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Mechanical responses of the bio-nano interface: A molecular dynamics study of graphene-coated lipid membrane
Theoretical and Applied Mechanics Letters 5 (2015) 231–235
Contents lists available at ScienceDirect
Theoretical and Applied Mechanics Letters journal homepage: www.elsevier.com/locate/taml
Letter
Mechanical responses of the bio-nano interface: A molecular dynamics study of graphene-coated lipid membrane Zhigong Song, Yanlei Wang, Zhiping Xu ∗ Applied Mechanics Laboratory, Department of Engineering Mechanics and Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
article
info
Article history: Received 5 September 2015 Accepted 14 November 2015 Available online 28 November 2015 *This article belongs to the Biomechanics and Interdiscipline Keywords: Cell membrane Lipid bilayer Graphene Mechanical responses Bio-nano interfaces
abstract Bio-nano interfaces between biological materials and functional nanodevices are of vital importance in relevant energy and information exchange processes, which thus demand an in-depth understanding. One of the critical issues from the application viewpoint is the stability of the bio-nano hybrid under mechanical perturbations. In this work we explore mechanical responses of the interface between lipid bilayer and graphene under hydrostatic pressure or indentation loads. We find that graphene coating provides remarkable resistance to the loads, and the intercalated water layer offers additional protection. These findings are discussed based on molecular dynamics simulation results that elucidate the molecular level mechanisms, which provide a basis for the rational design of bionanotechnologyenabled applications such as biomedical devices and nanotherapeutics. © 2015 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
Recently there have been significant interests rising in developing bionanotechnologies such as bioelectronics platforms that interface biological materials such as cells or tissues with functional nanostructures [1–6]. Biosensory functions can be enabled by detecting the biophysiochemical signals transduced across at this interface, which allows extracting valuable information from biologically important reactions, as well as controlling cellular activities through nanoscale contacts with integrated devices. Bio-nano hybrids with high complexity in integration require massively interconnected arrays of processing devices, completed with integrated power supply and heat removal networks [7]. As a result, the bio-nano interface that conveys energy and information exchange between biological materials and nanostructures are pivotal in designing relevant technological applications. The structural and physiological stabilities of such an interface under external mechanical perturbation are important issues to be addressed practically in order to design reliable bionanotechnologies, which are crucial not only for preserving functions of bioelectronics, but also to conduct subcellular engineering of the biological processes [8]. Graphene and its derivatives such as graphene oxide are flexible single-atom-thick layers that are able to form compatible interface with lipid bilayers that constitute the cell membrane, which have been studied recently as functional nanostructures
∗
Corresponding author. E-mail address: [email protected] (Z. Xu).
interfacing with biological materials. Nanocomposite structures have been constructed by depositing lipids onto graphitic layers or intercalating them into an assembly in a layer-by-layer fashion [2–4,9–11]. Researchers have found that graphene layers could confine the cell as an easy-to-apply impermeable and electrontransparent encasement that retains the cellular water content [4]. More interestingly, the graphene sheet deposited on the cell wall permits a free functioning of the plasma membrane it encapsulates [3]. The interface between graphitic layers and the cell membrane is the essential pathway that conveys information and energy exchange, where evidences have been reported for the existence of a layer of trapped water within this interface. The thickness of this intercalated water layer (IWL) is only a few nanometers, although its dependence on the physiological condition is still not clear. However, it effectively weakens the dielectric coupling across the interface and thus the disruptive effects to the cellular membrane [2,9]. In additional to these biochemical effects, the nanostructural coating using graphene could also protect the cell under physical or chemical attacks. The stability of both the living system and the bio-nano interface could also be broken down under external mechanical perturbations. This fact, however, has only very limited understandings in the community. In this work, we explore mechanical responses of the lipid bilayer–graphene interface as a model system for general bio-nano interfaces. Empirical forcefield based molecular dynamics (MD) simulations are performed to probe the nanoscale structures and dynamics of the hybrid. We find that under external loads, the graphene coating provides an outstanding protection function for
http://dx.doi.org/10.1016/j.taml.2015.11.003 2095-0349/© 2015 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
232
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
a
b Number of H-bonds
tIWL
h
3.5 3.0
2.5 0.5
c
1.0 tIWL (nm)
1.5
d
Fig. 1. (a) The model of graphene-coated lipid bilayer membrane with intercalated water layers. (b) Number of hydrogen bonds (per water molecule) analyzed for different IWL thicknesses, tIWL . (c, d) Illustration of applied hydrostatic pressure and nanoindentation loads.
