MD Simulations on the Transport Behaviors of Mixed Na+ and Li+ in a

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MD Simulations on the Transport Behaviors of Mixed Na and Li in a Transmembrane Cyclic Peptide Nanotube under an Electric Field. Lingling Zhang, Jianfen Fan, and Mengnan Qu J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.8b00593 • Publication Date (Web): 26 Nov 2018 Downloaded from http://pubs.acs.org on November 29, 2018

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Journal of Chemical Information and Modeling

MD Simulations on the Transport Behaviors of Mixed Na+ and Li+ in a Transmembrane Cyclic Peptide Nanotube under an Electric Field Lingling Zhang, Jianfen Fan,* Mengnan Qu College of Chemistry, Chemical Engineering and Materials Science, Soochow University, Suzhou 215123, People’s Republic of China

ABSTRACT: Due to its inherently stronger hydration, Li+ faces a higher dehydration energy than Na+ at the entrance of the 8(WL)4/POPE-CPNT. Present MD simulations show that it can enter the channel from a NaCl/LiCl solution only under an electric field stronger than 0.3 V nm-1, while Na+ is easier to move into the channel, which is well elucidated by two cations’ PMF profiles. The cation-Ow radial distribution functions, the electrostatic interactions with water and the orientations of neighboring water all refer to a more compact solvation structure and stronger hydration of Li+. Regardless of whether there is an external electric field, Na+ mainly appears in an α-plane zone, while Li+ does so in a midplane region. The increase of the electric field strength significantly accelerates the cations’ axial diffusions, shortening the residence times of two cations in the channel. Furthermore, it makes channel water tend to take positive dipole states.

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1. INTRODUCTION Inorganic ions are indispensable for life activities. Na+ can maintain the osmotic pressure between the inner and outer portions of a cell membrane and regulate neurological functions and muscle excitabilities.1 Li+ plays an important role in improving hematopoiesis and immune functions.2,3 Theoretical and experimental studies have shown that an ion in a dilute solution exists as a hydrated capsule structure.4,5 The hydration strength of an ion is important to the structure and stability of the ion. Zhou et al.6 suggested a hydration factor defined as the ratio between the hydration number and coordination water number to describe the intensity of ionic hydration. Their MD simulations indicated that the hydration of Li+ is stronger than that of Na+ in a dilute aqueous solution. Studying the transport behavior of an aqueous ion in a biological channel helps to comprehend the microscopic mechanism of the ion in a living organism. Recently, artificial ion channels have received wide attention, because of their capacity to simulate biological channels to some extent. It was reported that the hydration and axial diffusion of Li+ are both stronger than those of Na+ in a (10,10) armchair carbon nanotube (CNT).7 The free energy barrier of Cl- upon entry is much higher than that of Na+, revealing the phenomenon that Cl- can be blocked outside (7,7) and (8,8) CNTs, while Na+ has a chance to enter these channels.8 Composed of several cyclic peptides (CPs) through an antiparallel 2


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H-bonding network, an open-ended and hollow cyclic peptide nanotube (CPNT) exhibits good biocompatibility.9 Numerous theoretical and experimental studies have verified that CPNTs are ideal to conduct small species, such as water,10-12 and ions.13-15 The computed diffusion coefficient of water in an octa-CPNT is quite close to that in Gramicidin A.16 Regarded as a fine artificial ion channel, a CPNT of 8xcyclo[-(Trp-D-Leu)3-Gln-D-Leu-] shows good conductivities for K+ and Na+, which are three times as fast as the results of Gramicidin A.17 Generally, there are two typical kinds of regions in a CPNT—α-plane zones and midplane regions alternately arranged along the tube major axis, with the spacings of 1.8 Å and 3.0 Å, respectively, as shown in Figure 1a. The orientation distribution of water dipoles indicates that the surrounding

water

molecules

of

Li+

or

Na+

in

the

CPNT

of

4xcyclo[-(L-Ala-D-Ala)4-] are more highly structured in a midplane region than in bulk. Nevertheless, in an α-plane zone, the distribution of Li+ is similar to the case in bulk, while Na+ shows an enhanced structure.18 Nevertheless, in an α,γ-CPNT of 10xcyclo[-(L-Trp-D-γ-Ach-)4-], it was reported that Na+ generally populated in midplane regions, while Li+ showed little location preference.19 Furthermore, the presence of Na+ or Li+ hardly disturbed the original water arrangement in the channel, merely somewhat increasing the disorder. Bioelectric fields exist widely in biological systems and are closely related to various biological activities. It is of great biological significance to study the transport of an aqueous ion in a nanochannel under an electric field. It was 3



reported that the introduction of an oscillating electric field may significantly alter the radial distribution functions (RDF) between Na+ and Ow (water

oxygen) atoms, decreasing the hydration of Na+ in a solution.20-22 Nevertheless, the presence of a constant external field has no distinct effect on the solvation structures of K+ and Cl- in a cylindrical nanopore, but may induce the orientation of channel water to rearrange23 and significantly accelerate the movements of Na+ and water in a nanopore.24 An electric field exceeding 0.2 V nm-1 can prevent the blockage of Na+, thereby resulting in a fast water flow in a (6,6) CNT. A strong electric field reaching 0.25 V nm-1 may help Na+ to escape from a (8,8) CNT.25 Na+ absorbed in a negatively charged (40,40) single-wall CNT can move freely only under an electric field stronger than 2.5 V nm-1.26 These results infer that the introduction of an electric field may change the states and transport behaviors of an aqueous ion and water in a nanochannel. Regarding the transport of ions through CPNTs, early works13-15 mainly focused on studying the behavior of a single ion under no electric field. The hydrophobic characteristics makes a CPNT composed of eight CP subunits easily to be inserted into a lipid bilayer membrane, acting as an artificial channel.16,27 For this reason, the transmembrane CPNT of 8(WL)4/POPE was selected to simulate an artificial biological channel. The existence of a bioelectric field may greatly affect the movement of an ion in a biological channel. In this work, MD simulations were carried out to investigate the transport properties of Na+ and Li+ through the transmembrane CPNT of 4


