^{1}Department of Mathematical Science, College of Engineering, University of Business and Technology, Dahban, Jeddah, Saudia Arabia
^{2}Department of Applied Chemistry, Faculty of Science, Tafila Technical University, Tafila, Jordan
Received date: April 11, 2017; Accepted date: April 28, 2017; Published date: May 05, 2017
Citation: Al Garalleh H, Garalehab M (2017) Modeling of Encapsulation of Alanine Amino Acid inside a Carbon Nanotube. J Biotechnol Biomater 7:255. doi:10.4172/2155-952X.1000255
Copyright: © 2017 Al Garalleh H, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
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Carbon nanotubes play a significant role in facilitating and controlling the transportation of drugs and biomolecules through their internal and external surfaces. Carbon nanotubes are also selective nano-devices because of their outstanding properties and huge potential use in many bio-medical and drug delivery applications. The proposed model aims to investigate the encapsulation of Alanine molecule inside a single-walled carbon nanotube, and to determine the minimum energy arising from the Alanine interacting with single-walled carbon nanotubes with variant radius r. We consider two possible structures as models of Alanine amino acid which are a spherical shell and discrete configuration modelled as comprising three components: the linear molecule, cylindrical group and CH3 molecule as a sphere, all interacting with infinite cylindrical single-walled carbon nanotube. The adsorption of Alanine amino acid and magnitude of total energy for each orientation calculated based on the nanotube radius r and the orientation angle φ which the amino acid makes with central axis of the cylindrical nanotube. Our results indicate that the Alanine molecule encapsulated inside the nanotubes of radius greater than 3.75 Å, which is in excellent agreement with recent findings.
Carbon nanotube (CNT); Alanine amino acid; Encapsulation; Potential energy; van der Waals Force; Lennard-Jones potential
The area of nanotechnolgy and nanoscience has witnessed unexpected growth of researches and applications which aim to design and enhance new nano-devices by manipulating in their nano-scales size, unique features and distinct properties. These Engineered nano-devices are very important and preferable tools, such as carbon nanotubes (CNTs), nanobuds and fullerenes which can be used as carriers in the diseases diagnosis and treatment [1,2]. The debut of CNTs has initially generated much interest in their potential applications in designing life sciences since its discovery [3]. The usefulness of nano-particles in medicinal applications, especially in drug delivery and disease therapy has spread rapidly [4]. Their distinct properties have motivated scientists to investigate the possibility of combination between carbon nanostructures and drugs, and the mechanisms of their reactions and encapsulation [5-7]. For example, they can be used as carriers in drug delivery applications to increase the efficiency of treating the infected sites, attacking the pathogens and inhibiting the growth of viruses and cancer cells by reducing the toxicity and solubility rate, especially in aqueous media [8-11]. Dresselhaus et al. [12] predict that the CNT with Chiral vector (5, 5) would be the most significant physical nanotube. CNTs have a huge potential for enhancing new techniques for drug delivery applications and can be covalently and non-covalently bonded to bio-molecules, such as α-amino acids and drugs [7,9,13]. Longterm studies have addressed the ability of proteins and amino acids to conjugate with carbon nanotubes by using different methods; Molecular Dynamic Simulations (MDSs), Density Functional-Based Plus (DFBP) and Spanish Initiative Simulations (SIESTA) [14-16]. Amino acids can interact with either the outer wall (binding) or the inner surface (encapsulation) of multi-walled (MWCNTs) and single-walled carbon nanotubes (SWCNTs) [17]. An on-going work aims to study the encapsulation of Alanine molecule inside a cylindrical SWCNT.
