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Transport Behavior of the Enantiomers of Lactic Acid through Cyclic Peptide Nanotube: Enantiomer Discrimination Hossein Farrokhpour, Alireza Mansouri, and Alireza Najafi Chermahini J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b00010 • Publication Date (Web): 27 Mar 2017 Downloaded from http://pubs.acs.org on March 31, 2017

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The Journal of Physical Chemistry

Transport Behavior of the Enantiomers of Lactic Acid through the Cyclic Peptide Nanotube: Enantiomer Discrimination

Hossein Farrokhpour*, Alireza Mansouri, Alireza Najafi Chermahini

Department of Chemistry, Isfahan University of Technology, Isfahan, Iran, 84156-83111

Corresponding author: H. Farrokhpour E-mail: [email protected];[email protected]

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ABSTRACT The behavior and mechanism of the transport of the enantiomers of lactic acid (LA) in a cyclic peptide nanotube (CPNT) embedded in water, consisted of eight cyclic peptide unit ([Ala-D-Ala-L]5), have been studied in details using quantum calculations and steered molecular dynamic (SMD) simulations, separately. The SMD simulations were performed in three different phases and it was observed that the transport behavior of two enantiomers in the CPNT is different from each other in each phase. The variation of the calculated pulling force of two enantiomers versus time in three phases showed that (a) if the enantiomers move near the walls of CPNT, the velocity of S-enantiomer is more than R-enantiomer and the walls of the nanotube can act as chirality discriminator (b) if the enantiomers are limited to move in the center of CPNT the velocity of R-enantiomer is more than S-enantiomer and (c) when the enantiomers move in the

nanotube and their center of mass is free for the

displacement in x and y direction as well as displacement in z-direction, again the velocity of R-enantiomer is higher than S-enantiomer. The radial distribution functions (RDFs) of the important atoms of the enantiomers, relative to the O atoms of CNPT, were calculated and it was observed that the affinities of the atoms of two enantiomers to O atoms of CNPT during their movement in the CPNT are different in each phases. The results obtained in this work, typically, show that the transportations of the enantiomers of biological molecules moving in the biological channels are different.


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1. INTRODUCTION The cyclic peptide nanotubes (CPNTs) are novel supramolecular nanobiomaterials with tubular structure which can be used as channel for the delivery and molecular diffusion of drugs, organic molecules, ions and water in the membranes, especially lipid membrane 1– 17

. CPNT as a kind of artificial channels for molecular transportation was produced by

Ghadiri et al. for the first time 18. Because of their ease synthesize and manipulations, CPNTs have attracted much interest in different fields, especially biology. The ability and properties of the CPNT can be changed by the control of the properties of its outer surface and inner diameter via changing the functional side chains and the number of amino acids in each cycle peptide. Cycle peptides consist of alternate L/D amino acids and can be stacked to each other by the hydrogen bonds so that the carbonyl and amine groups of the amino acids in the cyclic peptides are directed perpendicular of the ring and contribute in forming of the hydrogen 15–17

bond in the two adjacent cyclic peptides

. It has been determined, experimentally and

theoretically, that the CPNTs are stable 19 and their stabilities depends on the number of joint cyclic peptides and the type of the amino acids in cyclic peptide. The hydrophobic or hydrophilic groups of outer CPNTs surface (side chains of amino acids) leads to easy insertion of CPNT into lipid bilayer membrane or water solubilization 2,11,20–22. One of the important applications of CPNTs is using them for the transportation ions and small molecules. For example, it has been determined that the CPNTs are the best candidates as artificial ion channels

19

compared to natural ions channels. Zhang et al. used

molecular dynamic (MD) simulation to study the transport behaviour of NH4+ and NH3 in CPNTs 23. Yan et al. investigated the transport of Ca+2, K+ and Na+ in the water-filled CPNT by MD simulations 24. The potential of CPNTs for the drug delivery has also been examined, theoretically and experimentally

8,24,25

. For example, Liu and coworkers studied,

experimentally and theoretically (MD simulation), the transportation of the drug 5-



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fluorouracil (5-FU) through CPNT

12

and observed that 5-FU molecule moves from the

different energy minima along the nanotube. Rui et al. studied the dynamic behavior and transport properties of ethanol molecules in CPNTs using MD simulations with different radii 26

. Jian and coworkers investigated the transport of small molecules such as methane and

methanol

through the water-filled CPNT

27

using MD simulation and the potential

application of CPNT for the separation of water/alcohol mixture. Transmembrane delivery of anticancer drugs through the CPNTs has also been studied 28. Recently, the interaction of cyclic peptides with the enantiomers of a molecules has been studied and it was found that the cyclic peptide has a potential for the discrimination of the enantiomers of molecule based on the difference in the interaction of the enantiomers with cyclic peptide28–32. For example, Zhao et al. studied the interaction of the enantiomers of 1-phenyl-1-propanol with E-type cyclic decapeptide

