly, the intermolecular hydrogen bonds play a crucial role in the stability of inclusion complexes conformational change. It was suggested that the contribution of the \( {\rm O} - {\text{H}} \cdots {\text{O}} \) hydrogen bond interactions to the structural stability in CDP/S-PP is greater than those in CDP/R-PP. This explains why the BE for the CDP/S-PP is 9.40 kJ mol-1 lower than that of CDP/R-PP.

Table 2 The electron donors, electron acceptors and the corresponding E(2) energies, distances and angles obtained at the B3LYP/6-31 + G(d,p) level of theory
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Fig. 4
figure 6

Host–guest hydrogen bonds are presented by dotted lines: (a) CDP/S-PP and (b) CDP/R-PP. H in white, C in gray, N in blue, O in red

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The following NBO analyses confirm the occurrence of these intermolecular hydrogen bonds. The stabilization energies E(2) calculated at the B3LYP/6-31 + G(d,p) level of the established H-bond in the CDP/E-PP are listed in Table 2. Significant interaction energies are obtained for the expected hydrogen bonds, especially for the \( {\rm O} - {\text{H}} \cdots {\text{O}} \) one. The interaction energy of the \( {\rm O} - {\text{H}} \cdots {\text{O}} \) hydrogen bond of CDP/S-PP is 23.24 kJ mol-1, which is a conventional hydrogen bond (16–25 kJ mol-1 for \( {\rm O} - {\text{H}} \cdots {\text{O}} \) hydrogen bonds in carbohydrates) [48]. The interaction energy of the \( {\rm O} - {\text{H}} \cdots {\text{O}} \) hydrogen bond of the CDP/R-PP is 3.61 kJ mol-1, which belongs to a typical weak hydrogen bond for which energies vary between 2.1 and 8.4 kJ mol-1 [49]. Noteworthy, one extra \( {\text{C}} - {\text{H}} \cdots {\text{O}} \) hydrogen bond was observed for CDP/S-PP. Quantum mechanical calculations have been performed to determine the energetic of the \( {\text{C}} - {\text{H}} \cdots {\text{O}} \) bonds in the complexes, which are far below values of conventional hydrogen bonding [50, 51], but appreciably above energies of van der Waals contacts. Briefly, these hydrogen bond interactions play important roles in the inclusion processes of CDP with E-PP.

Molecular dynamics simulations

Regarding the identification of the preferred inclusion modes, it would be more realistic to select a set of inclusion complex structures, besides a single optimized configuration. Inclusion phenomena are dynamic in nature; therefore the establishment of host-guest intermolecular interactions cannot be analyzed from a single structure [52]. Perhaps, other unexplored inclusion complexes can lead to different hydrogen bonding patterns. Molecular dynamics (MD) simulations could provide such a view [53]. To obtain the possible inclusion modes between CDP and E-PP, the two guests, R-PP and S-PP, were firstly docked into CDP by using AutoDock 4.0 program [54]. The grid map of 32 × 32 × 32 points and a grid-point spacing of 0.375 Å have been employed during the dock processes. One better-scoring representative from 1000 predication inclusion models for CDP with E-PP has been selected as an initial structure for MD simulations. All MD simulations were carried out using the AMBER9 [55] package with the AMBER force fields of parm99 [56, 57] and gaff [58]. The systems were explicitly solvated by using the TIP3P water potential inside a box large enough to ensure the solvent shell extended to 10 Å in all directions of each system studied. For the equilibration of the investigated systems, the following procedures were carried out. First, 22500 steps energy minimization were carried out to remove unfavorable contacts. Then the systems were heated over 100 ps from 0 to 300 K with a little restrains of 10 kcal mol-1 Å-2. The equilibration time for each simulation was 500 ps (NPT) followed by 10 ns of data collection for trajectory analysis, that is, 5000 structures for each simulation were saved for further data analysis by uniformly sampling the trajectory.

With the help of a 10 ns long molecular dynamics, it is shown that the CDP/E-PP are stable in water environment. The detailed information of intermolecular hydrogen bonds interactions for the CDP/E-PP in the course of the simulations are listed in Table 3. The quantities and lifetimes of H-bonds reflect the ability of CDP to bind E-PP, respectively. These observations clearly show that the lifetimes and number of H-bonds for CDP/S-PP are longer and larger than those of CDP/R-PP. Specifically, the longest lifetime of H-bond for CDP/S-PP is up to 99.58% of the simulation times, while the longest lifetime of H-bond for CDP/R-PP is only 44.06% of the simulation times. Compared to R-PP, S-PP exhibits the anticipated binding propensity to associate with CDP. The MD results indicate that the CDP/S-PP system is appreciably more stable than CDP/R-PP. Briefly, the MD results support the conclusions obtained by B3LYP/6-31 + G(d,p).

Table 3 The intermolecular hydrogen bonds of CDP/S-PP and CDP/R-PP during molecular dynamics (MD) simulations
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Solvent effects

Complex phenomena take place in condensed phase. Thus, solvent plays a critical role in the intermolecular interactions that lead to the formation of inclusion complexes, especially in the case of polar compounds with hydrogen donor/acceptor groups. To consider the role of the solvent, the polarized continuum model (PCM) [59–61] has been employed to simulate the solvent effects as implemented within the solvent reaction field based on the optimized structures as listed in Table 1. As shown in Table 1, positive entropy changes (ΔSpcm) in the two inclusion processes are 106.72 and 116.69 J mol-1 K-1 respectively, which are attributed to the releasing of water molecules in the cavity of CDP. Based on the discussions above, it can be concluded that entropy effects on the stability of the CDP/E-PP are favorable factors, that is, the formations of CDP/E-PP are entropy driven processes in aqueous solution.

Conclusions

In this work, CDP/E-PP have been investigated theoretically using the density functional theory (DFT) B3LYP method. Almost all possible locations of E-PP with CDP were taken into account to obtain the most stable conformation of CDP/E-PP. The optimized structures and the binding energy (BE) indicate that CDP/S-PP is more stable than CDP/R-PP. The conformational characteristics of CDP/E-PP show that the distinct differences for hydrogen bond interactions occur in the different CDP/E-PP. For CDP/S-PP, the better stabilization may be attributed to the formation of two hydrogen bonds between CDP and E-PP. For CDP/R-PP, only one hydrogen bond has been formed between CDP and E-PP, which might account for the stabilization of CDP/E-PP. The NBO analyses confirm the occurrence of these intermolecular hydrogen bonds: the NBO results show that there is one conventional hydrogen bond and one weak hydrogen bond in the CDP/S-PP inclusion complex while there is only one weak hydrogen bond in the CDP/R-PP inclusion complex. Briefly, these hydrogen bond interactions will contribute to the overall stability and structure of the inclusion complexes of CDP with E-PP. Furthermore, the MD simulation results are in agreement with the conclusions obtained by the B3LYP/6-31 + G(d,p) method.

Additionally, the thermodynamic calculated results demonstrated that enthalpy changes (ΔΗ) are prominent in the inclusion processes. The enthalpy changes suggest that the formation of CDP/E-PP is an enthalpy driven process. Their obvious differences in binding energy and enthalpy change suggest that CDP could well distinguish E-PP. Take the solution effects into account, the entropy is still a favorable driving force for the formation of CDP/E-PP. The current studies provide a revealing insight into conformational characteristics and thermodynamics properties for CDP/E-PP at the molecular level. The observations in this work indicate that CDP is a desirable host molecule for chiral and molecular recognition.