3Department of Applied Chemistry, Faculty of Science, Tafila Technical University, Tafila, ...... E. Anslyn and D. A. Dougherty, Modern Physical Organic Chem-.
RESEARCH ARTICLE
Copyright © 2017 American Scientific Publishers All rights reserved Printed in the United States of America
Journal of Computational and Theoretical Nanoscience Vol. 14, 3416–3421, 2017
Modelling Interaction Between a Methane Molecule and Biological Channels Hakim Al Garalleh1 2 ∗ , Ngamta Thamwattana2 , and Mazen Garaleh1 3 1
Department of Mathematical Science, College of Engineering and Information Technology, University of Business and Technology, Jeddah 21433, Saudia Arabia 2 Nanomechanics Group, School of Mathematics and Applied Statistics, University of Wollongong, NSW 2500, Australia 3 Department of Applied Chemistry, Faculty of Science, Tafila Technical University, Tafila, 66110, Jordan Aquaporins are small ubiquitous membranes in biological channels that play significant role in the transportation of nano-sized materials, such as water and other biomolecules, into cell. The present work proposes a mathematical model to determine the potential energy of the interaction between a methane molecule and three different types of aquaporin channels, which are aquaporin-Z, aquaglyceroporin and aquaporin-1. We adopt a continuous model, where all atoms comprising the aquaporin channels are assumed to be uniformly distributed throughout their volumes. We also assume that a methane molecule comprises two parts: A single point representing the carbon atom at the centre and a spherical shell of four evenly distributed hydrogen atoms. Our results indicate the naturalistic acceptance of a methane molecule inside aquaglyceroporin and aquaporin-1 channels, but the repulsion occurs for the case of aquaporin-Z channel.
Keywords: Aquaporin-Z (AqpZ), Aquaglyceroporin (GlpF), Aquaporin-1 (AQP1), Methane Gas (CH4 ), Lennard-Jones Potential, van der Waals Interaction.
1. INTRODUCTION Aquaporin is a family of membrane proteins that enable water and small molecules to permeate cell membranes. Aquaporins from human cells were discovered in 1992 and since then several aquaporin channels have also been identified and pioneered by Peter’s Agre team.1 Examples of these channels are aquaporin-Z (AqpZ), aquaglyceroporin (GlpF) and aquaporin-1 (AQP1), as shown in Figure 1. Members of the aquaporin family are widely distributed in various organs and have been found in different sites of human body, such as brain, kidney and eubacterian.2, 3 The family of variant protein channels, from AQP1 to AQP12 and AqpZ,4 is clustered into three distinct groups according to their permeability characteristics and to the number of atoms forming these protein channels.5–8 Firstly, the biological water selective channels, AqpZ, AQP1, AQP2, AQP4, AQP5, AQP6 and AQP8, where AqpZ is only capable of transporting water molecules through cell membranes and blocking the ionic and non-ionic bonded molecules, while AQP1, AQP6 and AQP8 are able to permeate nitrate, chloride ions and ammonia, respectively.9–12 Second is aquaglyceroporin family (GlpF) which consists of AQP3, AQP7, AQP9 and AQP10 channels, usually permeable to water, urea, glycerol and other small neutral ∗
Author to whom correspondence should be addressed.