29

. Farrokhpour et al. performed the

theoretical modeling of the chirality recognition of enantiomers by cyclic peptide using gas phase photoelectron spectroscopy 32. Although, there are studies on the chirality recognition of enantiomers using cyclic peptides and the transport behavior of the ions and some molecules in the CPNTs, there is no theoretical and experimental studies on the transportation behavior and mechanism of enantiomers in the CPNTs in literature. The main aim of this work is the investigation of the behavior of the enantiomers of a molecule when transport through CPNT with the aid of both quantum calculations and MD simulation. LA (CH3CH(OH)CO2H) as one of the important organic molecules which is produced in human and animal body was selected for this study. LA is produced through anaerobic glycolysis which the glucose molecule transmute to lactate (S-LA) when inadequate amounts of oxygen (O2) are accessible 33. LA has two chiral isomers known as S-LA and R-LA (see Figure 1).


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Figure 1. The structure of S (left) and R(right) enantiomers of lactic acid (LA). The atoms have been numbered.

In the first part of this work, the intermolecular interaction of the enantiomers of LA with a cyclic peptide (cycle [alanine (Ala)-D-Ala-L] 5) were calculated to find the difference between their interactions and orientations relative to the cyclic peptide. In the second part of this work, the transport process of two enantiomers of LA through the CPNT consisted of eight cyclic peptide unit ([Ala-D-Ala-L]5) was investigated using steered molecular dynamic (SMD) simulations. To the author knowledge, this is the first theoretical study on the transportation of two enantiomers of a molecule through CPNT to understand the difference in their behavior.

2. COMPUTATIONAL DETAILS 2.1 Quantum calculations The structure of two enantiomers of LA and cyclic peptide were optimized using density functional theory (DFT) employing B3LYP34 functional and 6-31+G(d) basis set, separately. The optimized structure of enantiomers were docked to the cyclic peptide using the AutoDock 4.2

35,36

to find the approximate orientation of enantiomers relative to cyclic

peptide and predict their standard free binding energies (∆G°). The structures of the



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complexes obtained from the docking calculations were further optimized, quantum mechanically, using M06-2X37 functional and 6-31+G(d) basis set. The interaction energy (Eint) between each enantiomer and cyclic peptide was calculated using supermolecular approach considering the basis set superposition error (BSSE)

38

. The entire quantum

calculations were performed using Gaussian 09 quantum chemistry package 39.

2.2 Optimization of CPNT using the MD simulation The selected CPNT in this work, consisted of eight units ([Ala-D-Ala-L] 5), constructed based on antiparallel stacking of each unit with the next unit (see Figure 2). The optimized structure of ([Ala-D-Ala-L]5) with the diameter of 1.1 nm, obtained at the B3LYP/6-31+G(d) level of theory, was used for the construction of the CPNT.

Figure 2. Schematic representation of the selected CPNT with antiparallel stacking. Each cycle peptide includes ten alanine (Ala) amino acid and the hydrogen bonds have been shown as dotted red line. Here only the stacking of four-cycle peptides has been shown. The solvation box of CPNT was designed with TIP3P water model so that the minimum distance between the atoms of CPNT and the walls of the simulation box was 1.6 nm

18,40,41

which this space was filled with water molecules. The prepared system was processed for


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minimization, equilibration and production. The minimization process was included 10000 cycles without any position restrain. The equilibration process was performed in the NVT ensemble for 200 ps by restraining the CPNT as 1000 kJ/mol.nm-2 in harmonic force constant. In the production process, the MD simulation on the system, obtained from equilibration processes, was performed in the NPT ensemble for 10 ns without any position restrain. The periodic boundary condition (PBC) was considered in equilibration and production processes. The temperature and pressure of the system were kept at 310 K (the normal temperature of human body) and 1 bar using Berendsen thermostat and Parrinello– Rahman barostat, respectively 42,43. The partial-mesh Ewald (PME) summation algorithm was used for calculating the electrostatic interactions

44

and the cut-offs of the non-bonded

interaction was set to 1.4 nm. The linear constraint solver (LINCS) algorithm was used to constrain the bonds including hydrogen atoms45. GROMACS 4.5.7 was applied for all MD simulation using CHARMM 27 force field parameters 46,47.

2.3 Molecular docking of the enantiomers of LA to the optimized CPNT Molecular docking method is a useful tool in computational chemistry and pharmaceutical science to realize and predict the best position of the ligand close to receptor molecule and the binding free energy

35,48,49

. The AutoDock 4.2 was used to calculate and

predict binding free energy and the orientation of both enantiomers of LA into the lumen of the optimized CPNT 36. The optimized CPNT structure, obtained from the MD simulation, was selected for the docking simulation as receptor rule. Both enantiomers of LA, optimized at the B3LYP/6-31+G(d), were docked into the lumen of CPNT via Lamarkian Genetic Algorithm (LGA) procedure

35

. An initial population of random individuals has been used

with a population size of 50 individuals; a maximum number of generations of 27,000; a maximum number of 2.5 × 106 energy evaluations; a mutation rate of 0.02, and a crossover



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rate of 0.80 and gasteiger charges model was added using MGLTools package 1.5.6 35. The bonds of the enantiomers of LA were not allowed to rotate, freely in the docking process. Docking simulation was performed with setting of grid size to 40 × 46 × 40 points in the first cycle unit of CPNT. The grid spacing of grid box was set to 0.375 Å.