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8(WL)4/POPE from a mixed solution of NaCl and LiCl under individual external electric fields. The differences between the distributions, diffusion behaviors, potentials of mean force (PMFs), non-bonded interactions and hydration strengths of Na+ and Li+ are discussed. Information about the transports of Na+ and Li+ in a nanochannel under an electric field will be helpful to the drug delivery and disease treatment.

2. MATERIALS AND METHODS 2.1. Modeling Systems. The equilibrium configuration of the transmembrane CPNT of 8×(WL)4/POPE was obtained from our previous work,28 which includes one CPNT [consisting of residues L-Trp (W) and D-Leu (L)], inserted in a POPE (palmitoyloleylphosphatidylethanolamine) membrane. The CPNT includes seven gaps (each covering the space with an internal of 4.8 Å between two adjacent CP subunits) numbered consecutively along the major axis (z-axis), as shown in Figure 1a. On the other hand, the CPNT consists of eight α-plane zones and seven midplane regions, with intervals of about 1.8 Å and 3.0 Å, respectively. A water box with dimensions of 58 Å × 58 Å × 45 Å was set up, and 39 Na+, 39 Li+ and 78 Cl- were added in it, yielding a 0.43 M NaCl and LiCl solution. The solution box was then equilibrated in an NPT ensemble for 10 ns at 310 K, varying the z dimension, while maintaining the ratio of the x and y dimensions. Finally, the dimensions of the solution box converged to 58 Å × 58 Å × 38.1 Å, 5



resulting a 0.51 M NaCl and LiCl solution. The time evolution of the root mean squared deviations (RMSDs) of all atoms, as depicted in Figure S1, indicates that the solution box was fully equilibrated. Two equilibrated solution boxes, each with a thickness of 38.1 Å, were placed along the z-axis on the both sides of 8×(WL)4/POPE. The completed system (Figure 1b) was composed of two boxes of 0.51 M NaCl and LiCl solution, one CPNT and one POPE bilayer membrane including 104 lipid units. A harmonic restraint potential of 20 kcal mol-1 Å-2 was applied for each Cα atom of the CPNT to keep the channel steady during a MD simulation. The whole system was then equilibrated in an NPT ensemble for 10 ns. Finally, the dimensions converged to 58 Å×58 Å×117.8 Å.

2.2. Introduction of an Electric Field. In this work, non-equilibrium molecular dynamics (NEMD)29,30 were performed to study the transport behaviors of Na+ and Li+ through the transmembrane CPNT of 8×(WL)4/POPE under an external electric field, which was applied along the positive direction of the z-axis, with strengths of 0.1, 0.2 and 0.3 V nm-1, respectively. MD simulation tests indicate that the POPE bilayer may be destroyed gradually by one or more water columns, causing the system to fall apart under an electric field E≥0.4 V nm−1. To prevent the POPE membrane from drifting, the lipid N and P atoms were constrained with a spring constant of 20 kcal mol-1, similar to the constraint to the Cα atoms of the CPNT. The NEMD simulation under an external electric field was realized through an “eField” algorithm implemented 6


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in NAMD.

2.3. Computational Scheme of Potential of Mean Force (PMF). The PMF of a single Li+ (or Na+) moving through the transmembrane CPNT of 8(WL)4/POPE from a NaCl/LiCl solution was gained by the adaptive biasing force (ABF) method.31,32 Based on the thermodynamic integration scheme, ABF integrates the average force of each ∆ξ along the reaction coordinate (ξ) to compute the free energy. Here, the reaction coordinate (ξ) was defined as the position of Na+ (or Li+) on the z-axis. Before ABF computation, a cv-SMD33 (constant velocity steered molecular dynamics) simulation was carried out along the reaction coordinate (ξ) in order to obtain a picture of a cation’s permeation pathway, in which a constant pulling speed of 2.0 Å/ns was applied to the cation. Generally, the pulling speed should be slow as possible under the promise that the simulation can be finished at a reasonable time cost. Simulation tests indicate that the cv-SMD pulling speed of 2.0 Å/ns can provide a reasonable computational efficiency. In total, a 33.6-ns cv-SMD simulation was carried out for a cation, providing the system configuration for the subsequent ABF simulation. For improving the efficiency of the ABF algorithm, the interval of reaction coordinate (ξ) between -33.6 Å and 33.6 Å was divided into 14 equally spaced windows, each with a width of 4.8 Å. To generate a smooth PMF, each window was further separated into 48 bins with a width of 0.1 Å. The first 1000 samples should be discarded. The initial structure in each 7



window was gained from the result of cv-SMD trajectories. A 25-ns ABF simulation was carried out for each window, totaling, a 350-ns ABF simulation for the whole system. By combining the outputs in 14 individual windows, the whole PMF of Li+ (or Na+) moving through the CPNT can be generated .

