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Advancing the biphasic drug delivery system through the molecular encapsulation of pinocembrin with NO-releasing β-cyclodextrin derivatives: A computational insight
*Corresponding authors: E-mail addresses: wangkun@wmu.edu.cn (K. Wang), luoyuting@wmu.edu.cn (Y. Luo)
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Received: ,
Accepted: ,
Abstract
Comprehending the intricate interactions between pinocembrin (PNCB) and NO-releasing β-cyclodextrin is fundamental for advancing novel gas-solid biphasic drug delivery systems (DDSs). Theoretical methods, including molecular dynamics (MD) and density functional theory (DFT) calculations, were utilized to investigate the structural stability and interaction mechanisms of inclusion complexes formed between PNCB and two β-CD derivatives: mono-6-diethylenetriamine-β-cyclodextrin (D-β-CD) and mono-6-ethylenediamine-β-cyclodextrin (E-β-CD). Two favorable conformations for PNCB inclusion within β-CD derivatives were identified: the benzene ring insertion (Conf-P) and the chromone ring insertion (Conf-C). MD simulations confirmed that the inclusion complexes of PNCB with NO-modified β-CDs exhibit excellent stability and encapsulation efficiency, with Conf-C demonstrating superior efficacy. DFT analysis revealed that dispersion interactions govern host-guest molecular interactions, and D-β-CD emerged as the most effective carrier for PNCB due to the formation of strong hydrogen bonds. These outcomes offer a fundamental understanding of PNCB@β-CDs complexes, paving the way for developing advanced biphasic DDSs based on NO-releasing β-CD derivatives.
Keywords
DFT
Host-guest interactions
Molecular dynamics
Nitric oxide-releasing β-cyclodextrins
Pinocembrin

1. Introduction
The development of highly efficient drug delivery systems (DDSs) is of paramount importance for advancing the pharmaceutical industry. These systems enhance drug bioavailability, reduce dosage and side effects, and improve patient compliance and therapeutic outcomes, ultimately leading to better health [1-3]. In recent years, multi-DDSs have garnered significant attention, as the combined delivery of multiple drugs can produce synergistic effects, substantially improving treatment efficacy [4,5]. For instance, in cancer therapy, the combined use of chemotherapeutic and immunotherapeutic agents has demonstrated remarkable improvements in treatment responses [6,7]. Among various DDSs, gas-solid biphasic DDSs are particularly noteworthy due to their ability to combine the stability of solid drugs with the rapid absorption of gaseous therapies. These systems hold broad application potential in the treatment of lung diseases [8], cancers [9], tissue regeneration [10], and so on [11]. For example, Wen et al. developed an ultrasound-responsive natural pollen delivery system that encapsulates oxygen and the chemotherapeutic drug doxorubicin, synergistically enhancing the tumor-killing efficacy in triple-negative breast cancer treatment [12]. Similarly, Ruan et al. fabricated a thermo-sensitive hydrogel loaded with anti-inflammatory brevilin A and nitric oxide (NO), effectively eradicating drug-resistant pathogens while reducing inflammation, thereby achieving favorable wound repair outcomes [13].
Among various drug delivery carriers, beta-cyclodextrin (β-CD) has garnered enormous attention due to its ability to improve the water solubility and bioavailability of various drugs. It features a hydrophobic cavity and hydrophilic external surface, moderate cavity size, favorable water solubility, and cost-effectiveness. Consequently, it is now widely used in the food, cosmetic, and pharmaceutical industries [14-21]. To further improve the solubility and biosafety of β-CD, various derivatives, such as the well-established methylated-β-CD (ME-β-CD), sulfobutylether-β-CD (SBE-β-CD), and hydroxypropyl-β-CD (HP-β-CD), have been developed, greatly expanding its range of applications [22-24]. Recently, various novel derivatives have also emerged [25]. In particular, the N-diazeniumdiolate-functionalized β-CD (β-CD-NONOates), which possesses the ability to release NO, has been synthesized and exhibits benign bactericidal activity and biocompatibility [26-28]. Given various physiological functions of NO, such as anti-tumor activity, immunoregulation, and vasodilation, this in situ NO-releasing β-CD derivatives holds great promise for applications in cancer treatment, antibacterial therapy, and wound repair [29,30]. Therefore, encapsulating drug molecules within the NO-releasing β-CD-NONOates to construct a biphasic DDS may synergistically exert the therapeutic effects of both the encapsulated drugs and NO, which is of significant importance for the treatment of numerous diseases.