the lipid membrane. Moreover, the IWL at the lipid–graphene interface is found to play a critical role in modulating the transmission of mechanical signals and the mechanical stability of the hybrid. These conclusions are discussed with respect to their implications in designing related bionanotechnological applications. We construct a lipid bilayer–graphene hybrid by placing the bilayer at a certain distance from the graphene sheets. Water molecules are added in between, which could enter the spaces in 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid bilayers with a depth of ∼1 nm after thermal equilibration (Fig. 1(a)). The interfaces with top and bottom hydrophilic sides of the lipid bilayer are constructed symmetrically. A two-dimensional supercell is used with periodic boundary conditions (PBCs) along the interface, with lateral dimensions of 10.46 and 10.15 nm, respectively. Free boundary conditions are used in the dimension across the bilayer. Supercells with different lateral sizes are explored to characterize the size effect in the indentation tests, and we find notable size effect in the nanoindentation tests, where mechanical responses are weakened as the lateral membrane span increases under the same indentation force. However, our following discussions are focused on this specific system size for a quanlitative demonstration. All MD simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package [12]. Interatomic interactions between carbon atoms in graphene are described using the adaptive intermolecular reactive empirical bond order (AIREBO) potential with torsion and van der Waals terms included [13]. The CHARMM36 forcefield is used for the lipid bilayer, and water is simulated using the TIP3P model [14]. The SHAKE algorithm is applied for bond stretching and angle bending terms between oxygen and hydrogen atoms to avoid highfrequency vibrations that require shorter time steps. Interaction between water, graphene and the lipid bilayer includes both van der Waals and electrostatic terms. The former term is described
by the 12-6 Lennard–Jones potential 4ε[(σ /r )12 − (σ /r )6 ] and the Lorentz–Berthelot mixing rule [14], which is truncated at an interatomic distance r = 1.0 nm. Long-range Coulomb interactions are computed by using the particle–particle particle-mesh (PPPM) algorithm [15]. The time step is set to 0.5 fs to assure total energy conservation in absence of thermostat coupling. The whole system is equilibrated at 300 K and 1 a.t.m. (1 a.t.m. = 101325 Pa) (in the lateral dimensions) before the mechanical loadings are applied, using the Berendsen thermostat and barostat [16], respectively. We carry out MD simulations with both hydrostatic pressure and local indentation loads on the lipid–graphene hybrid. The hydrostatic pressure Pz is simulated by compressing two planar walls towards graphene coatings at both sides of the graphene–lipid–graphene hybrid at a rate of 0.03 nm/ps (Fig. 1(c)). These planar walls interact with the graphene sheet through a harmonic, repulsive-only potential in the form of Urep = K (r − rc )2 /2, where r is the position of wall and the interaction is turned off beyond a cut-off distance rc = 0.1 nm. The spring constant K is set to 200 eV · nm−2 . These settings allow us to probe mechanical responses of the hybrid under external pressure Pz , in terms of a compressive strain εz = −21h/h. Here h is equilibrium thickness of the lipid–graphene hybrid, which is defined by the vertical distance between two graphene sheets. 1h is the change. During the loading process we find that the lateral relaxation of simulation box is not significant due to the high in-plane stiffness of graphene. To probe mechanical responses of the hybrid to local or concentrated loads, we carry out nanoindentation tests where an indenter is pressed towards one side of the lipid–graphene hybrid, while the other side is fixed (Fig. 1(d)). The indentation force f is tracked as a function of indentation depth d. The indenter is a rigid spherical particle with a radius of R = 1 nm, interacting with the graphene sheet through a force in the form of f (r ) = −k(r − R)2 . Here r is the distance measured from the atom to the center of indenter. The specified force constant k = 104 eV · nm−3 is large
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
enough to exclude notable rate dependence that could arises in a soft contact. The loading rates are set to v = 0.05 nm/ps for the nanoindentation tests. Simulations carried out at lower loading rates show softened responses, but the results are quanlitative the same. For example, tests for tIWL = 0.68 nm and at v = 0.005 nm/ps predict failure force and depth of 67.546 nN and 1.355 nm, which are very close to 66.147 nN and 1.347 nm for v = 0.05 nm/ps. When a hydrostatic pressure Pz = −σzz is applied on the graphene surface with area A, it can be related to the compressive strain εz by considering the hybrid as a composite continuum with Young’s modulus Y and Poisson’s ratio ν (we assume ν = 0.3 in this work)
εxx = [σxx − ν(σyy + σzz )]/Y ,
(1a)
εyy = [σyy − ν(σxx + σzz )]/Y ,
(1b)
εzz = [σzz − ν(σxx + σyy )]/Y .
(1c)
Following the boundary and loading conditions used in our MD simulations, i.e., εx = εy = 0, the compressive strain response can be expressed as
εzz = σzz [1 − 2ν 2 /(1 − ν)]/Y = −Pz [1 − 2ν 2 /(1 − ν)]/Y .