2.4 Steered molecular dynamic (SMD) simulation

The SMD simulations were performed in two different pull geometries which have been explained in three phases as following. In phase I and III, the initial geometry of complex (enantiomer+CPNT) were taken from the molecular docking calculations (see section 3.2; Figure 8). The initial geometry related to phase II is different from phase I and III so that the enantiomer was placed 1nm away for the center of the first cyclic peptide of CPNT. The SMD simulations of phase I and II are position restrain strategy while the SMD simulation of phase III is direction restrain strategy. In position restrain algorithm, the molecule is retrained at a position of reference molecule (CPNT) and the direction of its movement depends on the position of reference molecule (CPNT) so that by changing the position of CPNT the direction of the molecule change according with it, simultaneously. In fact, the x and y coordinate of the center of mass of LA acid relative to the CPNT has been restrained and molecule can move in the z-direction (the axis of the CPNT) and rotate around its center of mass when is moving in the z-direction. In directional strategy, the direction of the pulled molecule is independent of the movement of CPNT.

Phase I The complexes of the enantiomers of the LA and CPNT, obtained from the docking calculations, were used for the SMD simulation of pulling the enantiomers through the lumen


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of CPNT. The parameters of the CHARMM force field for the enantiomers of LA were obtained from the SwissParam website50. The CHARMM force field is widely used for the organic substances. The complexes were solvated in water considering TIP3P force field for water molecules. The size of simulation box for each complex was set to 7 × 7 × 10 nm3 that can pull LA enantiomers to z-direction. Before starting to perform SMD simulation, the system was equilibrated by restraining LA and CPNT in NPT ensemble for 1 ns with similar conditions used for the equilibration of only CPNT mentioned in section 2.2. The pulling of enantiomers through the CPNT was performed using a harmonic sparing constant of 1000 kJ mol-1nm-2 and pulling rate of 0.001 nm ps-1 which CPNT was selected as a reference group for the pulling of enantiomers. During SMD simulation, the backbone atoms of CPNT (O, Cα and N) were restrained with a harmonic force constant of 1000 kJ mol-1nm-2. The pulling processes of LA were performed through the specific position of CPNT with position restrain strategy.

Phase II The enantiomers of LA were placed at 1 nm away from the center of the first cyclic peptide of CPNT. The complex of LA and enantiomer was put in the center of the simulation boxes and the system was equilibrated by restraining LA and CPNT in NPT ensemble for 1 ns and then SMD simulations were performed for 5000 ps with the same condition of Phase I. The size of simulation box for each complex is 11 × 11 × 12 nm3 that can pull LA in Z direction.

Phase III The initial structures of complexes selected for the simulations in this phase are same as those used in phase I (see section 3.2; Figure 8). The pulling process of the enantiomers of



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LA were performed along z-direction without any position restrain and only the backbone atoms of the first cyclic peptide were restrained. The simulation parameters of this phase are same as the parameters selected for phase I.

3. RESULT AND DISSCUSION 3.1 Interaction of enantiomers of LA with cyclic peptide Figure 3 demonstrated the optimized structures of the complexes of enantiomers of LA and cyclic peptide calculated at the M06-2X/6-31+G(d) level of theory. The optimized structures have been shown from two side views in Figure 3. The calculated interaction energy (Eint) of the R- and S- enantiomer with the cyclic peptide are -22.17 and -29.72


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kcal/mol,

respectively.

Figure 3. The optimized structures of the complex of enantiomers of lactic acid (LA) and cyclic peptide at the M06-2X/6-31+G(d) level of theory. The initial structures of the complexes for the optimization have been obtained from the docking calculations. Hydrogen bonds have been shown as dotted red lines. It can be seen that the Eint of S- enantiomer is greater than that of R-enantiomer. The effects of the interaction on the deformation of the cyclic peptide due to the interaction with the R and S-enantiomer have been depicted in Figure 4. It can be seen that the effect of Senantiomer on the deformation of the cyclic peptide from the circle is more than to what is seen when the cyclic peptide is interacting with the R-enantiomer. The more deformation of cyclic peptide interacting with S-enantiomer confirms that its interaction with the Senantiomer is more than R-enantiomer.



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Figure 4. Comparison of the deformed geometry of the cyclic peptide (red cycles) after interaction with the R and S-enantiomers with the geometry of cyclic peptide before interaction (black cycles).

As seen in Figure 3, there are two hydrogen bonds between each enantiomer and cyclic peptide. The distances between some atoms of the enantiomers with the atoms of cyclic peptide have been depicted in Figure 5.


