Water transport through a transmembrane channel formed by arylene ethynylene macrocycles

Abstract

Benefitting from the rigid backbone and π–π stacking interactions, arylene ethynylene macrocycles (AEMs) have a high tendency toward a stable nanotube assembly, which brings about potential in transmembrane channel use. Herein, we use molecular dynamics simulations to study the transport properties of water molecules through such a macrocycle nanotube (MNT) embedded in a DPPC bilayer membrane. For comparison, we also consider a structurally less complex channel of carbon nanotube (CNT) with similar size. We find that due to the spatial distribution of the MNT interior, water density profiles exhibit more remarkable wave patterns compared to the CNT, where the water occupancy within cross-sections along the channel have a unique variation of 2–3–2–3. Water molecules inside the MNT are subject to not only shape shifting but also rotation to satisfy the steric environment, which results in an inertial loss and slows down the water flow. We further consider the effect of channel–water interaction and channel length. The water flow through MNTs and CNTs both exhibit maximum behaviors with the increase of channel–water interactions. The MNT flow becomes larger when the channel–water interaction is at low or high levels. Both the water flow decrease steeply first and then smoothly with the increase of channel length. These results indicate that the channel structure and channel–water interaction have a distinct impact on the transport properties of water molecules. As the size of MNT can be well controlled by experimental techniques, this is promising for the design of novel nanofluidic devices.

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1. Introduction

The unique dynamics and structures of confined water have drawn considerable interest during the past decades, since the pioneering works by Hummer et al.¹ and Zeng et al.² in 2001. For example, by the use of molecular dynamics (MD) simulations, Fang et al. designed fascinating nanoscale water gates either via adding a charge to a carbon nanotube (CNT)³ or by the deformation of a CNT;⁴ while Zhao et al. designed a novel artificial water channel through inserting CNTs into biomembranes.^5,6 On the other hand, recent experiments reported several orders of enhancement of the water flow through CNTs over the conventional hydrodynamic predictions.^7,8 In subsequent experiments, similar highly efficient flow was observed either for functionalized CNTs⁹ or for hydrophilic nanochannels.¹⁰ It has been widely recognized that the rapid conduction of water inside CNTs is strongly dependent on their unique structure and stronger hydrogen bonds than bulk water, as well as weak water–CNT interactions.¹¹ In the limit of one-dimensional confinement, water can be in a single-file arrangement,^12,13 as observed by recent experiments,¹⁴ which shows the possibility for signal transmission.¹⁵ While, inside relatively wider CNTs, water can exhibit ice nanotube structures under high pressures.^2,16

Furthermore, for the sake of more practical use, including the demands in biotechnology,¹⁷ water desalination^18,19 or other industrial domains,²⁰ an ideal transportation channel should be mechanically and chemically stable, highly efficient and have a discrimination ability. However, such an ideal channel is not easily obtainable so far whether by re-engineering of biological channels or CNT-like inorganic channels. The biological proteins may lack mechanical stability, while CNTs though having rigid structures, may show limitation in discrimination or permeability manipulation ability. Although recent biomimetic design researches provide more possibilities for CNTs, the accurate decoration on the inner wall remains as a technical challenge.^21–23 Alternatively, in a recent experiment, Sébastien et al. fabricated a hybrid nanoporous membrane comprised of a solid-state polymeric thin film in which an ion channel is confined.²⁴

On the other hand, organic nanotubes formed by macrocycle molecules or other organic building blocks are promising for transmembrane channel use and should be added to the resolution handbook.^25–27 A prototype of macrocycle molecules is cyclic peptides,²⁸ however, with the rapid progress in macrocycle synthesis in recent years, new macrocycle units have been generated including other backbones, namely arylene ethynylene,^29,30 aryl amide and hydrazide,³¹ as well as Schiff-base ones.³² While reliable assembly shapes could benefit from stacking interactions, the inner modification and backbone adjustment will provide more potential artificial motifs with different passage manipulation characteristics. Although the water or ion permeability can be easily realized in different artificial organic nanotubes, the discrimination ability is still a challenging difficulty.^33,34 Fortunately, in a recent experimental work, Zhou et al. showed that the arylene ethynylene macrocycles (AEMs) nanotubes are attractive artificial transmembrane channels.³⁵ In their report, the AEMs with side-chain hydrogen bonding will form a stable nanotubular structure both in solid and solution states, which can be automatically plugged into the artificial membrane, leading to high water permeability and ion selectivity.