(2)
For a model problem of indentation on a half-space, the indentation force f , depth d, and their relation can be described through the Sneddon formula [17] d = a lg[(R + a)/(R − a)]/2,
(3a)
f = Y {(a + R ) lg[(R + a)/(R − a)] − aR}/[2(1 − ν )]. 2
2
2
(3b)
Here a is the radius of contact between the indenter and the membrane under indentation, which can be determined from the data of our MD simulations using Eq. (3a). ν = 0.3 is the Poisson’s ratio assumed for the substrate material. Molecular structures of the bio-nano interface between a cell membrane and graphene coating are illustrated in Fig. 1(a), which are composed of a lipid bilayer, monolayer graphene sheets, and a thin layer of trapped water, i.e., the IWL. In this work, the IWL thickness (tIWL ) is defined as the span of region where the water density is no lower than that in the bulk. The presence of IWL within the gap between the lipid layer and graphene allows the cell to exchange masses and energy with the surroundings and thus is crucial for their survival [3]. From the snapshots of water molecules within the interfacial gallery, we identify layered water structures adjacent to the graphene wall in our MD simulations. Further structural analysis at the molecular level shows that the number of hydrogen bonds per water molecule is smaller than the value in bulk water, but increases with tIWL (Fig. 1(b)). This is actually a common feature of nanoconfined water, which was reported for water trapped between graphene or graphene oxide (GO) layers at a similar length scale of confinement [18]. It should also be remarked that there are water molecules entering the lipid bilayer within a depth of ∼1 nm, which is similar as the situation where lipid bilayers are immersed into water at the physiological condition [19]. The thickness of layered water region in our simulations is ∼1 nm, which is close to the IWL thickness reported for water trapped at the lipid–graphene interface in recent experimental measurements [2]. This means that the presence of structured IWLs between hydrated lipid bilayers and the graphene sheet could lead to changes in the properties and stabilities of lipid bilayers and the cell, compared to their native structures immersed in the extracellular fluid. Accordingly, we construct a number of lipid–graphene hybrids with tIWL ranging from 0 nm to 2 nm based on these observations, and use them as model systems for further mechanical characterization.
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Bio-nano devices are usually immersed in fluid to maintain the physiological condition of living systems. The integration of nanoelectronics with cell contains functional interfaces between the cell membrane and nanostructures such as the graphene coating. External mechanical perturbation could originate from hydrostatic pressure or localized impacts. To explore the stability of such a bio-nano interface under these loads, we first explore the relation between hydrostatic pressure Pz applied onto the graphene sheet and the compressive strain εzz measured in the same direction. From a typical stress–strain curve shown in Fig. 2(a), we find that the bio-nano hybrid is stiffened as the pressure increases due to a densified structures of IWLs as demonstrated in the water density plots for tIWL = 1.4 nm (Fig. 3(a)). We notice further that as the hybrid is compressed, mechanical load is transmitted through the IWLs, and the responses are relatively incompressible. The layered structures of IWLs become more and more prominent as the pressure increases due to the enhanced graphene–water interaction and presence of anisotropic pressure. This enhanced layered order further contributes to the nonlinearly elastic responses and protects the structural stability of lipid membrane. Interestingly, this process of structural transition in IWLs is reversible under the pressure loading, which results in negligible hysteresis. We now summarize mechanical responses of the bio-nano interface as a function of the IWL thickness tIWL . It is clearly shown in Fig. 4(a) that, as the IWL is present, the lipid–graphene hybrid is significantly stiffened compared to the bare one because of both the intercalation of water molecules in the lipid bilayers and the mechanical resistance of IWLs. However, this enhancement is weakened as t further increases, which could be explained by the fact that for few-layer water the stiffening effect increases with tIWL , while the structure of the IWLs becomes less ordered as its thickness increases and thus the hybrid is softened with tIWL >∼ 0.6 nm. This can also be concluded from the extracted values of Young’s modulus Y using Eq. (2). The results in Fig. 4(a) show that Y is on the order of 1 GPa, which is significant enough to provide an effective mechanical protection to the cell membrane. This value of Y converges to 2.39 GPa as tIWL increases, which is close to the bulk modulus of water B = 2.2 GPa [20]. Local mechanical responses of the lipid–graphene hybrid are distinctly different from that under hydrostatic loading. Under nanoindentation, our MD simulations show that the structure of lipid–graphene hybrid is distorted locally at small indentation depth. The force–depth relation we obtain from the simulation results at small indentation depth (inset in Fig. 2(b)) is used to extract effective in-plane elastic modulus Y of the hybrid through Eq. (3) (Fig. 4(a)). Comparative studies of the mechanical responses under nanoindentation show that with water intercalation, the hybrid is stiffened. Similarly, the stiffening effect decreases with the IWL thickness tIWL , which suggests that the deformation mechanism under small indentation loads is the same as that under hydrostatic pressure. At large indentation depth, however, we find that water molecules under the indenter are able to diffuse and flow during the loading process (Fig. 3(b)). Consequently, the structures of IWLs and lipid bilayer change significantly in contrast to that under either hydrostatic pressure or small-depth indentation. The mechanical response is softened with IWL, in contrast to the conclusion at small indentation depth (Fig. 2(b)). This redistribution of water in the IWL also implicates mechanical energy dissipation during the loading processes. To quantify this effect, we perform additional MD simulations with cycling indentation loads applied. We characterize the force hysteresis from the f –d curve in one cycle of nanoindentation (Fig. 2(b)). The results show that the amount of energy dissipation is almost independent on tIWL and is slightly reduced as tIWL increases in the range we explored (Fig. 4(b)). This
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Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
a
b 60
2
f 0.02
1
f (nN)
0.00 tIWL
0.00
30
0.02
a tIWL
0.00 nm 0.00 nm
0.85 nm 0
0
1.40 nm 0.00
0.05
0.85 nm 0
0.10
1 d (nm)
2
Fig. 2. Mechanical responses of lipid–graphene hybrids with different IWL thicknesses, measured under (a) hydrostatic pressure and (b) cycling nanoindentation loads. The inset in panel (b) shows the elastic response of interface measured at small indentation depth, which is used to extract the Young’s modulus using Eq. (3).