Amino acids a family of biological compounds that have a critical role in many metabolic functions in the human body. They are classified into two sub-functional groups, proteinogenic and non-proteinogenic, based on the synthesization by the human body, such as Phylanine, Histidine, Alanine, Cystine, ...etc. Alanine is a non-essential amino acid in human because it can be synthesized in the body. It is known to be one of the most important amino acids synthesized long before it was first isolated from the natural resources in 1879 by Adolph Strecker [18,19]. It is a hydrophobic and ambivalent molecule with a chemical formula C_{3}H_{7}NO_{2}, this means that it can be found inside or outside of the protein molecule. Under biological conditions, Alanine’s structure can be divided into three sub-groups; α-amino group (NH^{+}: Protonated, value of pKa_{1}=9.69), α-Carboxylic acid group (COO−: Deprotonated, value of pKa_{2}=2.34) and a side chain methyl group (value of pKa3 is still unknown) which is classified as non-polar at physiological pH [20]. It is found in a wide variety of daily food, especially in meats, fish and seeds, can be manufactured in the human body from branched chain of amino acids, such as Pyruvate, Valine and Leucine and is also arisen together with generating glucose and lactate from protein via Alanine cycle [21]. Alanine has a vital role in Glucose-Alanine cycle between liver and tissues, which is used as fuel in muscles and other tissues. After being formed, passed to the blood then transported to the liver. The Glucose- Alanine cycle contributes in removing Glutamate and Pyruvate from the muscle, which then find their way to the liver and participating in urea cycle to form urea [22,23]. Long-term study conducted by Imperial College London confirmed that the high level of Alanine amino acid can increase energy intake, cholesterol and the blood pressure levels [23]. In addition, it supports prostate health, guards against producing the toxic substances which leads to breaking down the proteins in the muscles, strengthens the immune system by producing the anti-bodies if needed, and plays a key role by transferring the nitrogen from peripheral tissues to the liver [23,24]. Taking an oral dose of Alanine with insulindependent diabetes can be more effective than a conventional bed-time snack [24]. The adsorption of different amino acids inside single-walled carbon nanotubes (SWCNTs) has been studied and investigated [17,25- 28].
The recent studies have gained much more attention and also intensively studied the combination of carbon nanodevices with different bio-molecules as inhibitors for disease therapy or as safe agents for drug delivery system, such as amino acids and drugs [17,18,26,29,30]. This has led to motivating the scientific researchers to enhance the ability and conductivity of these carbon nanodevices by manipulating in their conductivity and intrinsic structural properties [31-35]. Trzaskowski et al. [36] indicate that amino acids may bind to the outer surface and interact with the interior wall of CNTs. In addition, Roman et al. [37] calculate the adsorption of different amino acids on graphite sheet and the (3, 3) SWCNT by using the density functional theory (DFT). Further example, Vardanega et al. [38] show that the adsorption (outer surface) and encapsulation (inner wall) of amino acids with a dielectric SWCNT is carried out. Chang et al. [39] theoretically study and investigate the encapsulation of amino acids. Inside Zigzag SWCNTs and their results reveal that the stability of amino acids along the interior cavity wall. Ganji [17] also calculates the encapsulation of Histidine, Phenylalanine, Cysteine and Glycine amino acids inside the SWCNTs by using the Spanish Initiative Simulations (SIESTA) with thousands of atoms and the Density Functional Theory Based Methods (DFT and DFTB+). Recent computational, numerical and experimental results show that the interaction energies arising from different amino acids interacting with inner surface of SWCNTs with variant radius r are very small in the range of approximately -0.1 to -0.8 kcal/mol compared to those of gas molecules and nucleic acid bases of approximately 20.8 and 20.1 kcal/ mol, respectively [40-44].
In this paper, we only examine the encapsulation of Alanine amino acid inside a SWCNT as shown in Figure 1. Here, we propose a mathematical model by assuming the Alanine molecule as comprising three parts (discrete approach): a group of atoms as a linear molecule, a cylindrical group of atoms and a spherical shell and all atoms containing the Alanine molecule assumed to be as a spherical shell (continuum approach). Each orientation interacting individually with an infinite nanotube of radius r which is assumed to be uniformly distributed, welldefined and characterized as a perfect cylinder.
In the next section, we briefly outline the two significant physical concepts of van der Waals force and Lennard-Jones potential, and also determine the values of minimum energies by using a discretecontinuum approach and depending on the inner radius of nanotube r and the orientation angle φ. Followed by a discussion and analysis are in results section. Finally, conclusions are given in the last section.