3416
J. Comput. Theor. Nanosci. 2017, Vol. 14, No. 7
solutes.5, 6, 9, 13 AQP9 is a water channel and also permeable to neutral solutes, urea, glycerol, pyrimidines and purines, while AQP10 is able to transport water not glycerol and urea as well as AQP7 and AQP9 are also permeable to arsenite.14–16 Third group has only two intracellular proteins, AQP11 and AQP12. In compared to efficiency of AQP12, AQP11 has a major role in integrity maintenance, transports water in liposoms when reconstituted, but fails to display water in oocytes.17–19 On the other hand, substrate specificity of AQP12 is still vague.19–21 For full detail related to the geometrical structures of these aquaporin channels and their functions and characteristics, we refer the reader to Refs. [22–26]. Specifically, experimental results of Wang’s work show that the inner pore diameter of GlpF or AQP1 is approximately 13 Å,25 which is larger than that of AqpZ channel (1 Å).27 Some of aquaporin channels allow the passage of gas molecules, such as carbon dioxide, ammonia, nitric oxide and methane.23, 24, 28 Methane is a chemical compound composed of one carbon and four hydrogen atoms with a chemical formula CH4 . Methane was first spontaneously identified in the marshes of Lake Maggiore Straddling Switzerland and Italy by the Italian physicist Don Alessandro Volta in 1776, having been inspiring to find out the substance after reading Benjamin Franklin’s paper about “flammable air.”29 Methane gas had been captured arising from the marshes, 1546-1955/2017/14/3416/006
doi:10.1166/jctn.2017.6644
Garalleh et al. (a) AqpZ
Modelling Interaction Between a Methane Molecule and Biological Channels (b) GlpF and AQP1
then been isolated as a pure gas in 1778 and it easily ignited with an electrical spark.29, 30 Humans and animals are the main resources of methane emissions.31, 32 It is the simplest member in alkanes, and a principal component of natural gas and its huge abundance makes it one of the most attractive fuel resources.33 At the beginning, scientific researchers had been facing challenges in capturing and storing methane due to its gaseous property.31 In its natural state, methane was found at standard conditions of pressure and temperature in two main areas, below the ground and under the sea floor, and it easily finds its way to the atmosphere which is called atmospheric methane.31 Methane reactions are very difficult to control, such as combustion, halogenation and steam reforming to syn-gas. Mechanism of partial oxidation to methanol has challenge because of the typical progress depending on carbon dioxide and water even with insufficient amount of oxygen.34 Methanol is completely arising from methane by the anzyme methane mono-oxygenase.31 It is very weak acid due to its high density being heavier than air and can be used in industrial chemical process and transported as a liquid natural gas.29, 30, 35 The study of aquaporin channels on the transportation of waters and biomolecules across cell membranes has led to the development of modern medical and biological applications, such as drug delivery and water desalination.36 The molecular selectivity of AQP1 and GlpF channels has been investigated.36 Further, Hub’s work has shown that GlpF and AQP1 channels can facilitate the transport of gases, such as NH3 and CO2 into cells.37 Several recent studies indicate that small gas molecules transported by membrane proteins and should not be ignored.28, 37, 38 The potential mean forces have also been computed for the permeation of these biomolecules into AQP1 and GlpF using numerical and computational approaches. Recent experiments show that the transportation of the larger molecules through aquaporins occurs for those small with and long thin shapes.39, 40 These channels are also useful for separation of gases, such as removing carbon dioxide molecules from mixtures with methane. J. Comput. Theor. Nanosci. 14, 3416–3421, 2017
3417
RESEARCH ARTICLE
Fig. 1. Functional unit of geometrical structure of aquaporin channels: (a) AqpZ, (b) GlpF and AQP1.27