2.4. MD Simulation Details. All MD simulations were carried out using the NAMD 2.9 program.34 The CHARMM27 force field35 were applied for ions, the CPNT and “POPE membrane,” respectively. As one of the simplest models only including three sites, TIP3P water model36 was used for water. This water model has been perfectly fit with the CHARMM force field, exhibiting a higher computational efficiency.37 The establishment of a simulation system and the analysis were fulfilled with the molecular graphics program VMD 1.92.38 The periodic boundary conditions were applied for a simulation system in all three dimensions. The particle mesh Ewald (PME) approach was applied to calculate full electrostatic interactions.39 Electrostatic and van der Walls (vdW) interactions were truncated at 12 Å with a smoothing function switching on at 10 Å. All non-bonded interactions were only searched within 14 Å of atomic spacing in order to improve the computational efficiency. The Nose-Hoover Langevin piston method40 and Langevin dynamics41 were used to keep the temperature and system pressure and at 310 K and 1 bar, The SHAKE algorithm42 was applied to keep the distance between hydrogen and a heavy atom constrained to the equilibrium value. Individual electric fields of 0.1, 0.2 and 0.3 V nm-1 were applied for the simulation system along the positive 8


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direction of the z-axis. The whole system underwent a 40-ns simulation in an NVT ensemble in which the trajectories were recorded simultaneously for further analysis.

3. RESULTS AND DISCUSSION 3.1. An Encapsulated Cation in the CPNT. 3.1.1 Cation-Ow Radial Distribution Function (RDF). An electric field may allow a cation to overcome the dehydration energy barrier and further enter a nanochannel. Present MD simulations disclose that, under an electric field of 0.1, 0.2 or 0.3 V nm-1, Na+ can enter and move through the 8×(WL)4/POPE-CPNT easily. Under no electric field, one or two Na+ may randomly enter and be trapped in the channel. Li+ can enter the channel only under an electric field stronger than 0.3 V nm-1. To determine the effect of the electric field intensity on the cation-Ow (oxygen of water) RDF, the Na+-Ow RDFs in the 8×(WL)4/POPE-CPNT under individual electric fields were respectively analyzed and are illustrated in Figure S2. Distinctly, the positions of the first and second peaks are almost the same under different electric fields, indicating that the strength of an external electric field has little effect on the profile of the cation-Ow RDF in a CPNT which discloses the solvation structure of a cation. A similar result was once reported for a mixed solution of NaCl and CaCl2 in a lysozyme crystal by Hu et al.43 Based on the above result, the Na+-Ow and Li+-Ow RDFs under the electric 9



field of 0.3 V nm-1 were further analyzed to describe the solvation structures of Li+ and Na+ in the 8×(WL)4/POPE-CPNT. Since the structural difference between a midplane region and an α-plane zone may lead to discrepancies of a cation’s hydration structures, results in a midplane region and an α-plane zone were separately analyzed and shown in Figure 2. Notably, for both Na+ and Li+, there is an evident first maximum and an adjacent second one, indicating two cations can each form two solvation shells in the CPNT. The second peaks of Na+ and Li+ are both lower and broader than the first ones, indicating loose second solvation shells. The first peaks in the cation-OW RDFs of Li+ and Na+ are located at 1.95 and 2.25 Å, respectively, well consistent with the previous studies.44-47 The first peak of Li+ is more pronounced than that of Na+ and characterized with a lower value of the quantity r, inferring that water molecules in the first solvation shell of Li+ form a more compact structure. The solvation number of a cation can be calculated by integrating the RDF, plotted as a dotted line in Figure 2. On average, the numbers of water molecules in the first solvation shells of Li+ locating in a midplane region and an α-plane zone have almost the same values, both around 4.1. The results for Na+ are 5.1 and 4.4, respectively. For comparison, we also computed the solvation numbers of Li+ and Na+ in their first solvation shells in bulk. The results are 4.3 and 5.6, respectively, consistent with the literature reports.48,49 For Li+, whether locating in a midplane region or an α-plane zone, its first solvation number is always about 4.1, close to the counterpart in bulk. The 10


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possible reasons are the tight binding of water with Li+ and the small size of the hydrated structure of Li+, making it less affected by the inner space limitation of the CPNT. However, for Na+, there exists an emerging difference in the first solvation numbers when locating in a midplane region and an α-plane zone. When Na+ is locating in an α-plane zone, there are more water molecules in its two adjacent midplane regions to coordinate with Na+, resulting in 5.1 as the solvation number. While in a midplane region, the result is about 4.4. Similar results were reported in the literature.14 Thus, compared to the counterpart in bulk, Na+ may feel more comfortable in an α-plane zone than in a midplane region. Figure S3 clearly shows the microstructures of the first solvation shells of Na+ and Li+ in a midplane region and an -plane zone, respectively. The variations of the solvation numbers of Li+ and Na+ along the tube axis (z-axis) are shown in Figure S4, showing 3-5 for Li+ and 3-6 for Na+. This result indicates that the influence of the internal environment of a CPNT on the coordination of water molecules with Li+ is slightly less than that with Na+. In the process of a cation passing through a CPNT, it is also possible for the cation to coordinate with the carbonyl oxygen (OC=O) atoms of the CPNT, in addition to the hydration with the surrounding water. MD trajectory analysis indicated that Li+ is extremely difficult to coordinate with the OC=O atoms, which may be related to its strong hydration, while Na+ may coordinate with OC=O atoms. It was found that the coordination of Na+ with the OC=O atoms 11



mainly occurs in midplane regions, and the coordination number can be 1-2, even occasionally reaching 3, no matter what intensity of the electric field was applied. For instance, the variation of the coordination number of the OC=O atoms with Na+ along the major axis of the CPNT under the electric field of 0.3 V nm-1 is illustrated in Figure S5, inferring that the carbonyl oxygen (OC=O) may replace water to coordinate with Na+ in a midplane region.