In this model, we obtain the biophysical model which describes the encapsulation of Alanine molecule inside SWCNT of radii r as a mathematical model to determine the interaction energy between specific atoms at point P inside cylindrical nanotube. Next, we use the Cartesian coordinate system (x, y, z) as a reference to model the two interacting molecules, Alanine molecule and the SWCNT as a perfect and well-defined cylinder. We assume that the specific point at atom P parameterized by (0, 0, δ), where 0 ≤ δ ≤ r. Next, we apply the discrete continuum approximation by using van der Waals force and Lennard Jones potential to model the encapsulation of Alanine amino acid inside infinite SWCNT of radius r. The Lennard-Jones potential is given by
where, ρ denotes the distance between two well-defined different molecules, Ψ(ρ) is the potential function, the significant physical parameters, A (attractive) and B (repulsive), are calculated by using the empirical combining laws given by where E is the well depth, σ is the van der Waals diameter and ζ is the non-bond energy [45,46]. Here, we apply discrete-continuum approximation, specific atom is assumed to be uniformly distributed over the surfaces of the two interacting molecules. To obtain the total energy for all orientations as in Figure 2(ii), we first need to determine the interaction energy between the atoms at point P inside an infinite SWCNT as shown in Figure 1(i). The magnitude of total energy arising from the interaction between a specific atom at point P and the cylindrical nanotube can be mathematically obtained by performing a surface integral of the Lennard-Jones potential over the nanotube and given
Where η_{c} and η_{l} are the mean surface densities of atoms on the two interacting molecules, and
dδ_{c} and dδ_{l} are typical surface elements located on the two interacting molecules.
Alanine as a spherical shell
In this proposed model, we apply the continuum approach and Lennard-Jones potential together to determine the minimum energy arising from Alanine-SWCNT interaction. The cylindrical nanotube is assumed to be as a perfect cylindrical shell which can be parameterized by (r cos θ, r sin θ, z), the Alanine amino acid assumed to be a spherical molecule of radius rs located at (r_{s} sin φ cos θ, r_{s} sin φ sin θ, r_{s} cos φ) as shown in Figure 2 and the distance between the spherical shell and cylindrical tube is given by
From Cox et al. [47], we find the interaction energy between the sphere of atoms of radius rs and cylindrical nanotube as
where η_{N}=13/volume of the sphere is the atomic volume density of the spherical molecule (CH_{3}).
Alanine comprised as three configurations
We assume that the centre of Alanine molecule is located at the origin (center of the infinite cylindrical nanotube). The minimum energy arising from the interaction between Alanine molecule and a cylindrical SWCNT with infinite length is accounted in three orientations a shown in Figure 2. Firstly, the two carbon and one nitrogen atoms forming a linear molecule which is assumed to be located at (0, 0, t cos φ+z_{0}), where t ∈ [0, σ_{CN}+σ_{CC}] and the distance ρ1 between the linear chain and the nanotube is given by ρ_{1}^{ 2}=r^{2} + (z−(tcosφ+z_{0}))^{2}. From work of Al Garalleh et al. [48] defining Dn as
so, the interaction energy between linear molecule and cylindrical nanotube can be given by
where η_{c} and η_{l}=3/length of linear molecule are the atomic surface densities for the carbon nanotube and linear chain (a nitrogen and two carbon atoms), respectively.
Secondly, we assume a group of two oxygen and four hydrogen atoms as a cylindrical shell of radius r_{1}. This cylinder is assumed to be located at (r_{c} cos θ, r_{c} sin θ, t+z_{0}) and t ∈ [0, σ_{CO}+σ_{CH}],
where the distance ρ^{2} between the nanotube of radius r and the cylindrical group of radius r_{c} is given by
From the work of Cox et al. [49], if Tn is given by
the interaction energy between cylindrical group pf atoms and cylindrical nanotube is given by
where ηg=6/surface area of the cylinder group is the atomic surface density of the cylindrical group. Finally, we consider the carbon and three hydrogen atoms (CH_{3} molecule) as a sphere of radius b=σ_{CH} which is assumed to be located at (bsinφ cos θ, b sin φ sin θ, b cos φ) and the distance between the spherical shell and cylindrical tube is given by ρ_{3}^{2}=(r cos θ−b sin φ cos θ)^{2} + (r sin θ−b sin φ sin θ)^{2} + (z−b cos φ)^{2}. We find the interaction energy betweenthe sphere of radius b=σ_{CH} and cylindrical nanotube by using the equation 3 which can be given
Where η_{H}=4/surface area of the sphere is the atomic surface density of the spherical molecule (CH_{3}). Thus, we gather all sub-interactions arising from the encapsulation of Alanine molecule inside SWCNT of radius r to determine the magnitude of total energy which is given as
Figure 1: i) Modelling interaction between Ala-nine amino acid (C3H7NO2) and a SWCNT (each atom specified by distinct colour; Carbon: Grey, Nitrogen: Blue, Oxygen: Orange and Hydrogen: Green) ii) A SWCNT of radius r interacting with an interior atom at point P off-setting from the central-axis by a distance δ.