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Figure 5. A more clear picture for the interaction of enantiomers with cyclic peptide (only a part of cyclic peptide interacting with the enantiomers has been shown). The distance between important atoms of enantiomers of lactic acid (LA) and the cyclic peptide have been depicted in the figure.

The O1 atom in R-enantiomer (see Figure 1) is far from the cyclic peptide and has not the interaction with the cyclic peptide so that it cannot affect the cyclic peptide unlike to what observed for the S-enantiomer. The length of the hydrogen bond between the O1 atom of Senantiomer and H atom of NH2 group is 2.64 Å. The distance of O2 and O3 atoms of Senantiomer with Hα and H atoms of NH2 group of cyclic peptide are 2.92 and 2.28 Å, respectively. Also, in R- enantiomer, the distance of O2 and O3 atoms from the H atom of NH2 group and Hα atom of cyclic peptide are 2.18 and 2.39 Å, respectively. The other important distances between the enantiomers and cyclic peptide is the distances of H1 and H3 atoms of enantiomers from the oxygen atoms of two carboxylic groups in the cyclic peptide (see Figure 5). The corresponding values for S and R-enantiomer are (1.74 and 1.82 Å) and (1.83 and 1.89 Å), respectively.



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Figure 6. The two-dimensional (2D) interaction diagrams of the complexes obtained by ligplot software. The atoms responsible for the van der Waals (vdW) interactions have been shown by ( ) in the figure.

The Ligplot software

48,51

were used to identify the atoms responsible for the van der

Waals (vdW) interactions between the enantiomers and cyclic peptide. Figure 6 demonstrates the schematic 2D interaction diagrams of the complexes obtained from the ligplot. Figure 6 shows that there is vdW interaction between the S-enantiomer and cyclic peptide while there is no vdW interaction for the R-enantiomer. There are vdW interaction between the C1 atom of S-enantiomer and C24 (C of carboxyl group) and C25 (Cα of cyclic peptide). Three important results can be deduced from the theoretical calculations performed in this part. (a) Based on the calculated distances between the enantiomers and cyclic peptide (Figure 5), the S-enantiomer is more close to the cyclic peptide than R-enantiomer due to the higher attraction of the S-enantiomer. (b) The O1 atom (oxygen of carbonyl group) of Senantiomer has directed toward the cavity of cyclic peptide while the opposite direction is seen for the O1 of R-enantiomer due to the position of methyl group. (c) the S-enantiomer can bind to the cyclic peptide through both hydrogen bonding and vdW interaction but, Renantiomer can bind only through hydrogen bonding interactions.


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Regarding to the difference in the interaction energies of enantiomers of LA with cyclic peptide, it is expected that the transport behavior of R-enantiomer in the CPNT could be different from the S-enantiomer due to the difference in the interactions. Studying the transport behavior of the enantiomers in the CPNT can provide information about the potential of this kind of nanostructures for the chirality discrimination of the mixtures of enantiomers transporting through them. This study provides information which will be useful for the transportation of the enantiomers of biological molecules in the artificial and natural channels in the biological systems.

3.2 Transport mechanism To understand the transport behavior of the enantiomers of LA through CPNT, three separate SMD simulations were performed which have been named as phase I, phase II and Phase III in this paper. The SMD simulation can be performed in two different methods including velocity constant and force constant

52

. In the velocity constant method, the

molecule moves with a constant velocity and the pulling force on the molecule changes during its movement to provide the constant velocity for the molecule during its transportation. In the force constant method, the force exerted on the molecule during its movement is constant and the velocity is changing. The velocity constant method was selected for the SMD simulation in this work and the velocity equal to 0.001 nm/sec was selected for the movement of two enantiomers through the CPNT. To check the equality of the velocity of two enantiomers, the calculated distance between the centers of mass (COM) of two enantiomers of LA and that of CPNT for the SMD simulations related to phase I have been depicted in Figure 7. It can be seen that both plots are coincide on each other and confirms that the velocity of two enantiomers are equal with each other. Therefore, both enantiomers reach at the same points of CPNT at the same time.



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Figure 7. The distance between the center of mass (COM) of the enantiomers of lactic acid (LA) and the center of mass of CPNT during 4ns simulation time related to the SMD simulation of phase I.

SMD of Phase I.


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In the SMD simulation of this phase, the relative position and orientations of the enantiomers relative to the first cyclic peptide of CPNT were obtained from the molecular docking calculations. The position and orientation of R and S-enantiomer relative to the first cyclic peptide of CPNT have been demonstrated in Figure 8.

Figure 8. The position and orientation of the enantiomers of lactic acid (LA) relative to the first cyclic peptide of CPNT obtained using the docking of the enantiomers to CPNT. Only the first cycle of CPNT has been shown.

Based on the docking calculation, the best place for the enantiomers is close the inner wall of CPNT and the enantiomers move through the CPNT near the inner wall in this case. The docking calculations show that there are three hydrogen bonds between the R- and Senantiomer with the first cyclic peptide of CPNT, respectively (see Figure 8).