a
b
Δh = 0.0 nm
0.00
d = 0.00 nm
1.25
0.2 nm
0.50 nm
0.4 nm
1.00 nm
0.8 nm
1.84 nm
Fig. 3. Density distribution of the intercalated water layer (tIWL = 1.4 nm) at the lipid–graphene interface under (a) hydrostatic pressure and (b) nanoindentation forces, measured by its ratio to the bulk value ρ/ρbulk .
capability of energy dissipation could protect the bio-nano hybrid from dynamical loads such as vibration and impacts. As the amplitude of indentation force further increases, the structure of bio-nano hybrids could be significantly disturbed and even fail. From our nanoindentation tests, we find that the amplitude of fracture indentation force and depth are almost invariant as the IWL thickness changes (Fig. 5), which aligns with the fact that the fracture is nucleated inside the graphene sheet.
These simulation results thus show that the graphene coating could protect the underneath lipid membrane very effectively because of its outstanding in-plane mechanical resistance. In summary, we analyzed molecular structures of the bio-nano interface between a lipid membrane and graphene coatings by performing atomistic simulations and explore their mechanical responses upon hydrostatic pressure and nanoindentation loads. We find that the graphene coatings with extremely high stiffness
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
235
b 10 Energy dissipation (10-9 nJ)
a
Y (GPa)
4
2 Hydrostatic pressure
5
Indentation 0.0
0.5
1.0
1.5
0.0
0.5
tIWL (nm)
1.0
1.5
tIWL (nm)
Fig. 4. (a) The Young’s moduli of lipid–graphene hybrids calculated under hydrostatic pressure and indentation forces. (b) Mechanical energy dissipation during the first loading–unloading cycle in the nanoindentation tests, plotted as a function of the IWL thickness, tIWL .
b Depth to failure (nm)
Fracture force (nN)
a 80
60
0.0
0.5
1.0
1.5
tIWL (nm)
2
1
0.0
0.5
1.0
1.5
tIWL (nm)
Fig. 5. The critical indentation (a) force and (b) depth measured for the lipid–graphene hybrids as a function of the thickness of IWL, tIWL .
and strength could effectively protect the structural and physiological stabilities of the bio-nano hybrid in response to both hydrostatic and concentrated loads. The presence of an intercalated water layer at the interface is found to play an important role in further mediating the mechanical resistance and energy dissipation. These findings could direct rational design of bionanotechnologyenabled biomedical devices, where stability and robustness of bionano interfaces under mechanical perturbation are essential for non-invasive applications. Acknowledgments This work was supported by the National Natural Science Foundation of China (11222217 and 11472150). The simulations were performed on the Explorer 100 cluster system of Tsinghua National Laboratory for Information Science and Technology. References [1] A.E. Nel, L. Madler, D. Velegol, et al., Understanding biophysicochemical interactions at the nano–bio interface, Nat. Mater. 8 (2009) 543–557. [2] P.K. Ang, M. Jaiswal, C.H.Y.X. Lim, et al., A bioelectronic platform using a graphene–lipid bilayer interface, ACS Nano 4 (2010) 7387–7394. [3] R. Kempaiah, A. Chung, V. Maheshwari, Graphene as cellular interface: Electromechanical coupling with cells, ACS Nano 5 (2011) 6025–6031. [4] N. Mohanty, M. Fahrenholtz, A. Nagaraja, et al., Impermeable graphenic encasement of bacteria, Nano Lett. 11 (2011) 1270–1275. [5] A. Fabbro, S. Bosi, L. Ballerini, et al., Carbon nanotubes: Artificial nanomaterials to engineer single neurons and neuronal networks, ACS Chem. Neurosci. 3 (2012) 611–618.
[6] B. Tian, J. Liu, T. Dvir, et al., Macroporous nanowire nanoelectronic scaffolds for synthetic tissues, Nat. Mater. 11 (2012) 986–994. [7] A.D. Maynard, Could we 3D print an artificial mind? Nat. Nanotechnol. 9 (2014) 955–956. [8] X. Shi, A. von dem Bussche, R.H. Hurt, et al., Cell entry of one-dimensional nanomaterials occurs by tip recognition and rotation, Nat. Nanotechnol. 6 (2011) 714–719. [9] R. Frost, G.E. Jönsson, D. Chakarov, et al., Graphene oxide and lipid membranes: Interactions and nanocomposite structures, Nano Lett. 12 (2012) 3356–3362. [10] K. Tsuzuki, Y. Okamoto, S. Iwasa, et al., Reduced graphene oxide as the support for lipid bilayer membrane, J. Phys. Conf. 352 (2012) 012016. [11] Y.K. Lee, H. Lee, J.-M. Nam, Lipid-nanostructure hybrids and their applications in nanobiotechnology, NPG Asia Mater. 5 (2013) e48. [12] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics, J. Comput. Phys. 117 (1995) 1–19. [13] B. Ni, K.-H. Lee, S.B. Sinnott, A reactive empirical bond order (REBO) potential for hydrocarbon–oxygen interactions, J. Phys.: Condens. Matter. 16 (2004) 7261–7275. [14] B.R. Brooks, R.E. Bruccoleri, D.J. Olafson, et al., CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Comput. Chem. 4 (1983) 187–217. [15] R.W. Hockney, J.W. Eastwood, Computer Simulation using Particles, Taylor & Francis, 1989. [16] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gunsteren, et al., Molecular dynamics with coupling to an external bath, J. Chem. Phys. 81 (1984) 3684–3690. [17] I.N. Sneddon, The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile, Int. J. Engr. Sci. 3 (1965) 47–57. [18] N. Wei, X. Peng, Z. Xu, Breakdown of fast water transport in graphene oxides, Phys. Rev. E 89 (2014) 012113. [19] G. Franzese, M. Rubi, Aspects of Physical Biology: Biological Water, Protein Solutions, Transport and Replication, Springer, 2008. [20] H. Wang, Q. Li, Prediction of elastic modulus and Poisson’s ratio for unsaturated concrete, Int. J. Solids Struct. 44 (2007) 1370–1379.