3.1.2. Water Orientation in the Cation’s First Solvation Shell. To further study the orientation distribution of water molecules in the first solvation shell of a cation, the angle (θ) between the dipole of a water molecule and the Ow-cation bond, as depicted in Figure 3a, was defined. The orientation distributions of water molecules in the first solvation shells of Na+ and Li+ locating in an -plane zone and in a midplane region under the electric field of 0.3 V nm-1 were analyzed and the results are shown in Figures 3b and 3c, respectively. Distinctly, the orientation distribution profiles of Na+ and Li+ both have peaks of cosθ around -0.9, meaning that water molecules in the two cations’ first solvation shells use the oxygen atoms to approach the cations. The orientation distribution of water around Li+ is characterized with a relatively higher peak than that of Na+, indicating that Li+ has a stronger hydration than Na+, consistent with the result reported by Zhou et al.6 Furthermore, the hydration of Li+ is stronger in a midplane region than in an -plane zone, as the former is characterized with a higher peak. For Na+, as shown in Figure 3b, an enhanced solvation structure is observed when Na+ in 12


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an -plane zone. Summarily, Na+ exhibits stronger hydration in an -plane zone, while Li+ does so in a midplane region.

3.2. Cation’s Potential of Mean Force (PMF) through the CPNT. Figure 4 describes the PMF profiles of a single Na+ and Li+ moving along the major axis (z-axis) of the transmembrane CPNT of 8(WL)4/POPE from a mixed solution of NaCl and LiCl under individual electric fields of 0.1, 0.2 and 0.3 V nm-1, respectively, calculated by using the ABF method. The results under no electric field are also included. Under no electric field, Li+ and Na+ face different free energy barriers (so-called dehydration energies8) at the crucial time when entering the entrance of the CPNT. For Na+, its dehydration energy there is about 2.5 kcal mol-1, close to the result (2.4 kcal mol-1) by Hwang et al.15 for Na+ at the entrance of the 4xcyclo[-(D-Ala-Glu-D-Ala-Gln)2-]-CPNT obtained from a cv-SMD simulation. Such dehydration energy (2.5 kcal mol-1) is not so high for Na+ to overcome by means of thermal motion. As a result, one or two Na+ may occasionally enter the channel under no electric field. Compared with Na+, Li+ meets a relatively high dehydration energy barrier (about 4.5 kcal mol-1) at the channel entrance, too high for Li+ to overcome. As a result, no Li+ may enter the channel under no electric field. Na+ and Li+ both have lower free energies in the lumen. Therefore, these two cations may be confined at the moment of entering the lumen. The alternations of the barriers and wells in the PMF profiles indicate that these two cations diffuse through the CPNT with a series 13



of hopping. It is worth nothing that the maximum and minimum positions in two cations’ PMF profiles are quite different. The landscape of the free energy of Li+ between the second and seventh CP subunits (approximately −12.0 Å ≤ z ≤ +12.0 Å) shows local maxima in -plane zones and minima in midplane regions, in line with the result from Asthagiri et al. for Li+ in a CPNT of 4xcyclo[-(L-Ala-D-Ala)4-].18 Nevertheless, the results for Na+ is contrary, reaching local minima in -plane zones and maxima in midplane regions. Such a difference can be ascribed to the solvation number in the first solvation shell and the hydration strength of a cation. For Na+, the solvation number in its first solvation shell is 5.1 in an -plane zone, while 4.4 in a midplane region, signifying that Na+ is stabilized when locating in an -plane zone. As for Li+, whether locating in an -plane zone or in a midplane region, the first solvation number of Li+ is basically about 4.1. However, the hydration strength of Li+ in a midplane region is stronger than that in an -plane zone (see the section 3.1). Therefore, Li+ is stabilized when locating in a midplane region. The PMF profiles under individual electric fields, shown in Figures 4b-4d, indicate that the introduction of an electric field may significantly change the PMF landscape of a cation moving through the 8(WL)4/POPE-CPNT. The free energy difference of a cation between two ends of the CPNT increases with the enhancement of the electric field, which is shown as the PMF profile gradually changing to become an oblique line. It is clear that the dehydration energy barriers of Na+ and Li+ at the channel entrance both decrease as the 14


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electric field intensity increases, meaning that these two cations may enter the channel more easily. Under the electric field of 0.1 V nm-1, Li+ encounters a higher dehydration energy barrier (about 3.3 kcal mol-1) than that of Na+ (about 1.1 kcal mol-1) at the channel entrance, meaning that it is difficult for Li+ to enter the tube, while it is easier for Na+. In the channel, the free energies of Na+ and Li+ both gradually decrease along the direction of the external electric field. Nevertheless, the alternations of the barriers and wells are still reserved, inferring that Na+ passes through the CPNT still with a string of hopping. Under the electric field of 0.2 V nm-1, the energy barriers of Li+ and Na+ both further decrease at the channel entrance. Nevertheless, Li+ still faces a higher energy barrier (about 2.6 kcal mol-1) at the channel entrance, which is a little difficult for it to overcome. The alternating characteristics of the barriers and wells for two cations in the channel gradually become less obvious, and almost disappear under the electric field of 0.3 V nm-1. At this time, the motion of a cation is mainly promoted by the external electric field. Under the electric field of 0.3 V nm-1, the dehydration energy barrier of Na+ at the channel entrance is almost non-existent. As for Li+, the dehydration energy barrier becomes smaller (about 0.9 kcal mol-1), consistent with the phenomenon that Li+ can enter and pass through the CPNT in this case. The result discloses that a strong enough external electric field may decrease the dehydration energy barrier of a cation and allow the cation to enter the channel. 15



