Surface Topography Effects in Protein Adsorption on Nanostructured

Lokesh Baweja , Kanagasabai Balamurugan , Venkatesan Subramanian , and .... Tina Mesarič , Lokesh Baweja , Barbara DraÅ¡ler , Damjana Drobne , Darko ...
0 downloads 0 Views 2MB Size
Download PDF
Article pubs.acs.org/Langmuir

Surface Topography Effects in Protein Adsorption on Nanostructured Carbon Allotropes Giuseppina Raffaini* and Fabio Ganazzoli Dipartimento di Chimica, Materiali e Ingegneria Chimica ‘G. Natta’, Politecnico di Milano, and Unità Politecnico, INSTM, piazza Leonardo da Vinci 32, 20133 Milano, Italy S Supporting Information *

ABSTRACT: We report a molecular dynamics (MD) simulation study of protein adsorption on the surface of nanosized carbon allotropes, namely single-walled carbon nanotubes (SWNT) considering both the convex outer surface and the concave inner surface, together with a graphene sheet for comparison. These systems are chosen to investigate the effect of the surface curvature on protein adsorption at the same surface chemistry, given by sp2 carbon atoms in all cases. The simulations show that proteins do favorably interact with these hydrophobic surfaces, as previously found on graphite which has the same chemical nature. However, the main finding of the present study is that the adsorption strength does depend on the surface topography: in particular, it is slightly weaker on the outer convex surfaces of SWNT and is conversely enhanced on the inner concave SWNT surface, being therefore intermediate for flat graphene. We additionally find that oligopeptides may enter the cavity of common SWNT, provided their size is small enough and the tube diameter is large enough for both entropic and energetic reasons. Therefore, we suggest that proteins can effectively be used to solubilize in water single-walled (and by analogy also multiwalled) carbon nanotubes through adsorption on the outer surface, as indeed experimentally found, and to functionalize them after insertion of oligopeptides within the cavity of nanotubes of appropriate size.

■

INTRODUCTION Biomaterials interact with a physiological environment, and the first event taking place at their surface after the initial hydration is protein adsorption, which drives the subsequent cell adhesion, possibly followed by proliferation and/or differentiation.1,2 The surface adsorption of proteins is affected by many factors,3−5 such as their abundance in the physiological medium, their diffusivity (related with the hydrodynamic volume, hence their size), and the solution pH and ionic strength. However, a major issue obviously consists of the surface chemistry and topography, whose effects are often largely intertwined, but can be separated by considering different polymorphs or allotropes for single-element materials. An example of the former case is the TiO2 passivating film on titanium, which may be present in the anatase or, more often, in the rutile structure, thus exposing different crystallographic planes,6−8 and of the latter case is graphite or its nanostructured allotropes such as graphene and carbon nanotubes.9 The theoretical study of protein adsorption on specific biomaterial surfaces is hampered by the hierarchical structure of proteins, which requires an atomistic picture of the molecule and of the surface.3,10 Accordingly, in the last years we modeled these phenomena through fully atomistic molecular dynamics (MD) simulations, since this method yields detailed information about the surface−adsorbate interaction at a © 2013 American Chemical Society

given temperature and the possible protein denaturation and eventual surface spreading or ordering.3,10−13 Using this approach, we first modeled the adsorption of albumin and fibronectin subdomains14,15 with an unlike secondary structure (α-helices and β-sheets, respectively) and then of whole lysozyme on graphite.16 We also investigated the unlike behavior of the same subdomains on the surface of an amorphous hydrophilic polymer, poly(vinyl alcohol).17 In the meantime, other groups modeled protein adsorption on other surfaces, focusing on ceramic materials, either ionic or covalent,18 and on self-assembled monolayers,19 but graphite was also considered.20 More recently, we began to model the effect of surface topography on protein adsorption at a given surface chemistry. Considering the same albumin and fibronectin subdomains previously modeled on graphite, we carried out a study of their adsorption on simple surfaces of the TiO2 polymorphs (rutile, anatase, and brookite), showing an unlike surface geometry, and found small but significant differences in the adsorption strength.8 Using again the same protein subdomains, in the present paper we consider nanostructured carbon allotropes Received: December 21, 2012 Revised: February 26, 2013 Published: March 21, 2013 4883

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

al.13 showed that a much smaller protein (the villin headpiece) on graphene in explicit water lead to a significant, though not yet fully complete, surface spreading. Thanks to the small size of the protein, which only comprises 35 residues, a large denaturation could be eventually achieved, preserving only part of the secondary structure. Once again the adsorption was accompanied by the protein dehydration close to the surface, producing final arrangements on graphene similar to those obtained by us on graphite with the effective dielectric medium. In conclusion, these lengthy MD simulations in explicit water do support our use of an implicit solvent as a way to significantly speed up computationally the protein adsorption process on these materials without introducing significant artifacts. In view of the above remarks, the simulation protocol adopted in this study is the same as in previous papers:14−16 (i) first, the arrangement of the protein subdomains close to the surface in different initial orientations is optimized through simple energy minimizations in the effective dielectric medium; (ii) then, some selected optimized geometries are subject to an MD run in the same medium in search of the final and most stable adsorption state. The first step corresponds to the initial adsorption on a bare surface, possibly under kinetic control, but in a moderately concentrated solution it can also provide the final adsorption stage at a large surface coverage hindering the full molecular spreading because of the small available adsorption area. Conversely, the second step yields the final adsorption stage on a bare surface in a very dilute solution with the most favorable interaction and surface spreading under thermodynamic control. In the following, we first describe the simulation methods, and then we report the main results obtained first on the outer (convex) and then on the inner (concave) nanotube surfaces and on graphene, considering in either case both the initial and the final adsorption stages mentioned before. In all cases, a comparison is made with previous results obtained for the same protein subdomains on graphite and with other theoretical and experimental results, whenever available. In the final section we summarize our main results.

