Introduction

The present work is an application of density functional theory (DFT) [1] for investigation of cyclic trimerization involving imidazole based heterocyclic amino acids. Two different density functionals, B3LYP [2] and B97D [3] are used in the work, intended to study the role of long range correlation effects in predicting minimum energy conformations. For molecular systems separated by van der Waals distances, where electronic overlap is fairly large [4], accurate measurement of long range correlation energy improves reliability of results. Grimme et al. [3] and Jurecka et al. [5] have developed dispersion corrected, DFT-D, functionals for better description of the systems where damped dispersion interactions are significant. The functionals also describe contribution of intramolecular dispersion for larger molecules [4]. Several studies on polypeptides show that energy ordering of conformations has become much better after inclusion of the dispersion corrections [6–10]. The functional, B3LYP, includes long range non-covalent interactions (at distances > 5 Å) through Hartree-Fock exchange but remain local in correlation [11]. The functional does not describe the R −6 asymptotic distance dependence of the dispersion forces [11]. Zhao et al. have reported that B3LYP functional often provides inaccurate hydrogen bond energies [12]. To include the effect of long range dispersion interactions in energetics of the systems, dispersion corrected functional, B97D, was used, besides the functional, B3LYP, in the current study. The long range correlation interaction estimated by B97D, accounts for improving accuracy in estimation of energy of systems compared to that by the functional, B3LYP.

Our earlier DFT study [13] reported that heterochiral cyclic trimerization of 5-(aminoethyl)-2-furan carboxylic acid is kinetically preferred over its homochiral cyclic trimerization based on results obtained from dispersion corrected functional, M06 [14]. The ability of cyclic tripeptide of chiral furan amino acids to form hydrogen bonding with solvent molecule, N, N, dimethyl formamide (DMF), enhances with change of stereochemistry at one of the three chiral amino acids in the cyclic tripeptide [13].

Importance of cyclic peptides comes from the facts that they are therapeutically potential molecules, show significant resistance towards both exo and endo proteases, functional fine tuning and remarkable size dependent receptor selectivity [15]. Macrocyclization of peptides is a method of synthesizing cyclic peptide with desired properties [16–18]. Indeed, cyclization of small peptides is difficult as the E-geometry of peptide bond prevents to form ring like structure [19]. Structural features that stabilize a linear tripeptide which is precursor to a cyclic tripeptide determine kinetics of cyclization reaction [20, 21].

With a goal to investigate such properties on cyclic tripeptide of Nitrogen based heterocyclic amino acids, we investigated homochiral versus heterochiral cyclic trimerization of imidazole based heterocyclic amino acids using DFT. The importance of scaffolds with three imidazole rings comes from their receptor affinity towards hydroxybenzes [22]. Haberhauer et al. reported that homochiral cyclic tripeptides (RRR-Cy/SSS-Cy) of imidazole based heterocyclic amino acids are good molecular receptors for phloroglucinol [22]. The cyclic peptide was synthesized using pentafluorophenyl diphenylphosphinate (FDPP) and H\(\ddot {\textnormal u}\)nig base in acetonitrile with 60 % yield [22].

The present study of DFT calculations on homochiral (RRR-Cy) versus heterochiral cyclic (RRS-Cy) trimerization of imidazole based heterocyclic amino acids in gas phase and solvent phase with acetonitrile as the solvent reports that homochiral cyclic tripeptide is thermodynamically favorable over heterochiral cyclic tripeptide. The B97D functional that includes long range correlation interactions reduced the activation energy barriers significantly. Kinetically both the homochiral as well as heterochiral cyclic tripeptides are preferable with marginal difference in free energy of activation in solvent phase. We highlight the role of long range correlation, solvent effects and intramolecular interactions in cyclization reactions.

Methods

Initial geometries of R-, S- isomers of 5-aminoethyl-3-methyl-2-imidazole carboxylic acid (AEMIC) and cyclic tripeptides (both homochiral, RRR-Cy and heterochiral, RRS-Cy) (See Fig. 1) were generated using Avogadro (Application version 1.0.3) [23]. The methyl groups at C δ - position (chiral center) is kept in such way that it is at s-trans orientation with respect to imidazole ring. The geometries were subjected to optimization in gas phase using B3LYP and B97D functionals; and 6-31G(d,p) [24] basis set in both gas phase as well as solvent phase with Acetonitrile as solvent. Polarizable continuum model (PCM) [25] of Self Consistent Reaction Field (SCRF) [26] was used to model the solvent phase (Solvent: Acetonitrile). Use of PCM is appropriate as it is widely used continuum solvent model and computationally tractable, to predict bulk solvent effects on molecular properties [27]. The model defines a cavity as union of series of interlocking spheres [28]. The electrostatic interactions between solute and solvent including mutual polarization effects are calculated using apparent charge distribution spread over the cavity surface [27]. Effect of non-electrostatic interactions are will be considered in our future work.

