1 Introduction

Cucurbit[n]urils (CBn, n = 5–8, 10) are a family of water-soluble macrocyclic host molecules, consisting of n glycoluril units linked through methylene bridges [1,2,3,4]. They are known to bind neutral and cationic organic guests in aqueous solutions with high affinity [5,6,7,8] via a combination of hydrophobic and electrostatic interactions [9,10,11]. Within the CBn family, CB7 is the homologue with most applications due to its high water-solubility and intermediate cavity size, and its ability to bind a wider variety of guest molecules with extraordinary association constants [10, 11]. The CBn are used in many applications, including dye tuning, as catalysts, molecular switches and drug binding and delivery [9, 12, 13].

Benzimidazole (BZ) and its derivatives, viz. albendazole (ABZ), carbendazim (CBZ), thiabendazole (TBZ), and fuberidazole (FBZ) (Scheme 1), are known as being fungicides and anthelmintic drugs [14, 15]. In general, benzimidazoles have limited water solubility and may undergo chemical and photo-degradation [16]. It is well-known that their encapsulation within macrocyclic molecules, such as CBs and cyclodextrins (CDs), enhances their solubility as well as thermal and photochemical stability [17,18,19,20]. Furthermore, host–guest complexation can alter the protonation of guest molecules with ionizable groups, which is known as complexation-induced pKa shifts [13, 18, 20]. These shifts in pKa values can be exploited to activate pro-drug molecules, stabilize the active form of drug molecules, enhance their solubility, and increase their degree of ionization [13, 18, 20]. Nau and coworkers have reported that the binding for drug molecules with CB7 enhances the stability of the active form through complexation induced protonation [6]. Koner et al. studied the complexation between CB7 and BZ derivatives in aqueous solution, and found complexation-induced shifts in their pKa values, enhanced water solubility and chemical stability, as well as altered photo-physical properties [18].

Scheme 1
scheme 1

Chemical structures of the investigated guest molecules

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Molecular dynamics (MD) simulations and quantum-chemical calculations have been widely used to study CBn host–guest complexation [21,22,23,24,25,26,27,28,29]. Olivia and co-workers have recently applied constant-pH MD simulation (CpHMD) protocol to investigate the pH dependent binding of BZ and its derivatives to CB7 and estimate the induced pKa shifts; they obtained good agreement with the experimentally reported values, with absolute errors less than 5.4 kJ·mol−1 [30]. Fatiha et al. have employed the HF/6-31G and B3LYP/6-31G methods to compare two binding modes of CBZ with CB7, with the benzimidazole and carbamate moieties, respectively, introduced into the CB7 cavity, and found that the former resulted in a more stable conformation [31]. Shewale et al. have used dispersion-corrected DFT calculations to study the CB7 complexes with BZ and its derivatives (ABZ, CBZ, FBZ and TBZ) and found that inclusion of the benzimidazole moiety resulted in increased binding stability in the following order: ABZ > CBZ > BZ > FBZ ~ TBZ [32].

In this work, MD simulations are used to study the dynamics of the inclusion complexes formed in aqueous solution between CB7 and the protonated and neutral forms of benzimidazole derivatives (Scheme 1). Free binding energies are estimated using the molecular mechanics Poisson–Boltzmann surface area (MM-PBSA) method. Finally, DFT is used to estimate the pKa values for the guests in their free and bound states. A comparison of both MD and quantum mechanical approaches is made and discussed.

