Indentation of Graphene-Covered Atomic Force Microscopy Probe

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Interfaces: Adsorption, Reactions, Films, Forces, Measurement Techniques, Charge Transfer, Electrochemistry, Electrocatalysis, Energy Production and Storage

Indentation of graphene covered AFM probe across a lipid bilayer membrane: Effect of tip shape, size and surface hydrophobicity Kang Lv, and Yinfeng Li Langmuir, Just Accepted Manuscript • Publication Date (Web): 04 Jun 2018 Downloaded from http://pubs.acs.org on June 4, 2018

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Indentation of graphene covered AFM probe across a lipid bilayer membrane: Effect of tip shape, size and surface hydrophobicity Kang Lva,b, Yinfeng Lia,b,c,* a. Department of Engineering Mechanics, School of Naval Architecture, Ocean and Civil Engineering (State Key Laboratory of Ocean Engineering), Shanghai Jiao Tong University, Shanghai 200240, China b. Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China c. Key Laboratory of Hydrodynamics (Ministry of Education), Shanghai Jiao Tong University, Shanghai 200240, China

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Abstract Understanding the interaction of graphene with cell membranes is crucial to the development of graphene-based biological applications and the management of graphene safety issues. To help reveal the key factors controlling the interaction of between graphene and cell membrane, here we adopt the dissipative particle dynamics method to analyze the evolution of interaction force and free energy as the graphene covered AFM probe indents across a lipid bilayer. The simulation results show that graphene covered on the AFM probe can cause severe deformation of cell membrane which drives the lipid molecule to adsorb and diffuse at the surface of graphene. Breakthrough force and free energy analysis are calculated for the effects of tip shape, size and surface hydrophobicity on the piercing behaviors of graphene covered AFM. In addition, the deformation of cell membrane can decrease the dependency of breakthrough force on tip shape. The analysis of surface functionalization suggests that the horizontal patterns on graphene can change the preferred orientation in the penetration process but the vertical patterns on graphene may disrupt the cell membrane. What’s more, the bending stiffness of graphene has little influence on the penetration process as graphene pierces into cell membrane. These results provide useful guidelines for the molecular design of graphene materials with controllable cell penetrability. Keywords: graphene covered AFM, cell membrane, indentation, dissipative particle dynamics Highlights: 1. Using graphene attached on the AFM probe to indent the cell membrane is firstly studied by dissipative particle dynamics method. 2. The mechanism of graphene interacted with cell membrane is revealed by the calculation of interaction force and free energy change. 3. Key factors controlling the interaction between graphene and cell membrane is provided, such as tip shape, size, surface functionalization, bending stiffness.


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Introduction Graphene, which is a monolayer material consisting of hexagonally arranged carbon atoms, has received intense interest due to its excellent electrical1, mechanical2, and thermal properties3. In particular, graphene and its derivatives have been applied in a variety of biomedical fields on specific targeting4, drug delivery5, and enhanced bioimaging6-7. Relative experimental observations show that graphene and its derivatives can be either benign8-10 or toxic11-14 to cells. Thus, it has been important to understand the interaction of graphene with cell membrane in cellular uptake internalization, including the effects of graphene shape15, size16-17, surface functionalization18-19 and thickness20-21. In the recent years, the studies on the interactions of graphene and cell have made significant advancements. It has been observed through simulations22-23 and experiments17 that the grapheme nanosheets can enter cells. Titov et al. studied the interaction of small graphene nanosheets with a lipid bilayer and reported stable hybrid structures of graphene and lipid bilayer.22 Li et al. studied the uptake of graphene microsheets in cellular membranes and showed the low energy barrier of local asperities in entry process.15 Dallavalle et al. studied the penetration of graphene nanosheets in lipid bilayers and analyzed the size effects on the reorganization of the lipid bilayer.16 These findings are mostly based on the preliminary stage when the graphene contacts with the cell membrane. Up to now, very little is known about the fundamental behavior when the graphene has entered the cell membrane. When the graphene has gone deep into the cell membrane, it is challenging to measure the interaction of graphene and cell membrane due to the complex physical and chemical mechanisms. Thus, suitable means should be chosen in the penetration process.