Fig. 1
figure 1

Schematic representation of R, S- 5-aminoethyl-3-methyl-2-imidazole carboxylic acids (Monomers), and cyclic tripeptides, RRR-Cy (homochiral) and RRS-Cy (heterochiral)

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Hessian calculations carried out on optimized geometries show real frequencies, indicating that they are at local minimum of their potential energy surface. Thermodynamic properties, free energy, enthalpy and entropy are calculated at temperature of 298.15 K and pressure, 1 atm. Change in zero point vibrational energy corrected electronic energy, ( ΔE z ), and free energy, ( ΔG), for formation of the cyclic tripeptides were calculated using the following equation.

$$ {\Delta} \text{X} = (\text{X}_{\text{P}} + {3 X_{water}}) - {3X_{M}} $$
(1)

where X stands for either zero point corrected electronic energy ( E z ) or free energy (G). M represents monomer, AEMIC, and P stands for cyclic tripeptide.

Reaction pathways

Table 1 Change in zero point corrected electronic energy (ZPE), ΔE z , and free energy, ΔG, for formation of cyclic tripeptides at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory in gas phase as well as solvent phase, i. e., Acetonitrile (PCM)
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Reaction pathways for cyclization of homochiral (RRR) and heterochiral (RRS) linear tripeptides were explored using the concerted straight forward peptide bond formation mechanism shown in Fig. 2. Concerted pathway involves direct elimination of water molecule, using the -OH from the carboxyl terminal and -H of amine group [29, 30]. Reaction mechanism for the reverse process, i. e., amide hydrolysis via concerted mechanism is also investigated by Krug et al. [31]. As the straightforward mechanisms offer less computational cost, geometries involved in reaction pathways for the cyclization reactions were modeled using this mechanism in gas phase and solvent phase.

Fig. 2
figure 2

Uncatalyzed concerted peptide bond formation mechanism suggested in literature

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The products are cyclic structures and expected to be conformationally more rigid compared to the reactants and their linear precursors. The number of possible conformers for the linear tripeptides and transition states are relatively larger compared to the cyclic tripeptides. Thus the modeling of the precursor species was based on the minimum energy structures of the products. For example, the transition state, RRR-TS was obtained by keeping a water molecule close to the carbonyl group of stable cyclic tripeptide, followed by transition state optimization. The geometries obtained in this process are consistent models for comparing each other.

The optimization and Hessian calculations were carried on the geometries of the pathways using B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory in both the gas phase as well as solvent phase. Implicit solvent phase model, PCM, was used to model the solvent phase, Acetonitrile. The transition states (TS) were confirmed by one imaginary frequency and visual analysis of nuclear motion corresponding to the imaginary frequency. Change in free energy ( ΔG) of formation of each structure on pathways was calculated to gain insights into thermodynamic and kinetic aspects of cyclization reaction. Also, change in enthalpy ( ΔH) and entropic energies (T ΔS) corresponding to the change in free energy were estimated.

To verify basis set effect on the results obtained at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory, all the geometries explored on the pathway were subjected to single point energy calculations at B3LYP / 6-311++G(2d,2p) // B3LYP / 6-31G(d,p) and B97D / 6-311++G(2d,2p) // B97D/ 6-31G(d,p) levels of theory in both gas phase as well as solvent phase.

Following are the structural parameters used to study the stabilizing interactions in the peptide systems: Hydrogen bond parameters ( ∠ N⋯H-N and distance, N ⋯H), Dihedral angle, ∠ N⋯H-N-C, at C-terminal end of the amino acid and peptide bond length. Magnitude of the dihedral angle provides inferences on planarity of the cyclic tripeptide and stability due to overlapping of the π electrons of conjugated double bonds at the C-terminal end of the amino acids. Resonance in peptide bond results in its partial double bond character and associated stability.

All quantum chemical calculations were carried out using the Gaussian09 [32] suite of programs.

Results and discussion

Coordinates and harmonic vibrations of optimized geometries are shown in Tables, S1 and S2 respectively. Tables S3-S6 show absolute energies of all the species under study. First, free energy of formation of the cyclic tripeptides in gas phase and solvent phase was discussed. Next, the reaction pathways explored in gas phase as well as solvent phase are analyzed to gain kinetic aspects in the formation of the cyclic tripeptides. Finally, structural aspects responsible for cyclic trimerization reactions were presented.