such as single-walled nanotubes (SWNT) and a graphene sheet in comparison with graphite to model the topography effects on protein adsorption due to the surface curvature with the same surface chemistry (sp2 carbon atoms). Actually, it should be noted that in this way we neglect any specific electronic effect of the surface curvature that may affect the chemical reactivity and possibly physisorption. In fact, recently Cheng et al.21 modeled the adsorption of molecular hydrogen within small carbon nanotubes assuming in particular nonbonded interactions that were curvature dependent: thus, the parameters for the surface carbon atoms were obtained by a weighted average between those pertaining to sp2 and (pseudo) sp3 atoms, the weighing factor being a function of the surface curvature. However, the contribution of the (pseudo) sp3 carbon atoms is only relevant for very small nanotubes,21 whereas it amounts to at most 8% for our smallest nanotube, being much less for the larger ones. Accordingly, we simply considered our surfaces as formed by sp2 carbon atoms only as a reasonable approximation for a comparison among different nanotubes, in keeping also with what is currently done in most simulations. In the present paper, the effect of the curvature sign, or more simply of the surface concavity and convexity, is investigated by considering both the inner and the outer surface of SWNTs of appropriate diameters. The use of nanostructured materials like carbon nanotubes in a biological environment is receiving an increasingly large attention because of their novel and unusual properties that can be exploited in nanomedicine, for instance for drug or gene delivery, diagnosis, and therapy.22,23 Thus, here we consider both common SWNTs to study protein adsorption on the outer convex surface and larger nanotubes to model adsorption on the inner concave surfaces without a significant steric hindrance. Other simulation studies of the interaction between biological macromolecules and SWNT or graphene recently appeared in the literature, as commented upon later, but their goal was largely different from ours. The simulations are carried out in an effective dielectric medium using a distance-dependent dielectric constant24 as done in previous works.14−17 In this way, the presence of added salts cannot be considered, and specific hydration effects are neglected, but this approximation allows probing lengthy largescale surface rearrangements thanks both to the smaller system size and to the much faster relaxation rate due to the lack of friction with the solvent molecules. We already proposed two arguments to support this approach, based on one hand on a comparison with simulations in explicit water (the changes in the solvation energy was estimated to amount to about 10%)17 and on the other hand on the simulations of molecular recognition phenomena in supramolecular host−guest complexes (exactly the same geometry was obtained at room temperature both with explicit water and with the effective dielectric medium).25 A stronger argument supporting our use of an implicit solvent, however, is given by recent MD simulations in explicit water.12,13 In fact, Szleifer et al.12 showed that atomistic MD simulations of protein adsorption on a hydrophobic surface require huge simulation times because of lengthy dehydration processes. Considering lysozyme on crystalline polyethylene, they found that after an initial diffusion to the surface, the protein−surface interaction leads to their dehydration on time scales of the order of tens of nanoseconds, eventually followed by local denaturation mostly involving the loss of α-helices. In the adsorbed state, the protein is thus in contact with the surface, with very few water molecules (of the order of unity) sandwiched between them. Moreover, Zhou et

■

SIMULATION METHOD The simulations were performed with the InsightII/Discover and Materials Studio packages,26 using the consistent valence force field CVFF,27 originally designed for proteins and organic molecules. Uncapped armchair nanotubes and the graphene sheet were prepared from the available templates: the (8, 8) and (10, 10) SWNT used to model protein adsorption on their outer convex surface had diameters of 1.08 and 1.36 nm, while the (30, 30), (40, 40), and (50, 50) SWNT chosen to study adsorption on their inner concave surface had diameters of 4.07, 5.42, and 6.78 nm, in that order, and a length of 6.0 nm. The size of the graphene surface was 5.9 × 8.4 nm2. The albumin subdomain, its structure, and hydropathy are described in detail in a previous work (the A subdomain in ref 14), while the fibronectin type I modules are described in ref 15, where they were incorrectly mentioned as forming a single module instead of two. In both cases the appropriate charges for the ionizable residues were considered at the physiological pH = 7.4. The protein subdomains were optimized close to the surfaces in eight unbiased trial orientations for the albumin subdomains and six for the fibronectin modules so as to mimic a random approach from the solution, as previously done on graphite.14,15 The energy minimizations were carried out up to 4884

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

Figure 1. Albumin subdomain and the fibronectin moduli (above and below, respectively) in the most favorable initial adsorption stage on the outer convex surface of the (8, 8) and (10, 10) SWNT (left and right, respectively) shown in a side and in an end-on view. The secondary structure of the proteins is indicated by the red cylinders for the α-helices and the orange arrows for the β-sheets, while the regular turns are shown in blue and the backbone in green. The H atoms have been removed for clarity.

an energy gradient lower than 4 × 10−3 kJ mol−1 Å−1 in an implicit solvent using a distance-dependent dielectric constant14−16 by keeping fixed the carbon atoms of the materials, unless otherwise stated. The MD runs were performed in the same implicit solvent at a constant temperature (T = 300 K) controlled through the Berendsen thermostat. Integration of the dynamical equations was carried out with the Verlet algorithm using a time step of 1 fs, and the instantaneous coordinates were periodically saved for further analysis or geometry optimization. Within the MD runs, we monitored the time changes of the total and potential energy together with its components, and the distance between the protein center of mass and the surface. In general, these quantities showed an initial decrease, possibly with a few separate kinetic stages, and then fluctuated around a constant value, indicating achievement of equilibrium, which required adopting different lengths of the dynamic trajectories. The final optimizations were carried out with the same convergence criteria as before.

amino acids that are in contact with the surface, n5 Å, where 5 Å is conveniently taken as the upper distance for a contact interaction. The linear dependence, due to the additive nature of the attractive dispersive interactions, is shown in Figure 2 in

Figure 2. Interaction energy Eint and the strain energy Estrain plotted as a function of the number of aminoacids in contact with the surface, n5 Å (see text). The best-fit lines through the origin are also shown. The Eint values on the outer convex surfaces of the (8, 8) and (10, 10) SWNT are shown with empty circles and filled triangles, respectively, in comparison with previous results obtained for the same subdomains and a further albumin subdomain on graphite11,14,15 (empty squares). The diamonds show the Estrain values for the two subdomains on the (8, 8) and (10, 10) SWNT (empty and filled symbols, respectively) with the common best-fit line through the origin.