3.3. Electrostatic and VdW Interactions of a Cation with Water and the CPNT. To study the electrostatic and vdW interactions of a cation with water molecules in its first solvation shell and the CPNT during the transition of the cation through the channel, a single Na+ (or Li+) was fixed at the positions of z = −28.8, −26.4, . . . , +26.4, +28.8 Å along the major axis (z-axis), with a total of 25 sampling points, guaranteeing the samplings in bulk and in all midplane regions and -plane zones. The interval between two adjacent sampling points is 2.4 Å, half of the distance between two adjacent CP subunits. A 2.0-ns simulation was carried out at each of above individual positions, and the last 1.0-ns trajectories were collected for further analysis. The results are collectively shown in Figure 5. The vdW interactions of Li+ and Na+ with neighboring water molecules and the CPNT are all basically weak. In particular, the electrostatic interaction between a cation and neighboring water molecules plays a dominant part. Tang et al.23 also found that the interaction between Na+ and water is significantly stronger than those of ion-ion and water-water in a 0.5M KCl solution in a cylindrical nanopore. The electrostatic interaction energies of Li+ and Na+ with the CPNT become stronger when two cations enter the CPNT from the bulk. While those between the cations and water molecules in the first solvation shells gradually decrease due to the dehydration. In the channel, the variations of such interactions reflect the geometry of the cavity―alternating arrangement of -plane zones and midplane regions. However, the variations of such 16


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interactions for Na+ and Li+ are entirely different. Li+ possesses the stronger electrostatic interaction with water when in a midplane region, due to the stronger hydration. Conversely, the stronger electrostatic interaction of Na+ with water occurs in an -plane zone, which can be attributed to a larger amount of water molecules in the first solvation shell. Obviously, the electrostatic interaction energy of Li+ with water molecules is significantly higher than that of Na+, whether in bulk or in the channel, further proving that the hydration of Li+ is stronger than that of Na+.

3.4. Distribution of a Cation in the CPNT. 3.4.1. Axial Distribution. The axial probability distributions of Na+ and Li+ inside the 8×(WL)4/POPE-CPNT have been carefully investigated under no electric field and individual electric fields of 0.1, 0.2 and 0.3 V nm-1, respectively, and are illustrated in Figure 6. During the whole process of 40-ns simulation, no Cl- was observed entering the tube, mainly stemmed from the presence of the negatively carbonyl groups at two ends of the CPNT. Further observation discloses that the distributions of Na+ and Li+ inside the CPNT are quite different. The profiles of Na+ almost touch the bottom in midplane regions and Na+ exhibits the most specific distributions in -plane zones, where the local free energy wells are located. Compared to Na+, Li+ almost doesn’t appear in -plane zones and exhibits the largest occurrence probabilities in midplane regions, due to lower free energies. Present MD simulations indicate that either Na+ or Li+ is more likely to occur in the left 17



section of the CPNT. As we know, if a positively charged species enters a uniform electric field, it will do a linear motion with a constant acceleration along the direction of the electric field. Nevertheless, in addition to being promoted by the external electric field, a cation must overcome a series of energy barriers coming from the inner space limitation of the CPNT. Consequently, either Na+ or Li+ tends to stay at the left section of the CPNT.

3.4.2. Radial Distribution. The radial distributions of Na+, Li+, OW of channel water and OC=O atoms of the CPNT framework under individual electric fields were respectively investigated. The results are displayed in Figure 7. Here, the physical quantity r represents the distance of a species to the major axis (z-axis) of the CPNT and was calculated according to the formula r = x 2  y 2 , in which the x and y coordinates of the species were used. Clearly, Na+ and Li+ both are both prone to stay near the CPNT axis. Water molecules distribute between the cations and the tube wall, to meet with the requirements to coordinate with the cations (forming encapsulated cations) and to form H-bonded interactions with the OC=O atoms of the CPNT framework simultaneously. It can be seen that the radial distribution of water molecules is basically unchanged under individual electric fields, keeping a distance of about 3 Å from the carbonyl oxygen. Relatively, the radial distribution of Na+ is wider and closer to the carbonyl oxygen than that of Li+, owing to its large radius and higher activity. As the electric field intensity 18


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increases, the radial distribution of Na+ gradually widens, meaning that the activity of Na+ increases.

3.5. Residence Time of a Cation in the CPNT. The residence time of Na+ (or Li+) inside the 8×(WL)4/POPE-CPNT was further studied, and it was defined as the time of a cation staying in a channel,50 calculated by averaging all the species of the same kind. Table S1 gives the average numbers of Na+ and Li+ passing through the CPNT under individual external electric fields. The averaged residence times of Li+ and Na+ under individual electric fields are listed in Table 1. As expected, the stronger the electrical field, the smaller the residence time of Na+ in the channel. Similar phenomenon was once reported for Mg2+ in the (7,7) and (8,8) CNTs.51 Under the electric field of 0.3 V nm-1, the residence time of Li+ is slightly smaller than that of Na+. It was speculated that the lower mass of the hydration structure of Li+ is the major reason. Based on the former analysis, there is no significant difference between the energy barriers for Na+ and Li+ moving through the channel (see Figure 4). Furthermore, the forces acting on the identically charged the hydration structures of Li+ and Na+ from an electric field (E) are basically equal. Thus, the mass of the hydration structure of a cation will affect the speed of the cation moving forward through the CPNT to some extent.