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Atomic Force Microscopy (AFM)24 has been regarded as an useful tool to study micro and nano systems. Compared with other techniques, the main advantage is that the surface structure of biological samples can be visualized in liquid media with nanometer resolution25-26, such as lipid bilayer or cell27. Moreover, it is an excellent tool to sense and apply forces with pN sensitivity at the single molecule level, which is known as force spectroscopy (FS).28-29 In previous studies, AFM is widely used in examining

the

mechanical

response

of

cells

exposed

to

graphene-based

nanomaterials.30-32 The experimental studies have shown that the carbon-based materials are absorbed on the AFM probe.33-34 Inspired by the experiments above, the graphene can be also adsorbed on the surface of the AFM probe. Thus, the interaction between the graphene and the cell membrane can be measured by the AFM as the graphene approaches the cell membrane. In our study, the dissipative particle dynamics(DPD) methods35-36 are carried out on the indentation of graphene nanocone across a lipid bilayer membrane. By applying the standard thermodynamic integration (TI) scheme in coarse-grain molecular dynamics (CGMD)18, 37, we calculate the interaction forces and free energy change as a function of the AFM tip position covered with graphene across the bilayer. The mechanism of graphene interacting with cell membrane is revealed through analysis of movement of lipid molecule. Attentions will be focused on several key factors affecting the interaction between graphene covered on the AFM tip and cell membrane, including tip shape of graphene layer as well as the size, surface functionalization, the bending stiffness.


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Simulation method Formulations of the DPD method In the paper, the simulations are carried out by using the method of dissipative particle dynamics (DPD), which is a mesoscopic coarse-grained simulation method for bio-membrane systems and soft matters.38-44 In DPD simulations, a single bead denotes a group of atoms and is set at the mass center of the group. The interaction between beads i and j can be represented as a pairwise additive force consisting of conservative force FijC , dissipative force FijD and random force FijR . Thus, the total force on bead i can be given as

(

Fi = ∑ FijC + FijD + FijR

)

i≠ j

= ∑ aijω (rij )rîj − γω 2 (rij )(rîj ⋅ vij )rîj + σω (rij )ξ ij ∆t −1/ 2 rîj

(1)

i≠ j

where the sum covers all particles within the cutoff radius rc. aij is the maximum repulsive force, rij is the interval distance between beads i and j, rîj is a unit vector and vij denotes the relative velocity between beads i and j, ξij represents a random number with zero mean and unit variance, and

1 − rij / rc  0

ω (rij ) = 

rij < rc rij ≥ rc

(2)

is a normalized distribution function; γ and σ are parameters related to each other as σ 2 = 2γk BT , where kBT is the unit of energy. In our simulations, the standard values σ = 3.0 and γ = 4.5 are used as reported in literature.15

Length and time scales In DPD simulation, the mass, length and time scales are all reduced into dimensionless indexes. The unit of length is the cutoff radius rc, the unit of mass is the


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mass of the solvent beads, and the unit of energy is kBT. Other quantities are expressed in terms of these basic units. To examine the membrane thickness and the lipid diffusion coefficient, the reduced DPD units can be converted into the simulation units. The simulated bilayer thickness is 5rc , and the effective time scale of the simulation can be determined by the simulation lateral diffusion constants of the lipid bilayer.45 The DPPC bilayer thickness is approximately 4 nm and its lipid diffusion coefficient is about 5 µm 2 s −1 .46 Compared with experimental values, the DPD length unit equals 0.8 nm and the time unit corresponds to τ= 24.32 ps. All simulations are carried out in LAMMPS.47 A modified Velocity-Verlet algorithm48 is adopted in the time integration of the equations of motion. The timestep in our simulations is taken as ∆t = 0.003τ .

Coarse grained model The simulation box for the indentation of graphene nanocone is a 40 × 40 × 40 cube with periodic boundary conditions. The system contains 193678 particles with 973 graphene beads, 24025 lipids beads and 168680 water beads. The particle density of the system is about 3.49 For clarity, the solvent beads (S) are not shown in the figures below. The lipid molecule is represented by the H3(T5)2 coarse grained model50-51 proposed by Groot and Rabone35, as shown in Fig. 1. The hydrophilic lipid heads (H) are represented by red beads and the hydrophobic lipid tails (T) are shown as yellow beads.