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Figure 9. The variation of the pulling forces of two enantiomers of lactic acid (LA) during 4 ns SMD simulation time related to Phase I.

Figure 9 demonstrated the variation of pulling force exerted on each enantiomer during its movement through the CPNT in the z-direction (the axis of CNPT). Before starting to explain about Figure 9, the concept of pulling force is explained, briefly. The pulling force is a mean force which is an equal and opposite biasing force, allowing both enantiomers to move across the barriers and escape from minima in potential energy surface 53. Figure 10 explains the role of the repulsion and attraction forces when the molecule is moving between two sequential cyclic peptides, schematically. The arrows in Figure 10 show the forces between the molecule and the first and second cyclic peptide. When the molecule is very close to the backbone of the first cyclic peptide and entering to it, there is repulsive force between them and the velocity of the molecule decreases. In this case, the pulling force in the direction of movement of the molecule (positive pulling force) should be exerted on the molecule to compensate the velocity decrease of the molecule and provide the constant velocity for the molecule during SMD simulations. When the molecule is leaving the first cyclic peptide and is still close to the backbone of cyclic peptide, the force between them is


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still repulsive and exerted in the direction of movement of molecule and increase the velocity of molecule. Therefore, the pulling force is exerted on the molecule in the opposite direction of its movement to decrease the velocity of molecule (negative pulling force). The repulsive force decreases when the distance of molecule from the first cyclic peptide increases. When the distance of the molecule from the first cyclic peptide increases further, the nature of the force between the cyclic peptide and molecule changes from the repulsive to attractive and the velocity of the molecule decreases again and the positive pulling force is necessary to increase the velocity of molecule in SMD simulation (case A in Figure 10). By further increase of the distance of molecule from the first cyclic peptide the attraction forces with the first cyclic peptide decreases and the attraction forces with the second cyclic peptide start to increase. At distance correspond to the middle between two cyclic peptide, the molecule is under two attraction forces in two opposite directions and the resultant force on the molecule is zero which is correspond to zero pulling force (case B in Figure 10). By approaching the molecule to the second cyclic peptide, the attraction forces with this cyclic peptide increases and the velocity of molecule increases and the negative pulling force is necessary to reduce the velocity of molecule. By the decrease of the distance of molecule from the second cyclic peptide, the attractive force decreases and the repulsive force start to appear (case C in Figure 10) and the velocity of molecule decreases which the positive pulling force is necessary to compensate the decrease in the velocity. Based on these explanations, the amount and sign of the pulling force is as a criterion to distinguish the amount and direction of the force exerted from the channel on the moving molecule. Negative pulling force means that the net force exerted to the molecule from the channel is in the direction of the movement of molecule and the molecule tends to move more quickly. The positive pulling force corresponds to the net force exerted on the molecule from the channel in the opposite direction of its movement. It is important to notice that the rotation of molecule around its center of mass during its



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movement has also effect on the amount and sign of the pulling force. For example, suppose that the interaction of the molecule at a certain distance from a cyclic peptide is attraction and when the orientation of molecule change due to the rotation, the attraction of the molecule with the cyclic peptide decreases or may be changed to repulsive.

Figure 10. One of the enantiomers of lactic acid (LA) is moving from one cyclic peptide to the other one. The arrows show the forces between the molecule and cyclic peptides.

It can be seen in Figure 9 that the pulling force changes oscillatory with the time for both enantiomers and it is important to notice that the amplitude of the oscillations of pulling force for S-enantiomer is smaller than R-enantiomer. Considering the explanations about the pulling force, the positive and negative sign of pulling force means that the enantiomer is under the net force in the opposite direction and in direction of its movement in the channel, respectively. The other important point is that the maximum and minimum of the oscillations of the pulling force, related to the movement of S-enantiomer in CPNT, are mostly in the negative region while for the R-enantiomer, the maximum and minimum of pulling force are in the positive and negative region, respectively (see the dashed red lines in Figure 9). It can


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be concluded that the net force exerted on the S-enantiomer moving near the inner wall of the CPNT is in the direction of its movement while the R-enantiomer is under the force in both the direction and opposite direction of its movement. Therefore, the movement of the S- and R-enantiomer when they are traveling near the inner wall of the CPNT is different from each other so that the movement of S-enantiomer is easier (more velocity) than that of Renantiomer. Thus, it can be deduced that the inner wall of CPNT can be used as a discriminator for the separation of R and S-enantiomers from each other. Briefly, the Senantiomer is under the force in the direction of its movement in the channel and it can be speculated that when the S-enantiomer is exiting from one cyclic peptide is under the attraction force from the next cyclic peptide. Again, it should be emphasized that in the SMD simulations of phase I two enantiomers are moving through the CPNT near the inner wall of channel.