The recent work on one-dimensional aquaporin channels shows that the Tris(5-acetyl-3-thienyl) methane is able to pass through these channels.41 Chen et al.42 employs the Brownian dynamics fluctuation dissipation theorem and steered molecular dynamic simulations to calculate the free energy for the permeation of water and hydration of methane molecules through GlpF. In addition, Adisa et al.43 investigate the encapsulation of methane gas inside carbon nanotube bundles and his results show that carbon nano-structures could be a superior for storage methane molecules at natural conditions (carbon is an essential component in chemical formulas of all aquaporin protein channels). Moreover, Skowronski et al.44 suggest that several sub-types AQP1, AQP5 and AQP9 are involved in the regulation of water and other biomolecules homeostasis in the reproductive system of gilts. Al Garalleh et al.45–47 show that the biological channels, GlpF and AQP1, are able to transport water and small gas molecules, such as carbon dioxide, nitric oxide and ammonia through cell membrane protein. The rate of diffusion of methanol (CH3 OH) or methane (CH4 ) through the hydrophobic region of the phospholipid bilayer of cell membrane is approximately 50 times faster than that of urea.26, 48 Barrer et al.49 state that the permeation of methane or nitrogen across vulcanized rubber (bilayer) membranes of aquaporin channels is about 7.15–11.3 percentage. Further, Wang et al.50 use the molecular dynamics performed with NAMD to show that the gas transportation through AQP1 is valid with two complementary methods, implicit ligand sampling and explicit gas diffusion simulation. The simulation results suggest that the AQP1 central pore may function as a pathway for gas molecules and the four monomeric pores of AQP1 serve as water channels to cross the membrane.51 The transportation of other molecules, either charged or uncharged, depends on the kind of aquaporin channel and its inner radius which plays a significant role in controlling the permeation of these molecules and determining the global minimum energy.28, 41, 42, 45–47 Oliva et al.52 show that AqpZ channel has positive charges around its wall which can block all kinds of molecules and ions to pass through AqpZ membranes, excepting water molecules. In this paper, we investigate the acceptance of a methane molecule inside the biological channels (AqpZ, GlpF and AQP1), which are assumed to have a profile of right cylindrical channel. To obtain the interaction energy we adopt the discrete-continuum approach and the LennardJones potential. For a methane molecule, the four hydrogen atoms are assumed to be on a spherical shell and the carbon atom is assumed to be a single point located at the centre of the spherical shell. We perform volume integration throughout the channel to calculate the total interaction potential energy due to these interactions. The analytical expressions for the potential energy obtained involve series of hypergeometric functions, which can be readily computed using an algebraic computer package, such
as MAPLE. Our study indicates that gas molecules are accepted inside GlpF and AQP1 channels while prevented to enter the AqpZ channel. We note that the chemical compositions of AqpZ, GlpF, and AQP1 with chemical compositions of C906 H1885 N272 O463 S4 , C1289 H2527 N315 O591 S11 and C1235 H2468 N320 O601 S7 , respectively. In order to determine the total interaction energy, we perform surface and volume integrations of the potential energy between the carbon atom as a discrete point and the four hydrogen atoms as a spherical shell interacting with AqpZ, GlpF and AQP1, respectively. In the following section, we outline the Lennard-Jones potential and the method used to derive an expression for the interaction potential of a methane molecule and the AqpZ, GlpF and AQP1 channels. In Section 3, we present the numerical results of our model. A summary is given in the final section of this paper.
2. INTERACTION ENERGY 2.1. Interaction Between an Aquaporin Channel and a Single Atom We begin by considering the Lennard-Jones interaction between an aquaporin channel (either, AqpZ, AQP1 or GlpF) which is assumed to be a flaired right cylinder and a discrete point representing a single atom located on the z-axis. Here, by using a rectangular coordinate system x y z as a reference, the atom is assumed to be located at 0 0 z0 on the z-axis. This cylinder can be parameterized by r cos , r sin , z, where z ∈ −L/2, L/2, ∈ − , and ∈ a, 1, where 0 < a < 1 and r is represented a parabolic curve as shown in Figure 2 and defined by the quadratic equation. r = r0 + 4r1 − r0 z/L2 = r0 + z2
(1)
where r0 and r1 are the outer radii at the middle and at the opening of aquaporin, respectively, and = 4r1 − r0 /L2 . The quantities ar0 and ar1 are defined as the inner radii at 15
Aquaporin radius r (Angstrom)
RESEARCH ARTICLE
Modelling Interaction Between a Methane Molecule and Biological Channels
14.5 14 13.5 13 12.5 AqpZ radius GlpF or AQP1 radius
12 –10
–5
0
5
10
Z (Angstrom) Fig. 2. The relationship between the aquaporin radius and the value of z along the z-axis.
3418
Garalleh et al.