Pervious simulation works on organic nanotubes are mainly related to cyclic peptide nanotubes including assembly structure,³⁶ insertion process,³⁷ water structure³⁸ and water permeability.³⁹ AEM simulation works are rarely reported. In view of the AEM assembly nanotube (MNT) as a promising type of artificial channels, herein we use molecular dynamics (MD) simulations to investigate the water permeability and the flow details along the nanotube. Interestingly, we find that the water density profiles inside MNTs exhibit more remarkable wave patterns than those in CNTs. This is because the alternately distributed mid-plane and α-plane zones along the MNT show different accommodation capabilities, which is believed to have a significant impact on the water flow. By varying the channel–water interaction, we find that both the water flow in MNTs and CNTs exhibit maximum behaviors and the MNT flow can be even larger at low or high levels of interactions. We also compare the water flow between MNTs and CNTs at different lengths. We finally investigate the pressure-driven water flow and present the flow evolution by cutting the nanotubes into many thin layers along the flow direction.

2. Model and simulation methods

We used the AEM molecule in the ab initio calculation by Zhou et al.³⁵ We obtained the MNT from the AEM assembly in chloroform solvent. The MNT structures, including a stacking distance (0.361 nm) due to strong π–π stacking interactions⁴⁰ and a helical stacking feature accompanied with hydrogen bonding interactions of the side chains, are consistent with the ab initio calculations of Zhou et al. The typical structure of MNT is shown in Fig. 1a and b. The inner pore diameter is 1.109 nm (geometry distance of carbon atoms in the inner benzene) and the outer size is 2.4 nm. Fig. 1c is a snapshot of the simulated system, where the MNT embedded in the bilayer membrane is solved in a water box. Considering the membrane in our model is a DPPC bilayer,⁴¹ of which the hydrophobic domain thickness is around 3.1 nm, we used a 9-layer assembly MNT that will just hide in the hydrophobic zone to avoid unmatched disturbance from the hydrophilic domain of the membrane and water reservoir. In order to have a fair comparison, the CNT dimension is determined according to the 9-layer MNT size, where a (15, 0) CNT with 1.166 nm in diameter and 2.891 nm in length is suggested. The MNT system contains 80 DPPC molecules and 5558 water molecules; while the CNT system includes 105 DPPC molecules and 6083 water molecules, shown in Fig. 1d. We first conducted 20 ns MD simulations to calculate the water occupancy, density profiles and tilt angle, where the MNT, CNT and membrane are free to undergo rotation and translation. To obtain the channel water permeability under equilibrium condition, 60 ns MD trajectory data were collected for each ε_NT–OW interaction, where the positions of membrane and nanotube were fixed to keep the system stable. To consider the channel length effect, a series of MNTs (1.1, 3.0, 5.2 and 7.0 nm, corresponding to 4, 9, 15 and 20 layers assembly, respectively) and CNTs with similar lengths were examined, where each length were run in 120 ns simulations. As the DPPC membrane has a given thickness, we thus used graphite sheets as a simple membrane for different channel lengths, where the channel and membrane are fixed. Finally we studied the pressure driven water flux by applying water molecules with additional accelerations of 0.025, 0.05, 0.075 and 0.1 nm ps⁻² along the +z direction to study the water permeability in nonequilibrium condition, where the nanotube and DPPC molecules were also fixed. In this part, simulations were run for 120 ns at each pressure.

Fig. 1 Stable AEMs assembly structure obtained in chloroform: (a) an axial view and (b) a radial view. The simulation systems of (c) MNT and (d) CNT.