Contents lists available at ScienceDirect
Theoretical and Applied Mechanics Letters journal homepage: www.elsevier.com/locate/taml
Letter
Mechanical responses of the bio-nano interface: A molecular dynamics study of graphene-coated lipid membrane Zhigong Song, Yanlei Wang, Zhiping Xu ∗ Applied Mechanics Laboratory, Department of Engineering Mechanics and Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
article
info
Article history: Received 5 September 2015 Accepted 14 November 2015 Available online 28 November 2015 *This article belongs to the Biomechanics and Interdiscipline Keywords: Cell membrane Lipid bilayer Graphene Mechanical responses Bio-nano interfaces
abstract Bio-nano interfaces between biological materials and functional nanodevices are of vital importance in relevant energy and information exchange processes, which thus demand an in-depth understanding. One of the critical issues from the application viewpoint is the stability of the bio-nano hybrid under mechanical perturbations. In this work we explore mechanical responses of the interface between lipid bilayer and graphene under hydrostatic pressure or indentation loads. We find that graphene coating provides remarkable resistance to the loads, and the intercalated water layer offers additional protection. These findings are discussed based on molecular dynamics simulation results that elucidate the molecular level mechanisms, which provide a basis for the rational design of bionanotechnologyenabled applications such as biomedical devices and nanotherapeutics. © 2015 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/).
Recently there have been significant interests rising in developing bionanotechnologies such as bioelectronics platforms that interface biological materials such as cells or tissues with functional nanostructures [1–6]. Biosensory functions can be enabled by detecting the biophysiochemical signals transduced across at this interface, which allows extracting valuable information from biologically important reactions, as well as controlling cellular activities through nanoscale contacts with integrated devices. Bio-nano hybrids with high complexity in integration require massively interconnected arrays of processing devices, completed with integrated power supply and heat removal networks [7]. As a result, the bio-nano interface that conveys energy and information exchange between biological materials and nanostructures are pivotal in designing relevant technological applications. The structural and physiological stabilities of such an interface under external mechanical perturbation are important issues to be addressed practically in order to design reliable bionanotechnologies, which are crucial not only for preserving functions of bioelectronics, but also to conduct subcellular engineering of the biological processes [8]. Graphene and its derivatives such as graphene oxide are flexible single-atom-thick layers that are able to form compatible interface with lipid bilayers that constitute the cell membrane, which have been studied recently as functional nanostructures
∗
Corresponding author. E-mail address: [email protected] (Z. Xu).
interfacing with biological materials. Nanocomposite structures have been constructed by depositing lipids onto graphitic layers or intercalating them into an assembly in a layer-by-layer fashion [2–4,9–11]. Researchers have found that graphene layers could confine the cell as an easy-to-apply impermeable and electrontransparent encasement that retains the cellular water content [4]. More interestingly, the graphene sheet deposited on the cell wall permits a free functioning of the plasma membrane it encapsulates [3]. The interface between graphitic layers and the cell membrane is the essential pathway that conveys information and energy exchange, where evidences have been reported for the existence of a layer of trapped water within this interface. The thickness of this intercalated water layer (IWL) is only a few nanometers, although its dependence on the physiological condition is still not clear. However, it effectively weakens the dielectric coupling across the interface and thus the disruptive effects to the cellular membrane [2,9]. In additional to these biochemical effects, the nanostructural coating using graphene could also protect the cell under physical or chemical attacks. The stability of both the living system and the bio-nano interface could also be broken down under external mechanical perturbations. This fact, however, has only very limited understandings in the community. In this work, we explore mechanical responses of the lipid bilayer–graphene interface as a model system for general bio-nano interfaces. Empirical forcefield based molecular dynamics (MD) simulations are performed to probe the nanoscale structures and dynamics of the hybrid. We find that under external loads, the graphene coating provides an outstanding protection function for
http://dx.doi.org/10.1016/j.taml.2015.11.003 2095-0349/© 2015 The Authors. Published by Elsevier Ltd on behalf of The Chinese Society of Theoretical and Applied Mechanics. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
232
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
a
b Number of H-bonds
tIWL
h
3.5 3.0
2.5 0.5
c
1.0 tIWL (nm)
1.5
d
Fig. 1. (a) The model of graphene-coated lipid bilayer membrane with intercalated water layers. (b) Number of hydrogen bonds (per water molecule) analyzed for different IWL thicknesses, tIWL . (c, d) Illustration of applied hydrostatic pressure and nanoindentation loads.