the middle and at the opening of aquaporin, respectively, and we take a = r0∗ /r0 ≈ 0 25, where r0 is the inner radius at the centre of the aquaporin. The distance between the atom and a typical point in the channel volume is given by 2 = r 2 2 + z − z0 2
(2)
To find the interaction potential between the single atom and the aquaporin channel, we adopt the Lennard-Jones potential which is given by 6 12 (3) +
= −A −6 + B −12 = 4 − where is the well depth and is the van der Waals diameter. We also make use of the empirical combining laws53–55 given by 12 = 1 2 1/2 and 12 = 1 + 2 /2 to determine the well depth and van der Waals diameter for two atoms of different species. A = 4 6 and B = 4 12 are the attractive and repulsive constants, respectively. By summing all pair interactions, the total potential energy can be given by (4) Vtot = i i
where is the potential function given in (3). In the continuum approximation, we may replace this summation by the volume integral, where we assume a uniform atomic density throughout the volume of the aquaporin. Thus, from (4) we have 1 L/2
dV V1 = c −L/2 −
a
= c
1
L/2
−L/2 −
a
r 2 −A −6 + B −12 d dz d (5)
where c represents the atomic density per unit volume and dV represents the volume element of the cylindrical aquaporin given by dV = r 2 d dz d. For detailed analytical evaluation of (5), we refer the reader to Ref. [46]. 2.2. Interaction Between an Aquaporin Channel and a Methane Molecule In this section, we consider the interaction of a methane molecule with aquaporin channels. We propose to model this problem in two parts. Firstly, we study the interaction of the aquaporin (either AqpZ, GlpF or AQP1) with the carbon atom which is assumed to be located at 0 0 z0 as shown in Figure 3. From the work of Al Garalleh et al.,46 the equation of the potential energy is given by 1 L/2 E1 = c r 2 −A −6 + B −12 d dz d a
= 2 c
−L/2 −
1 a
L/2
−L/2
r 2 −A −6 + B −12 d dz
(6)
Secondly, we consider the interaction of the aquaporin with the four hydrogen atoms which are assumed to be J. Comput. Theor. Nanosci. 14, 3416–3421, 2017
Garalleh et al.
Modelling Interaction Between a Methane Molecule and Biological Channels Table II.
X
Numerical values for other physical parameters.27
H
r0
r1
r0*
r1*
H
Z
H
H Z0
L/2 Fig. 3. Geometry of atom on the z-axis interacting with aquaporin assumed to have a flaired right cylindrical structure.
on a spherical shell of radius b = 1 087 Å (Fig. 3). From Ref. [56], the potential energy is given by A 1 1 H − E2 = H b 2 +b4 −b4 BH 1 1 − dV − 5 +b10 −b10 1 L/2 1 A 1 = H b r 2 H − 2 +b4 −b4 a −L/2 − BH 1 1 − ddzd (7) − 5 +b10 −b10 where H represents the atomic surface density of the sphere of the four hydrogen atoms and b is the radius of the sphere of the four hydrogen atoms. We then combine the interactions in (6) and (7) to determine the interaction energy for the whole system.
3. NUMERICAL RESULTS Here, we evaluate the total energy arising from a methane molecule interacting with aquaporin channels and we obtain the plots of the potential energy using MAPLE, MATLAB and GNUPLOT packages. The parameters used in this model are shown in Tables I and II which are taken from Ref. [27]. We note that NA = 3530, NG = 4737 and NQ = 4601 are the numbers of atoms in AqpZ, GlpF, and AQP1 with chemical compositions of C906 H1885 N272 O463 S4 , C1289 H2527 N315 O591 S11 and C1235 H2468 N320 O601 S7 , respectively. Vc is the cylinder volume and As is the surface area of the sphere of four hydrogen atoms. A and B are the attractive and repulsive constants, respectively, which Table I. The Lennard-Jones constants (: Bond length and : Bond energy) (single bond: sb, double bond: db).54, 55, 57–60 Interaction