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Fig. 1 Schematic representations of the coarsed grained graphene nanocone and lipid molecule. Within a lipid molecule, a harmonic force is applied to connect two consecutive beads,

FijS = k s (1− rij / rs )rîj

(3)

where ks is the spring constant and rs is the equilibrium bond length. Here, ks = 100.0, and rs = 0.7rc are used for the lipid molecule.52 The bending resistance of the lipid chain is represented as an additional force caused by a harmonic constraint on two consecutive bonds,

F θ = −∇Vbend Vbend =

1 2 kθ (θ − θ 0 ) 2

(4) (5)

where kθ, θ0 and θ are the bending constant, equilibrium angle , and inclination angle, respectively. For three consecutive lipid tail beads or three consecutive lipid head beads in a lipid molecule, k1 = 6 and θ = 180° are used following Groot and Rabone35; for the top tail-beads and the last head-bead (beads 3, 4 and 9 in Fig. 1), k2 = 3 and θ = 120°; for the bottom two consecutive head beads and the first bead in each tail (beads 2, 3, and 4 or beads 2, 3, and 5 in Fig. 1), k3 = 4.5 and θ = 120°. We first constructed flexible coarse-grained graphene composed of beads


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connected by bond, angle and dihedral angle. Then the flexible coarse-grained graphene plate is tailed and zipped into graphene nanocone. Each bead of graphene represents six atoms with a interval distance of 0.4 nm and internal angle of 60°. By applying a suite of standard mechanical tests on a square coarse-grained graphene model, we determine Young’s modulus, bending stiffness, and shear modulus in our CGMD model to keep elastic properties53-54 of the constructed CG graphene consistent with experimental results2, 55.The bond and angular constants are set as ks = 12000.0 and kθ = 1200.0. The dihedral angle force constants, multiplicity, and potential minima are set as kd = 71.0, n=1, and θd = 180o, respectively.15 To express the hydrophilic/hydrophobic property of beads in the DPD system, the interaction parameters for the beads of same type are aij = 25, the interaction parameters for two beads of different types are set as aHT = aST = aGS = 100 and aHS = 25,37 where S represents the solvent bead, G represents the graphene bead, and H and T stand for the lipid head and the lipid tail, respectively. The interaction parameters between lipid molecules and graphene cone are taken to be aGH =155 and aGT =45, which were derived from matching with the correct graphene–membrane interaction parameters γH and γT in the all-atom MD simulations.15

Results and discussions Breakthrough force and free energy analysis In our simulation, the graphene is attached on the surface of AFM probe and the overall structure of graphene is based on the shape of the AFM probe30. Motivated by the AFM probe used in the experiments, graphene nanocones with 60 degree apex are considered. Up to now, graphene nanocones with five different apex angles α(19°, 38°, 60°, 83° and 112°) have been reported experimentally56. For graphene nanocone with


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small apex angles (such as 19°, 38°), the cone is too small to fit the AFM tip. Meanwhile, the bottom edge of graphene nanocone with large apex angle (such 83°,112°) will not be able to fully attach on the surface of the AFM. Thus, nanocones with tip angle of 60° are selected as an optimized structure for the study of graphene covered AFM tip. To understand the interaction of graphene nanocone with cell membrane, we first calculate the interaction force and free energy change as the graphene nanocone indents into a lipid bilayer. In each case, all nanocones are placed at a distance about 5rc above and vertical to the upper surface of membrane.

Fig. 2 Schematic illustration for the thermodynamic integration (TI) approach used in the analysis of interaction force and free energy.

Due to the molecular interactions, the interaction force and the free energy varies as the graphene nanocone indents into the lipid membrane. Here the thermodynamic integration (TI) approach37, 57 is adopted to analyze the interaction force and the free energy as a function of the distance from the tip of nanocone to the upper surface of the lipid bilayer. When the graphene nanocone arrives at the lipid bilayer, the interaction force in this process is expressed as:


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(

F = kz Z − z

)

(6)

The harmonic force is applied to confine the motion of the graphene nanocone along z-direction, where kz = 1000 and z represents the spring constant and equilibrium position of the potential, respectively. Under the harmonic constraint, the graphene nanocone is forced to oscillate around a pseudo-equilibrium position

Z

in the vicinity of z, where

Z

is the position of the nanocone tip, as shown in Fig. 2.