the lipid membrane. Moreover, the IWL at the lipid–graphene interface is found to play a critical role in modulating the transmission of mechanical signals and the mechanical stability of the hybrid. These conclusions are discussed with respect to their implications in designing related bionanotechnological applications. We construct a lipid bilayer–graphene hybrid by placing the bilayer at a certain distance from the graphene sheets. Water molecules are added in between, which could enter the spaces in 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid bilayers with a depth of ∼1 nm after thermal equilibration (Fig. 1(a)). The interfaces with top and bottom hydrophilic sides of the lipid bilayer are constructed symmetrically. A two-dimensional supercell is used with periodic boundary conditions (PBCs) along the interface, with lateral dimensions of 10.46 and 10.15 nm, respectively. Free boundary conditions are used in the dimension across the bilayer. Supercells with different lateral sizes are explored to characterize the size effect in the indentation tests, and we find notable size effect in the nanoindentation tests, where mechanical responses are weakened as the lateral membrane span increases under the same indentation force. However, our following discussions are focused on this specific system size for a quanlitative demonstration. All MD simulations are performed using the large-scale atomic/molecular massively parallel simulator (LAMMPS) package [12]. Interatomic interactions between carbon atoms in graphene are described using the adaptive intermolecular reactive empirical bond order (AIREBO) potential with torsion and van der Waals terms included [13]. The CHARMM36 forcefield is used for the lipid bilayer, and water is simulated using the TIP3P model [14]. The SHAKE algorithm is applied for bond stretching and angle bending terms between oxygen and hydrogen atoms to avoid highfrequency vibrations that require shorter time steps. Interaction between water, graphene and the lipid bilayer includes both van der Waals and electrostatic terms. The former term is described
by the 12-6 Lennard–Jones potential 4ε[(σ /r )12 − (σ /r )6 ] and the Lorentz–Berthelot mixing rule [14], which is truncated at an interatomic distance r = 1.0 nm. Long-range Coulomb interactions are computed by using the particle–particle particle-mesh (PPPM) algorithm [15]. The time step is set to 0.5 fs to assure total energy conservation in absence of thermostat coupling. The whole system is equilibrated at 300 K and 1 a.t.m. (1 a.t.m. = 101325 Pa) (in the lateral dimensions) before the mechanical loadings are applied, using the Berendsen thermostat and barostat [16], respectively. We carry out MD simulations with both hydrostatic pressure and local indentation loads on the lipid–graphene hybrid. The hydrostatic pressure Pz is simulated by compressing two planar walls towards graphene coatings at both sides of the graphene–lipid–graphene hybrid at a rate of 0.03 nm/ps (Fig. 1(c)). These planar walls interact with the graphene sheet through a harmonic, repulsive-only potential in the form of Urep = K (r − rc )2 /2, where r is the position of wall and the interaction is turned off beyond a cut-off distance rc = 0.1 nm. The spring constant K is set to 200 eV · nm−2 . These settings allow us to probe mechanical responses of the hybrid under external pressure Pz , in terms of a compressive strain εz = −21h/h. Here h is equilibrium thickness of the lipid–graphene hybrid, which is defined by the vertical distance between two graphene sheets. 1h is the change. During the loading process we find that the lateral relaxation of simulation box is not significant due to the high in-plane stiffness of graphene. To probe mechanical responses of the hybrid to local or concentrated loads, we carry out nanoindentation tests where an indenter is pressed towards one side of the lipid–graphene hybrid, while the other side is fixed (Fig. 1(d)). The indentation force f is tracked as a function of indentation depth d. The indenter is a rigid spherical particle with a radius of R = 1 nm, interacting with the graphene sheet through a force in the form of f (r ) = −k(r − R)2 . Here r is the distance measured from the atom to the center of indenter. The specified force constant k = 104 eV · nm−3 is large
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
enough to exclude notable rate dependence that could arises in a soft contact. The loading rates are set to v = 0.05 nm/ps for the nanoindentation tests. Simulations carried out at lower loading rates show softened responses, but the results are quanlitative the same. For example, tests for tIWL = 0.68 nm and at v = 0.005 nm/ps predict failure force and depth of 67.546 nN and 1.355 nm, which are very close to 66.147 nN and 1.347 nm for v = 0.05 nm/ps. When a hydrostatic pressure Pz = −σzz is applied on the graphene surface with area A, it can be related to the compressive strain εz by considering the hybrid as a composite continuum with Young’s modulus Y and Poisson’s ratio ν (we assume ν = 0.3 in this work)
εxx = [σxx − ν(σyy + σzz )]/Y ,
(1a)
εyy = [σyy − ν(σxx + σzz )]/Y ,
(1b)
εzz = [σzz − ν(σxx + σyy )]/Y .