3.6. Axial Diffusion of a Cation in the CPNT. The axial diffusion coefficient (Dz) of a cation in a channel can be derived from the axial mean square displacement ( MSDz ),52 which is the average square of the 19



displacement a cation travels along the major axis (z-axis) over the time t and can be calculated as follows,

Dz  MSDz / 2t =

1 1 2t N

 zi t   zi 0

2

where zi(t)-zi(0) is the axial distance traveled by the cation i over the time interval t, and its square is averaged over all cations (N) of the same kind in the channel. The angle bracket represents the ensemble average over many time intervals. Here, the species i denotes Na+ or Li+. As mentioned earlier, Na+ is willing to stay at an -plane zone, while Li+ in a midplane region, which means that the axial diffusions of these two cations in an -plane zone and in a midplane region are different. Accordingly, the time-dependent MSDz of Na+ in a midplane region and in an -plane zone under no electric field and individual electric fields of 0.1, 0.2 and 0.3 V nm-1, and those of Li+ under the electric field of 0.3 V nm-1, were respectively calculated and are collectively depicted in Figure 8. The axial diffusion coefficients (Dz) of Li+ and Na+ in a midplane region and in an α-plane zone were further obtained, based on the MSDz ∼ t profiles. The results indicate that the axial diffusion of Na+ mainly takes place in a midplane region, while Li+ occurs in an -plane zone. Na+ has a larger axial diffusion coefficient (Dz) in a midplane region as 287.5, 210.8.5 and 107.5 Å2 ns-1 under external electric fields of 0.3, 0.2 and 0.1 V nm-1, respectively. For comparison, the axial diffusion coefficient (Dz) of Na+ in a midplane region under no electric field was computed to be 83.8 Å2 ns-1, consistent with the reported value.13 This result discloses that the 20


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introduction of an external electric field may greatly enhance the axial diffusion of a cation. As expected, as the electric field strength increases, the cation's axial diffusion was accelerated. The slopes of the MSDz ∼ t curves of Li+ indicate that Li+ has a larger diffusion coefficient (Dz) in an α-plane zone as 456.6 Å2 ns-1 under the external electric field of 0.3 V nm-1. Compared with Na+, Li+ has a faster axial diffusion, consistent with the above result that Li+ has a relatively shorter residence time.

3.7. Water Chain in the CPNT. 3.7.1 Channel Water Structure. The axial probability distributions of the Ow-atoms of channel water molecules under individual electric fields of 0.1, 0.2 and 0.3 V nm-1 are collectively depicted in Figure 9. For comparison, the results under no electric field and free of ions, and no electric field but with the presence of Na+, Li+ and Cl- are also included in Figure 9. It is clear that the axial distribution of water is basically unaffected by the introduction of an electric field. Under no electric field, one or two Na+ ions may occasionally enter the channel and stay at the left section of the CPNT, which slightly influences the axial distribution of the nearby water. In order to study the influence of an external electric field on the microstructure of the water chain, the average probabilities of different amounts of water molecules occurring in a midplane and an α-plane zone were further analyzed and are shown in Figure S6. It can be seen that the introduction of an electric field has no distinct effect on the amount of water molecules in an α-plane zone. The occurring probabilities of one and two 21



water molecules are essentially maintained at about 72% and 8%, respectively. In a midplane region, the occurring probability of two water molecules is basically unchanged with the enhancement of the electric field, and is maintained at about 55%. Nevertheless, that of three water molecules increases slightly, causing the total amount of water molecules in the channel to slightly increase, consistent with the phenomenon that the total number of water molecules are 21.5, 22 and 24 under the external electric fields of 0.1, 0.2 and 0.3 V nm-1, respectively. In general, water inside the CPNT still prefers to take the 1-2-1-2 array,16 which is an average of one water molecule in an -plane zone and two in a midplane region, disclosing that the water chain in the CPNT has a certain resistance to an external electric field. A similar phenomenon was once reported by García-Fandiño et al.19 noting that the presence of ions hardly disturbed the original water arrangement, but merely increased disorder somewhat. 3.7.2. Dipole Orientation of Channel Water. The incorporation of a cation or an external electric field will inevitably affect the orientation of a polar molecule (i.e., water) in a channel. Here, the angle () between the dipole of a channel water molecule and the CPNT axis (z-axis) was used to describe the orientation of channel water. We calculated the dipole orientation distributions of channel water in the 8×(WL)4/POPE-CPNT under individual electric fields, recording the results in Figure 10. For comparison, the results for channel water in the 8×(WL)4/POPE-CPNT under no electric field and free 22


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of ions, and under no electric field but with the presence of Na+, Li+ and Cl-, are depicted in Figures S7a and 7b, respectively. Under no electric field and free of ions (Figure. S7a), channel water molecules in gap1 and gap7 exhibit positive and negative dipole states, corresponding to  = 40° and 150°, respectively, owing to the orientations from the bare negative carbonyl groups at two ends of the channel.13 The curves in the center gaps all have two peaks, meaning that channel water molecules in these regions may change their dipole orientations by means of thermal motion. When the CPNT is embedded in a NaCl/LiCl solution, several Na+ ions can enter the channel. The dipole of a channel water molecule is simultaneously influenced by the negative carbonyl groups at the channel ends and the Na+ ions in the channel. The existence of a cation results in the dipole of a channel water molecule pointing away from the cation, contrary to the orientation from the negative carbonyl groups at the channel ends. MD simulation indicates that Na+ mainly stays in the second α-plane zone under no electric field. Channel water molecules in gap1 mainly exist in negative dipole states (Figure S7b), meaning that the dipole orientation from Na+ plays a dominant role. Due to the dipole-dipole interactions, such negative dipole orientation would pass along the water chain. Nevertheless, the dipole orientations of water molecules in gap2 are also influenced by the presence of Na+ in the adjacent second α-plane zone. These two contrary orientations make the 23