■

RESULTS AND DISCUSSION 1. Adsorption on Convex Surfaces. a. The Initial Adsorption Stage. The albumin subdomain and the fibronectin modules were initially placed close to the outer convex surface of the (8, 8) and (10, 10) SWNT in many different orientations (see the Simulation Method section) so that the minimum protein−surface distance was slightly larger than 5 Å. The initial optimization of these trial geometries yielded in all cases a significant protein−nanotube interaction, as shown in Figure 1 by the local deformation close to surface to enhance the contact area. Similar optimizations carried out close to the open ends of these SWNT shall be mentioned later (section 2c). The interaction strength with the SWNT surface can be measured through the interaction energy Eint. As done in other papers,10,11,14−16 this energy is defined as Eint = (Efree + Esubstr) − Etot, where Efree is the energy of the free native protein subdomain, Esubstr is the energy of the nanotube substrate (in the present case it is a constant conveniently set to zero since the SWNT is kept fixed), and Etot is the total energy of the whole system. Accordingly, Eint > 0 is the energy required to desorb the protein fragment from the surface and bring it back to the free native state. Taking into account the different starting orientations of the protein subdomains, producing different adsorption geometries with a local energy minimum, Eint turns out to be linearly correlated with the number of

comparison with the results for the same subdomains on graphite.11,14,15 The best-fit lines through the origin, also shown in the figure, are given by E int = (30.7 ± 1.1) × n5Å (kJ/mol) for the (8, 8) SWNT

(1a)

E int = (33.8 ± 1.3) × n5Å (kJ/mol) for the (10, 10) SWNT

(1b)

(the ± sign refers to the standard error of the fit) independently from the secondary structure within the statistical uncertainty. The slopes yield the intrinsic interaction energy per amino acid in contact with the surface (intrinsic Eint in the following) and show that the protein−nanotube interaction energy is slightly more favorable for the (10, 10) than for the (8, 8) SWNT, even though the difference is 4885

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

Figure 3. The most stable arrangements found for the albumin subdomains and the fibronectin modules (above and below, respectively) on the (8, 8) and (10, 10) SWNT (left and right, respectively). Each arrangement is shown in a side and in an end-on view. The surviving secondary structure (a short β-sheet for the fibronectin module) is shown by the orange arrows and by a blue ribbon for the regular turns in the albumin subdomain. The H atoms are not shown for clarity.

statistically significant only at the 1.8 σ level, suggesting a very small effect of the (quite similar) curvature of these convex surfaces. Still, these values are much smaller than the value of 57 ± 1 kJ/mol obtained for the same subdomains (and also the albumin E subdomain of ref 14) on flat graphite11 and with the value of 54.7 ± 0.9 kJ/mol for the graphene sheet (see later) in the initial adsorption stage. The local surface deformation shown in Figure 1 also entails a strain energy Estrain, i.e., an energy penalty undergone by the protein when it deforms from the native state to optimize the interaction with the surface. The Estrain values, shown with diamonds in the lower part of Figure 2, slowly increase with n5 Å as also found on graphite, but with a smaller slope (equal to 9.2 ± 0.7 kJ/mol) than Eint. Therefore, larger deformations with significant surface spreading can maximize the surface interaction. In other words, the initial adsorption stage may correspond to a local energy minimum, separated from the absolute one by a (free) energy barrier. Therefore, according to step ii of our simulation protocol (see the Introduction), we carried out the MD runs at room temperature in search of more stable adsorption geometries, as described below. b. The Final Adsorption Stage. Much larger deformations with a greater coating of the outer surface of the SWNT are achieved during the MD runs at 300 K, starting from both the most and the least stable geometry obtained after the initial energy minimizations. The MD simulation time required to achieve the final state, encompassing also the subsequent equilibrium fluctuations, amounted to 5 ns for the albumin subdomain and to 7 ns for the fibronectin moduli, even though much lengthier rearrangements cannot be ruled out. The final most stable adsorption geometries achieved in this way (Figure 3) maximize the surface coverage with a very large nanotube wrapping. Some secondary structure may survive for quite a long time in the MD runs, but the optimization of the interaction through a large surface covering mostly leads to an almost complete denaturation of the protein fragments. Correspondingly, the interaction energies reported in Table 1 for the most stable adsorption state are very large, while the intrinsic Eint is somewhat larger than in the initial stage. This energy is about the same for the albumin subdomain on either SWNT thanks to the relatively small difference in their radii of curvature, but mainly to the “soft” nature of albumin,4 which

Table 1. Interaction Energy (kJ/mol) on the Convex Outer Surfaces of the SWNT (8, 8) SWNT

albumin subdomain fibronectin modules

(10, 10) SWNT

Eint (×10−3)

n5 Å

intrinsic Eint

Eint (×10−3)

n5 Å

intrinsic Eint

1.61

36

44.8

1.85

42

43.9

2.02

52

38.8

2.11

45

47.0

allows for a very efficient surface spreading. Conversely, the fibronectin modules display a smaller spreading, being more “hard”,4 and show a smaller intrinsic Eint on the (8, 8) than on the (10, 10) SWNT (Table 1). Therefore, at least in this case a larger radius of curvature leads to a more favorable adsorption on convex surfaces. Anyway, all these values of the intrinsic Eint are smaller than those eventually achieved on graphite (57 kJ/ mol)11 and on the graphene sheet which also lacks lower carbon planes (53.3 kJ/mol, see later). Accordingly, they can only be due to the surface curvature. Thus, a small radius of curvature leads to a weaker intrinsic interaction, since the graphene sheet can be viewed as a convex (or equivalently a concave) surface with an infinite radius of curvature. We shall come back later to this issue. The protein spreading on the surface is also accompanied by an energy penalty (the strain energy) related with the loss of the secondary structure and of most of the intramolecular hydrogen bonds which is however much smaller than the energy gain due to the favorable dispersive forces between the adsorbate atoms and the hydrophobic surface. The adsorption geometries obtained through these MD runs do not yet provide the most stable state that may in principle be achieved on these SWNT, but are rather robust metastable states, kinetically but not thermodynamically stable. The most stable state can possibly be reached at exceedingly long simulation times after some free energy barrier (mainly entropic) is overcome. However, such a state can also be reached starting from an appropriate geometry (or configuration, in statistical mechanics terms). Since a fully optimized protein−surface interaction may imply the surface interaction of all the residues, as found on graphite,14−16 we selected the monolayer of amino acids achieved by the albumin subdomain 4886

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

on graphite14 and placed it close to the (10, 10) SWNT as a trial starting geometry, so that no two residues did overlap, when projected on the surface. After a 2 ns MD run, the final optimizations indeed yielded the most stable state shown in Figure 4, where all the residues are in contact with the surface,

It is useful to put the above-reported interaction energies in a different perspective. To this purpose, we estimated the interaction energy among amorphous (10, 10) SWNT in the random arrangement shown in Figure 5. Direct energy

Figure 4. Thermodynamically most stable adsorption geometry achieved by the albumin subdomain on the (10, 10) SWNT. The H atoms are not shown for clarity.