2 Computational Methods

The initial molecular geometry of CB7 was obtained from its experimental XRD structure [2]. Optimized structures for the guest molecules were generated using ab initio (HF/6-31G*) calculations, in order to use them as starting geometries for the MD simulations and to calculate the electrostatic potentials. The initial host–guest complexes, generated by manually inserting the guest into the desired position inside the host cavity, are shown in Scheme 2. MD simulations were performed with the sander module of the AMBER program [33] employing the general amber force field (GAFF) parameter set [34]. RESP charges were used for the atomic charges of the host and guest molecules generated from the electrostatic potentials calculated using an ab initio (HF/6-31G*) method [35]. Each system was solvated in a truncated octahedral periodic box of TIP3P water molecules [36]. Chloride ions were added to maintain the charge neutrality of each system. The non-bonded cut-off was set to 12.0 Å. Prior to starting the MD simulation, each solvated complex was subjected to energy minimization using the conjugate gradient algorithm, followed by gradual heating up to 298 K for 60 ps, and 500 ps of equilibration at 1 atm (1.01325 MPa). During the minimization and production runs, the Particle Mesh Ewald method (PME) was employed to treat the long-range electrostatic interactions in periodic boundary conditions [37]. All bond lengths involving hydrogen atoms were constrained by means of the SHAKE Algorithm [38]. Production runs were carried out for 20 ns at 298 K and 1.0 atm (1.01325 MPa), using 2 fs time steps, saving structures every 2 ps, and updating the non-bonded pair list every 25 steps. Trajectories were analyzed with the PTRAJ module of the AMBER 11 program. The VMD 1.8.6 program was used to visualize the structures [39] The MM-PBSA method and normal mode analysis were employed according to the procedure described elsewhere [21, 22, 24, 40]. For the quantum calculations (geometry optimization and binding energy calculations), the dispersion-corrected DFT method (wB97XD/6-31G*) in Gaussian 09 was used, with default convergence criteria. Minima were characterized by the absence of imaginary frequencies. The polarizable continuum model (PCM) was implemented to simulate the effect of solvent [41]. For the pKa calculations, the procedure was adopted from the literature [42, 43].

Scheme 2
scheme 2

Initial geometry of a typical host–guest inclusion complex

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3 Results and Discussion

The starting structures for the MD simulations of the complexes had the benzimidazole ring of the guest at the center of the host (Scheme 2). Figure 1 shows for each complex a superposition of representative samples (snapshots) extracted from its 20 ns trajectory. These snapshots revealed complete inclusion of the benzene ring, thus allowing maximum van der Waals interactions with the hydrophobic cavity of CB7. The snapshots for ABZ on the other hand showed only a partial inclusion of the benzene ring and a complete inclusion of the hydrophobic propyl-thio moiety. The imidazole ring in all guests was positioned next to the carbonyl portals, interacting via hydrogen bonds as well as ion–dipole interactions in the case of the protonated guests. The R2 substituents in all guests were excluded from the cavity and exposed to the surrounding water. The protonated guests assumed more restricted conformations compared to the neutral forms, a result of the strong ion–dipole interactions. Our results are in agreement with the 1H-NMR data obtained by Koner et al. [18] in acidic medium. Specifically, the 1H NMR spectra revealed the encapsulation of the benzimidazole moiety of the guest inside the CB7 cavity, except for ABZH+, in which the hydrophobic propyl-thio moiety shuttles inside CB7.

Fig. 1
figure 1

Dynamics of studied guests shown as a clustered molecular display

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4 Hydrogen Bond Analysis

A summary of the intermolecular hydrogen bonds (HB) between the guest molecules and the carbonyl oxygens on the CB7 portals is presented in Table 1. The hydrogen bond analysis was carried out using the PTRAJ module of the AMBER 11 program, using a hydrogen bond cut off distance < 3.2 Å and an angle > 120°. The analysis showed that the protonated guest partakes in more hydrogen bonds than its neutral from, a result of the additional hydrogen atom on the imine group (see Table 1). The enhancement was more pronounced for BZH+, as this guest adopted a more rigid conformation inside the cavity (Fig. 1). For CBZ, the amide group on the side can also form hydrogen bonds with the carbonyl rim, but not after protonation of the amine/imine groups in the imidazole ring which acts as a stronger competitor (Fig. 1). This resulted in a reduction of the number of hydrogen bonds on Hc from 0.8 to 0 upon protonation of the amine group in the imidazole ring.

Table 1 Hydrogen bond analysis between guests and CB7
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5 MM/PBSA Results