C

120

Interaction force(kBT/rc)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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D

80

E B

40

A

0

A

D

-40

B

-80

C 0

E 2

4

6

8

10

12

14

Tip position(rc)

Fig. 3 The interaction force change as a function of a distance between the tip of graphene nanocone and the upper surface of bilayer when a graphene nanocone with apex 60o and height 10rc pierces into a lipid bilayer. (A-E) The simulation results when the graphene nanocones penetrate into the cell membrane at different positions.

Fig. 3 shows the change of interaction force on graphene nanocone of apex 60o and height 10rc with the distance between the tip of graphene nanocone and the upper ACS Paragon Plus Environment

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surface of bilayer. When the cone reaches the upper surface of bilayer, lipid molecules are attracted upward and the integral structure of lipid bilayer changes a little. As the nanocone pierces into bilayer, the lipid molecules are adsorbed on the surface of graphene nanocone and move along the generatrix of graphene nanocone, which induces the large deformation of cell membrane and sharp increase of the interaction force. Such phenomenon is consistent with the previous study that graphene nanosheets can extract lipid molecules from the cell membranes.58 When the nanocone enters at a certain position, a turning point can be noticed on the interaction force curve. The turning point can be interpreted as the fully penetration of the graphene nanocone through the cell membrane. The interaction force where the turning point happens is the maximum force. And the maximum force is the breakthrough force (Fb) which the bilayer is able to withstand before breaking.59 At this moment, the cell membrane has the largest deformation in the indentation process. After that, the deformation of bilayer starts to reduce and the force decreases gradually as the penetration continues. The analysis of interaction force in the penetration process reveals that the interaction of graphene nanocone and lipid bilayer is predominantly attractive which is due to the strong interaction between the graphene cone and the hydrophobic tail of lipid molecules. By integrating the interaction force, free energy change can be calculated as a function of the distance from the tip of nanocone to the upper surface of lipid bilayer: E = ∫ − Fdz = ∫ k z (z − Z )dz


(7)

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0

B

A -100

Free energy(kBT)

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-200 -300

C

A

-400

B

-500

C

C

-600 -4

-2

0

2

4

6

8

10

12

14

Tip position(rc)

Fig. 4 The evolution of free energy as a function of the distance between the tip of nanocone and the upper surface of lipid bilayer during the penetration of nanocone across the lipid bilayer. Position C is the energy favorable position of graphene nanocone. Time sequences of CGMD simulation results show that the graphene nanocone located at position A (0.6 rc) and B (13.9 rc) can automatically penetrates the cell membrane and equilibrium at the position C without external force.

Fig. 4 shows the free energy evolution of the system as a function of the distance between the tip of nanocone and the upper surface of lipid bilayer membrane. The results show that there exists a deep energy valley in the indentation of graphene nanocone. As the nanocone contacts the lipid bilayer, it will tend to penetrate to a preferred position, at which graphene nanocone is trapped inside the bilayer. To verify the low-energy state in the indentation process, we place the nanocone


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at the high-energy state. Then we observe whether the nanocone can automatically move into the low-energy state. Two different penetration heights have been chosen: 0.6rc where the nanocone has attached to the hydrophobic part of the bilayer and 13.9rc where the nanocone starts to leave from the bilayer. Then, the nanocones undergo Brownian motion. After a period of time, the nanocones automatically pierce into the bilayer and stay inside the lipid bilayer. It is clear that the low-energy state exists in the penetration process and makes the nanocone easy to pierce into the lipid bilayer or difficult to leave. In the low-energy state, the deformation of the lipid bilayer gets relatively small and the structure of graphene nanocone and cell membrane remains stable leading to activate an uptake process like endocytosis.

Tip shape analysis Table 1 Morphological properties of graphene nanocone with 60° apex angle and different tip curvatures.