(Å)
(Å)
Interaction
(Å)
(Å)
H–H O–O (sb) N–N N–H C–C (db) C–O (db) C–H S–H
0.74 1.48 1.45 1.00 1.34 1.20 1.09 1.34
2.886 3.500 3.660 3.273 3.851 3.675 3.368 3.461
O–H O–O (db) N–O C–C (sb) C–O (sb) C–N S–S S–C
0.96 1.21 1.40 1.54 1.43 1.47 2.05 1.82
3.193 3.500 3.580 3.851 3.675 3.755 4.035 3.943
J. Comput. Theor. Nanosci. 14, 3416–3421, 2017
Symbol
Length of aquaporin Outer radius of aquaporin Inner radius of AqpZ Inner radius of GlpF or AQP1 Radius of sphere of hydrogen atoms Volume density for an AqpZ
L r1 r0 r0
c = NA /Vc
Volume density for an GlpF
c = NG /Vc
Volume density for an AQP1 Surface density for a sphere of hydrogen Channel wall thickness
c = NQ /Vc
Value 28 15 13 12
b
Å Å Å Å
1.087 Å
s = 4/As a = r0∗ /r0
3530/ Lr 2 = 0 2234 atom/Å3 4737/ Lr 2 = 0 3389 atom/Å3 4601/ Lr 2 = 0 3292 atom/Å3 0.2695 atom/Å2 0.25
are calculated from finding the well-depth and the van der Waals diameter for a methane molecule, a carbon and four hydrogen atoms, interacting with all of the atoms comprising the cylindrical aquaporin channels, as shown in Table III. In Figures 4–6 the interaction energies are given for both numerical and computational solutions. The computational solution is referred to the evaluation of the first 10 terms in the infinite summation formulation for the five special cases as mentioned in Appendix A of Ref. [46]. The numerical solution is referred to the volume integral in Eq. (7) using the numerical integration Table III. Numerical values of the attractive (A) and repulsive (B) constants derived from Refs. [54, 55, 57]. Element
Symbol
OO AOO OH AOH OS AOS ON AON OC AOC HH AHH HS AHS HN AHN HC AHC CN ACN CS ACS SN ASN CC ACC NN ANN SS ASS C-AqpZ AC-AqpZ H-AqpZ AH-AqpZ C-GlpF AC-GlpF H-GlpF AH-GlpF C-AQP1 AC-AQP1 H-AQP1 AH-AQP1 CH4 -AqpZ ACH4 -AqpZ CH4 -GlpF ACH4 -GlpF CH4 -AQP1 ACH4 -AQP1
Value (eVÅ6 )
Symbol
Value (eVÅ12 × 103 )
22 63 9 41 79 89 23 41 33 79 4 41 41 10 11 70 17 16 41 26 139 04 97 11 58 71 28 74 324 72 32 00 8 94 32 41 8 92 32 45 9 07 16 94 17 02 17 18
BOO BOH BOS BON BOC BHH BHS BHN BHC BCN BCS BSN BCC BNN BSS BC-AqpZ BH-AqpZ BC-GlpF BH-GlpF BC-AQP1 BH-AQP1 BCH4 -AqpZ BCH4 -GlpF BCH4 -AQP1
41 599 9 972 228 279 49 283 83 240 2 548 70 517 14 383 52 046 115 661 522 516 314.772 191 493 69 083 1401 426 97 362 17 214 99 162 17 734 99 031 17 747 41 554 42 524 42 504
3419
RESEARCH ARTICLE
Parameter
C
Modelling Interaction Between a Methane Molecule and Biological Channels 1
Total potential energy E (eV)
Total potential energy E (eV)
4 2 0 –2 –4 –6 Sphere of hydrogens Carbon atom(Numerical) Methane molecule(Numerical) Carbon atom(Computational) Methane molecule molecule(Computational)
–8 –10 –20
–10
0
10
20
0 –1 –2 –3 –4 –5 –6
Sphere of hydrogens Carbon atom(Numerical) Methane molecule(Numerical) Carbon atom(Computational) Methane molecule molecule(Computational)
–7 30
–8 –30
–20
–10
Z (Angstrom)
0
10
20
30
Z (Angstrom)
Fig. 4. Potential energies for carbon atom, sphere of hydrogen atoms and methane molecule interacting with AqpZ.
