Comparison the stability of peptide with various secondary structures in bulk water and under CNTs confinement.
Carbon-based nanoparticles and nanostructures, such as carbon nanotubes (CNTs), have drawn great attention in both academia and industry due to their wide potential applications. Owing to their well-defined one-dimensional (1D) interior, CNTs serve as desirable materials for encapsulating molecules, such as water [1-4], ionic liquid , drug molecules , and biomolecules . The nanoscale confinement of CNTs have considerable impact on the inner molecules, including changes in their structure, size distribution, surface area, and dynamics, thus leading to many interesting and striking properties that are quite different from those in bulk [1-5, 7-9]. For example, nanoscale confinement of CNTs can give rise to ordered structure and extra-fast motion of water molecules [1-4], significantly enhanced activity of catalytic particles , phase transition of ionic liquids from liquid to high-melting-point crystal , and denatured structures of peptide helices . In particular, recent studies [10-13] have shown that these CNT-based nanomaterials can be used as a new paradigm of diagnostic and therapeutic tools, which is beyond the traditional organic chemistry based therapeutics in the current pharmacology. Before their wide applications in the biomedical filed, the effects of CNTs on biomolecules (and drug molecules) need to be understood thoroughly [14-20].
In this book chapter, we review some of our recent works [21-24], with large scale molecular dynamics (MD) simulations using massively parallel supercomputers such as IBM Blue Gene, on the nanoscale confinement of both small molecules and peptides inside the CNT, which demonstrate wide implications in nanoscale signal processing, single-file transportation, drug delivery, and even cytotoxicity. The structure of this chapter will be organized as following. First, we show that water molecules confined within a Y-shaped CNT can realize the molecular signal conversion and multiplication, due to the surprisingly strong dipole-induced orientation ordering of confined water wires . Second, we find a striking phenomen that urea can induce the drying of CNTs and result in single-file urea wires. The unique properties of a urea wire as well as its biological and technological implications are discussed [22, 23]. Third, we show that nanoscale confinement can catalyze the chiral transition of chiral molecules. We further explore the molecular mechanism of CNT-catalyzed enantiomerization and provide some implications for drug delivery . Last, we investigate the effect of confinement of CNT on three important secondary structural motifs of proteins – a hairpin turn, a helix, and a beta-sheet.
2.1. Water-mediated signal multiplication with Y-shaped nanotubes
Uunderstanding the molecular-scale signal transmission (amplification, shunting, etc) has attracted intensive attentions in recent years because it is of particular importance in many physical, chemical, and biological applications, such as molecular switches, nano-gates, and biosensors [26-29]. However, due to the intrinsic complexity of these nano-systems and the significant noises coming from thermal fluctuations as well as interferences between branch signals, the molecular details are far from well understood. On the other hand, water molecules confined within nanochannels exhibit structures and dynamics quite different from bulk , which might provide a medium for molecular signal transmission. Water molecules inside CNT with a suitable diameter can form a single-file hydrogen-bonded molecular wire, with the concerted water dipole orientations, i.e., either parallel or antiparallel to the CNT axis [1, 30, 31]. The characteristic time for reorientation of the dipole orientation of water wire is in the range of 2–3 ns for CNT with a length of 1.34 nm , and the water wire inside a nanochannel can remain dipole-orientation-ordered up to macroscopic lengths of ~ 0.1 mm, with durations up to ~ 0.1 s . If we can “tune” the orientation of a water molecule at one end, we might be able to control the orientations of all water molecules in the molecular wire and even amplify and shunt the orientation signal.