(1c)
Following the boundary and loading conditions used in our MD simulations, i.e., εx = εy = 0, the compressive strain response can be expressed as
εzz = σzz [1 − 2ν 2 /(1 − ν)]/Y = −Pz [1 − 2ν 2 /(1 − ν)]/Y .
(2)
For a model problem of indentation on a half-space, the indentation force f , depth d, and their relation can be described through the Sneddon formula [17] d = a lg[(R + a)/(R − a)]/2,
(3a)
f = Y {(a + R ) lg[(R + a)/(R − a)] − aR}/[2(1 − ν )]. 2
2
2
(3b)
Here a is the radius of contact between the indenter and the membrane under indentation, which can be determined from the data of our MD simulations using Eq. (3a). ν = 0.3 is the Poisson’s ratio assumed for the substrate material. Molecular structures of the bio-nano interface between a cell membrane and graphene coating are illustrated in Fig. 1(a), which are composed of a lipid bilayer, monolayer graphene sheets, and a thin layer of trapped water, i.e., the IWL. In this work, the IWL thickness (tIWL ) is defined as the span of region where the water density is no lower than that in the bulk. The presence of IWL within the gap between the lipid layer and graphene allows the cell to exchange masses and energy with the surroundings and thus is crucial for their survival [3]. From the snapshots of water molecules within the interfacial gallery, we identify layered water structures adjacent to the graphene wall in our MD simulations. Further structural analysis at the molecular level shows that the number of hydrogen bonds per water molecule is smaller than the value in bulk water, but increases with tIWL (Fig. 1(b)). This is actually a common feature of nanoconfined water, which was reported for water trapped between graphene or graphene oxide (GO) layers at a similar length scale of confinement [18]. It should also be remarked that there are water molecules entering the lipid bilayer within a depth of ∼1 nm, which is similar as the situation where lipid bilayers are immersed into water at the physiological condition [19]. The thickness of layered water region in our simulations is ∼1 nm, which is close to the IWL thickness reported for water trapped at the lipid–graphene interface in recent experimental measurements [2]. This means that the presence of structured IWLs between hydrated lipid bilayers and the graphene sheet could lead to changes in the properties and stabilities of lipid bilayers and the cell, compared to their native structures immersed in the extracellular fluid. Accordingly, we construct a number of lipid–graphene hybrids with tIWL ranging from 0 nm to 2 nm based on these observations, and use them as model systems for further mechanical characterization.
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Bio-nano devices are usually immersed in fluid to maintain the physiological condition of living systems. The integration of nanoelectronics with cell contains functional interfaces between the cell membrane and nanostructures such as the graphene coating. External mechanical perturbation could originate from hydrostatic pressure or localized impacts. To explore the stability of such a bio-nano interface under these loads, we first explore the relation between hydrostatic pressure Pz applied onto the graphene sheet and the compressive strain εzz measured in the same direction. From a typical stress–strain curve shown in Fig. 2(a), we find that the bio-nano hybrid is stiffened as the pressure increases due to a densified structures of IWLs as demonstrated in the water density plots for tIWL = 1.4 nm (Fig. 3(a)). We notice further that as the hybrid is compressed, mechanical load is transmitted through the IWLs, and the responses are relatively incompressible. The layered structures of IWLs become more and more prominent as the pressure increases due to the enhanced graphene–water interaction and presence of anisotropic pressure. This enhanced layered order further contributes to the nonlinearly elastic responses and protects the structural stability of lipid membrane. Interestingly, this process of structural transition in IWLs is reversible under the pressure loading, which results in negligible hysteresis. We now summarize mechanical responses of the bio-nano interface as a function of the IWL thickness tIWL . It is clearly shown in Fig. 4(a) that, as the IWL is present, the lipid–graphene hybrid is significantly stiffened compared to the bare one because of both the intercalation of water molecules in the lipid bilayers and the mechanical resistance of IWLs. However, this enhancement is weakened as t further increases, which could be explained by the fact that for few-layer water the stiffening effect increases with tIWL , while the structure of the IWLs becomes less ordered as its thickness increases and thus the hybrid is softened with tIWL >∼ 0.6 nm. This can also be concluded from the extracted values of Young’s modulus Y using Eq. (2). The results in Fig. 4(a) show that Y is on the order of 1 GPa, which is significant enough to provide an effective mechanical protection to the cell membrane. This value of Y converges to 2.39 GPa as tIWL increases, which is close to the bulk modulus of water B = 2.2 GPa [20]. Local mechanical responses of the lipid–graphene hybrid are distinctly different from that under hydrostatic loading. Under nanoindentation, our MD simulations show that the structure of lipid–graphene hybrid is distorted locally at small indentation depth. The force–depth relation we obtain from the simulation results at small indentation depth (inset in Fig. 2(b)) is used to extract effective in-plane elastic modulus Y of the hybrid through Eq. (3) (Fig. 4(a)). Comparative studies of the mechanical responses under nanoindentation show that with water intercalation, the hybrid is stiffened. Similarly, the stiffening effect decreases with the IWL thickness tIWL , which suggests that the deformation mechanism under small indentation loads is the same as that under hydrostatic pressure. At large indentation depth, however, we find that water molecules under the indenter are able to diffuse and flow during the loading process (Fig. 3(b)). Consequently, the structures of IWLs and lipid bilayer change significantly in contrast to that under either hydrostatic pressure or small-depth indentation. The mechanical response is softened with IWL, in contrast to the conclusion at small indentation depth (Fig. 2(b)). This redistribution of water in the IWL also implicates mechanical energy dissipation during the loading processes. To quantify this effect, we perform additional MD simulations with cycling indentation loads applied. We characterize the force hysteresis from the f –d curve in one cycle of nanoindentation (Fig. 2(b)). The results show that the amount of energy dissipation is almost independent on tIWL and is slightly reduced as tIWL increases in the range we explored (Fig. 4(b)). This
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a
b 60
2
f 0.02
1
f (nN)
0.00 tIWL
0.00
30
0.02
a tIWL
0.00 nm 0.00 nm
0.85 nm 0
0
1.40 nm 0.00
0.05
0.85 nm 0
0.10
1 d (nm)
2
Fig. 2. Mechanical responses of lipid–graphene hybrids with different IWL thicknesses, measured under (a) hydrostatic pressure and (b) cycling nanoindentation loads. The inset in panel (b) shows the elastic response of interface measured at small indentation depth, which is used to extract the Young’s modulus using Eq. (3).