Fig. 6. Potential energies for carbon atom, sphere of hydrogen atoms and methane molecule interacting with AQP1.
package in MAPLE. As seen in Figures 4–6, there is a minimal difference in the magnitude of the potential energies between the numerical and computational solutions. In Figure 4, we present the interaction energies for a methane molecule, a carbon atom and the hydrogen sphere, each interacting with the aquaporin channel AqpZ. We note that the interaction energy is approximately zero at the extremities of the aquaporin channel and reaches its maximum value at the centre of AqpZ channel (when z = 0). At z = 0, the minimum interaction energies for the carbon-AqpZ and the hydrogen-AqpZ are approximately −4.15 eV and −6.18 eV, respectively. This model suggests that there is an energetic barrier which prevents the methane molecule to be accepted in the interior of the AqpZ channel. In Figures 5 and 6, the encapsulations of methane molecule inside the GlpF and AQP1 channels are presented. We find that the interaction energies are approximately zero at the open ends of the channel and have minimum values of approximately −6.13 eV and −6.16 eV, respectively. The interaction of carbon-AQP1 is approximately −3.94 eV which is slightly greater than that
of carbon-GlpF (−3.91 eV). Furthermore, the hydrogen sphere-GlpF and hydrogen sphere-AQP1 interactions are equal having the value approximately −2.23 eV at the centre of these channels. Our results indicates that the encapsulation of the methane molecule is more favorable inside the AQP1 channel. These results suggest that methane can enter the GlpF and AQP1 channels without energy barriers to prevent its encapsulation. Our results agree with the Brownian dynamics fluctuation dissipation theorem, (dynamics simulation systems)42 and the potential mean forces using both numerical and computational approaches.28 Our calculations and these recent studies indicate that ions and gas molecules are accepted inside the GlpF and AQP1 channels. The numerical values for the interaction energies are in excellent agreement with recent experimental and computational studies.42, 44, 52
1 0
Total potential energy E (eV)
RESEARCH ARTICLE
6
–12 –30
Garalleh et al.
–1 –2 –3 –4 –5 –6
Sphere of hydrogens Carbon atom(Numerical) Methane molecule(Numerical) Carbon atom(Computational) Methane molecule molecule(Computational)
–7 –8 –30
–20
–10
0 Z (Angstrom)
10
20
30
Fig. 5. Potential energies for carbon atom, sphere of hydrogen atoms and methane molecule interacting with GlpF.
3420
4. CONCLUSION In this paper, we investigate the acceptance of a methane molecule inside various aquaporin channels. We evaluate the potential energy by applying two approaches, namely discrete-continuum and completely discrete approaches. We model the methane molecule where the carbon atom as an arbitrary point and the four hydrogen atoms as a spherical shell, with both entities interacting with the three different kinds of aquaporins. We also use the LennardJones potential to calculate the energy for each interaction. We find that the aquaporin radius r plays a prime role in controlling the energy for these interactions. In conclusion, our results show that the total potential energy for the methane has a local minimum energy around the centre of the GlpF and AQP1 channels, where the channels are narrowest. This indicates that the methane molecule is encapsulated inside the GlpF and AQP1. However, it is rejected from the AqpZ channel, as the energy profile is maximized inside the channel. The results presented here agree with findings shown in previous studies. J. Comput. Theor. Nanosci. 14, 3416–3421, 2017