Thermodynamic analysis shows that homochiral cyclic tripeptide is favorable over its heterochiral counterpart

The B3LYP/6-31G(d,p) level of theory predicted that homochiral and heterochiral cyclic tripeptides are favored by 12.0 (12.1) and 11.2 (11.3) kcal/mol in gas phase (solvent phase) respectively (Table 1). The magnitudes of free energy of formation are significantly increased when B97D functional is used instead of B3LYP, i. e, B97D/6-31G(d,p) level of theory predicted that the homochiral and heterochiral cyclic tripeptides are favored by 21.1 (21.5) and 18.7 (19.4) kcal/mol in gas phase (solvent phase) respectively. Both the theories predict that formation of homochiral cyclic tripeptide from 3 units of R-AEMIC is slightly favored over formation of heterochiral cyclic tripeptide from 2 units of R-AEMIC and 1 unit of S-AEMIC.

The trends observed with zero point energy corrected electronic energy remains same as that with free energy data.

Kinetic aspects of cyclic trimerization in solvent phase show reduced preference of homochiral cyclic trimerization over heterochiral cyclic trimerization

Kinetic control in preferential homochiral and heterochiral cyclic trimerization is evaluated by comparing energetics of transition states along concerted reaction pathways shown in Fig. 3. In gas phase, while B3LYP/6-31G(d,p) level of theory predicted free energy of activation for RRR-TS (RRS-TS) as 39.0 (41.3) kcal/mol, the B97D/6-31G(d,p) level of theory predicted the energy of activation for RRR-TS (RRS-TS) as 19.3 (23.9) kcal/mol. The B3LYP and B97D functionals preferred homochiral cyclic trimerization with an activation energy difference of 2.3 and 4.6 kcal/mol respectively over heterochiral cyclic trimerization reaction in gas phase. In solvent phase, while B3LYP/6-31G(d,p) level of theory showed the free energy of activation for RRR-TS (RRS-TS) as 42.8 (44.2) kcal/mol, the B97D/6-31G(d,p) level of theory predicted the energy of activation for RRR-TS (RRS-TS) as 25.3 (26.6) kcal/mol. The homochiral cyclic trimerization is preferred over heterochiral cyclic trimerization by free energy activation of 1.4 kcal/mol as per B3LYP/6-31G(d,p) level of theory and 1.3 kcal/mol as per B97D/6-31G(d,p) level of theory in solvent phase. Over all, the data show that formation of homochiral cyclic tripeptide is slightly preferred over that of heterochiral cyclic tripeptide in solvent phase compared to that observed in gas phase.

Fig. 3
figure 3

Information of the cyclization reaction pathway is presented. Relative values of free energy ( ΔG) of various structures obtained in pathways of reactions RRR-CyR and RRS-CyR calculated at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory in gas phase as well as Acetonitrile solvent phase modelled using Polarizable Continuum Model

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Also, the results indicate the functional, B97D, showed significantly reduced activation energy barriers compared to that obtained from the functional B3LYP. It indicates that long range correlation plays important role in predicting the energies of the species on reaction pathways.

The relative changes of enthalpy ( ΔH) and entropic energy (T ΔS) of all the geometries on the pathways calculated at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory are shown supporting information (Table S7: Gas phase data, Table S8: Solvent phase data). The relative changes of enthalpy follow the trends of free energy data.

Single point energy calculations carried out at B3LYP / 6-311++G(2d,2p) // B3LYP/ 6-31G(d,p) and B97D / 6-311++G(2d,2p) // B97D/ 6-31G(d,p) levels of theory agree with energetic trends discussed above (See Tables S9 and S10).

Linear tripeptides explored in reaction pathways of solvent phase show preferential formation of heterochiral linear tripeptide over homochiral linear tripeptide

The results of gas phase and solvent phase differ significantly in predicting relative magnitudes of free energy ( ΔG) for homochiral and heterochiral linear tripeptides. In gas phase, free energy of formation ( ΔG) of homochiral (RRR) and heterochiral (RRS) linear tripeptides, calculated by B3LYP/6-31G(d,p) (B97D/6-31G(d,p)) level of theory is − 7.2 ( − 19.0) and − 2.1 ( − 10.7) kcal/mol respectively. Both the theories show that formation of homochiral linear tripeptide is preferred over that of its heterochiral counterpart in gas phase. On the other hand, in solvent phase, heterochiral linear tripeptide is favored over homochiral linear tripeptide by 4.1 kcal/mol ( ΔG R R R =− 2.1 kcal/mol, ΔG R R S =− 6.5 kcal/mol) and 3.4 kcal/mol ( ΔG R R R =− 12.6 kcal/mol, ΔG R R S =− 16.0 kcal/mol) as per B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory respectively.