evenly coating it. For this arrangement, Eint amounts to 2.19 MJ/mol, while the intrinsic Eint drops to 37.8 kJ/mol. A rationale of this value smaller than for the previous geometries can be given considering that now all the residues, but two are in contact with the surface (n5 Å = 58, out of 60). Such interaction involves also the hydrophilic residues, while the tight wrapping of the nanotube imposes a strong geometrical constraint to the albumin subdomain, with a strain energy more than 5 times as large as in the geometry of Figure 3b. Therefore, also in this case the interaction with the nanotube would be weaker than with graphite, partly due to the lack of a deeper carbon plane, but mainly to the surface curvature, as it will be further shown upon comparison with the results on graphene. The present results are in qualitative agreement with those obtained in previous simulations for other proteins or protein subdomains. For instance, a single α-helix with 40 residues in explicit water displayed a strong interaction and large rearrangements on graphene and an increasingly weaker adsorption on SWNT with an increasingly larger curvature.28 Very long MD simulations in water (5 runs of 500 ns each) of the villin headpiece with 35 residues do also show large denaturation and spreading on graphene, but a weaker interaction with a small (5, 5) SWNT,13 again in keeping with our results. On the other hand, another MD simulation of the adsorption of an albumin subdomain with the same features as ours was carried out on somewhat larger SWNT in water.29 These simulations lasted only for 2 ns and could only study the initial adsorption behavior, as also noted in the paper, since the results did display an ongoing kinetic evolution. Nevertheless, also in this case a weaker adsorption was found with minor conformational changes from the native state on the smaller SWNT with the larger curvature (no well-defined trend could be obtained, possibly due also to the small difference in the curvature radii). In conclusion, these results, qualitatively consistent also with experimental results,30 do support our findings. On the other hand, most recently a lengthy MD simulation in water (lasting for 60 ns) was carried out to model the lysozyme interaction with the (10, 10) SWNT, yielding an interaction between two α-helices and the nanotube surface, but only minor conformational changes were detected without any significant protein rearrangement.31 It is not clear whether the reason of the discrepancy with the previous results is to be attributed to the simulation methodology or, more probably, to the unlike nature of lysozyme, usually classified as a “hard” protein compared for instance to albumin.4

Figure 5. The random arrangement of four (10, 10) SWNT.

minimization would lead to an almost parallel arrangement of the nanotubes with only a slight misalignment of their main axes due to the small system size and the finite length of the SWNT with a small aspect ratio compared to real samples. To account for this shortcoming and the limited possibility of rearrangement imposed to much longer nanotubes by the surrounding ones not explicitly considered in the simulations, we carried out a constrained minimization. In particular, we allowed only small changes to the intermolecular distances among selected carbon atoms at the ends of different nanotubes to implicitly account for the steric constraints on longer SWNT and imposed a strong penalty to the out-of-plane deformations to avoid large local bucklings which could enhance the intermolecular interactions in spite of the other constraint. The energy of the random aggregate is then obtained by a single-point calculation after removal of the constraint and of the penalty for the out-of-plane deformation. A similar procedure was applied to the system formed by three nanotubes after deleting a SWNT to the arrangement of Figure 5, while for the single SWNT an unconstrained minimization was carried out. The energy required to detach a single SWNT is then the interaction energy defined as before as Eint = (E1,SWNT + E3,SWNT) − E4,SWNT, where En,SWNT is the (single-point) energy of the aggregate with n SWNT. The almost parallel arrangement of four SWNT shows a large Eint of about 2.3 MJ/mol, but for the random arrangement of Figure 5 Eint drops to 0.54 MJ/mol, and therefore it is much less than the interaction energy between the nanotube and the protein subdomains (see Table 1). Such conclusion also holds for much 4887

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

longer nanotubes. In fact, longer nanotubes would show a proportionally larger number of contacts with other nanotubes, so that the interaction energy would be proportionally larger. (This conclusion would also be valid in the limiting case of parallel nanotubes, since the van der Waals interaction energy between parallel cylinders scales linearly with their length.32) However, longer SWNTs can interact with a proportionally larger number of protein subdomains, and therefore the total protein−SWNT interaction energy would be proportionally larger as well. In conclusion, since the protein−SWNT interaction is much stronger than the SWNT−SWNT interaction, while the proteins would mostly expose to the environment the polar residues, from the energetic viewpoint we conclude that amorphous carbon nanotubes can be solubilized in water by proteins, a conclusion in agreement with the experimental results.33 2. Adsorption on Concave Surfaces. a. The Initial Adsorption Stage. The procedure adopted in the previous section to study the adsorption on convex surfaces was also adopted for the inner concave surfaces of larger nanotubes and a single graphene sheet (see the Simulation Method section). We only report the results for the albumin subdomain, in view of the similarity of the results obtained for both protein subdomains on graphite and on the outer convex surface. On the concave SWNT surfaces and on flat graphene in the initial adsorption stage, the local deformations are somewhat larger than before: an example is shown in Figure 6 for the (30, 30)

Figure 7. Interaction energy Eint (filled symbols) of the albumin subdomain in the initial adsorption stage plotted as a function of n5 Å, the number of amino acids in contact with the inner concave surface of large SWNT and with a flat graphene surface (see text). The empty symbols show the corresponding strain energy Estrain (see text). The common best fit lines through the origin are also shown.