Garalleh et al.
Modelling Interaction Between a Methane Molecule and Biological Channels
30.
31.
References 1. P. Agre, Bioscience Reports 24, 127 (2004). 2. F. Zhu, E. Tajkhorshid, and K. Schulten, Biophysical 83, 154 (2002). 3. S. T. Horsefield, E. Tajkhorshid, Y. Wang, K. Hedfalk, U. Johanson, M. Karlsson, R. Neutze, and P. Kjellbom, Nature 439, 688 (2006). 4. M. B. Gorin, S. B. Yancey, J. Cline, J. P. Revel, and J. Horwitz, Cell 39, 49 (1984). 5. C. Maurel, J. Reizer, J. I. Schroeder, M. J. Chrispeels, and M. H. Saier, J. Biol. Chem. 269, 11869 (1994). 6. L. S. King, D. Kozono, and P. Agre, Nat. Rev. Mol. Cell. Biol. 5, 687 (2004). 7. E. M. Campbell, A. Ball, S. Hoppler, and A. S. Bowman, J. Comp. Physiol. 178, 935 (2008). 8. A. S. Verkman and A. K. Mitra, Am. J. Physiol. Renal. Physiol. 278, 13 (2000). 9. C. M. Krane and D. L. Goldstein, Mamm. Genome. 18, 452 (2007). 10. M. Yasui, A. Hazama, T. H. Kwon, S. Nielsen, W. B. Guggino, and P. Agre, Nature 402, 184 (1999). 11. M. Yasu, T. H. Kwon, M. A. Knepper, S. Nielsen, and P. Agre, Proc. Natl. Acad. Sci. USA 96, 5808 (1999). 12. S. M. Saparov, K. Liu, P. Agre, and P. Pohl, J. Biol. Chem. 282, 5296 (2007). 13. A. Rojek, J. Praetorius, J. Frokiaer, S. Nielsen, and R. A. Fenton, Annu. Rev. Physiol. 70, 301 (2008). 14. S. Hatakeyama, Y. Yoshida, T. Tani, Y. Koyama, K. Nihei, K. Ohshiro, J. I. Kamien, E. Yaoita, T. Suda, K. Hatakeyama, and T. Yamamoto, Biochem. Biophys. Res. Commun. 287, 814 (2001). 15. H. Tsukaguchi, S. Weremowicz, C. C. Mortona, and M. A. Hediger, Am. J. Physiol. 277, 685 (1999). 16. Z. Liu, J. Shen, J. M. Carbrey, R. Mukhopadhyay, P. Agre, and B. P. Rosen, Proc. Natl. Acad. Sci. USA 99, 6053 (2002). 17. T. Itoh, T. Rai, M. Kuwahara, S. B. Ko, S. Uchida, S. Sasaki, and K. Ishibashi, Biochem. Biophys. Res. Commun. 330, 832 (2005). 18. Y. Morishita, T. Matsuzaki, M. Hara-chikuma, A. Andoo, M. Shimono, A. Matsuki, K. Kobayashi, M. Ikeda, T. Yamamoto, A. Verkman, E. Kusano, S. Ookawara, K. Takata, S. Sasaki, and K. Ishibashi, Mol. Cell. Biol. 25, 7770 (2005). 19. K. Yakata, Y. Hiroaki, K. Ishibashi, E. Sohara, S. Sasaki, K. Mitsuoka, and Y. Fujiyoshi, Biochim. Biophys. Acta 1768, 688 (2007). 20. K. Ishibashi, Biochem. Biophys. Acta 1758, 989 (2006). 21. K. Nozaki, D. Ishii, and K. Ishibashi, Pflugers Arch. 456, 701 (2008). 22. D. Fu, A. Libson, L. J. W. Miercke, C. Weitzman, P. Nollert, J. Krucinski, and R. M. Stroud, Science 290, 481 (2000). 23. N. Chakrabarti, E. Tajkhorshid, B. Roux, and R. Pomes, Structure 12, 65 (2004). 24. K. Murata, K. Mitsouka, T. Hirai, T. Walz, P. Agre, J. B. Heymann, A. Engel, and Y. Fujiyoshi, Nature 407, 599 (2000). 25. Y. Wang, K. Schulten, and E. Tajkhorshid, Structure 13, 1107 (2005). 26. D. Gomes, A. Agasse, P. Thiebaud, S. Delrot, H. Geros, and F. Chaumont, Biochim. Biophys. Acta 1788, 1213 (2009). 27. D. F. Savage, P. F. Egea, C. Y. Robles, J. D. O’Conell, and R. M. Stroud, Public Library of Science Biology 1, 334 (2003). 28. A. S. Verkman, Journal of Physiology 542, 31 (2002). 29. D. A. Volta, Lettere del Signor Don Alessandro Volta Sull Aria Inflammabile Nativa delle Paludi [Letters of Signor Don Alessandro
32. 33.
34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53.
54. 55. 56.
57. 58. 59. 60.