It has been reported that local configuration of graphene has an influence on the interaction of graphene and cell membrane.15 Graphene sheets choose to contact the cell membrane with an asperity orthogonally to minimize the entry barrier. Inspired by the consideration, the tip shape of the AFM probe may influence the interaction of


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graphene and cell membrane. So, we change the shape of nanocone tip and repeat the simulation of indentation above. The graphene nanocone with the apex angle of 60° and the height of 10rc is chosen and four different curvatures are considered: (1)0; (2)1/5rc; (3)1/4rc; (4)1/3rc. The graphene nanocone with smaller tip curvature has larger degree of local sharpness.

Fig. 5 The breakthrough force for indentation of graphene nanocones with different tip curvatures across cell membrane. The black line denotes the case that the penetration of nanocone across a suspended lipid bilayer and the red line represents the situation of supported membrane. (A-H) The snapshots taken from the simulated penetration process of graphene nanocones with different tip curvatures.


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When the lower surface of the lipid bilayer is unfixed, the breakthrough force shows negligible change with the tip curvature of nanocone, as shown in Fig. 5. To explain the phenomena in our simulation results, we note that the deformations of cell membrane in the four unfix cases are similar. When graphene nanocone breaks through the lipid bilayer, the lipid molecules are attracted around the edge of nanocone bottom and have little contact with the nanocone tip, as shown in Fig.5(E-G). Inspired by the deformation observation, we apply out-of-plane constrain to the lower surface of lipid bilayer to constrain the out of plane deformation of cell membrane, which corresponds to the effect of cytoskeletal60. As shown in Fig. 5(A-C), the nanocone tips have good contact with the lipid bilayer when the breakthrough force happens. And the breakthrough force decreases when the curvature of nanocone tip increases. The contact area between graphene nanocone and lipid bilayer decreases with the increase of tip curvature at same penetration depth before the lipid bilayer is broken through, leading to a decrease of the breakthrough force. The comparison of the fix and unfix cases reveals that the interaction between the graphene nanocone and lipid bilayer is closely related to the contact area, and the large out-of-plane deformation of cell membrane can weaken the influence of the tip shape on breakthrough force.


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Size analysis

130

120

Breakthrough force(kBT/rc)

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C 110

D

B

100

A

B

C

D

90

A

80 4

6

8

10

12

14

16

18

20

Nanocone height(rc)

Fig. 6 The breakthrough force change as a function of the height of graphene nanocone when graphene nanocones with apex 60o piercing into a lipid bilayer. The simulation results show the graphene nanocones with different heights have broken through the lipid bilayer: (A)5rc; (B)7rc; (C)10rc; (D)15rc.

The simulation of graphene sheets entering the lipid bilayer has shown that the size of graphene sheet has a huge influence on the interaction between the graphene sheets and lipid bilayer. So, the effect of nanocone height on the breakthrough force is also investigated in our simulation.16 As shown in Fig. 6, the breakthrough force increases as the height of graphene nanocone increases and has little change once the height is more than 10rc. To explain the change trend of breakthrough force, we focus on the strength of the interaction between graphene nanocone and lipid bilayer. If the height of nanocone is small enough, the interaction between graphene nanocone and


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lipid bilayer has enough strength to drive the lipid molecules to the bottom of nanocone at which point the interaction force reaches the maximum. As the height of nanocone increases, the difficulty for the lipid molecules reaching the bottom of nanocone increases. When the height of nanocone is larger than a critical height, lipid molecules no longer come in contact with the bottom of nanocone. The phenomenon can also be analyzed through the deformation of lipid bilayer. The deformation of lipid bilayer, when the interaction force reaches the breakthrough force, increases greatly as the height of graphene nanocone increases and has little change once the height is more than 10rc. The analysis of breakthrough force change with the height of nanocone reveals that the effect of size on the breakthrough force occurs only when the size of nanocone is small. So in our following study, we choose the height of 10rc for graphene nanocone to reduce the effect of size. 200 0

A

-200

Free energy(kBT)

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-400

B C

-600

D

-800

5 7 10 12 15

-1000 -1200

E

-1400 0

2

4

6

8

10

12

14

16

Tip position(r c ) Fig. 7 The free energy change with the distance between the tip of graphene nanocone and the upper surface of bilayer when graphene nanocones with apex 60o and different heights pierce into a lipid bilayer. The lowest points of energy valley are shown as (A-E). ACS Paragon Plus Environment