contribution to the interaction with the adsorbate through short-range dispersive forces. As for the effect of the surface curvature, the results may suggest a somewhat stronger adsorption on the inner surface of the (30, 30) SWNT (filled circles in Figure 7) thanks to a larger number of residues in contact with the surface. This result may be related to the different radii of curvature of the surfaces, but this issue is best analyzed in the thermodynamically most stable states achieved through the MD runs (see below). In fact, the values of the strain energy Estrain, shown in Figure 7, increase again linearly with n5 Å (the slope of the best-fit line is 11.3 ± 0.5 kJ/mol), but more slowly than Eint, suggesting again that larger deformations and surface spreading may maximize the surface interaction. b. The Final Adsorption Stage. On the inner concave surface of larger SWNT, the MD runs also led to a significant reorganization of the albumin subdomain, with a significant spreading, basically yielding again a monolayer of amino acids. As an example, the most stable hairpin arrangement achieved on the inner surface of the (30, 30) SWNT is shown in Figure 8a while the similar geometries found on the (40, 40) and the (50, 50) SWNT are reported in the Supporting Information (Figure S3). In this arrangement, the surface coverage is again maximized, and the protein assumes an essentially ordered disposition, with a roughly parallel arrangement of distant strands. Such geometry is similar to that achieved on graphene (Figure 9) and also to that previously found on graphite.10,11,14 This conformation allows the system to optimize at the same time both the dispersive interactions with the surface and the intramolecular interactions through the amino acid side groups (in particular, the dipolar and the charged interactions). The interaction energy Eint reported in Table 2 turns also out to be very large and slightly dependent on the radius of curvature of the concave surface. In particular, Table 2 shows that a surface concavity enhances the intrinsic Eint, so that adsorption is increasingly favored by a decreasing radius of curvature of the concave surface, with increasingly larger differences with the graphene sheet. As already pointed out before, on the latter surface Eint is slightly smaller than on graphite because of the lack of further subsurface layers providing a weak additional contribution (by about 3 kJ/mol of residue in contact with the surface) through van der Waals interactions. As a word of caution, we also add that possible nanoscale deformations of a free-standing graphene sheet (which was kept rigid in the simulations) could slightly enhance the interaction strength,

Figure 6. Albumin subdomain in the most stable initial adsorption stage on the concave inner surface of (30, 30) SWNT shown in a side and in an end-on view. The secondary structure is drawn as described in Figure 1, and the H atoms are not shown for clarity.

SWNT, to be compared with the arrangement of Figure 1, while the similar geometries found on the (40, 40) and the (50, 50) SWNT are in the Supporting Information (Figure S1). Interestingly, on the concave surface the local deformation is quite similar to what is obtained on graphite, thanks also to the larger radius of curvature of these surfaces, and to what is found on graphene (Figure S2). The interaction energy Eint follows again the same trend, as shown in Figure 7. No curvature effect is basically seen in this initial adsorption stage on the concave surface and on graphene, and the common best-fit line through the origin of the values for the (30, 30), (40, 40) and (50, 50) SWNT and for graphene34 is given by E int = (54.4 ± 0.5) × n5Å (kJ/mol)

(2)

The intrinsic Eint (the numerical coefficient of the equation) is significantly larger than on the convex outer surfaces of the smaller SWNT, but it is slightly smaller than on graphite, even though the difference is not statistically significant at the 3σ level. Anyway, the difference is consistent with the lack of a lower carbon plane in graphene and SWNT compared to graphite, where it is expected to give a minor, but not negligible 4888

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

Figure 8. (a) The most stable hairpin conformation of the albumin subdomain on the inner surface of the (30, 30) SWNT: this optimized snapshot, taken at the end of a 10 ns MD run, did not show major changes in the final nanoseconds of the run. (b) The metastable ringlike conformation eventually obtained within the same SWNT at the end of a 10 ns MD run. In both cases, at left the front atoms of the SWNT are not shown to better display the inner adsorbed subdomains, while the H atoms are not shown for clarity.

efficient parallel arrangement of the distant strands compared to the convex surfaces with a larger curvature, thus enhancing the interaction among the side groups and stabilizing the adsorbed protein. Furthermore, on the concave surfaces a gentle increase in curvature allows the nanotube atoms to favorably interact with more atoms of the same residues that are in contact with the surface through again van der Waals interactions. In order to best appreciate the large stability of the hairpin conformation of Figure 8a achieved on the concave SWNT surfaces, it is of interest to analyze the metastable higher energy ringlike conformation of Figure 8b that was reached starting from a different initial arrangement. This conformation lacks (most of) the nonbonded interactions among the side groups of spatially close but topological distant strands, unlike the hairpin conformation. However, this loss can be somewhat compensated by the intramolecular interactions of the residual α-helix (mainly hydrogen bonds). Because of that, the ringlike conformation does not fully optimize the contact with the surface, and therefore it is less stable than the hairpin conformation by about 440 kJ/mol, while the intrinsic Eint (61.0 kJ/mol) is the same. From a methodological viewpoint, it should be noted that in many cases the final most stable geometry can be found starting from the least stable initial geometry, as it happened for instance for the hairpin conformation found on the (40, 40) SWNT: subtle conformational changes in the initial adsorption state may in fact have a relatively large influence on the surface spreading within the MD runs, so that some care must be used to consider more than one starting geometry. A fuller description of the conformational changes undergone by the protein subdomains on the surfaces of SWNTs and of graphene will be reported in a separate paper, including also the possible refolding of the albumin subdomain to a new secondary structure with short β-sheets. Here, we briefly discuss the main conformational changes from the native to the

Figure 9. The final adsorption geometry achieved by the albumin subdomain on graphene (side and top views). The H atoms are not shown for clarity.

Table 2. Interaction Energy (kJ/mol) of the Albumin Subdomain on the Concave Inner Surfaces of the SWNT and on Graphene (30, 30) SWNT (40, 40) SWNT (50, 50) SWNT graphene

Eint (×10−3)

n5 Å

intrinsic Eint

3.49 3.27 2.94 3.10

57 52 50 58

61.3 60.6 58.8 53.3

with an Eint possibly approaching the graphite value. As for the molecular origin of the observed curvature dependence, we first note that adsorption on a concave surface allows a more 4889

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

Figure 10. Ramachandran plots for the albumin subdomain (a) in the native state, (b) in the hairpin conformation, and (c) in the ringlike conformation.

Figure 11. Distribution of the ψ torsion angles for the albumin subdomain (a) in the native state, (b) in the hairpin conformation, and (c) in the ringlike conformation.