water molecules in gap2 flip between the positive and negative dipole states. The water molecules in gap7 still keep negative states, indicating the orientation from the distant Na+ is suppressed by that from the carbonyl groups at the neighboring channel end. Under the electric field of 0.1 V nm-1, there are about 5 Na+ visiting the CPNT and distributing mainly in the left section of the channel, resulting in the dipole orientations of channel water in gap1 mainly exhibiting negative dipole states. These water molecules also display positive states (Figure 10a), due to the orientation from the external electric field, similar to the phenomenon that water is prone to orientate along the external electric field in a lysozyme crystal.43 Water molecules in gap7 mainly take the positive dipole states at this time, indicating that the orientation from the external electric field overpowers that from the carbonyl groups at the neighboring channel end. Water molecules in other gaps flip between the positive and negative dipole states, resulted from the collective effects from the external electric field, the presence of channel Na+ ions, the dipole-dipole interactions between channel water molecules, and the bare negative carbonyl groups at two ends of the channel. As the electric field strength increases, channel water molecules in all gaps tend to take positive dipole states. At that time, the influence of the electric field is dominant. The dipole orientation distribution of channel water in gap7 is relatively wide, due to the collective effect of the positive orientations from 24


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the electric field and the presence of Na+ in the channel, and the negative orientation from the bare negative carbonyl groups at the adjacent channel end.

4. CONCLUSION The transport behaviors of Na+ and Li+ through the transmembrane CPNT of 8(WL)4/POPE from a mixed solution of NaCl and LiCl under an electric field have been investigated. The introduction of an electric field helps to decrease the dehydration energy barrier of a cation at the CPNT entrance. Relatively, it is easier for Na+ to enter the channel. Even under no external electric field, one or two Na+ ions may occasionally enter the channel. Li+ can enter the channel only under an electric field stronger than 0.3 V nm-1. Either Na+ or Li+ is prone to occur in the left section of the channel and both can form two solvation shells. Li+ forms a more compact solvation structure than Na+, related to its stronger electrostatic interaction with surrounding water molecules. Accordingly, the solvation structure of Li+ is less affected by the electric field than that of Na+. Compared to the case in bulk, Na+ in a midplane region is obviously insufficiently solvated by water. Na+ exhibits stronger hydration in an -plane zone, while Li+ does so in in a midplane region. Whether or not there is an external electric field, Na+ mainly appears in an -plane zone while Li+ does so in a midplane region, consistent with their axial profiles of PMFs and the electrostatic interactions with water. As a result, the 25



axial diffusions of Na+ and Li+ mainly occur in a midplane region and in an -plane zone, respectively, and both can be significantly accelerated as the electric field strength increases. Accordingly, the residence times of two cations are shortened. The presence of cations and the introduction of an external electric field hardly disturb the original 1-2-1-2 water array in the channel. Nevertheless, these two factors obviously influence the dipole orientations of water molecules in the CPNT. Results in this work are of great significance for achieving a profound understanding of the discrepancies of the transport characteristics of coexisting Na+ and Li+ in an artificial biological channel under an external electric field and are helpful to provide information for the drug delivery and disease treatment related with the transport of Li+ or Na+ in a living organism.

ASSOCIATED CONTENT Support information Average numbers of Na+ and Li+ passing through the CPNT under individual electric fields (Table S1). RMSDs of all atoms in a NaCl/LiCl solution box (Figure S1). Channel Na+-Ow RDFs under individual electric fields (Figure S2). Snapshots of the first solvation shells of Na+ and Li+ in a midplane region and an -plane zone (Figure S3). Axial variations of water numbers in the first solvation shells of Na+ and Li+ (Figure S4). Axial variation of the coordination number of OC=O atoms with Na+ (Figure S5). Average probabilities of various filling states in an α-plane zone and in a midplane region under individual 26


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electric fields (Figure S6). Distributions of channel water orientation angles () in individual gaps under no external (Figure S7).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

ORCID Jianfen Fan: 0000-0003-4974-4978.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work has been supported by the National Basic Research Program of China (973 program, Grant 2012CBB25803) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. It was further supported by the Project of Scientific and Technology Infrastructure of Suzhou (SZS201708). The authors are grateful to Associate Professor Jian Liu and Miss Xialan Si for their insightful suggestions.