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In addition, the free energy changes of a system are calculated as a function of the distance of the nanocone tip and the upper surface of bilayer, as shown in Fig. 7. The simulation results show that penetration of graphene nanocones will encounter deep energy valleys and the free energy change of a graphene nanocone with smaller height is much smoother. As the height of nanocone increases, the position where the lowest point of the energy valley occurs increases and is close to the height of nanocone. In other word, when the nanocone spontaneously pierces into the lipid bilayer, the nanocone has a possibility to stay in the lipid bilayer. And, the tip position where the lowest point of free energy change occurs is close to the height of nanocone, indicating that the bottom of nanocone will lie on the upper surface of lipid bilayer membrane. At the lowest point, the contact area between the lipid bilayer and nanocone reaches maximum. Under the stable location, the graphene may be adsorbed by cell membrane.

Surface functionalization analysis For graphene with hydrophobic surface, it is difficult for it to enter the inside of cell membrane as the hydrophilic surface of lipid bilayer inhibits its further penetration after it attaches to the membrane surface. However, different surface functionalization of graphene can modify its chemical properties and manipulate the penetration process. With the rapid development of synthesis techniques, different types of patterns can be coated on the surface of graphene to achieve controlled functionalities.8, 10 Motivated by graphene materials used in the experiments26, 40, we design two different style of patterns: horizontal pattern and vertical pattern.


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Table 2 Morphological properties of graphene nanocones with circular hydrophilic functionalization.

In the DPD simulations, the interaction parameters for beads of the same type are aij = 25. For the hydrophilic beads in Section 3.4, the interaction parameters between

hydrophilic beads and the solvent, the lipid head as well as the lipid tail are set as aHS = 25, aHH = 25 and aHT = 100, respectively. The hydrophobic patterning is the same as the pure graphene beads used in the rest of the paper. Thus, the interaction parameters for the hydrophobic beads are the same as that for the pure graphene beads. The interaction parameter between the hydrophobic and hydrophilic beads is set as a = 155. First, four different horizontal patterns have been considered: (1) only the apex part is hydrophilic (denoted by Apex); (2) only the edge part is hydrophilic(denoted by Edge); (3) four part with alternating hydrophilic and hydrophobic surface and the apex part is hydrophobic (denoted by Phob4); (4) four part with alternating hydrophilic and hydrophobic and the apex part is hydrophilic(denoted by Phil4). In each case, all nanocones have the same height of 10rc.


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Fig. 8 The evolution of free energy as a function of the distance between the nanocone tip and the upper surface of bilayer. The equilibriumed configuration of graphene nanocone with different surface functionalized patterns: (A) Apex, (B) Edge, (C) Phob4, (D) Phil4. When the nanocones with different horizontal patterns pierce into a lipid bilayer, the free energy changes are calculated as a function of the distance of the nanocone tip and the upper surface of bilayer, as shown in Fig. 8. This analysis indicates that, as the nanocone with horizontal patterns penetrates into the membrane, it tends to stay at a preferred orientation. The free energy evolution associated with the cases of Apex and Phil4 reveals that the low energy barrier is due to the repulsive interaction between the hydrophilic apex of nanocone and the hydrophobic core of lipid bilayer, which prevents the free energy of the nanocones from sinking to a deep valley. Currently, there is no experimentally study about the interaction between the nanocones and cell membrane. Castrill ó n et al studied the interaction of GO with bacterial cell


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membranes and showed GO-cell interactions are predominantly repulsive. Such experimental observation is consistant with the simulated biological behaviors of functionlized nanocone Apex and Phil4. The evolution of free energy for the case of Edge reveals that the hydrophilic bottom of nanocone can reduce the position where the lowest point of the free energy locates. Interestingly, the penetration of nanocone-Phob4 and nanocone-Phil4 encounter two energy valleys and the penetration of nanocone-Apex and nanocone-Edge encounter one energy valley. It seems that the number of the energy valleys is related to the number of hydrophilic parts. What’s more, the free energy change of nanocone-Phob4 and nanocone-Phil4 is much smoother than that of nanocone-Apex and nanocone-Edge. Our results show that the horizontal patterns on graphene nanocones can reduce the change range of free energy and change the preferred orientation in the penetration process.