hairpin and the ringlike conformation through the Ramachandran plots,35,36 which map the distribution of the (φ, ψ) torsion angles along the backbone. Upon adsorption, for these conformations we found a significant shift of the ψ angles from the α-helix to the β-sheet region of the map compared to the native state, as shown in Figure 10. The albumin subdomain only contains α-helices in the native state, characterized by ψ values clustered around −30° (Figure 10a) which largely shift upon adsorption to values clustered around +120° (Figure 10b,c) but in part also to more negative values loosely centered at about −90°. A more quantitative display of such changes is shown through the histograms reporting the ψ distribution in Figure 11. The number of the ψ torsion angles around 120° is quite larger in the hairpin than in the ringlike conformation, while the latter one shows a somewhat larger number of ψ values in the range between −30° and −90°. The significant contribution for ψ around 120° for the hairpin conformation is highly suggestive of a new refolding of the subdomains to form β-sheet-like structures, which however usually lack the hydrogen bonds among the backbone atoms, being solely due to the interactions among the side groups. c. Oligopeptide Adsorption Inside a Small SWNT. Extrapolation to much smaller nanotubes of the main result arrived at in the previous section, namely that adsorption is increasingly favored by a decreasing radius of curvature of a concave surface, would become quickly unwarranted because eventually the small size of the nanotube cavity would prevent an easy access to the protein both for energetic and for entropic reasons. In this context, we mention a somewhat unexpected result obtained by placing the protein subdomains close to the open end of the uncapped (10, 10) SWNT. In fact, depending on the starting orientations of the protein subdomains, it

turned out that at the end of some MD runs short strands comprising the hydrophobic residues can enter rather easily the cavity of the (10, 10) SWNT, forming a loop which leaves outside the free ends. An example of such arrangement for the albumin subdomain and the fibronectin modules is reported in the Supporting Information (Figure S4). In this way, the inserted strand is fully wrapped by, and strongly interacts with, the concave inner surface, while the folded loop (a sort of a minor hairpin) effectively prevents any deeper penetration for both entropic and energetic reasons. No such inclusion is found in the (8, 8) SWNT for steric reasons due to its very small diameter. This finding prompted us to investigate whether a smaller protein fragment made of a single α-helix might enter the cavity of these SWNT. We selected a small fragment because the entropy penalty of confinement increases linearly with the number of residues, but even more quickly with a decreasing tube diameter. In fact, de Gennes37 showed that the entropy loss of a polymer chain with N repeat units confined inside a tube scales as ΔS ∼ −N/Dβ, where D is the tube diameter, while β = 2 in an ideal solution and β = 5/3 in a good solvent. Therefore, insertion of long protein strands is an unlikely process, while the tube diameter obviously plays a major role with small nanotubes. Energetic factors can also be important, since they can either favor the insertion process through dispersion forces or forbid it altogether for steric reasons depending on the nanotube diameter. Thus, we may anticipate a relatively facile insertion of short oligopeptides within the larger SWNTs and little or no insertion at all in the smaller ones. In order to model such insertion, a single hydrophobic αhelix of the albumin subdomain comprising 16 residues (helix A2 in ref 14) was placed head-on close to the (10, 10) SWNT 4890

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

before, and the most stable geometries only show adsorption on the outer surface (Figure 12c,d), possibly with a minor inclusion of the alkyl side chain of a terminal leucine (Figure 12c). In order to quantify the energy penalty that should be overcome to have strand inclusion in the (8, 8) SWNT, we manually inserted the elongated conformation obtained with the (10, 10) SWNT (Figure 12a) within the smaller nanotube. In this way, we could check that the covolume repulsions are indeed very large, thus ruling out any possibility of spontaneous inclusion, in addition to the entropy loss. In fact, the MD run, allowing also for the nanotube deformation, yielded a total interaction energy of 0.92 MJ/mol, with an intrinsic Eint of 57 kJ/mol, somewhat larger than on the outer surface (see Table 1). On the other hand, the strain energy of the protein strand would be huge, amounting to 1.25 MJ/mol because of the repulsive steric interactions with the nanotube, which also would undergo significant deformations in spite of its stiffness (strain energy of 0.16 MJ/mol) due to the C−C bond stretching and some C−C−C angle bending producing a detectable bulge in the central part of the nanotube. We conclude that oligopeptide inclusion in the (8, 8) SWNT imposes too large an energy penalty to be possible, in addition to the unfavorable entropic effect. These results are fully consistent with those obtained by other simulation studies for a single α-helix in water within SWNTs of varying diameters with a lowest value of 1.49 nm for the (11, 11) SWNT.38 In this case, the denaturation of the solvated and confined helix was found to be essentially complete for the smallest nanotube, even though its size can allow hosting the helix. On the other hand, another simulation study carried out for a single α-helix and a β-hairpin with larger SWNT (diameters of 1.72 and 2.35 nm) found little changes for the inserted free oligopeptides.39 The encapsulation of somewhat longer hydrophilic oligopeptides in SWNT of increasing diameters and of different lengths was also considered,40 but the conformational changes were poorly described. In any case, according to ref 12, in these papers39,40 the length of the MD runs in explicit water (2 ns and up to 700 ps, respectively) are most likely not sufficient to achieve full equilibration possibly with extensive denaturation (see also ref 41), in view also of the steric constraint of the nanotube. As a concluding remark of this section, we note that the SWNT interaction with other biological macromolecules has given rise to a widespread interest, as attested for example by the insertion of a DNA oligonucleotide or its surface adsorption in the same carbon nanotubes (i.e., an (8, 8) or a (10, 10) SWNT), modeled by similar techniques.42

opening in two opposite orientations, with a rough alignment of the helical and the tube axes. Simple energy minimizations already provided a significant interaction energy, with a shallow insertion of the helical free ends within the cavity. The MD runs yielded a fast insertion of the whole helix, which achieved a fully extended conformation to maximize the interaction with the wrapping surface. At first, the included strand showed a shuttling motion within the cavity lasting for about 200 ps, eventually damped by the interaction with the wall producing only a residual tumbling motion. The most stable geometry (Figure 12a) shows that the (10, 10) SWNT has the right size for including the protein strand in the elongated conformation.

Figure 12. (a) A α-helix inserted within the cavity of the (10, 10) SWNT. (b) The same strand adsorbed on the outer surface of the same nanotube. (c, d) The same strand adsorbed on the outer surface of the (8, 8) nanotube (side and end views in all cases). The H atoms are not shown for clarity.