Acceptance and suction energies
To demonstrate the adsorption of the Alanine molecule inside a SWCNT, we first need to determine the acceptance and suction energies. We then evaluate the acceptance energy moving from -∞ to z_{0} to determine whether the Alanine amino acid will be sucked into a cylindrical SWCNT. Next, we calculate the suction energy which is the total energy for a molecule moving from -∞ to ∞. Based on work of Cox et al. [55], a molecule is accepted inside a CNT if the acceptance energy (A_{r} ) is greater than zero, which is given bynoting that z_{0} is the root of equation ∂E/∂z=0, which is the point where the molecule is about to enter the nanotube. The suction energy (S_{r}) is calculated as the total integral of the axial force from -∞ to ∞ and is given by
Noting that z_{0} is the root of equation ∂E=∂z=0, which is the point where the molecule is about to enter the nanotube. The suction energy (Sr) is calculated as the total integral of the axial force from -∞ to ∞ and is given by
The suction energy S_{r} can be converted directly to the kinetic energy of the moving molecule, in the case there is no energy dissipation.
Here, we apply the discrete-continuum approach to evaluate the interaction energy of encapsulation of Alanine inside SWCNT. The well-depth E, van der Waals diameter σ and non-bond energy ζ are shown as in Table 1. The significant physical parameters and radii r of carbon nanotubes involved in this model are calculated as in Table 2. The attractive (A=4_{E}σ^{6}) and repulsive (B=4_{E}σ^{12}) constants are calculated by using the concepts of well-depth E and the van der Waals diameter σ and are given in Table 3. We calculate the atomic densities from dividing the number of atoms for each interaction pair by the volume or surface of the assumed structure and also determine the radius of the CNTr by using the chirality concept ((n, m)), as shown in Table 4, which can be calculated by using the relationship as shown in Figure 3 [56],
Maple package used to evaluate and plot the minimum energy arising from the interactions between Alanine and SWCNT of radii r (the SWCNT assumed to be characterized and well- defined with an infinite length). The magnitude of Alanine-SWCNT interaction depends on the nanotube radius r and the orientation angle φ as shown in Figures 4 to 11. By considering the nanotubes (9, 0), (8, 2), (6, 5), (7, 4), (8, 3), (9, 2), (10, 3) and (13, 0) which have radii r=3.523, 3.591, 3.735, 3.775, 3.861, 3.973, 4.615 and 5.089 Å, respectively, and assuming that φ=0o, π/6, π/3 and π/2. In this model, we deduce the minimum radius of the nanotube that will accept the Alanine molecule for each configuration and find out that the encapsulation of Alanine occurs when r is greater than 3.75 Å. The lowest interaction energy is obtained when r=4.615 Å ((10, 3) nanotube) and is more favorable when Alanine molecule as a spherical structure for continuum approximation and φ=0o then followed by π/6, π/3 and π/2 for discrete approximation. The magnitude of the minimum energies for both configurations is given in Table 4. For all orientations, we note that there is a minimal difference in the value of interaction energy inside SWCNTs and the Alanine amino acid is unstable and repulsive when r<3.75 Å. For both configurations, our calculations indicate that the (10, 3) SWCNT is the most favorable physical tube with a minimum energy of approximately -0.77 Kcal/mol.