Recently, Y-shaped nanotubes have been successfully fabricated by means of many different methods [32-34]. These nanotubes have been found to exhibit both electrical switching and logic behaviour [27, 35]. In the following, we will show that single-file water wires confined within a Y-shaped single-walled CNT (hereafter referred to it as Y-SWNT, see Fig. 1) can perform both signal amplification and shunting, ignited by a single electron, because of the surprisingly strong interactions between water molecules at the Y-junction. We construct Y-SWNT by jointing three (6, 6) uncapped armchair single-wall CNTs (SWNTs) together symmetrically along three directions neighbouring 120° one another. An external charge,
The simulations show that water molecules in the Y-SWNT form single-file hydrogen-bonded molecular wires. Although the water wires in different tubes interact at the Y-junction, all water’s orientations are either parallel or anti-parallel to the nanotube axis, similar as the case of water wire in conventional SWNT . To describe quantitatively the confined water’s dipole orientation, we choose an angle between the dipole orientation of
To further characterize the molecular signal transmission, we define an integer
Careful examinations reveal that the external charge “monitors” the water molecule facing this charge (referred to as the “Monitored-water”); the Monitored-water determines the water orientations in the main tube; the uppermost water molecule in the main tube governs the dipole orientations of the bottommost water molecules in branch tubes and hence the water dipole orientations within both branch tubes (see ref.  for more discussions). In addition, we find that the response to the switching of the charge signal is very rapid, from a few nanoseconds to a few hundred nanoseconds: In response to -
The charge signal can also be transmitted and amplified/shunted through additional channels. We have simulated a system with three Y-junctions where each of the outlet branch tubes forms a Y-junction connecting two more tubes (see Fig. 3). We refer the two middle tubes as MT1 and MT2, and the four branch tubes as BT1, BT2, BT3 and BT4. Fig. 4 shows the
To summarize, by using MD simulations we show that a signal at the single-electron level can be converted and multiplied into two or more signals by water wires confined within a narrow Y-shaped CNT. This remarkable capability of signal transduction by Y-SWNT derives from the surprisingly strong dipole-induced ordering of such water wires, so that the concerted water orientations in the two branches of the Y-SWNT can be modulated by the orientation of water wire in the main channel. The response to the switching of the charge signal is found to be very rapid, from a few nanoseconds to a few hundred nanoseconds. To our knowledge, this is the first observation of the remarkable signal amplification and shunting with a Y-shaped nanotube at the atomic level and this observation may have significance for future applications in molecular-scale electronic devices. In addition, it is noteworthy that there are Y-shaped biological channels [38, 39], therefore, our findings might also provide useful insight into the molecular signal transmission in biological systems.
2.2. Molecular wire of urea and induced drying in carbon nanotubes
2.2.1. Molecular wire of urea inside narrow carbon nanotube
Molecules confined inside nanoscale space such as narrow nanotubes or membrane proteins can form one-dimensional (1D) molecular wires, which have attracted intense interest recently because of their scientific importance and potential applications in nanotechnology [1, 21, 40-56]. Among them, it is of particular interest in determining the structure and dynamical behavior of water wires [1, 21, 40-49] which have been found to exist in narrow nanotubes[1, 21, 40-42, 46-48] and biological channels [43-45]. Water wires have many interesting properties, such as wavelike density distributions [1, 46], rapid and concerted motions [1, 40, 43], orientation-ordered structures and collective flips [1, 21, 41, 48], and excellent on-off gating behaviors [46, 47]. In addition, it has been observed that the methane , methanol , and gas molecules (O2, H2, and CO2)  preferentially bind to the interiors of narrow SWNT over water and form 1D molecular wires. Despite the above progress, the properties of molecular wires have not been fully understood, particularly for the molecular wires formed by larger polar organic molecules.
Urea plays an important role in the metabolism of nitrogen-containing compounds by animals [57, 58], and serves as a common protein chemical denaturant and an important raw material in chemical industry. It is important to note that the biological urea channel dvUT (a urea transporter from the bacterium
We have performed MD simulation of 336-carbon (6, 6) SWNT (3.32 nm in length), solvated in aqueous urea with various urea concentrations (8M, 1 M and 0.5 M, with the simulation lengths 100 ns, 200 ns, and 200 ns, respectively). Fig. 5 shows the number of solvent (water/urea) molecules inside the SWNT in case of 1 M urea concentration during the course of simulation. Almost all water molecules inside the SWNT are replaced by urea within the first 25 ns. The confined urea molecules form a 1D “perfect” urea wire with a contiguous hydrogen-bonded network in most of the simulation time, or occasionally forms a “defective” urea wire [with a very small number of “water defect(s)”, commonly near the SWNT edge].
Table 1 summarizes the average number of urea () and water molecules () inside the SWNT after the systems have reached equilibrium with various urea concentrations. Regardless of urea concentration and urea model used, finally, the SWNTs are nearly completely filled with urea molecules. Table 1 also shows the occurrence probability for “perfect” urea wire,
Next, we explore the structure of the confined urea wire. We use the case of the 336-carbon (6, 6) SWNT in 8 M KBFF urea for illustration because
The above findings have technological implications. Our previous reports [21, 25] have demonstrated water wires can mediate the signal conversion and multiplication because of their ordered 1D structure and collective flipping behavior. However, the very small size of the water and fast flipping of water wire make the experimental realization very difficult . Urea wire has similar ordered 1D structure and flipping behavior as water wire but has a lower flipping frequency and a high molecular polarity which can facilitate the signal detection in practice (urea wire has longer response time  to switch its dipole orientation under the influence of a change in charge signal). We therefore expect that urea wire can serve as a better candidate for signal transduction and multiplication.