Table 3 Physical and morphological properties of graphene nanocones with radial hydrophilic functionalization.

Later, we also consider four vertical patterns with alternating hydrophilic and


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hydrophobic parts: (1)four parts(denoted by V4); (1)six parts(denoted by V6); (1)eight parts(denoted by V8); (1)ten parts(denoted by V10). In each case, all nanocones have the same size of 10rc height and the hydrophobic content is 50% of total surface.

Fig. 9 The free energy changes as a function of the distance of the nanocone tip and the upper surface of bilayer. The simulation results show the disruption of cell membrane. (A) V4; (B) V6; (C) V8; (D) V10.

The free energy changes with the distance of the nanocone tip and the upper surface of bilayer when nanocones with different vertical patterns pierce into a lipid bilayer, as shown in Fig. 9. The free energy analysis indicates that there is a turning point when the nanocones V4, V6 and V8 penetrate into the cell membrane. At the turning point, the disruption of the cell membrane initiates at the contact area between the hydrophilic part of nanocone and the hydrophobic core of lipid bilayer due to the strong repulsive interaction, which is consistent with the failure mechanism of graphene oxide and lipid bilayer. And the position where the disruption of cell


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membrane occurs increases as the number of hydrophilic part increases. But the nanocone-V10 penetrates into the cell membrane with no disruption. It is due to the smaller contact area between the hydrophilic part of nanocone and the hydrophobic core of lipid bilayer.

Bending stiffness analysis Due to the stable surface chemical property, the graphene is easily stacked together leading to the change of the bending stiffness. So, we focus on the effect of bending stiffness on the interaction of graphene nanocone and cell membrane. The previous studies on the bending stiffness of few-layer graphene have shown that the bending stiffness of graphene sheets with 1, 2, 3, 4 and 5 layers is about 1.6, 3.1, 7.0, 12.4 and 19.4eV, respectively.61 We apply a suit of standard mechanical test on a square CG graphene model to make sure that elastic properties of the CG graphene agrees with the reported experimental results. After that, we repeat the simulation of indentation above. 160

1.6 3.1 7.0 12.4 19.4

0 150 -100

Breakthrough force(kBT/r c)

140

Free energy(kBT)

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2

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Tip position(r c) B

Fig. 10 The breakthrough force and free energy change of the graphene nanocones with different bending stiffness when the graphene nanocone pierces the lipid bilayer. (A)The breakthrough force as a function of bending stiffness of few-layer graphene.


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(B)The free energy change as a function of the distance of the nanocone tip and the upper surface of bilayer.

Fig. 10 shows the breakthrough force change and the free energy change as a function of bending stiffness of few-layer graphene when nanocones with different bending stiffness pierce into a lipid bilayer. The breakthrough force decreases with the increase of bending stiffness. In penetration process, the more rigid nanocones create smaller deformations with the membrane and it is more difficult for them to enter. But when the bending stiffness of graphene changes greatly, the breakthrough force changes little. The phenomenon can be found from the free energy change as well. The analysis of breakthrough force and free energy change reveals that the bending stiffness of graphene has little influence on the penetration process when the graphene nanocones pierce into cell membrane.

Conclusions In summary, DPD simulation has been carried out to investigate indentation of graphene covered on the AFM probe across a lipid bilayer membrane. Interaction force and free energy change are calculated by the TI method as the graphene penetrates into a lipid bilayer membrane. When the graphene pierces into bilayer, the lipid molecules are noticed to attach on the surface of graphene and move along the surface of graphene due to the strong interactions between graphene and the tail of lipid molecules, which induces the large deformation of cell membrane. Interaction force and free energy analysis reveals that graphene can be trapped inside the lipid bilayer. The analysis of tip shape demonstrates that the deformation of cell membrane can weaken the influence of the tip shape on breakthrough force and graphene with


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large tip radius faces a high breakthrough force in the indentation process. The analysis of size shows that the effect of size of graphene on breakthrough force works only when the size of graphene is small. The analysis of surface functionalization suggests that the horizontal patterns on graphene can reduce the change range of free energy and change the stable location in the penetration process. But the vertical patterns on graphene may disrupt the cell membrane which is relate to the number of the vertical patterns. The analysis of bending stiffness reveals that the bending stiffness of graphene has little influence on the penetration process when the graphene pierces into cell membrane. Our results are supposed to inspire and motivate further theoretical and experimental work about the interaction of graphene and cell membrane.