All MD simulations were carried out using Gromacs 4.0.5 software package under constant volume and temperature condition.⁴² The force field used for the macrocycles was OPLS-AA⁴³ and charge value of each atom was obtained by the RESP method.⁴⁴ The force field parameters of the DPPC bilayer is taken from Tieleman's work.⁴¹ For the CNT, the carbon atoms were modeled as uncharged Lennard-Jones particles, and the carbon–carbon and carbon–water interaction parameters were taken from Hummer's work.¹ The TIP3P water model was used.⁴⁵ The Berendsen thermostat were employed to maintain the system temperature at 300 K.⁴⁶ The particle-mesh Ewald method⁴⁷ was used to treat the long-range electrostatic interactions and the cut-off radius for Lennard-Jones interactions was 1.2 nm. The periodic boundary conditions were applied in all directions.

3. Results and discussion

The MNT structure obtained in our MD simulation coincides with the ab initio calculation in the work of Zhou et al.³⁵ The MNT structure is well maintained in the DPPC membrane. The MNT and CNT in the DPPC bilayer accommodate similar amounts of water molecules inside as shown in Fig. 2a. The average occupancy is 40.9 and 46.9, respectively. There exist tilt angles between the channel axis and the bilayer normal for both the MNT and CNT, similar to previous experiments or simulation works on other transmembrane channels.^48,49 As shown in Fig. 2b, the MNT is more even with less fluctuations in the tilt angles. The reason should be that the MNT as a stacking assembly is capable of making geometry adjustment corresponding to environment fluctuations and this to some degree will release the influence from outside. However, CNT being a covalent bonded molecule is more rigid and the response to the environment is inevitably realized by tilting. Furthermore, the MNT benefiting from the controllable modification of outside chains, should have a wide compatibility with different membranes.

Fig. 2 (a) The water occupancy for the MNT and CNT. Inset: the occupancy distribution. (b) The tilt angle of the MNT and CNT (angle between the nanotube axis and membrane normal). Inset: the tilt angle distribution.

The axial density distributions of water inside the two channels are shown in Fig. 3a, which works as a closer inspection of the channel's transportation characteristics. It should be noted that, in order to have a fair comparison between the MNT and CNT, the cross-section used for unit volume in the calculation of density is a circle with the same diameter as the CNT geometry diameter. The density fluctuation pattern inside the channel that we mainly focus on will be unaffected by the choice of cross-section. The (15, 0) CNT with a diameter of 1.166 nm, almost outreaches the sub-continuum size, and shows no large axial density fluctuation, in agreement with previous study.⁵⁰ The MNT, however, showed large fluctuations with several peaks and minima. The fluctuation is clearly induced by the nine layer and eight inter-layer spaces, denoted as the α-plane and mid-plane zones, similar to previous peptide nanotubes (PNTs).^36,38,39

Fig. 3 (a) The axial density distributions inside the MNT and CNT. (b) Snapshots of water molecules inside and near the entrance of the nanotubes: top (CNT) and bottom (MNT).

To further understand the water density fluctuation, it is reasonable to consider the geometry difference between the MNT and CNT. Fig. 3a shows the water molecules inside and near the mid-plane zone will suffer a geometry shrink that works as an energy barrier during the translocation process. Such kind of geometry shrink will build a preference to water in the mid-plane zone. Consequently, water molecules will accumulate in mid-plane zones, leading to density peaks. Extra information shown in Fig. 3a is that near the two ends of the channels, the water density exhibits higher values for the MNT. Such a difference should be due to the water–channel interactions. Besides the hydrophobic interactions, the water–MNT also has electrostatic potentials. Furthermore, as seen in Fig. 1b, the atom number of a macrocycle (114) is clearly larger than a cross-section of the CNT (20), and thus the macrocycle molecules at channel ends will gather more water molecules. This can also be seen directly from Fig. 3b. For example, from a frame of the trajectory, the water number within 0.7 nm from the channel ends are 1382 and 478, for the MNT and CNT, respectively. In a previous study, the PNT channel shows a 1–2–1–2 water occupancy distribution along the channel axis.³⁶ Similarly, we can identify a pattern of 2–3–2–3 for the current MNT, as it has a larger interior space.