The data indicate that preferential formation of heterochiral linear tripeptide over its homochiral counterpart in solvent phase increases the yield of heterochiral cyclic tripeptide compared to that of homochiral cyclic tripeptide.

Geometric analysis substantiates reduced kinetic favorability of homochiral cyclic trimerization over heterochiral cyclization

Monomers optimized at B3LYP/6-31G(d,p) level of theory in gas phase are shown in Fig. S1. Cyclic tripeptides optimized in gas phase and solvent are shown in Figs. 4 and S2 respectively. Also, the geometries of linear tripeptides, and transition states optimized in both the gas phase and solvent phase are shown in Figs. S3–S6 and S7–S10 respectively.

Fig. 4
figure 4

Up: Axial Side views of RRR (Homochiral) cyclic tripeptide of AEMIC, Down: RRS (Heterochiral) cyclic tripeptide of AEMIC optimized at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory in gas phase

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Magnitudes of structural parameters that stabilize all the systems optimized at B3LYP/6-31G(d,p) and B97D/6-31G(d,p) levels of theory, in gas phase, implicit solvent phase (PCM) are shown in Tables, S12 and S13 respectively. Related to the linear tripeptides, we are interested in intramolecular H-bond interaction between terminal groups as it plays important role in ring closure mechanism.

B3LYP/6-31G(d,p), Gas phase

Both the homochiral and heterochiral cyclic tripeptides are stabilized by weak hydrogen bond interactions (see Table S12 and Fig. 4). The structures of both the cyclic tripeptides have bifurcated N-H ⋯N intramolecular H-bond interactions with N ⋯H distance in the range of 2.26 - 2.33 Å and bond angles in the range of 104.8 ∘ - 106.4 ∘ in their interior part. Also, the structures show C-H ⋯O intramolecular interactions with O ⋯H distance in the range of 2.32 Å - 2.39 Å and bond angle is about 126.0 ∘ in their exterior part. Geometrical parameters of intramolecular hydrogen bond interactions in both the homochiral and heterochiral cyclic peptides are nearly equal in magnitudes.

The dihedral angle at three residues of homochiral cyclic tripeptide is 4.7 ∘. The magnitudes of the angle in heterochiral cyclic tripeptide are −3.4 ∘ , 0.6 ∘ and 7.2 ∘. The date indicate that while homochiral cyclic tripeptide is symmetric (C3-Symmetry) and the heterochiral cyclic tripeptide is planar and lacks the symmetry.

The structural parameters of the linear tripeptides, RRR and RRS, shown in Table S12, supports for N-H ⋯O and O-H ⋯N Hydrogen bonding interaction at its terminals (See Figs. S3 & S4) respectively. The bond angle, ∠N-H ⋯O and distance H ⋯O parameters of H-bond interaction in RRR peptide are 159.6 ∘ and 2.34 Å. Similarly, the bond angle, ∠O-H ⋯N and distance, H ⋯N in RRS are 127.6 ∘ and 2.34 Å. Magnitudes of the geometrical parameters support larger stability of homochiral linear tripeptide compared to heterochiral tripeptide shown in energy profile, Fig. 3.

B97D/6-31G(d,p), Gas Phase

The homochiral cyclic tripeptide shows significant structural variation compared to that of its heterochiral counterpart. While, in interior part, homochiral cyclic tripeptide show N-H ⋯N hydrogen bond interactions only at C-terminal end of each of the amino acids (N ⋯H distance = 2.26Å, ∠ N⋯H-N = 109.2 ∘), those at N-terminal end of the amino acid such interaction is not observed. The homochiral cyclic tripeptide is not associated with bifurcated H-bond interactions at its interior part. At exterior part both the cyclic tripeptides, show bifurcated H-bond interactions (C-H ⋯O(=C) and N-H ⋯O(=C)) are observed (See Fig. 4) with similar magnitudes. The network of H-bond interactions at the interior of heterochiral cyclic tripeptide is similar to that optimized at B3LYP/6-31G(d,p) level of theory, i. e., the H-bond interactions are bifurcated.

The dihedral angle at three residues of homochiral cyclic tripeptide is 11.0 ∘, and magnitudes of the dihedral angles in heterochiral cyclic tripeptide are-3.7 ∘, 0.5 ∘ and 6.5 ∘, which indicate that heterochiral cyclic tripeptide is planar compared to that of its homochiral counterpart. The larger dihedral angle of homochiral cyclic tripeptide infers that it shows C3 symmetric bowl shaped structure.