Next, we have calculated the position distribution of urea along the nanotube axis. There are seven distinct, sharp peaks (with an average peak-to-peak value of ~ 4.6 Å), indicating that the urea wires are translationally ordered along the SWNT axis. The position distribution is found to be much sharper than water wire owing to the larger molecular size of urea (see ref.  for details).
We have also calculated the interaction energies with the rest of the system for a urea molecule with respect to its axial distance from the geometrical center of SWNT (see Fig. 6). Interestingly, the vdW potential curves are approximately symmetric; whereas electrostatic potential curves are observably asymmetric, i.e., correlate to the inner urea’s dipole orientations. Urea’s asymmetric molecular partial charge distribution together with the extremely confined space result in the orientationally ordered structure (concerted dipole orientations) of molecular wire, thus breaking the symmetry of the system within a finite time period (more than 100 ns for the present case) and causing an asymmetric electrostatic potential.
Although single-file transport of water through SWNT has been intensively investigated in recent years [1, 40, 46-48], much less is known about the single-file transportation for organic small molecules. Here we explore the transport properties of urea wire and make a comparison with water wire. We have calculated the urea flow, defined as the total number of urea molecules per nanosecond that have entered from one end and leave the SWNT from the opposite side. Given that the biological urea channel dvUT  has a length of ~ 16 Å (the number of urea molecules accommodated in the selectivity filter is about 3), we chose the 144-carbon (6, 6) SWNT (13.5 Å in length) as the nanochannel, wherein the resulting urea wire also consists of ~ 3 urea molecules. To facilitate a direct comparison with water wire, we performed additional simulations for the SWNT immersed in pure water. The calculated average flows (averaged over three independent 100 ns simulations) are 0.73 ns-1 and 0.79 ns-1, for KBFF and OPLS urea, respectively, and it is 16.2 ns-1 for water. Transportation of urea seems to be 20+ times slower than water. Fig. 7(A) displays the time evolution of urea flow from a typical simulation trajectory. The urea flow is low, with a maximal value of only 4 ns-1; it vanishes frequently, and the duration time of zero value can be up to 6 ns (e.g., t = 11 ns ~ 17 ns). In contrast, for water wire, its minimal flow is up to 7 ns-1, and its maximal flow reaches a value of 32 ns-1. Furthermore, we have studied the influence of urea concentrations (1 M ≤
To understand the physical mechanism behind the enormously lower permeability of urea relative to water for SWNT, we have calculated the interaction energies of a inner urea/water molecule with the SWNT (the data for water derives from the control runs of SWNT immersed in pure water). Because the carbon atoms of SWNT are modeled as uncharged Lennard-Jones particles, there are only vdW interactions between urea/water and SWNT. As displayed in Fig 7(B), the potential valley for urea is much deeper than that for water, because urea has a stronger dispersion interaction with SWNT than water, which in turn leads to a much lower permeability of urea than water.
In this section, we have investigated the structure and dynamical behavior of urea wire inside the narrow SWNT. Even at relatively low urea concentration (e.g., 0.5 M), we have observed spontaneous and continuous filling of SWNT with a 1D urea wire. The resulting urea wire is translationally and orientationally ordered, with a contiguous hydrogen-bonded network and concerted dipole orientations of urea molecules. Despite the symmetric nature of SWNT, the urea’s potential energy profile along SWNT is asymmetric, coming from asymmetric molecular partial charge distribution (or dipole moment) and the ordering of urea’s dipole orientation under extremely confinement. Furthermore, we have studied the single-file transportation of confined urea, and find that urea flow decreases significantly (by a factor of ~ 20) compared to that of water, due to the fact that urea has a stronger dispersion interaction with SWNT than water. We also find a maximum in urea permeation around a concentration of 5 M. The studies on the urea wire confined inside SWNT not only help our understanding of the unique properties of confined polar organic molecules, but also present biological (biological urea channel) and technological (e.g., electronic devices for signal transduction and multiplication at nanoscale) implications.