We then studied the nanotube water permeability in equilibrium condition. Besides the channel charge,⁵¹ the Lennard-Jones (LJ) interaction of channel–water also has a considerable influence on the water transportation process.⁵² Herein we compared the transport properties of MNTs and CNTs at different LJ interactions. For CNTs, the LJ potential depth of carbon–oxygen (ε_NT–OW) is originally 0.48 kJ mol⁻¹, based on which it is changed to 0.5, 0.75, 1.5 and 2 times. For MNTs, the original ε_NT–OW is 0.43 kJ mol⁻¹, and for comparison we used the same ε_NT–OW as those in CNTs, except for the original value. The water flows as a function of ε_NT–OW are shown in Fig. 4. Remarkably, both the flow exhibit maximum behaviors with the increase of ε_NT–OW. This maximum behavior can be well understood according to previous studies, especially for the CNT channels.^51,52 For the CNT channel with original ε_NT–OW, the channel charge can reduce the water flow,⁵¹ while for uncharged channels, the water flow increases drastically to a plateau with the increase of ε_NT–OW up to about 0.84 kJ mol⁻¹.⁵² Thus, it is believed that the water flow should naturally show a maximum when the channel–water interaction changes from purely repulsive to strongly attractive, which is confirmed by our results. However, compared to the previous study,⁵² the water flow is more sensitive to ε_NT–OW, since it decreases when ε_NT–OW > 0.5 kJ mol⁻¹. This should be due to different channel lengths. The previous CNT has short length of 1.34 nm, thus the water flow should highly depend on thermofluctuations of water reservoirs and becomes less sensitive to the channel–water interaction.

Fig. 4 Water flow and occupancy of the MNT and CNT as a function of LJ interactions. The third set of data points (x-axis) are the original LJ interactions.

Clearly, compared to the CNT, the maximum behavior of MNT is very smooth. This should stem from the partial charges in MNT and the steric distribution of MNT atoms. For example, at the smallest ε_NT–OW, the water flow of CNT is almost zero due to the nearly zero occupancy (also shown in Fig. 4); while the flow and occupancy of MNT are still large, due to the MNT–water electrostatic attraction. At moderate (or original) ε_NT–OW, the CNT has larger water flow owing to its regular interior surface. At high ε_NT–OW, the water flow of MNT is several times larger than the CNT, as the MNT is a stacking structure with less interaction points with water compared to the solid wrapped wall-like CNT. As a whole, the water flow of MNT is less sensitive to ε_NT–OW. The water occupancy has a sudden increase with the increase of ε_NT–OW, corresponding to the flow jump, and then it varies smoothly.

The channel length has a profound impact on the transport of water molecules.^50,53 To further elucidate this effect, we show in Fig. 5 the water flow as a function of channel length. At L = 1.1 nm the water flow of CNT is about three times larger than MNT, while for larger L, the difference is less than two times. Generally, for short channels, water molecules have little time to travel inside the channel, the transport properties may be more dominated by the effect of exit and entrance; while for long channels, water molecules have enough time to be subject to the channel environment, and thus the channel interior structure becomes dominant. The water density profiles in Fig. 3 show larger fluctuation in the entrance of MNT, which in turn reflect large flow difference at small L. Once the water molecules overcome the entrance, they will quickly spread out within a short time to feel the effect of the channel environment. The entrance effect should become trivial for L > 3 nm, where the flow decrease is not very drastic, and the flow difference between MNT and CNT becomes steady and should mainly come from the interior structure difference.

Fig. 5 Water flow of the MNT and CNT with different lengths.