The linear tripeptide, RRR, shows N-H ⋯O interaction with bond angle, ∠N-H ⋯O = 159.6∘ and distance H ⋯O = 2.34 Å (See Fig. S5) and RRS shows O-H ⋯N interaction with ∠O-H ⋯N = 131.1 ∘ and distance H ⋯N = 1.99 Å (See Fig. S6). Linearity of the bond supports larger stability of the peptide, RRR compared to RRS as shown in Fig. 3.

Over all, the structural data analyzed above indicates that change of stereochemistry at one chiral center of the cyclic tripeptide enhances its planarity which causes for bifurcation of intramolecular H-bond interactions. The linear precursor of homochiral cyclic tripeptide is associated with strong H-bond interactions compared to that of heterochiral cyclic tripeptide. The data support homochiral cyclic trimerization.

B3LYP/6-31G(d,p), solvent phase

Both the homochiral as well as heterochiral cyclic tripeptides show bifurcated H-bond interactions, N ⋯H-N, in the interior part with N ⋯H distance in the range of 2.27 - 2.30 Å, the bond angles in the range of 104.8∘ - 106.2∘. The bond length, O ⋯H, and bond angle, O ⋯H-C of interactions, O ⋯H-C, at the exterior part are in the range of 2.42 - 2.45 Å and 124.8 - 125.0 ∘.

The dihedral angle at three residues of homochiral cyclic tripeptide is 3.6 ∘ and the values for its counterpart, i. e., heterochiral cyclic tripeptide are −1.2 ∘, −0.7 ∘ and 5.3 ∘. The solvent environment also enhanced the planarity of the cyclic tripeptides compared to that of the gas phase structures.

The linear tripeptides, RRR shows N-H ⋯O interaction with bond angle, ∠N-H ⋯O = 161.8 ∘ and distance H ⋯O = 2.49 Å (See Fig. S9) and RRS shows O-H ⋯N interaction with ∠O-H ⋯N = 172.1 ∘ and distance H ⋯N = 1.66 Å (See Fig. S10). Linearity and proximity of the bond supports larger stability of the peptide, RRS compared to RRR as shown in Fig. 3. This is contrary to the result observed in gas phase.

B97D/6-31G(d,p), solvent phase

The structures of homochiral and heterochiral cyclic tripeptide are nearly similar to those optimized at B3LYP/6-31G(d,p) level of theory.

The dihedral angle at three residues of homochiral cyclic tripeptide is 1.6 ∘ and the values for its counterpart, i. e., heterochiral cyclic tripeptide are − 0.3 ∘, − 1.7 ∘ and 3.0 ∘. The B97D/6-31G(d,p) level of theory increased planarity of the segments, N ⋯H-N-C in the both the cyclic tripeptides compared to that obtained from B3LYP/6-31G(d,p) level of theory. This might be due to accurate estimation of B97D functional for long range dispersion interaction comes from overlapping of π electrons of conjugated double bond at C-terminal end of the amino acids.

The linear tripeptides, RRR shows N-H ⋯O interaction with bond angle, ∠N-H ⋯O = 160.7 ∘ and distance H ⋯O = 2.31 Å (See Fig. S7) and RRS shows O-H ⋯N interaction with ∠O-H ⋯N = 170.2 ∘ and distance H ⋯N = 1.56 Å (See Fig. S8). Linearity and proximity of the bond supports larger stability of the peptide, RRS compared to RRR as shown in Fig. 3, which contradicts the result observed in gas phase.

In all, the data shows that kinetic favorability for formation of homochiral cyclic tripeptide over heterochiral cyclic tripeptide is reduced with the inclusion of solvent effect. We hope to further investigate this result in future studies using the explicit solvent phase model.

Conclusions

B3LYP and B97D functionals of density functional theory are used to gain inferences on homochiral versus heterochiral cyclic trimerization of 5-aminoethyl-3-methyl-2-imidazole carboxylic acid (AEMIC) in both the gas phase as well as solvent phase. Thermodynamically and kinetically homochiral cyclic tripeptide is favorable in gas phase. Even though, both the functionals, B3LYP and B97D show similar trends, the height of activation energy barriers is significantly reduced by the functional B97D compared to predicted by B3LYP. In solvent phase, the kinetic favorability of homochiral cyclic trimerization over heterochiral cyclic trimerization is reduced. The energetics of the peptides are substantiated by the structural parameters.

We suggest the use of B97D functional for the kind of systems studied in the present work.