2.2.2. Urea-induced drying of carbon nanotubes
In the previous section, we have demonstrated that urea can expel water inside a narrow SWNT [(6, 6) SWNT]. One may wonder if this phenomenon can persist in wider SWNT. To answer this, we performed MD simulations of (17, 8) SWNT (1.73 nm in diameter, it can accommodate several layers of urea and water) immersed in 8 M urea solution. Considering that there are some urea models commonly used in literature whose charge distributions are quite different , herein we have used five different urea models to test if the drying phenomenon is sensitive to force fields used.
The five urea models used in the current study are the OPLS [60, 61], KBFF , CHARMM (parameters derived from the CHARMM22 force field ), AMBER* , and AMBER [parameters derived from the file embedded in the AMBER 10 simulation package (University of California at San Francisco)] urea models. The simulation were performed using Gromacs 4.0.7  in an NPT (300K, 1 atm) ensemble with the simulation lengths of 100 ns for all systems. In all cases, we observe that most of water molecules initially inside the SWNT (
To understand the observed phenomenon of urea-induced drying of SWNTs, we have calculated the difference in average interaction energies for a solvent (urea/water) in bulk and in (17, 8) SWNT with the rest of the system. As the solvent molecules move from bulk into the (17, 8) SWNT, both urea and water lose electrostatic interaction energies, but urea gains more vdW energy than water (about 3~4 times larger than water), which mainly comes from the stronger dispersion interaction of urea than water with nanotube. As a consequence, after a solvent penetrates the SWNT, on average each urea gains 2.55~4.58 kcal/mol whereas each water loses 0.12~1.64 kcal/mol. It is noteworthy that the replacement of structurally confined water by larger urea (on average each urea molecule can replace ~2.5 water molecules) is also favorable in overall free energy due to an overall solvent entropy gain. In addition, the free energy analysis [by calculating the potential of mean force (PMF)] also support that the phenomenon of urea-induced drying of SWNT derives from the stronger dispersion interaction of urea with SWNT than water (see ref.  for details).
In conclusion, by using MD simulation we have observed a striking phenomenon of urea-induced drying of hydrophobic nanotubes and demonstrated the robustness of this phenomenon by using five different urea models. By decomposing the interaction energies for a solvent molecule into electrostatic and vdW components, we find that the drying phenomenon results from the stronger dispersion interaction of urea than water with nanotube. These results also have implications on understanding the urea-induced denaturation of proteins by providing further evidence of the potential existence of a “dry globule”-like transient state  during early stage of protein unfolding and the “direct interaction mechanism” whereby urea attacks protein directly via favorable dispersion interaction, rather than disrupts water structure as a “water breaker”. In addition, this study points out the crucial role of dispersion interaction in the selective absorption of molecules inside hydrophobic nanopores [54-56], which might be important for nanoscience and nanotechnology.
2.3. Chirality switch of drug-like molecules inside boron-nitride nanotubes
Many basic building materials of organism, such as amino acids and saccharides, are chiral in nature. Understanding the molecular chirality is very important for pharmaceutical products because the biological systems have stereoselectivity . Some molecules chiral stable in bulk systems may undergo conformational transitions in human body . For example, in late 1950s and early 1960s, thalidomide caused serious damages to the fetal growth, known as the “thalidomide tragedy” [67, 68], which correlates to a chiral transition of thalidomide occurred in human body. Hence, good conformational stability is an important requirement for chiral molecules used in pharmaceutical products and drug delivery.