Understanding the interactions between drugs and β-CD-NONOates is crucial for developing novel biphasic DDSs, providing a foundation to optimize drug encapsulation efficiency, stability, and release profiles. This necessitates a systematic investigation of specific host-guest interactions between model drugs and β-CD-NONOates [31]. In this study, mono-6-diethylenetriamine-β-cyclodextrin (D-β-CD) and mono-6-ethylenediamine-β-cyclodextrin (E-β-CD) were selected due to their high NO loading efficiency, conversion efficiency, and nontoxicity towards mouse fibroblasts [28]. Pinocembrin (PNCB) is a natural flavonoid compound with diverse pharmacological properties, including anti-inflammatory, antimicrobial, antioxidant, antiallergic, neuroprotective, and antiproliferative activities [32-37]. It was chosen as the model drug owing to its low solubility and bioavailability, which hinder its clinical application. MD simulations and density functional theory (DFT) calculations were adopted to characterize the structural stability of supramolecular complexes (PNCB@β-CDs) formed between PNCB and β-CDs (β-CD, D-β-CD, and E-β-CD), as well as to decipher the host-guest intermolecular interactions. Complementarily, theoretical simulations of infrared vibrational spectra were performed to establish essential spectral references for experimental characterization of the inclusion complexes. The whole experimental methodology has been summarized in Figure 1. The results are expected to provide fundamental insights into the structural stability and intermolecular interactions of PNCB@β-CDs complexes, advancing the design of biphasic DDS based on NO-releasing β-cyclodextrin derivatives.

- The methodology encompasses molecular docking, MD simulations, and DFT calculations to investigate the favorable conformations, structural stability, and host-guest interactions of the inclusion complexes formed between PNCB and β-CD, E-β-CD, and D-β-CD.
2. Materials and Methods
2.1. Molecular docking
The chemical structures of PNCB, β-CD, and two β-CD derivatives: D-β-CD and E-β-CD, were optimized using Gaussian 09 software at B3LYP/6-311G** level [38]. Molecular docking between the optimized PNCB and target β-CDs was performed by AutoDock Vina Package [39,40], generating 100 interaction poses for each host-guest structure. The PNCB molecule was permitted unrestricted rotational and translational flexibility during docking. To improve computational accuracy and efficiency, the exhaustiveness parameter was set to 8, enabling a thorough conformational search. Binding models were quantitatively analyzed to determine the distribution and affinity of different conformations.
2.2. MD simulations
The 500 ns MD simulations were conducted by the Gromacs 2021 package [41] to further demonstrate the structure stability and interaction details of the inclusion complexes formed between PNCB and various β-CDs. A cubic box with dimensions of 6.0 × 6.0 × 6.0 nm3 was created with the Packmol program, positioning the docked inclusion complexes at the center and filling the remaining volume with 8000 TIP3P water molecules [42]. Sodium ions were added to neutralize the charge in the D-β-CD and E-β-CD systems. The general Amber force field (GAFF) was adopted in all simulations [43], with topological parameters obtained by the Sobtop package [44] and the atomic charges calculated using the RESP2 algorithm [45]. Stepwise energy minimization was performed with the steepest descent method followed by the conjugate gradient algorithm. Pre-equilibration was achieved through 10 cycles of periodic annealing, during which the system temperature was rapidly increased from 50 K to 360 K over 100 ps, maintained at 360 K for another 100 ps, and then cooled to 300 K over a final 100 ps. Subsequently, production MD simulations were performed for 500 ns, with various time-dependent analyses conducted using built-in functions/scripts in GROMACS. The temperature of 300 K was kept constant using the V-rescale method [46], while pressure coupling was managed at 1 atm by the Parrinello-Rahman barostat [47]. Short-range interactions were handled using the cut-off radii of 1.2 nm. The particle-mesh Ewald (PME) method was adopted to treat long-range electrostatics [48]. Trajectory visualization was realized in the VMD package [49].