Apart from above equilibrium examination of the water permeability of MNT, we further investigate the water transport under nonequilibrium condition, by calculating the water flux under the drive of pressure differences. It should be noted that we adopted the method developed by Zhu et al.,⁵⁴ where an additional force was applied on the water molecules. This method has been widely used in previous studies for water transport.^3,4,12,53 As a matter of fact, some new techniques in applying external pressures have also been developed, such as local force⁵⁵ or piston like model,⁵⁶ which may be more close to experimental conditions but are difficult to conduct in the current simulation package. According to Zhu et al., accelerations of 0.025, 0.05, 0.075 and 0.1 nm ps⁻² on water molecules will respectively generate 118, 236, 353 and 469 MPa pressure differences between the two channel ends of our simulated system. As shown in Fig. 6a, the net water flux across MNT is almost proportional to the applied pressures, in agreement with predictions from the no-slip Hagen–Poisseuille (HP) theory.⁵³ For P = 469 MPa, we compared the water flux of the MNT and CNT, shown in Fig. 6b as a function of the simulation time. Both the fluxes increase with time linearly, where the average values are 46.6 and 75.4 ns⁻¹ for the MNT and CNT, respectively. It is not surprising that the MNT has smaller water flux, since its interior is rougher than the CNT. Although the flux is smaller than the CNT, it is still at a high level, where the estimated value of 5.76 m³ m⁻² bar⁻¹ day⁻¹ (in calculation; outer chain size 2.4 nm) is higher than typical diffusive RO membranes.^19,57 With high water transportation ability and showing a benign nature with the surrounding environment, if we further consider the easy modification, MNT is promising for transmembrane channel uses.

Fig. 6 (a) The average water flux as a function of applied pressures for MNT. (b) The cumulative water flux for MNT and CNT under P = 469 MPa.

The weaker transportation ability of MNT should be related to large fluctuations in the density profiles. To further explore the density profiles, we use oxygen density map analysis (projection on the plane perpendicular to the flow direction), from which we will obtain a direct picture of the water distributions in different zones of the channel. The density maps in different zones will show us the evolution process of water flow. Fig. 7a and b show the density maps for water molecules in the whole channel of MNT and CNT, respectively, except for the 0.4 nm region at both ends. The regular circle distribution in CNT with high values near the interior surface agrees with the radial density distributions in the previous study.⁵⁰ However, the density distribution becomes wide inside the MNT, due to its stacking structure, where the α-plane and mid-plane zones arrange alternately. To consider the structural features of MNT, in Fig. 7c and d we show the density maps for water in the α-plane and mid-plane zones, respectively. The pattern in the α-plane zone is a connected hexagon; however, when water passes into the mid-plane zone, the pattern undergoes an expansion and changes into a hexa-island one. We also note an interesting phenomenon that each island in the mid-plane pattern is composed of two smaller islands, e.g., see the highlight with a circle mark in Fig. 7d. This result encourages us to cut the two zones further into four. The four zones are labeled as I, II, III and IV, shown in Fig. S1 in the ESI.† The I and II parts are disassembled from the α-plane zone and the latter two are the components of the mid-plane zone. In a more detailed way, the region between two neighboring macrocycles is divided into four equal parts, where I and II mean the nearby upper and lower parts to a given macrocycle, respectively; while III and IV represent the two following parts after II. The corresponding oxygen density maps for waters in I, II, III and IV are shown in Fig. 8a–d, respectively.

Fig. 7 Density maps for oxygen atoms of water molecules. Water molecules within the whole channel of (a) MNT, (b) CNT, except for the 0.4 nm region to both ends. Water molecules in (c) the α-plane zone, (d) mid-plane zone. The four contours use the same color bar. (a) and (b) are normalized by their largest value independently, in order to show the distribution difference between the MNT and CNT. (c) and (d) are normalized by the largest value in (d), in order to have a direct comparison between the two zones.