It is well-known that there are various nanoscale confinement environments in human body, but the effect of nano-confinement on molecular chirality is still poorly understood so far. Here we use MD simulations (employing Gromacs 3.3.1 ) to study the chiral transition of difluorobenzo[c]phenanthrene molecules (C18H12F2, referred to as “D molecule”) in single-walled boron-nitride nanotubes (SWBNNTs). Molecular systems can be chiral by asymmetrically arranging atoms in space around a center, axis, or plane, which are called point, axial, and planar chirality, respectively . It has been reported using infrared laser pulses that D molecule show the planar chirality transition between
Figs. 9(a) and (b) show the chiral character of
We have computed the critical temperature
Now we focus on how enantiomerization occurs in nanotubes and the mechanism behind those observations. The D molecule consists of four six-membered rings, with a nearly planar structure. At low temperatures, the D molecule prefers to cling to the inner surface of SWBNNT [with its rings parallel to the SWBNNT axis, see Fig. 11(a)]. It is observed that when chiral transition occurs, the D molecule changes its orientation first so that the angle between plane of D molecule [determined by atoms e, f and g, see Fig. 8(a)] and the axis of SWBNNT increases considerably, even reaches 90° in a SWBNNT with a large diameter, e.g., the (15, 6) SWBNNT [see Fig. 11(b)]. This observation is quite different from the chiral transition in bulk systems. When the D molecule clings to the SWBNNT surface again, its chirality may be changed [see Fig. 11(c)]. We have computed the interaction energies between (15, 6) SWBNNT and D molecule, and find that when chiral transition occurs (at this time, D molecule is almost perpendicular to the nanotube axis), D molecule loses interaction energies [~30 kJ/mol, see Fig. 11(d)], mainly comes from the lost in vdW interactions (the electrostatic interactions between D molecules and nanotube is very small, in the order of 0.1 kJ/mol).
We have also obtained the interaction energy barrier Δ
In summary, we have performed MD simulations of chiral transition of D molecule (with planar chirality) in SWBNNTs and revealed remarkable effects of nanoscale confinement on molecular chirality. The critical temperature, above which the enantiomerization occurs, increases considerably with the diameter of nanotube, and the frequency of chiral transition decreases exponentially with respect to the reciprocal of temperature. The chiral transitions are found to closely correlate with the orientational transformations of D molecule. Furthermore, the barriers of interaction energies between D molecule and SWBNNT for different orientational states can characterize the chiral transition, implying that the temperature thresholds of chiral transitions can be controlled by nanotubes with appropriate diameters. These findings provide new insights to the effect of nano-confinement on molecular chirality, and offer some guidance for the safe delivery of the chiral drugs since an unexpected chiral transition may cause serious cytotoxicity.
2.4. Conformational change of small peptides in carbon nanotubes
How proteins fold and unfold in nanoscale confinement has been an open question to the society. Currently, most of the experimental and theoretical studies on protein folding are performed in dilute solutions [71-73]. However, in
Previous studies using polymer physics models have proposed an entropic stabilization theory, pointing out that the stability of folded protein can be enhanced in confined space because of the reduction of conformational entropy to the unfolded structural ensemble [80, 85, 92, 94]. On the other hand, the additional hydrophobic interaction between the protein and the confined boundary may destabilize the folded state [76-78, 81]. Both the stabilization and destabilization effects due to the confinement were then examined in amino acid side chain level using molecular dynamics simulations by Vaitheeswaran and Thirumalai . In their work, three types of side chain interactions, hydrophobic (Ala:Phe), polar (Ser:Asn) and charged (Lys:Glu), were simulated in a cylinder nanopore confinement with different lengths and diameters, showing that the hydrophobic side chain pair was strongly destabilized and then separated in the confined environment, while both the interactions of polar side chain pair and charged side chain pair were enhanced in the cylindrical confinement .
Later, the effect of different confining geometries on protein-folding thermodynamics and kinetics were studied by Mittal and Best , in which two proteins, a 3-helix bundle protein prb and protein G, were tested in a coarse-grained model. A quantitative exponential relationship (R-γc, where γc ≈5/3) was found between the characteristic size R of the confining boundary and its stabilization effect on the folded state. Surprisingly, the stabilization effect was not relevant to the dimension of the confinement (
The role of solvent in protein folding kinetics and thermodynamics in confined environment was investigated by Pande’s group . In a small representative protein (villin) system, Pande and co-workers found that the protein was promoted to folded state and more unlikely to change to the unfolded state when only the protein was confined . However, the folded state was destabilized when both the protein and waters were confined. Comparing to the bulk, a compact unfolded state was promoted instead of native state, which points out the confined solvent may be another crucial aspect to the protein folding under nanoscale confinement.