2.3. DFT calculations
The inclusion complexes underwent further optimization utilizing the Gaussian 09 package. A two-layered hybrid ONION approach [50] with the SMD implicit water model was adopted for the optimization of these complexes, in which PNCB was handled by the DFT (B3LYP-D3/6-311G**) calculations [51] and β-CDs were treated with the semi-empirical (PM6-D3) calculations. Based on the relaxed structure, the binding energy (Eb) in SMD water solvent was calculated using the formula below (Eq. 1):
where EPNCB, Eβ-CDs and EPNCB@β-CDs represent the energy of the PNCB, β-CDs and PNCB@β-CDs complex calculated at M062X/6-31G* level, respectively. For large molecular systems like cyclodextrins, the selected computational method achieves an optimal trade-off between accuracy and efficiency [52]. Moreover, to explore the nature of the intermolecular interactions in diverse PNCB@β-CDs, the energy decomposition analysis based on GAFF force field (EDA-FF) [53,54] was carried out in Multiwfn 3.8 software [55]. The infrared spectra (IR) were calculated at the B3LYP/6-311G** level, with a frequency scaling factor of 0.9619 [56]. The full width at half maximum (FWHM) was set to 10 to enhance the visibility of the IR signals.
3. Results and Discussion
3.1. Favorable conformations of PNCB@β-CDs inclusion complexes
To determine the dominant conformations of PNCB within β-CD and its derivatives, 100 independent molecular docking simulations were performed, identifying two predominant conformations of PNCB@β-CDs inclusion complexes, as illustrated in Figure 2(a). These conformations were classified into two types: the conformation-P (Conf-P), characterized by benzene ring insertion, and the conformation-C (Conf-C), defined by chromone ring insertion. Statistical analysis of the occurrence frequencies and host-guest affinities for these conformations (Figures 2b-c) revealed that Conf-P occurred 46, 47, and 43 times in β-CD, D-β-CD, and E-β-CD, respectively, while Conf-C occurred 53, 49, and 51 times. Notably, Conf-C exhibited slightly higher occurrence frequencies than Conf-P. Conversely, Conf-P demonstrated marginally stronger host-guest binding affinities.

- (a) Typical conformations of the inclusion complex formed between PNCB and β-CDs obtained from molecular docking. Carbon atoms are indicated in gray, oxygen in red and hydrogen in white; (b) the occurrence number of both conformations, and (c) the host-guest affinity from 100 independent docking runs of the inclusion complexes.
To rationalize the coexistence of multiple conformations, the molecular electrostatic potential (ESP) surfaces of PNCB, β-CD, and two β-CD derivatives were analyzed, which is widely used for studying electrostatic interactions and predicting binding sites [57,58]. As depicted in Figure 3(a), both PNCB and β-CD exhibited symmetrical and uniform surface charge distributions. The negative charges of PNCB were mainly concentrated around its four oxygen atoms, which showed strong electrostatic complementarity with the electropositive hydrogen atoms of β-CD’s hydroxyl groups (Figure 3b). Notably, D-β-CD and E-β-CD displayed overall negative electrostatic potentials due to their negatively charged substituents, thereby promoting electrostatic interactions with the positively charged benzene ring and hydroxyl hydrogens on PNCB’s chromone rings. Such differential electrostatic matching provides a rational explanation for the observed conformational polymorphism in PNCB@CD inclusion complexes. Our computational evidence strongly supports that both Conf-P and Conf-C represent favorable conformations for PNCB inclusion within β-CD derivatives.

- Electrostatic surface potential distribution of (a) PNCB; (b) β-CD; (c) D-β-CD; (d) E-β-CD.
Favorable conformations of PNCB@β-CDs inclusion complex, at the end of ‘Notably, as shown in Figure 3(c, d), D-β-CD and E-β-CD displayed overall negative electrostatic potentials due to their negatively charged substituents, thereby promoting electrostatic interactions with the positively charged benzene ring and hydroxyl hydrogens on PNCB’s chromone rings.