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(42) Ryckaert, J. P.; Ciccotti, G.; Berendsen, H. J. C. Numerical Integration of the Cartesia Equations of Motion of a System with Constraints: Molecular Dynamics of n -Alkanes. J. Comput. Phys. 1977, 23, 327341. (43) Hu, Z. Q.; Jang, J. W. Electrophoresis in Protein Crystal: Nonequilibrium Molecular Dynamics Simulations. Biophys. J. 2008, 95, 41484156. (44) Wu, H. C.; Yoshioka, T.; Nakagawa, K.; Shintani, T.; Tsuru, T.; Saeki, D.; Chen, Y. R.; Tung, K. l.; Matsuyama, H. Water Transport and Ion Rejection Investigation for Application of Cyclic Peptide Nanotubes to forward Osmosis Process: A Simulation Study. Desalination. 2017,424, 8594. (45) Guardia, E.; Rey, R.; Padro, J. A. Na+-Na+ and CI--CI- Ion Pairs in water: Mean force Potentials by Constrained Molecular Dynamics. J. Chem. Phys. 1991, 95, 28232831. (46) Obst, S.; Bradaczek, H. Molecular Dynamics Study of the Structure and Dynamics of the Hydration Shell of Alkaline and Alkaline-Earth Metal Cations. J. Phys. Chem. 1996, 100, 1567715687. (47) Chang, T. M.; Dang, L. X. Detailed Study of Potassium Solvation Using Molecular Dynamics Techniques. J. Phys. Chem. B. 1999, 103, 47144720. (48) Bucher, D.; Guidoni, L.; Carloni, P.; Rothlisberger, U. Coordination Numbers of K+ and Na+ Ions Inside the Selectivity Filter of the KcsA Potassium Channel: Insights from First Principles Molecular Dynamics. Biophys. J. 2010, 98, 4749 (49) Grossfield, A.; Ren, P. Y.; Ponder, J. W. Ion Solvation Thermodynamics from Simulation with a Polarizable Force Field. J. Am. Chem. Soc. 2003, 125, 1567115682. (50) Azamat, J.; Sardroodi, J. J.; Rastkar, A. Water Desalination through Armchair Carbon Nanotubes: A molecular Dynamics Study. RSC Adv. 2014, 00, 17. (51) Azamat, J.; Sardroodi, J. J. Ion and Water Transport Through (7,7) and (8, 8) Carbon and Boron Nitride Nanotubes of Different Electric Fields: A Molecular Dynamics Simulation Study. J. Comput. Theor. Nano. 2014, 11, 26112617. (52) Mamonov, A. B.; Kurnikova, M. G.; Coalson, R. D. Diffusion Constant of K+ inside Gramicidin A: A Comparative Study of Four Computational Methods. Biophys. Chem. 2006, 124, 268278.

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Table 1. Averaged residence times (ps) of Na+ and Li+ under individual applied electric fields.

Electric field (V nm-1)

0.1

0.2

0.3

Na+

4478

1822

812

Li+

/

/

715

Figure 1 Descriptions of an α-plane zone, a midplane region and a gap of a CPNT (a) and the snapshot of the simulation system composed of the transmembrane CPNT of 8×(WL)4/POPE embedded in a NaCl/LiCl solution under an external electric field (E) along the positive direction of z-axis (b). The CPNT is oriented in the POPE membrane along the z-axis and only its backbone is represented. Water molecules are shown in red on both sides of the membrane. Na+ and Li+ are shown in yellow and green vdW spheres, respectively.

31



Figure 2. Cation-Ow RDFs of Na+ (a) and Li+ (b) locating in a midplane region (black lines) and in an -plane zone (red lines) under the external electric field of 0.3 V nm-1, respectively. The dotted black and red lines represent the integrations of the RDF profiles.

Figure 3. Scheme of the described orientation angle () of a water molecule in the first solvation shell of a cation (a), distributions of cos for Na+ (b) and Li+ (c) in a midplane region (black lines) and in an -plane zone (red lines) of the 8×(WL)4/POPE-CPNT under the external electric field of 0.3 V nm-1, respectively. 32


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Figure 4. PMF profiles of Na+ (black lines) and Li+ (red lines) along the major axis (z-axis) of the 8(WL)4/POPE-CPNT under no electric field (a) and individual external electric fields of 0.1 (b), 0.2 (c) and 0.3 V nm-1 (d), respectively. The vertical dashed lines represent the positions of individual CP subunits.

33



Figure 5. Electrostatic and vdW interactions of Na+ (a) and Li+ (b) with water molecules in the cations’ first solvation shells are represented by black square lines and red circled lines. Those with the CPNT are represented by blue and cyan triangled lines, respectively. The vertical dashed lines represent the positions of individual CP subunits.

Figure 6. Axial probability distributions of Na+ (a) under no electric field (black line) and individual electric fields of 0.1 (red line), 0.2 (black line) and 0.3 V nm-1 (olive line), and Li+ (b) under the electric field of 0.3 V nm-1 along the major axis (z-axis) of the 8×(WL)4/POPE-CPNT, respectively. The vertical dashed lines represent the positions of individual CP subunits. 34


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Figure 7. Radial distributions of Na+ (black), Li+ (red line), Ow of channel water (blue line) and OC=O atoms of the CPNT framework (green line) under individual electric fields of 0.1 (a), 0.2 (b) and 0.3 V nm-1 (c), respectively.

Figure 8. Time-dependent MSDz curves of Na+ (a) and Li+ (b) in an α-plane zone and in a midplane region under no electric field and individual electric fields of 0.1, 0.2 and 0.3 V nm-1 along the major axis (z-axis) of the 8×(WL)4/POPE-CPNT.

35



Figure 9. Axial probability distributions of the O-atoms of water under individual electric fields of 0.1 (blue line), 0.2 (pink line) and 0.3 V nm-1 (olive line), and no electric field with (red line) and without ions (black line), respectively.

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Figure 10. Axial probability distributions of the dipole orientation angles () of channel water in individual gaps of the 8×(WL)4/POPE-CPNT under individual electric fields of 0.1 (a), 0.2 (b) and 0.3 (c) V nm-1, respectively.  is the angle between the water molecular dipole and the channel major axis (z-axis).

37



For Table of Contents Use Only

MD Simulations on the Transport Behaviors of Mixed Na+ and Li+ in a Transmembrane Cyclic Peptide Nanotube under an Electric Field Lingling Zhang, Jianfen Fan,* Mengnan Qu

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MD Simulations on the Transport Behaviors of Mixed Na+ and Li+ in a

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