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Corresponding Author *E-mail: [email protected]

Notes The authors declare no competing financial interest.

Acknowledgements The authors gratefully acknowledge the support of the National Natural Science Foundation of China (No. 11402145), the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) (IPOC2017B009), and the Medical-Engineering Cross Fund of Shanghai Jiao Tong University (YG2015MS13, YG2017QN64). The computational support for this work was provided by Center for HPC, Shanghai Jiao Tong University.


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Table of Contents

0

graphene nanocone

V4 V6 V8 V10

Free energy(kBT)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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V10

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Physical and morphological properties of graphene nanocone with 60° apex angle and different tip curvatures. 214x91mm (120 x 120 DPI)


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Physical and morphological properties of graphene nanocones with circular hydrophilic functionalization. 220x108mm (120 x 120 DPI)


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Physical and morphological properties of graphene nanocones with radial hydrophilic functionalization. 220x109mm (120 x 120 DPI)


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Schematic representations of the coarsed grained graphene nanocone and lipid bilayer 66x57mm (120 x 120 DPI)


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Schematic representation of the thermodynamic integration approach used in the interaction force and free energy analysis. 200x165mm (120 x 120 DPI)


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The interaction force change as a function of the distance between the tip of graphene nanocone and the upper surface of bilayer when a graphene nanocone with apex 60o and height 10rc pierces into a lipid bilayer. (A-E) The simulation results when the graphene nanocones penetrate into the cell membrane at different positions. 150x114mm (120 x 120 DPI)


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The evolution of free energy as a function of the distance between the tip of nanocone and the upper surface of lipid bilayer during the penetration of nanocone across the lipid bilayer. Position C is the energy favorable position of graphene nanocone. Time sequences of CGMD simulation results show that the graphene nanocone located at position A (0.6 rc) and B (13.9 rc) can automatically penetrates the cell membrane and equilibrium at the position C without external force. 150x114mm (120 x 120 DPI)


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The breakthrough force for indentation of graphene nanocones with different tip curvatures across cell membrane. The black line denotes the case that the penetration of nanocone across a suspended lipid bilayer and the red line represents the situation of supported membrane. (A-H) The snapshots taken from the simulated penetration process of graphene nanocones with different tip curvatures. 168x161mm (120 x 120 DPI)


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The breakthrough force change as a function of the height of graphene nanocone when graphene nanocones with apex 60o piercing into a lipid bilayer. The simulation results show the graphene nanocones with different heights have broken through the lipid bilayer: (A)5rc; (B)7rc; (C)10rc; (D)15rc. 150x114mm (120 x 120 DPI)


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The free energy change as a function of the distance between the tip of graphene nanocone and the upper surface of bilayer when graphene nanocones with apex 60o and different heights pierce into a lipid bilayer. The lowest points of energy valley are shown as (A-E). 150x114mm (120 x 120 DPI)


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The evolution of free energy as a function of the distance between the nanocone tip and the upper surface of bilayer. The equilibriumed configuration of graphene nanocone with different surface functionalized patterns: (A) Apex, (B) Edge, (C) Phob4, (D) Phil4. 168x114mm (120 x 120 DPI)


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The free energy changes as a function of the distance of the nanocone tip and the upper surface of bilayer. The simulation results show the disruption of cell membrane. (A) V4; (B) V6; (C) V8; (D) V10. 200x114mm (120 x 120 DPI)


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The breakthrough force and free energy change of the graphene nanocones with different bending stiffness when the graphene nanocone pierces the lipid bilayer. (A)The breakthrough force as a function of bending stiffness of few-layer graphene. (B)The free energy change as a function of the distance of the nanocone tip and the upper surface of bilayer. 269x114mm (120 x 120 DPI)


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Indentation of Graphene-Covered Atomic Force Microscopy Probe

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