Volta on the flammable native air of the marshes], Giuseppe Marelli, Milan, Italy (1777). A. H. David and B. J. Kenneth, Handbook of Transport and the Environment, Emerald Group Publishing, Bingley, West Yorkshire, England (2003), Vol. 168, pp. 172–173. M. A. K. Khalil, Annual Review of Energy and the Environment 24, 645 (1999). J. T. G. Hamilton, W. C. McRoberts, F. Keppler, R. M. Kalin, and D. B. Harper, Science 301, 206 (2003). P. Bousquet, S. C. Tyler, P. Peylin, G. R. Van Der Werf, C. Prigent, D. A. Hauglustaine, E. J. Dlugokencky, J. B. Miller, P. Ciais, J. White, L. P. Steele, M. Schmidt, M. Ramonet, F. Papa, J. Lathiere, R. L. Langenfelds, C. Carouge, and E. G. Brunke, Nature 443, 439 (2006). M. H. Baik, M. Newcomb, R. A. Friesner, and S. J. Lippard, Chem. Rev. 103, 2385 (2003). B. G. Frederick, Acc. Chem. Res. 21, 456 (1988). J. S. Hub and L. B. de Groot, The Journal of Physical Chemistry B 115, 8364 (2011). J. S. Hub and L. B. de Groot, Proc. Natl. Acad. Sci. USA 105, 1198 (2008). S. Phongphanphanee, N. Yoshida, and F. Hirata, Journal of Physical Chemistry B 114, 7967 (2010). B. Bolto, M. Hoang, and T. Tran, Water 37, 80 (2010). D. Li and H. Wang, J. Mater. Chem. 20, 4551 (2010). P. S. Sidhu, K. A. Udachin, and J. A. Ripmeester, Chem. Commun. 10, 1358 (2004). L. Y. Chen, Phys. Chem. Chem. Phys. 13, 6176 (2011). O. O. Adisa, B. J. Cox, and J. M. Hill, Micro and Nano Letters 5, 291 (2010). M. T. Skowronski, T. H. Kwon, and S. Nielsen, J. Histochem. Cytochem. 57, 61 (2009). H. Al Garalleh, N. Thamwattana, B. J. Cox, and J. M. Hill, J. Math. Chem. 51, 2317 (2013). H. Al Garalleh, N. Thamwattana, B. J. Cox, and J. M. Hill, J. Comput. Theor. Nanosci. 10, 2722 (2013). H. Al Garalleh, N. Thamwattana, B. J. Cox, and J. M. Hill, J. Math. Chem. 51, 2020 (2013). H. Lodish, A. Berk, and S. L. Zipursky, Molecular Cell Biology, edited by W. H. Freeman, New York (2000). R. M. Barrer and G. Skirrow, Journal of Polymer Science 3, 549 (1984). Y. Wang, J. Cohen, W. F. Boron, K. Schulten, and E. Tajkhorshid, Journal of Structural Biology 157, 534 (2007). Y. Wang and E. Tajkhorshid, The Journal of Nutrition 137, 1509 (2007). R. Oliva, G. Calamita, J. M. Thornton, and M. Pellegrini-Calace, PNAS 107, 4135 (2010). J. O. Hirschfelder, C. F. Curtiss, and R. B. Byron, The molecular theory of gases and liquids, Society for Industrial and Applied Mathematics, University of Winsconsin, Madison, New York (1964). L. T. Cottrell, The Strengths of Chemical Bonds, Butterworths Scientific Publications, London (1954). L. Pauling, The Nature of the Chemical Bonds, Cornell University Press, Ithaca, New York (1960). B. J. Cox, N. Thamwattana, and J. M. Hill, Mechanics of atoms and fullerenes in single-walled carbon nanotubes, Proceedings of the Royal Society A, London, UK (2006), Vol. 463, pp. 461–476. A. K. Rappi, C. J. Casewit, K. S. Colwell, W. A. Goddard, III., and W. M. Skid, J. Am. Chem. Soc. 114, 10024 (1992). E. Anslyn and D. A. Dougherty, Modern Physical Organic Chemistry, University Science Books, Sausalito, California, USA (2006). S. W. Benson, J. Chem. Educ. 42, 502 (1965). B. deB. Darwent, National Standard Reference Data Series, National Bureau of Standards, Washington, DC (1970).
Received: 16 November 2016. Accepted: 3 December 2016. J. Comput. Theor. Nanosci. 14, 3416–3421, 2017
3421
RESEARCH ARTICLE
Acknowledgment: The authors are grateful to the University of Wollongong’s Research Council and University of Business and Technology Research Centre for support through small project fund.