a
b
Δh = 0.0 nm
0.00
d = 0.00 nm
1.25
0.2 nm
0.50 nm
0.4 nm
1.00 nm
0.8 nm
1.84 nm
Fig. 3. Density distribution of the intercalated water layer (tIWL = 1.4 nm) at the lipid–graphene interface under (a) hydrostatic pressure and (b) nanoindentation forces, measured by its ratio to the bulk value ρ/ρbulk .
capability of energy dissipation could protect the bio-nano hybrid from dynamical loads such as vibration and impacts. As the amplitude of indentation force further increases, the structure of bio-nano hybrids could be significantly disturbed and even fail. From our nanoindentation tests, we find that the amplitude of fracture indentation force and depth are almost invariant as the IWL thickness changes (Fig. 5), which aligns with the fact that the fracture is nucleated inside the graphene sheet.
These simulation results thus show that the graphene coating could protect the underneath lipid membrane very effectively because of its outstanding in-plane mechanical resistance. In summary, we analyzed molecular structures of the bio-nano interface between a lipid membrane and graphene coatings by performing atomistic simulations and explore their mechanical responses upon hydrostatic pressure and nanoindentation loads. We find that the graphene coatings with extremely high stiffness
Z. Song et al. / Theoretical and Applied Mechanics Letters 5 (2015) 231–235
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b 10 Energy dissipation (10-9 nJ)
a
Y (GPa)
4
2 Hydrostatic pressure
5
Indentation 0.0
0.5
1.0
1.5
0.0
0.5
tIWL (nm)
1.0
1.5
tIWL (nm)
Fig. 4. (a) The Young’s moduli of lipid–graphene hybrids calculated under hydrostatic pressure and indentation forces. (b) Mechanical energy dissipation during the first loading–unloading cycle in the nanoindentation tests, plotted as a function of the IWL thickness, tIWL .
b Depth to failure (nm)
Fracture force (nN)
a 80
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0.0
0.5
1.0
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tIWL (nm)
2
1
0.0
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tIWL (nm)
Fig. 5. The critical indentation (a) force and (b) depth measured for the lipid–graphene hybrids as a function of the thickness of IWL, tIWL .
and strength could effectively protect the structural and physiological stabilities of the bio-nano hybrid in response to both hydrostatic and concentrated loads. The presence of an intercalated water layer at the interface is found to play an important role in further mediating the mechanical resistance and energy dissipation. These findings could direct rational design of bionanotechnologyenabled biomedical devices, where stability and robustness of bionano interfaces under mechanical perturbation are essential for non-invasive applications. Acknowledgments This work was supported by the National Natural Science Foundation of China (11222217 and 11472150). The simulations were performed on the Explorer 100 cluster system of Tsinghua National Laboratory for Information Science and Technology. References [1] A.E. Nel, L. Madler, D. Velegol, et al., Understanding biophysicochemical interactions at the nano–bio interface, Nat. Mater. 8 (2009) 543–557. [2] P.K. Ang, M. Jaiswal, C.H.Y.X. Lim, et al., A bioelectronic platform using a graphene–lipid bilayer interface, ACS Nano 4 (2010) 7387–7394. [3] R. Kempaiah, A. Chung, V. Maheshwari, Graphene as cellular interface: Electromechanical coupling with cells, ACS Nano 5 (2011) 6025–6031. [4] N. Mohanty, M. Fahrenholtz, A. Nagaraja, et al., Impermeable graphenic encasement of bacteria, Nano Lett. 11 (2011) 1270–1275. [5] A. Fabbro, S. Bosi, L. Ballerini, et al., Carbon nanotubes: Artificial nanomaterials to engineer single neurons and neuronal networks, ACS Chem. Neurosci. 3 (2012) 611–618.
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