Interaction | E (Å) | σ (Å) | ζ (Kcal/mol) | Interaction | E (Å) | σ (Å) | ζ (Kcal/mol) |
---|---|---|---|---|---|---|---|
H-H | 0.74 | 2.886 | 0.044 | O-H | 0.96 | 3.193 | 0.051 |
O-O (sb) | 1.48 | 3.5 | 0.06 | O-O (db) | 1.21 | 3.5 | 0.06 |
N-N | 1.45 | 3.66 | 0.069 | N-H | 1 | 3.273 | 0.055 |
C-C (sb) | 1.54 | 3.851 | 0.105 | C-H | 1.09 | 3.368 | 0.068 |
C-C (db) | 1.34 | 3.851 | 0.105 | C-O (sb) | 1.43 | 3.675 | 0.079 |
C-O (db) | 1.2 | 3.675 | 0.079 | C-N | 1.47 | 3.755 | 0.085 |
Table 1: The Lennard-Jones constants (E: Bond length, σ: Non-Bond distance and ζ: Non-Bond energy) (sb: single bond; db: double bond) [45,50-53].
Radius of CNT (9,0) | 3.523 Å [54] |
Radius of CNT (8,2) | 3.591 Å [54] |
Radius of CNT (6,5) | 3.735 Å [54] |
Radius of CNT (7,4) | 3.775 Å [54] |
Radius of CNT (8,3) | 3.861 Å [54] |
Radius of CNT (9,2) | 3.973 Å [54] |
Radius of CNT (10,3) | 4.615 Å [54] |
Radius of CNT (13,0) | 5.089 Å [54] |
Radius of the cylindrical group | rc=2.39 Å |
Radius of the hydrogen sphere | b=1.091 Å |
Radius of the spherical shell | rs=3.205 Å |
Length of the cylindrical group | L=6.41 Å |
Surface density for carbon nanotube | ηc=0.381 Å−2 |
Atomic line density of the linear carbon atoms | ηl=0.732 Å−1 |
Surface density of the cylindrical group | ηg=0.063 Å−2 |
Surface density of the sphere (CH_{3}) | ηH=0.268 Å−2 |
Volume density of the Alanine as spherical shell | ηD=0.095 Å−3 |
Table 2: Parameters for carbon nanotubes and Alanine amino acid.
Interaction | Attractive | Value (Å 6 kcal/mol) | Repulsive | Value (Å12 ×103 kcal/mol) |
---|---|---|---|---|
C-C | ACC | 22.63 | BCC | 65.533 |
H-C | AHC | 17.16 | BHC | 31.729 |
N-C | ANC | 41.26 | BNC | 115.661 |
O-C | AOC | 33.79 | BOC | 83.246 |
S-C | ASC | 139.04 | BSC | 522.516 |
O-H | AOH | 9.41 | BOH | 9.972 |
N-H | ANH | 11.7 | BNH | 14.383 |
CNT | ACNT | 17.4 | BCNT | 29 |
Linear Molecule | ALine | 28.84 | BLine | 66.286 |
Sphere of Hydrogen | ASphere | 4.41 | BSphere | 2.548 |
Cylindrical group | ACyl | 16.87 | BCyl | 39.908 |
Alanine molecule as spherical shell | AD | 17.05 | BD | 32624 |
Line-CNT | ALine−CNT | 23.12 | BLine−CNT | 47.643 |
Sphere-CNT | ASphere−CNT | 10.91 | BSphere−CNT | 15.774 |
Cylinder group-CNT | ACyl−CNT | 17.14 | BCyl−CNT | 34.454 |
Alanine-CNT | AD−CNT | 17.23 | BD−CNT | 30812 |
Table 3: Numerical values of the attractive and repulsive constants.
Radius (Å) | E (φ=0) | E (φ=π/6) | E (φ=π/3) | E (φ=π/2) | E (Spherical shell) |
---|---|---|---|---|---|
3.523 | 1.725 | 1.708 | 1.702 | 1.698 | 1.868 |
3.59 | 0.963 | 0.954 | 0.951 | 0.948 | 1.043 |
3.735 | -0.037 | -0.038 | -0.038 | -0.037 | -0.041 |
3.775 | -0.209 | -0.208 | -0.207 | -0.206 | -0.226 |
3.861 | -0.474 | -0.472 | -0.47 | -0.469 | -0.515 |
3.98 | -0.675 | -0.678 | -0.68 | -0.684 | -0.734 |
4.615 | -0.709 | -0.704 | -0.702 | -0.699 | -0.769 |
5.195 | -0.485 | -0.482 | -0.48 | -0.479 | -0.527 |
Table 4: Interaction energy (E) (kcal/mol) for Alanine amino acid interacting with infinite SWCNTs of radii r for different values of φ.