In this state, the interaction energy between the α-helix and the nanotube amounts to 1.80 MJ/mol, or equivalently to an intrinsic Eint of about 112 kJ/mol. This very large value is due to the optimized dispersive interactions with the carbon atoms that fully wrap all the residues of the hydrophobic strand. The disruption of the helical structure imposes a relatively small energy penalty of 244 kJ/mol, due to the broken hydrogen bonds and, to a lesser extent, to the unfavorable torsion angles. Moreover, when the (10, 10) SWNT was not kept fixed, but it was allowed to optimize its geometry, we found that the interaction energy did not show any significant change, whereas the energy penalty of the α-helix decreased to 194 kJ/mol, and the SWNT underwent only minor deformations with a strain energy of 19 kJ/mol, so that no steric penalty is actually present. Of course, we checked that on the outer surface the same single α-helix (Figure 12b) yielded results fully consistent with those discussed before for the larger albumin subdomain, including in particular the intrinsic Eint. On the other hand, no inclusion could be achieved with the (8, 8) SWNT, whose diameter is too small for hosting guest molecules, apart possibly from very thin and hydrophobic ones. In fact, we never detected any inclusion of the same α-helix as

■

CONCLUDING REMARKS In this paper, we describe a molecular dynamics study of protein adsorption on single-walled carbon nanotubes (SWNT) considering both their outer convex and their inner concave surface, and on a graphene sheet, in comparison with a graphite surface. Our main goal is to assess the topography effect of the surface curvature on protein adsorption at a given chemistry, determined by the sp2 carbon atoms. We find that proteins do favorably interact with these hydrophobic surfaces irrespective of their secondary structure. Our main result is that the adsorption strength does indeed depend on the surface topography. In particular, compared to bulk graphite we find that adsorption is slightly weaker on the outer convex surfaces of SWNT, while it is enhanced on their inner concave surface in a hairpin arrangement that optimizes both the surface and the 4891

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

intramolecular interactions, being therefore intermediate for flat graphene. Moreover, we find that small protein fragments may also enter the cavity of common nanotubes in a strongly elongated conformation, provided the number of residues is small enough for entropic reasons and the tube diameter is large enough for energetic (steric) reasons. As a final result of the present simulations, we suggest that proteins can solubilize in water single-walled (and by analogy also multiwalled) carbon nanotubes through adsorption on the outer surface, as indeed found experimentally, and can functionalize them after insertion of oligopeptides within the cavity of nanotubes of appropriate size.

■

(10) Ganazzoli, F.; Raffaini, G. Computer simulation of polypeptide adsorption on biomaterials. Phys. Chem. Chem. Phys. 2005, 7, 3651− 3663. (11) Raffaini, G.; Ganazzoli, F. Understanding the performance of biomaterials through molecular modeling: crossing the bridge between their intrinsic properties and the surface adsorption of proteins. Macromol. Biosci. 2007, 7, 552−566. (12) Wei, T.; Carignano, M. A.; Szleifer, I. Lysozyme adsorption on polyethylene surfaces: why are long simulations needed? Langmuir 2011, 27, 12074−12081. (13) Zuo, G.; Zhou, X.; Huang, Q.; Fang, H.; Zhou, R. Adsorption of villin headpiece onto graphene, carbon nanotube, and C60: effect of contacting surface curvatures on binding affinity. J. Phys. Chem. C 2011, 115, 23323−23328. (14) Raffaini, G.; Ganazzoli, F. A simulation study of the interaction of some albumin sub-domains with a flat graphite surface. Langmuir 2003, 19, 3403−3412. (15) Raffaini, G.; Ganazzoli, F. Molecular dynamics simulation of the adsorption of a fibronectin module on a graphite surface. Langmuir 2004, 20, 3371−3378. (16) Raffaini, G.; Ganazzoli, F. Protein adsorption on a hydrophobic surface: a molecular dynamics study of lysozyme on graphite. Langmuir 2010, 26, 5679−5689. (17) Raffaini, G.; Ganazzoli, F. Protein adsorption on the hydrophilic surface of a glassy polymer: a computer simulation study. Phys. Chem. Chem. Phys. 2006, 8, 2765−2772. (18) (a) Cormack, A. N.; Lewis, R. J.; Goldstein, A. H. Computer simulation of protein adsorption to a material surface in aqueous solution: biomaterials modeling of a ternary system. J. Phys. Chem. B 2004, 108, 20408−20418. (b) Shen, J.-W.; Wu, T.; Wang, Q.; Pan, H.H. Molecular simulation of protein adsorption and desorption on hydroxyapatite surfaces. Biomaterials 2008, 29, 513−532. (c) Artali, R.; Del Pra, A.; Foresti, E.; Lesci, I. G.; Roveri, N.; Sabatino, P. Adsorption of human serum albumin on the chrysotile surface: a molecular dynamics and spectroscopic investigation. J. R. Soc. Interface 2008, 5, 273−283. (d) Kubiak, K.; Mulheran, P. A. Molecular dynamics simulations of hen egg white lysozyme adsorption at a charged solid surface. J. Phys. Chem. B 2009, 113, 12189−12200. (e) Wu, C.; Chen, M.; Xing, C. Molecular understanding of conformational dynamics of a fibronectin module on rutile (110) Surface. Langmuir 2010, 26, 15972−15981. (19) Agashe, M.; Raut, V.; Stuart, S. J.; Latour, R. A. Molecular simulation to characterize the adsorption behavior of a fibrinogen γchain fragment. Langmuir 2005, 21, 1103−1117. (20) Mücksch, C.; Urbassek, H. M. Molecular dynamics simulation of free and forced BSA adsorption on a hydrophobic graphite surface. Langmuir 2011, 27, 12938−12943. (21) Cheng, H.; Cooper, A. C.; Pez, G. P.; Kostov, M. K.; Piotrowski, P.; Stuart, S. J. Molecular dynamics simulations on the effects of diameter and chirality on hydrogen adsorption in single walled carbon nanotubes. J. Phys. Chem. B 2005, 109, 3780−3786. (22) Wong Shi Kam, N.; O’Connell, M.; Wisdom, J. A.; Dai, H. Carbon nanotubes as multifunctional biological transporters and nearinfrared agents for selective cancer cell destruction. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 11600−11605. (23) Kostarelos, K.; Bianco, A.; Prato, M. Promises, facts and challenges for carbon nanotubes in imaging and therapeutics. Nat. Nanotechnol. 2009, 4, 627−633. (24) See for instance: (a) Li, L.; Chen, R.; Weng, Z. RDOCK: refinement of rigid-body protein docking predictions. Proteins: Struct., Funct., Genet. 2003, 53, 693−707. (b) Moreira, I. S.; Fernandes, P. A.; Ramos, M. J. Computational determination of the relative free energy of binding - Application to alanine scanning mutagenesis. In Molecular Materials with Specific Interactions - Modeling and Design; Sokalski, W. A., Ed.; Springer: Dordrecht, 2007; Chapter 6, pp 305−399. (25) Raffaini, G.; Ganazzoli, F.; Malpezzi, L.; Fuganti, C.; Fronza, G.; Panzeri, W.; Mele, A. Validating a strategy for molecular dynamics simulations of cyclodextrin inclusion complexes through single-crystal

ASSOCIATED CONTENT

S Supporting Information *

Figure S1: albumin subdomain in the most stable initial adsorption stage on the concave inner surface of the (40, 40) and (50, 50) SWNT; Figure S2: albumin subdomain in the most stable initial adsorption stage on the flat surface of graphene; Figure S3: albumin subdomain in the most stable hairpin conformation eventually achieved on the concave inner surface of the (40, 40) and (50, 50) SWNT; Figure S4: optimized albumin subdomain and fibronectin modules at the open end of the (10, 10) SWNT with a short strand insertion within the cavity. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail giuseppina.raff[email protected]; Tel +39-0223993024; Fax +39-0223993081. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS G. Raffaini gratefully acknowledges financial support from MIUR - FIRB Futuro in Ricerca (Surface-Associated Selective Transfection - SAST, RBFR08XH0H).