3.2. Structural stability of PNCB@β-CDs inclusion complexes
The root mean square deviation (RMSD) measures the atomic positional deviations, enabling the analysis of structural fluctuations in biomolecules over time [59]. To assess system stability and ligand mobility within the β-CDs cavity, RMSD fluctuations and their statistical distributions for PNCB@β-CDs complexes were computed, and the results have been displayed in Figure 4(a). As shown, all inclusion complexes exhibited RMSD fluctuations below 0.35 nm, with the average values less than 0.4 nm, suggesting the simulations are generally converged and all the complexes possess benign stability. Notably, Conf-C of the PNCB@D-β-CD and PNCB@E-β-CD complexes displayed higher average RMSD values than Conf-P, suggesting increased ligand mobility when the chromone ring of PNCB is inserted into the cavity. Additionally, the radius of gyration (Rg), a key metric for evaluating molecular compactness, was employed to evaluate structural stability. The Rg box plot (Figure 4b) reveals fluctuations below 0.1 nm across all complexes, with mean values near 0.6 nm. The slightly larger Rg values for PNCB@D-β-CD and PNCB@E-β-CD compared to PNCB@β-CD likely arise from the introduction of substituents in two β-CD derivatives.

- The boxplot of (a) RMSD, (b) Rg and (c) SASA values of β-CD and its derivatives in the inclusion complexes (d) SASA values of the encapsulated PNCB molecule.
The solvent-accessible surface area (SASA) quantifies the interfacial contact between solute and solvent molecules. Comparative analysis of SASA data for β-CD and its derivatives in the supramolecular complexes revealed that substituent incorporation elevates system volume of modified β-CDs, leading to a marked increase in SASA (Figure 4c). Meanwhile, Conf-C displayed slightly higher SASA values than Conf-P, implying enhanced solute-solvent interactions and improved solubility. Furthermore, SASA measurements of encapsulated PNCB molecules showed negligible variation across all systems, further supporting effective ligand encapsulation within the β-CD cavity (Figure 4d). MD trajectories at selected time intervals were analyzed to assess structural stability and PNCB encapsulation. As can be found from Figure 5, PNCB in both conformations remained stably encapsulated within the β-CD central cavity throughout the simulations, providing molecular-level validation for the observed RMSD and SASA profiles. Overall, these findings collectively confirm the structural stability of PNCB@D-β-CD and PNCB@E-β-CD complexes.

- The binding poses of (a) PNCB@β-CD, (b) PNCB@D-β-CD, and (c) PNCB@E-β-CD in Conf-P (upper) and Conf-C (lower) over 500 ns. PNCB is displayed in the CPK model, while the β-CDs are shown in the Licorice model.
The radial distribution function (RDF), a cornerstone analytical tool in molecular dynamics (MD), elucidates spatial distribution patterns between particles by measuring the distribution density g(r) of particles at a distance r from a reference particle, thereby offering detailed insights into their interactions. Using the centroid of the P-terminal benzene ring (BP) and C-terminal benzene ring (BC) as well as specific oxygen atoms in PNCB as the reference particles (as illustrated in Figure 6a), the g(r) values of oxygen atoms from surrounding water molecules were calculated to evaluate the encapsulation efficacy of β-CDs on PNCB. As shown in Figures 6(b, c), BP exhibits no prominent g(r) peak due to its hydrophobic nature. Despite the presence of hydrophilic hydroxyl groups on BC, its g(r) peak remains negligible. Furthermore, its g(r) peaks for Conf-C exhibit a notable reduction compared to that of Conf-P. Among all complexes, the g(r) of the O1-O(H2O) pair lacks a distinct peak (Figures 6d), indicating minimal water accessibility for the O1 atom [18,60,61]. This observation confirms effective encapsulation of PNCB by β-CDs, as the O1 atom resides at the molecule’s central region. In contrast, other oxygen atoms demonstrate stronger hydration effects. The O4-O(H2O) pair exhibits the most intense and sharpest g(r) peak, reflecting robust interactions between O4 and water. The g(r) intensity for the O3-O(H2O) pair is significantly lower than that of the O4-O(H2O) pair, likely due to the formation of a stable intramolecular hydrogen bond between the H on the O3 atom and the O2 atom, which limits O3’s contact with water. Moreover, Conf-C shows a pronounced reduction in O3-O(H2O) g(r) intensity relative to Conf-P, underscoring superior encapsulation of PNCB in Conf-C. The O2-O(H2O) g(r) intensity remains consistently low across configurations, as O2 is well-shielded regardless of configurations. Additionally, g(r) profiles for different complexes within the same conformation align closely, emphasizing the dominant role of β-CDs’ hydrophobic cavity in guest molecules encapsulation. In summary, β-CD and its two derivatives can effectively encapsulate PNCB, with Conf-C exhibiting better efficacy.