SMD of Phase II In the simulation related to this section, the enantiomers were placed at nearly 1nm away from the center of the first cyclic peptide (See Figure 11). The selected parameters of the simulation are same as phase I and the SMD simulation of this phase is position restrain strategy and the center of mass of molecule has been limited to move only in the axis of CPNT. It is important to note that the molecule can rotate around its center of mass during its movement. The variation of pulling force with time related to the SMD simulation of Phase II has been depicted in Figure 12.



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Figure 11. The initial structures of two enantiomers relative to CPNT for the SMD simulation of Phase II.


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Figure 12. The variation of the pulling forces of two enantiomers of lactic acid (LA) during 5 ns SMD simulation time related to Phase II.

Both enantiomers reach to the first cyclic peptide of CPNT at ~ 1 ns and when the enantiomer is entered into the CPNT, the oscillations in the pulling force increases. The variation of pulling force with time for S- and R-enantiomer is different to what observed in phase I. For example, the oscillations of the pulling force for the S-enantiomer were mostly in the negative region and the force exerted from the CPNT to the S-enantiomer was in the direction of movement of molecule in phase I. In the SMD simulation of phase II, the oscillation of the pulling force exerted on the S-enantiomer is in both negative and positive region (see Figure 12). This means that the force exerted from the CPNT to the S-enantiomer is both in the direction and opposite direction of its movement unlike to what was observed in Phase I. Comparison of Figure 12 with 9 shows that the oscillation of the pulling force of Renantiomer in the negative region is more than what observed in the SMD simulation of phase I especially in the middle of CPNT. In addition, the amplitude of the oscillation of pulling force for R-enantiomer is smaller than that of S-enantiomer in the SMD simulations



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of phase II. These observations propose that if both enantiomers are limited to move in the center of CPNT,

the movement of the R-enantiomer is easier and faster than S-enantiomer

in the channel, especially in the middle of CPNT, due to the exerted force to the Renantiomer from the CPNT in the direction of its movement which corresponds to the negative pulling force. In the SMD simulation of phase II, the strongest interaction between the molecule and the inner walls of CPNT occurs when the molecule locates exactly in the hole of cyclic peptides. When the enantiomers reach to the places between two subsequent cyclic peptides, their interaction with the backbone of these cyclic peptides decreases considerably compared to when they move near the inner wall of CPNT (phase I). The lower velocity of Senantiomer compared to the R-enantiomer may be attributed to the more attraction between the S- enantiomer and cyclic peptide when the molecule is in the center of cyclic peptides during its movement. It should also be emphasized that the rotation of the enantiomers around their center of mass during their movement have also effect on their interaction with cyclic peptides especially when the enantiomers reach to the center of cyclic peptides.

SMD of Phase III The initial geometry of complex (enantiomer+CPNT) taken from the molecular docking calculations (see section 3.2; Figure 8) was used for the SMD calculations of this phase. As previously mentioned, the SMD simulation of this phase was performed without any position restrain and the direction of the moving molecule is not determined by the reference molecule (CPNT). In this case, the enantiomers have capability to move in the xand y-directions when they are moving in the z-direction. The calculated pulling forces exerted on both enantiomers have been depicted in Figure 13.


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Figure 13. The variation of the pulling forces of two enantiomers of lactic acid (LA) during 5 ns SMD simulation time related to Phase III.

It is seen that the shape of the variations of the pulling force for both enantiomers is different to what observed in phase I and II so that the visible maximum and minimum in variation of the pulling force with time is more visible. It is important to note that the shape of the variation of pulling force with time for both enantiomers is nearly the same but there is some difference between them. The most important difference between them is related to the amount of maximum pulling force exerted on the enantiomers. The blue dashed lines in Figure 13 show the level of the maximum positive pulling force exerted on both enantiomers and the yellow dashed lines are related to the maximum of the negative pulling force exerted on both enantiomers. It is seen that the maximum level of positive pulling force exerted on both enantiomers is nearly the same (+200 kJ/mol.nm) but, the level of the negative pulling force exerted on the R-enantiomer (-200 kJ/mol.nm) is more negative than that exerted on Senantiomer (-150 kJ/mol.nm). This comparison shows that the movement of R-enantiomer is easier than S-enantiomer in phase III.



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3.3 Radial distribution function of R and S-enantiomers To analyze the interaction of the enantiomers of LA with the CPNT during their movement in the nanotube, the radial distribution functions (RDFs) of some selected atoms of each enantiomer were also obtained from the SMD simulations. For this purpose, the RDF of each selected atom of the LA relative to a reference atom was calculated at each step of SMD simulation and then, the average of the calculated RDFs were obtained. The RDF shows the probability of finding specific atoms close to a reference group

48,54,55

. The fundamental

characteristic of competition between water molecule and the enantiomers for binding to the CPNT are main reasons for transferring LA through the CPNT 54. LA can interact with water molecules through its oxygen and hydrogen atoms. Therefore, their automatically watersolubility in water boxes offers that some water molecules close to lactic acids are ordered with specific position.