From Fig. 8, we have a clear picture of the density evolution when waters cross over a macrocycle layer. The I and II parts are quite similar with each other, which are also analogous to the α-plane zone map in Fig. 7c. This is a reasonable result since in the α-plane zone, water molecules have strong interaction with the macrocycle molecule, and there is almost no steric difference between the two sides of macrocycle molecule. From zone II to zone III, shape shifting happens, as the confinement space is expanded. Although zones III and IV have quite similar hexa-island structure, we can observe a rotation between them. This rotation clearly stems from the relative rotation of the coming macrocycle molecule. If labeling the density maps in the α-plane zone and mid-plane zone as pattern A and pattern B, respectively, the water flow evolution in the four parts can be described as: pattern A → pattern A → pattern B → rotation → pattern B (see Movie S1 in the ESI†). As seen in Fig. 1a, the macrocycles are continuously rotating to stack, thus the water flow pattern will share the same evolution, and the rotation only happens between the III and IV parts. Due to the water flow shape shifting and rotation in MNT, the water flow will suffer inertial losses, similar to water entering and leaving CNTs,⁵⁰ which should be responsible for its weaker transportation ability of MNT.

Fig. 8 Oxygen density maps in (a) I, (b) II, (c) III and (d) IV zones. The color bar is same as Fig. 7. The largest value among the four contours is used for normalization.

4. Conclusions

In summary, we obtained a stable MNT assembly structure that is consistent with ab initio calculations in the previous work including the helical rotation, a stacking distance revealing strong π–π stacking interaction and side chains' hydrogen network features. Both the MNT and CNT are stable in the DPPC membrane, and the MNT is more quiescent by comparing the tilt angle fluctuation, as it can well adjust its geometry in response to outward influence. From this perspective, we then expect that the permeability of the stacking assembly kind of nanotube may be controllable in response to the distortion of the membrane. By measuring the water density distribution along the nanotube axis, we found a more drastic density fluctuation in the MNT compared with CNT, due to its rougher interior structure, namely the α-plane zone and mid-plane zone. In particular, the water occupancy pattern along the MNT axis can be identified as 2–3–2–3.

With the increase of channel–water LJ interactions, both the water flow in MNT and CNT exhibit maximum behaviors. In particular, at small or large LJ interactions, the MNT flow is larger than CNT clearly, which are ascribed to the partial charge and unique structure of MNT, respectively. At moderate (or original) LJ interactions, the water flow in CNT is the larger. With the increase of channel length, both the water flow decrease drastically, where the flow difference between MNT and CNT also decreases and becomes steady. This is because the entrance effect is changed from dominant to trivial with the channel length increasing. We also studied the pressure-driven water transport. Although, the water flux in MNT is smaller than CNT, the value is still higher than typical RO membrane materials. Considering the MNT reported ion discrimination ability and controllable modification it should be a promising candidate for transmembrane uses.

We further explored the water flow evolution along the MNT axis by using oxygen density maps. The alternate α-plane and mid-plane zones of MNT lead to distinct density maps, i.e., hexagon and hexa-islands, respectively. We further divided the two zones into four equal parts, by which we obtained a clear water flow evolution process: pattern A → pattern A → pattern B → rotation → pattern B. Patterns A and B are hexagon and hexa-islands shapes, respectively. Besides the shape shifting between patterns A and B, water flow rotates in the mid-plane zone between two neighboring macrocycle molecules. The density maps revealed the inertial losses of water flow passing through the MNT, which is responsible for its weaker transportation ability, compared with the CNT. The vivid flow evolution has greatly enriched our knowledge about the water transportation through channels with specific interior structures.

Acknowledgements

This work is financially supported by the National Science Foundation of China (21204093, 21174154, 20874110) and Chinese Academy of Sciences (KJCX2-YW-H19). The allocated computer time at the Supercomputer Center of Chinese Academy of Sciences is gratefully acknowledged.

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Footnote

† Electronic supporting information (ESI) available: The α-plane, mid-plane, I, II, III and IV zones are described in Fig. S1 and the water flow evolution inside MNT is shown in Movie S1. See DOI: 10.1039/c3ra43545h

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