- (a) The distribution of the chromone and benzene rings in PNCB. The RDF of water around (b) BP and (c) BC. The RDF of water around the O1-O4 atoms of PNCB over the last 100 ns, including (d) Conf-P (I-III) and Conf-C (IV-VI).
3.3. The intermolecular interactions between PNCB and β-CDs
To elucidate the mechanisms underlying intermolecular interactions, host-guest complexes were analyzed using the independent gradient model based on Hirshfeld partition (IGMH) method [62,63]. Accordingly, blue regions indicate strong interactions (e.g., hydrogen bonding); green regions stand for van der Waals forces; and red regions signify repulsive effects, such as steric hindrance. As shown in Figure 7, extensive green regions between PNCB and β-CDs indicate that van der Waals interactions dominate their binding. In the PNCB@β-CD complex, a stable hydrogen bond formed between the hydroxyl group (-O4H) of PNCB and the β-CD backbone. Similarly, the PNCB@D-β-CD complex also exhibited robust hydrogen bonding between PNCB and D-β-CD, with an additional hydrogen bond observed in Conf-C. These interactions significantly enhance host-guest binding, thereby improving the structural stability of inclusion complexes. In contrast, no hydrogen bonds were detected in the PNCB@E-β-CD complex for either Conf-P or Conf-C. Moreover, Conf-C displayed more extensive green regions than Conf-P. Collectively, the superior stability of PNCB@D-β-CD compared to PNCB@E-β-CD underscores D-β-CD’s potential as an ideal carrier for biphasic DDSs.

- IGMH analysis of intermolecular interactions with isovalue = 0.001.
Furthermore, the binding energies (Eb) between the host and guest molecules of different systems were assessed using the SMD implicit solvent model at the M062X/6-31G* level. The results presented in Figure 8(a) demonstrate that the Eb of the PNCB@β-CD complex in both Conf-C and Conf-P are comparable, measuring -83.11 kJ∙mol-1 and -91.38 kJ∙mol-1, respectively. In contrast, the PNCB@E-β-CD complex exhibits a significantly higher Eb in Conf-C (-93.06 kJ∙mol-1) than in the Conf-P (-50.08 kJ∙mol-1). Strikingly, for the PNCB@D-β-CD complex, the Eb of the Conf-C (-288.50 kJ∙mol-1) far exceeds that of the Conf-P (-80.67 kJ∙mol-1). These quantitative findings align well with the IGMH analysis, collectively suggesting that the PNCB@D-β-CD complex, particularly in Conf-C, exhibits superior stability.

- (a) The binding energy (Eb, kJ∙mol-1) and (b) the energy decomposition based on EDA-FF of different conformations for PNCB@β-CDs complexes.
The EDA-FF analysis was performed to investigate the nature of intermolecular interactions across systems, comprehensively evaluating the contributions of electrostatic, repulsive, and dispersion energy components to total energy and their role in molecular stability. As illustrated in Figure 8(b), the total interaction energy derived from the EDA-FF aligns with the trend calculated using the SMD model, confirming the method’s accuracy and reliability. Furthermore, the dispersion forces were dominant in all inclusion complexes, corroborating the results of IGMH analysis. Particularly, PNCBC@D-β-CD exhibited the highest repulsive forces alongside the largest absolute values of electrostatic and dispersion interactions, rendering D-β-CD the optimal carrier for PNCB. In summary, dispersion interactions govern host-guest molecular interactions, and D-β-CD emerges as the most effective carrier for PNCB.