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Figure 14. The calculated radial distribution functions (RDFs) of some selected atoms of R and S enantiomers of lactic acid (LA) near O atom of water during their transportation through the CPNT in Phase I.

RDF of Phase I

The probability of finding the atoms of enantiomers of LA in the distance r from the O atom of water molecules have been shown in Figure 14. It is seen that the probability of finding the O atom of water near the atoms of LA cannot reach to one unit for both enantiomers which means that the affinity of enantiomers to the inner wall of CPNT is higher than O atoms of water molecules during their transport in the CPNT. On the other hand, the intensity of RDF peaks of S-enantiomer are lower than R-enantiomer. The intensity of RDF



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for O1, O2 and O3 of S-enantiomer are ~ 0.6, 0.45 and 0.7 at r = 0.3 nm relative to the water O atom, respectively. The corresponding values for the RDF of R-enantiomers at the same distance are ~0.7, 0.5 and 0.7, respectively. This comparison shows that the R-enantiomer is slightly more water-soluble than S-enantiomer. The position of the first peak of the RDF of H1 and H3 atoms of both enantiomers are located at ~ 0.2 nm distance from the water O atoms while the first peak of the RDF of O atoms of enantiomers have been located at 0.3 nm distance from O atoms of water molecules (see Figure 14). This indicates that the H1 and H3 atoms of the enantiomers have been oriented toward the inner wall of CPNT during their movements but the O atoms and the other H atoms of the enantiomers have directed to the tube center. The intensity of the first peak of the RDF of H1 and H3 atom of R-enantiomer is ~ 0.6 unit and reach to ~0. 5 unit for S-enantiomer. Thus, it can be concluded that the affinity of water molecules to R-enantiomer is slightly more than their affinity to S-enantiomer. Generally, the solvation of molecule meaningfully reduces its velocity in the transport pathway

54

and it can be considered that one of the factors for the lower velocity of R-

enantiomer compared to S-enantiomer in phase I calculations could be the more affinity of this enantiomer to water molecule compared to S-enantiomer. In order to study the affinity of the enantiomers to the wall of CPNT during their transportation, the RDF of atoms of enantiomers at different distance r from the O atom of CPNT were calculated (see Figure 15).


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Figure 15. The calculated radial distribution functions (RDFs) of some selected atoms of R and S enantiomers of lactic acid (LA) near O atoms of CPNT during their transportation in the CPNT in Phase I.

The RDF peaks of O1, O2 and O3 atoms of both enantiomers have been located in the range of r= 0.4 to 5.8 nm from the O atoms of CPNT with the intensity about 70, 68 and 60 units, respectively (see Figure 15). This shows that the transport pathway of both enantiomers is similar. The position of the first peak of the calculated RDF of H1 and H3 of both enantiomers is at r~ 0.2 nm from O atoms of CPNT with the intensity of (40 and 38) for Renantiomer and (50 and 43) for S-enantiomer. This indicates that there are hydrogen bonds between both enantiomers and O atoms of CPNT due to their H1 and H3 atoms. Therefore,



the affinity of S-enantiomer to the O atoms of CPNT is more than that of R-enantiomer due to the probability of finding of H1 and H3 of S-enantiomer in distance of 0.2 nm from O atoms of CPNT. Also, the comparison of the intensity of the RDF of H2 atom of Renantiomer (98 unit) with that of S-enantiomer (105 unit) confirms the more affinity of Senantiomer to CPNT compared to R-enantiomer (see Figure 15). Based on Figure 14 and 15, it can be concluded that there is a competition for forming the hydrogen bonds between O atoms of water and O atoms of CPNT with the H1 and H3 of enantiomers and the transfer of the enantiomers through the CPNT is because of this competition. The RDF of O atoms of water molecules close to O atoms of CPNT has been demonstrated in Figure 16. It can be seen that two RDFs are coincide on each other and the first peak of O atoms of water near O atoms of CPNT are observed at 0.3 nm with low probability which shows the numbers of water molecules moving in the lumen of CPNT are low.

g (r)

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r (nm) Figure 16. The calculated radial distribution function (RDF) of O atoms of water with O atoms of CPNT during their transportation for R- and S-enantiomers.


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RDF of Phase II The calculated RDF of the atoms of both enantiomers versus r (the distance from the O atoms of CPNT) have been depicted in Figure 17.

Figure 17. The calculated radial distribution functions (RDFs) of some selected atoms of R and S enantiomers of lactic acid (LA) near O atoms of CPNT during their transportation through the CPNT in Phase II.

It is seen that the intensity of the first peak of RDF of H1 and H3 of enantiomers relative to the rest of RDF has changed considerable compared to phase I. Similar to phase I, the location of the first peak of RDFs of H1 and H3 of two enantiomers (0.2 nm) propose that there are hydrogen bond between O atoms of CPNT and the H1 and H3 atoms of enantiomers



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during their movement in the CPNT. The difference between two enantiomers in phase II can be found from the first peak of RDFs of H1 and H3. It is seen that the value of RDF of H1 at r=0.2 nm is greater than H3 for R-enantiomer while the reverse trend is seen for the Senantiomer. This means that the H3 atom of R-enantiomer has more tendencies to form hydrogen bond with O atoms of CPNT compared to H1 atom and reverse trend is seen for Senantiomer. Figure 17 shows that although, the enantiomers move in the center of CPNT but their H1 and H3 atoms are still close to the atoms of CPNT for forming hydrogen bond.