■

REFERENCES

(1) Kasemo, B. Biological surface science. Surf. Sci. 2002, 500, 656− 677. (2) Ratner, B. D., Hoffman, A. S., Schoen, F. J., Lemons, J. E., Eds.; Biomaterials Science; Elsevier Academic Press: San Diego, CA, 2004. (3) Rabe, M.; Verdes, D.; Seeger, S. Understanding protein adsorption phenomena at solid surfaces. Adv. Colloid Interface Sci. 2011, 162, 87−106. (4) Nakanishi, K.; Sakiyama, T.; Imamura, K. On the adsorption of proteins on solid surfaces, a common but very complicated phenomenon. J. Biosci. Bioeng. 2001, 91, 233−244. (5) Oscarsson, S. J. Factors affecting protein interaction at sorbent interfaces. J. Chromatogr., B 1997, 699, 117−131. (6) Diebold, U. The surface science of titanium dioxide. Surf. Sci. Rep. 2003, 48, 53−229. (7) De Nardo, L.; Raffaini, G.; Ganazzoli, F.; Chiesa, R. Metal surface oxidation and surface interactions. In Surface Modification of Biomaterials. Methods, Analysis and Applications; Williams, R., Ed.; Woodhead: Cambridge, UK, 2001; pp 102−142. (8) Raffaini, G.; Ganazzoli, F. Molecular modelling of protein adsorption on the surface of titanium dioxide polymorphs. Philos. Trans. R. Soc., A 2012, 370, 1444−1462. (9) See for instance: Tománek, D. The nanotube site: http:// nanotube.msu.edu/. 4892

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893

Langmuir

Article

X-ray and NMR experimental data: a case study. J. Phys. Chem. B 2009, 113, 9110−9122. (26) Accelrys Inc. InsightII 2000 and Materials Studio, San Diego, CA. See also the URL http://www.accelrys.com. (27) Dauber-Osguthorpe, P.; Roberts, V. A.; Osguthorpe, D. J.; Wolff, J.; Genest, M.; Hagler, A. T. Structure and energetics of ligand binding to proteins: Escherichia coli dihydrofolate reductasetrimethoprim, a drug-receptor system. Proteins: Struct., Funct., Genet. 1988, 4, 31−47. (28) Balamurugan, K.; Azhagiya Singam, E. R.; Subramanian, V. Effect of curvature on the α-helix breaking tendency of carbon based nanomaterials. J. Phys. Chem. C 2011, 115, 8886−8892. (29) Shen, J.-W.; Wu, T.; Wang, Q.; Kang, Y. Induced stepwise conformational change of human serum albumin on carbon nanotube surfaces. Biomaterials 2008, 29, 3847−3855. (30) Mu, Q.; Liu, W.; Xing, Y.; Zhou, H.; Li, Z.; Zhang, Y.; Ji, L.; Wang, F.; Si, Z.; Zhang, B.; Yan, B. Protein binding by functionalized multiwalled carbon nanotubes is governed by the surface chemistry of both parties and the nanotube diameter. J. Phys. Chem. C 2008, 112, 3300−3307. (31) Calvaresi, M.; Hoefinger, S.; Zerbetto, F. Probing the structure of lysozyme−carbon-nanotube hybrids with molecular dynamics. Chem.Eur. J. 2012, 18, 4308−4313. (32) Israelachvili, J. Intermolecular and Surface Forces; Academic Press: London, 1992. (33) Karajanagi, S. S.; Yang, H.; Asuri, P.; Sellitto, E.; Dordick, J. S.; Kane, R. S. Protein-assisted solubilization of single-walled carbon nanotubes. Langmuir 2006, 22, 1392−1395. (34) On graphene only, the slope of the best fit line takes the abovementioned value of 54.7 ± 0.9 kJ/mol. (35) Ramachandran, G. N.; Ramakrishnan, C.; Sasisekharan, V. Stereochemistry of polypeptide chain configurations. J. Mol. Biol. 1963, 7, 95−99. (36) Lovell, S. C.; Davis, I. W.; Arendall, W. B., III; de Bakker, P. I. W.; Word, J. M.; Prisant, M. G.; Richardson, J. S.; Richardson, D. C. Structure validation by Cα geometry: φ,ψ and Cβ deviation. Proteins: Struct., Funct., Genet. 2003, 50, 437−450. (37) de Gennes, P. G. Scaling Concepts in Polymer Physics; Cornell University Press: Ithaca, NY, 1979. (38) Sorin, E. J.; Pande, V. S. Nanotube confinement denatures protein helices. J. Am. Chem. Soc. 2006, 128, 6316−6317. (39) Trzaskowski, B.; Jalbout, A. F.; Adamowicz, L. Molecular dynamics studies of protein-fragment models encapsulated into carbon nanotubes. Chem. Phys. Lett. 2006, 430, 97−100. (40) Liu, Y.-C.; Wang, Q. Dynamic behaviors on zadaxin getting into carbon nanotubes. J. Chem. Phys. 2007, 126, 124901. (41) Chen, Q.; Wang, Q.; Liu, Y.-C.; Wu, T.; Kang, Y.; Moore, J. D.; Gubbins, K. E. Energetics investigation on encapsulation of protein/ peptide drugs in carbon nanotubes. J. Chem. Phys. 2009, 131, 015101. (42) Gao, H.; Kong, Y.; Cui, D.; Ozkan, C. S. Spontaneous insertion of DNA oligonucleotides into carbon nanotubes. Nano Lett. 2003, 3, 471−473.

4893

dx.doi.org/10.1021/la3050779 | Langmuir 2013, 29, 4883−4893