Carbon nanotubes (CNTs) are good cylindrical condiment carriers with hydrophobic surface . CNTs are recognized as promising candidates to be biocompatible cargos for drugs, nucleic acids, and proteins because they can spontaneously penetrate mammalian cells [101, 102]. Towards this goal, lots of efforts have been put on studying the biosafety of using CNTs
In this section, the stability of protein motifs are systematically investigated in CNT confinement with various secondary structures, including a helix, a beta-sheet, and a hairpin turn. Our simulations show that the stability of tested peptides is mainly dependent on their secondary structural types. Interestingly, the stability of beta-sheet peptides is enhanced by the CNTs confinement, but those stabilized beta-sheets can become totally unfolded when a hairpin turn is added to connect these two beta-sheets. The helical structure was bended inside the CNTs in order to adapt to the curved surface, forming stable coil-coil structures (see Table 3).
|System||CNT (15, 15)|
D = 20 Åa
|CNT (22, 22)|
D = 30 Å
|Hairpin turn (GB1)||unfolded||unfolded||stable|
|Double-strand antiparallel beta|
|Alpha-helix (26-mer poly-alanine)||coil-coil||coil-coil||stable|
The structure of hairpin turn in CNT confinement was investigated by all-atom MD simulations with explicit solvent. The GB1 hairpin turn (PDB entry 2GB1, residue index 41 to 56) was put into CNTs with diameters of D=20 Å (D20) and 30 Å (D30), respectively . We found both hairpin turns were unfolded to random coils after 30 ns simulations in CNTs of different sizes [see Figs. 12 and 13(a)]. The hairpin turn was unfolded to a more relaxed form in the larger size CNT, with radius of gyrations (Rg) 10.1 Å in D30 CNT and 6.7 Å in D20 CNT. Both unfolding processes were started at the turn segment, where the hydrogen bonds formed in the beta region were broken gradually (Fig. 13b). Meanwhile, the aromatic sidechains of Trp43, Tyr45, and Phe52 in the beta-region were tightly stuck to the inner wall of CNT by their strong π-π stacking interactions. A helix-like structure was formed in the turn segment [Figs. 12(b) and (d)]. The
The polyalanine chain was then utilized as the model system to study the stability of helix in CNT confinement. A 26-residue alanine chain was started from alpha-helix form. At the beginning of the simulations, the alanine chain was put in the middle of the CNT along the tube direction [Figs. 14(a) and (c)]. To our surprise, in just a few nanosceonds of the simulations, the entire alanine chain was quickly stuck to the inner side of CNT wall for all sizes of CNTs. Then the helix was bent to adapt the curved surface of CNT and extended along the unit vector, and finally the alpha-hliex turned to the coil-coil superhelix structure [Figs. 14(b) and (d)]. We performed 3 extra independent simulations for each size of CNT systems to conform the fast conformational changes and the final coil-coil superhelix structure for all the alanine chains. The superhelix conformation is an important feature to design proteins that can wrap CNTs, which has been successfully applied to virus-like protein assemblies on CNT surfaces in DeGrado’s group . Our simulations indicate that similar strategy could be applied to wrap inner side of CNTs with preferred of coil-coil superhelix structure.
For beta-strand structure, we used Alzheimer amyloid-
In conclusion, we have investigated three important secondary structural motifs in protein – hairpin turn, helix, and beta-sheet – with CNT confinements by all-atom MD simulations. We find only beta-strand conformation is stabilized in the CNTs. The alpha-helical polyalanine is turned to form coil-coil superhelix structure in order to adapt the curved surface of CNTs. The hairpin turn becomes the most unstable structure in the CNT which totally unfolds to random coil structure and sticks to the CNT walls. Therefore, it is hard to make simple conclusions that CNT confinement could stabilize or destabilize the protein structures. The conformation of protein in the CNT confinement could be largely dependent on its residue types and building motifs.
In this book chapter, we review some of our recent computational works, including: i) the water-mediated signal conversion and multiplication with Y-SWNT; ii) structure, dynamics, and transportation of urea wire and the phenomenon of urea-induced drying inside SWNT; iii) remarkable effect of nanoscale confinement on molecular chirality; and iv) conformational changes of various peptides under nanoscale confinement. These studies provide a deeper understanding towards the unique structure and behaviors of small molecules (water and small organic molecules) and peptides under nanoscale confinement, and demonstrate potential wide implications in nanoscale signal processing, single-file transportation, drug delivery, and even cytotoxicity.
We thank Prof. Zhigang Wang, and Dr. Yusong Tu for helpful discussions. This research is supported in part by grants from Zhejiang Provincial Natural Science Foundation of China (Grant No. LY12A04007), the China Postdoctoral Science Foundation (Grant No. 201104738), and the Fundamental Research Funds for the Central Universities. RZ acknowledges the support from the IBM BlueGene Science Program.
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