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RDF of Phase III The RDF of the atoms of two enantiomers of LA versus the distance r from O atoms of CPNT have been depicted in Figure 18.

Figure 18. The calculated radial distribution functions (RDFs) of some selected atoms of R and S enantiomers of lactic acid (LA) near O atoms of CPNT during their transportation through the CPNT in Phase III.

It is seen that there are differences between the RDF of some atoms of R- and Senantiomer. The first peak of the RDF of H1 atom of R- and S-enantiomer are located at ~ 0.20 nm with the maximum intensity of 95 and 100, respectively which means that the H1



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atom of both enantiomers have tendencies for forming the hydrogen bond with the O atoms of CPNT and this tendency for S- enantiomer is more than R-enantiomer. The significant difference between two enantiomers is seen in the RDF of H2 and H3 atoms. The RDF of H3 atom has shifted to the higher values of r in the R-enantiomer compared to S-enantiomer. In addition, the intensity of the first peak of RDF of H2 atom has decreased and shifted to the higher value of r in R-enantiomer. This means that the H2 atom of S-enantiomer has more tendencies for the interaction with the O atoms of CPNT compared to R-enantiomer. This observation shows that the interaction of S-enantiomer with the CPNT is more than Renantiomer and this observation is in agreement with the results of the quantum calculations in previous sections. In addition, the distance between the H1 and H3 atoms of the enantiomers with the O atoms of cyclic peptide obtained from the quantum calculations (see Figure 5) is in agreement with the RDFs of the enantiomers shown in Figure 18. It can be seen that the distance of the H1 and H3 atoms of the enantiomers from the O atoms of cyclic peptide is smaller than the distance of the other atoms of enantiomers especially for the Senantiomer (see Figure 5) which shows that the first peak of RDF of H1 and H3 atoms should be located in the smaller r compared to the RDF of the other atoms. The other important point in the RDFs of the S- and R-enantiomers in Figure 18 which is confirmed in the quantum calculations is related to the H2 of enantiomers. Figure 5 shows that the H2 of LA in the S-enantiomer can participate in the interaction with the O atom of cyclic peptide more than the H2 atom of R-enantiomer. Therefore, the intensity of the first peak of RDF of H2 atom in S-enantiomer should be higher than R-enantiomer. The first peak of the RDF of H2 atom of the S-enantiomer has been located at ~0.27 nm while the RDF of H2 atom of Renantiomer does not have visible first peak at this value of r.


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4. CONCLUSION In the present work, the SMD simulation was employed to explore the difference in the transportation behavior of the enantiomers of LA when move in the CPNT. For this purpose, the variation of the pulling force versus time for each enantiomer was calculated in three different phases. (a) The SMD simulations showed when the enantiomers are limited to move near the wall of CPNT, the movement of the S-enantiomer was more feasible than the R-enantiomer because the sign of the pulling force exerted on the molecule was mostly negative in the simulation time. The calculated RDFs of the atoms of the enantiomers versus the distance from the O atoms of CPNT showed that the affinity of S-enantiomer to the O atoms of CPNT through its H1 and H3 atoms for forming the hydrogen bond is more than Renantiomer in this case. (b) When the enantiomers are limited to move in the center of CPNT, the reverse trend is seen so that the velocity of R-enantiomer is higher than the S-enantiomer because the variation of pulling force in the negative region for the R-enantiomer was more than the S-enantiomer. The calculated RDF of enantiomers showed that there is hydrogen bond between the O atoms of CPNT and, H1 and H3 atoms of enantiomers but the H1 atom of the R-enantiomer is more active in forming the hydrogen bond with the O atoms of CPNT than H1 atom and the revers trend was observed for the S-enantiomer. (c) when the enantiomers are moving in the axis of nanotube and their center of mass is free for the displacement in x and y direction, again the velocity of R-enantiomer is higher than Senantiomer. The calculated RDF of two enantiomers showed that the H1 of S-enantiomer has more tendencies to form hydrogen bond with the O atoms of CPNT compared to Renantiomer. Also, it was observed that there are significant differences between the RDF of H2 and H3 atoms of R- enantiomer compared to S-enantiomer. A shift to the higher value of r was observed in the RDF of H2 and H3 atoms of R-enantiomer compared to S-enantiomer



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which showed that the hydrogen bond of the H2 and H3 atoms of R-enantiomer with the O atoms of CPNT is weaker than those of S-enantiomer.

Acknowledgment

The authors gratefully acknowledge the support of the Isfahan University of Technology (IUT) to this work.


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