Next, we evaluate and plot the acceptance energy Wr by using equation (11) for various radii of SWCNTs and different values of orientation angle. We comment that the acceptance occurs when Wr is greater than zero. The Alanine amino acid is not completely encapsulated into such nanotubes of radius r<3.75 for all orientations as shown in Figure 12. Furthermore, our results show that the acceptance of Alanine is more favorable when the Alanine as spherical molecule then followed by φ=0o, φ=π/6, π/3 and π/2, respectively. We can also determine the suction energy of the Alanine as a function of the nanotube radius r by using equation (11). As shown in Figure 13, the SWCNT of radius greater than 3.75 Å will accept the Alanine for all orientations. The Alanine amino acid prefers to be inside the nanotube of radius r>3.75 Å. For the tubes with radius r>3.75 Å, there are no energetic barriers to prevent the encapsulation of the Alanine amino acid. Based on our results, the acceptance and suction energies are shown to agree with the results obtained from analyzing the total interaction energy. The latter calculations confirm the results above and show that the Alanine amino acid is encapsulated inside SWCNTs for any values of φ when r>3.75 Å. Our results are in excellent agreement with recent findings of Ganji’s work [17] which shows that the magnitude of minimum energy arising from the encapsulation of different amino acids, Histidine, Glycine, Cystine and Phyenalalanine, inside a SWCNT of radius r=5.089 ((13, 0)) are in the range of -0.1 to -0.8 kcal/mol compared to our results which is about -0.53 kcal/mol.
Based on our calculations as in Table 4, the magnitude of the interaction energies shows minimal difference for all both configurations (φ variant orientations) and the minimum binding energy arising from the encapsulation of Alanine inside the infinite SWCNT of radius r=4.615((10, 3)) is approximately -0.77 kcal/mol. Our results consistently agree with Roman et al. [37] who investigate nucleic acid bases adsorption on a (10, 0) SWCNT, and also with those of Trzaskowski et al. [36] and Vardanega et al. [38] who investigate the conjugation between the α-amino acids and carbon nanostructures. Their results indicate that the adsorption of amino acids are carried out and stable along the Zig-zag SWCNTs and graphite sheet. Most of recent theoretical and computational studies have intensively investigated the encapsulation of different amino acids, especially on a (3,3) nanotube [17,27,29,31,32]. Their computational and experimental results confirm that the amino acids can be encapsulated inside a carbon nanotube of radius greater than 3.75 Å. Based on work of Dresselhaus et al. [12] who predict that the (5, 5) would be the most distinct physical nanotube, this means that the researchers need to pay more attention to enhance its ability, by manipulating in its chemical and physical properties, to be more effective in reality and used as carrier for disease therapy and drug delivery.
In this paper, we use the van der Waals force and Lennard-Jones potential together with discrete-continuum formulation to obtain a mathematical model which describes the adsorption of Alanine amino acid inside the SWCNT with infinite length. We consider two possible structures as models of Alanine; spherical shell and can be accounted in three parts; linear molecule, cylindrical group of atoms and CH_{3} molecule as s sphere, we then gather all sub-interactions to determine the total potential energy. We also evaluate and plot the potential energy (for each configuration) of Alanine amino acid interacting with inner surface of the carbon nanotube of various sizes. The minimum binding energy depends directly on the radius of the nanotube r and the orientation angle φ. We note that (10, 3) of radius r=4.615 Å is the most favourable nanotube. For each configuration, we find that Alanine is unstable and rejected inside the SWCNT of radius r<3.75 Å. Overall, our results are in very good agreement with Ganji [17] who calculates the interaction energy (in the range of −0.1 to -0.8 kcal/mol).
for encapsulation of different α-amino acids inside SWCNTs and also with the long-term studies which have indicated that the encapsulation of protein as biosensors, peptides and different amino acids inside the graphite sheet and CNTs are carried out, especially when r is greater than 3.75 Å [25,27,29,31,32].
The author acknowledges financial support from the Research and Consultation Centre (RCC) at the University of Business and Technology.
This project funded by the Research and Consultation Centre (RCC) at the University of Business and Technology.