Infrared spectroscopy serves as a pivotal analytical technique for elucidating molecular structures and verifying the successful synthesis of inclusion compounds. To establish critical spectral benchmarks for experimental characterization of the inclusion complexes, theoretical simulations of infrared vibrational spectra were performed, and the results have been shown in Figure 9. For β-CD, the calculated spectra exhibited characteristic signals at 3501 cm-1 (νO-H) and 996 cm-1 (νC-O), showing good agreement with experimental observations at 3310 cm⁻1 (broad hydroxyl band) and 1022 cm-1 (C-O stretching) [64], thereby confirming the reliability of our computational approach. In comparison, a characteristic N-H stretching vibration emerged at around 3250 cm-1 for two β-CD derivatives. Notably, the PNCB spectrum displayed diagnostic peaks at 3684 cm-1 (νO-H), 1695 cm-1 (νC=O), and aromatic ring vibrations at 1602 cm-1 and 1426 cm-1 (νC=C). Upon complexation, a pronounced redshift in the hydroxyl stretching frequency was observed, indicative of potential hydrogen-bonding interactions. Concurrently, the benzene ring vibrational bands of PNCB exhibited significant modifications, suggesting restricted group vibrations due to host-guest binding within the cyclodextrin cavity. These spectroscopic observations collectively confirm the effective inclusion of PNCB within the hydrophobic cavities of β-CD and its derivatives, and provide a crucial reference for characterizing inclusion complexes through IR spectroscopy.

- The IR absorption spectrum of (a) β-CD, (b) D-β-CD, and (c) E-β-CD and their inclusion complexes formed with PNCB at the level of B3LYP/6-311G (d, p).
4. Conclusions
Herein, the structural stability, encapsulation efficacy, and intermolecular interactions governing the formation of inclusion complexes between PNCB and β-CD derivatives (D-β-CD and E-β-CD) were elucidated through comprehensive MD simulations and DFT calculations. Molecular docking simulations identified two energetically favorable conformations: conformation-P (Conf-P), involving insertion of the benzene ring, and conformation-C (Conf-C), involving insertion of the chromone ring. MD simulations confirmed the superior stability and encapsulation efficiency of these inclusion complexes, with Conf-C outperforming Conf-P. The IGMH analysis and energy calculations demonstrated that D-β-CD serves as the most effective carrier for PNCB due to the formation of strong hydrogen bonds. EDA-FF analysis revealed that dispersion interactions primarily drive host-guest interactions in these inclusion complexes. The IR spectroscopic simulation further confirmed the formation of the inclusion complex and provided crucial guidance for its experimental characterization. These findings validate NO donor-modified β-CDs as promising candidates for encapsulating poorly soluble anti-inflammatory drugs like PNCB and provide a mechanistic explanation of the complexation process, paving the way for novel biphasic DDSs.
Acknowledgment
K.W. is grateful for the financial support from Wenzhou Science & Technology Bureau of China (Y20240125). Y. L. acknowledges the financial support from Natural Science Foundation of Zhejiang Province (LQ24H180012) and Wenzhou Science & Technology Bureau of China (Y2023157).
CRediT authorship contribution statement
Hongjie Zhuo: Formal analysis, Visualization, Investigation, Writing – original draft. Yiting Zhu: Formal analysis, Visualization, Validation. Xu Huang: Formal analysis, Visualization, Validation. Wei Dong: Supervision, Resources. Yuting Luo: Validation, Supervision. Kun Wang: Conceptualization, Data curation, Validation, Funding acquisition, Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.
Declaration of generative AI and AI-assisted technologies in the writing process
The authors confirm that there was no use of artificial intelligence (AI)-assisted technology for assisting in the writing or editing of the manuscript and no images were manipulated using AI.
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