Table 2 displays the various contributions to the binding Gibbs energy of each complex as estimated by the MM-PBSA method. The higher Gibbs energy for the protonated form is a direct consequence of the increased electrostatic interactions, with − ∆EELE being greater by ~ 209 kJ·mol−1 than for the neutral form. The contribution from the van der Waals interaction (∆EVDW) did not differ much between the two forms, since the same part of the guest is responsible for binding inside the CB cavity. ABZ had the highest − ∆EVDW value (both forms), due to the encapsulation of the additional thiol residue. ΔGNP values for all complexes of both forms were slightly favorable, ~ − 8 kJ·mol−1, with the small differences between the two forms consistent with their similar binding modes. The solvation energy (ΔGsolv) was found to be unfavorable for all complexes: ~ 62–105 and 247–271 kJ·mol−1 for the neutral and protonated forms, respectively, with BZH+ having the largest (ΔGsolv) value as a result of its complete inclusion within the CB7 cavity. For all complexes, the large gas-phase interaction energies were largely compensated by the large solvation penalty. Overall, the ∆G values were negative, indicating favorable binding for the guests to CB7. The − ∆G values for the protonated guests were again much higher than those for the neutral ones. The highest and lowest binding Gibbs energies for the neutral (protonated) forms belonged to ABZ (ABZH+) and BZ (BZH+). Normal mode calculations yielded negative values of TΔS for all complexes, indicating overall reduction in guest and host freedom upon complexation, with the complexes of ABZ and ABZH+ showing the most negative values. This may be due to the different modes of binding with CB7 found for neutral and protonated ABZ (Fig. 1).

Table 2 MM-PBSA estimates of the binding Gibbs energies of the complexes and their decompositions, all in kJ·mol−1
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The fluctuations in the electrostatic contribution to the complex stability for protonated guests were lower than their neutral analogues (Table 2), in accord with the more restricted conformations adopted by the protonated guests as a result of their strong ion–dipole interactions with the host (Fig. 1). Similar observations were found for fluctuations of the van der Waals contribution to the complex stability.

The calculated binding Gibbs energy (∆G) values, excluding the entropic contribution (TΔS), were in a good agreement with the experimental ones (see Fig. 2). Including the TΔS term disrupted the agreement, presumably due to the inherent inaccuracy of the normal mode analysis. Although the MM-PBSA method employs a continuum solvation model, thereby neglecting the specific solute–solvent interactions important for a proper estimation of the Gibbs energies, the simulation nevertheless correctly predicted the significant increase in binding Gibbs energies of the protonated species and the selectivity of CB toward cationic species.

Fig. 2
figure 2

MD-calculated versus experimental binding energy: a ∆G and b ΔGTOT

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6 DFT Results

The preferential binding of CB7 with the protonated species results in larger shifts in their pKa values when compared with their neutral counterparts. In order to predict the binding affinities and the complexation-induced pKa shifts, we carried out DFT calculations (at the level of wb97xd/6-31G*) in implicit water using the polarizable continuum mode (PCM). The calculated binding Gibbs energies produced better agreement with the experimental trend than MM-PBSA (Fig. 3). Including the effect of solvation had a positive overall impact on the calculated binding trend. The pKa estimates (Table 3) are in good agreement with the experimental values for the free guests but overestimated them in the case of their complexes. Several factors could contribute to this disagreement: the choice of the basis set, the use of the continuum solvation model, especially for protonated species, which overestimates the binding energies and, as a consequence, exaggerates the pKa values for complexes, and finally, the use of optimized geometries only and the neglect of the conformational flexibility of the inclusion complexes. However, as Fig. 4 shows, the computed ∆pKa values (aside from the BZ compound) are in fair agreement with the experimental trend.

Fig. 3
figure 3

DFT-calculated versus experimental binding Gibbs energies: a in gas-phase and b in water

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Table 3 pKa values of benzimidazole derivatives in their free pKa(free) and CB7-complexed pKa(comp.) states in water, obtained from DFT calculations (PCM)
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Fig. 4
figure 4

Experimental versus DFT values for pKa of the free guests (a) and complexed guests (b); experimental versus DFT pKa shifts upon complexation (c). Data for BZ are omitted

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7 Conclusion

MD simulations were carried out to study the dynamics and stability of the complexes formed in aqueous solution between CB7 and the protonated and neutral forms of benzimidazole derivatives. The obtained complex geometries formed by CBZ, TBZ, and FBZ exhibit complete encapsulation of the hydrophobic benzene ring within the hydrophobic cavity of CB7, allowing maximum van der Waals interaction. The ABZ complex on the other hand has the hydrophobic propyl-thio moiety included instead. The large binding-induced pKa shifts reported in the literature are explained by the MM-PBSA results, which demonstrate the preferential binding of CB7 to the protonated guests. DFT results reproduced the experimental trend of the binding strengths and pKa shifts for the studied molecules but not the absolute values of the pKa.