Receptor-Mediated Endocytosis of Two-Dimensional Nanomaterials

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Receptor-Mediated Endocytosis of Two-Dimensional Nanomaterials Undergoes Flat Vesiculation and Occurs by Revolution and Self-Rotation Jian Mao, Pengyu Chen, Junshi Liang, Ruohai Guo, and Li-Tang Yan ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.5b07036 • Publication Date (Web): 07 Jan 2016 Downloaded from http://pubs.acs.org on January 8, 2016

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Receptor-Mediated Endocytosis of Two-Dimensional Nanomaterials Undergoes Flat Vesiculation and Occurs by Revolution and Self-Rotation

Jian Mao,† Pengyu Chen,† Junshi Liang, Ruohai Guo and Li-Tang Yan*

Key Laboratory of Advanced Materials (MOE), Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China

*Corresponding Author: [email protected] †

These authors contributed equally.

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Abstract: Two-dimensional nanomaterials, such as graphene and transitional metal dichalcogenide nanosheets, are promising materials for the development of antimicrobial surfaces and the nanocarriers for intracellular therapy. Understanding cell interaction with these emerging materials is an urgent-important issue to promoting their wide applications. Experimental studies suggest that two-dimensional nanomaterials enter cells mainly through receptor-mediated endocytosis. However, the detailed molecular mechanisms and kinetic pathways of such processes remain unknown. Here, we combine computer simulations and theoretical derivation of the energy within the system to show that the receptor-mediated transport of two-dimensional nanomaterials, such as graphene nanosheet across model lipid membrane, experiences a flat vesiculation event governed by the receptor density and membrane tension. The graphene nanosheet is found to undergo revolution relative to the membrane and, particularly, unique self-rotation around its normal during membrane wrapping. We derive explicit expressions for the formation of the flat vesiculation, which reveals that the flat vesiculation event can be fundamentally dominated by a dimensionless parameter and a defined relationship determined by complicated energy contributions. The mechanism offers an essential understanding on the cellular internalization and cytotoxicity of the emerging two-dimensional nanomaterials.

KEYWORDS: receptor-mediated endocytosis, two-dimensional nanomaterial, transmembrane transport, graphene nanosheet, flat vesiculation, theoretical analysis

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Two-dimensional (2D) nanomaterials, such as graphene and transition-metal dichalcogenides (TMDCs), have attracted intense attention because of their extraordinary properties that make them suitable materials for a wide range of technological applications.1-5 In particular, great promising has recently been found for the applications of such emerging nanomaterials in nanomedicine.6-16 The graphene with 2D shape and ultra-small size (down to 100nm and below) has been widely used to develop nano-devices or nano-agents for disease diagnosis9 and therapy10,11 as well as antibiotics.12 Owing to the similarities in the morphology and properties between graphene and TMDCs, the success of graphene encourages the exploration of TMDCs for nanomedical applications. Up to now, a few reports have highlighted the remarkable advantages of TMDCs in nanomedicine, such as MoS2-based DNA sensors,13 photothermal therapy with MoS214 or Bi2Se315 nanosheets, and drug delivery with PEGylated MoS2.16 The major challenge and current limitation in this area are clarifying the way cells interact with 2D nanomaterials because it is related to the safer biomedical diagnostics and therapies as well as to their health and environment impacts. However, owing to the intrinsically high complexity of such interactions,17,18 the essential mechanism and detailed kinetics for the transmembrane transport of 2D nanomaterials have not yet been established. Experimental evidences published so far suggest that the cellular uptake of 2D nanomaterials such as graphene nanosheet (GN) favors the mechanism of receptor-mediated endocytosis.19-21 Yet the detailed kinetics and endocytic pathways of this process remain unclear because it occurs on a length scale of tens of nanometers and a timescale of submillisecond and is thus very difficult to be 3


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measured in a single cell.17,18,22-30 When experiments encounter difficulties, tailored computer simulations as well as theoretical analysis offer alternative approaches to identify the process of interest.23-26 In the present study we use a combination of coarse-grained (CG) molecular simulations and theoretical derivation based on energy analysis to describe the mechanism and kinetic pathway of the receptor-mediated endocytosis of graphene, as the most well-known 2D nanomaterial. Our simulations show for the first time that the receptor-mediated transport of 2D nanomaterials across model lipid membranes experiences an event of flat vesiculation that is governed by the receptor density and the membrane tension. The simulations also present the accurate kinetic pathway of such processes and reveal the revolution and unique self-rotation of the 2D nanomaterial during membrane wrapping. In addition to the simulations, we rationalize the endocytic pathway and the complex rotation behaviors of the 2D nanomaterial through systematic analyses of energy based on the theoretical models developed by us. The findings may serve as a foundation for the future development of such emerging nanomaterials for widespread nanomedical applications.

Results and Discussion Flat vesiculation in receptor-mediated transmembrane transport of 2D nanomaterial Here, we use a mesoscopic simulation technique, dissipative particle dynamics (DPD),31 that is a CG method, includes explicit solvent particles, and faithfully reproduces all key properties of self-assembling fluid bilayer membrane and the interactions between membrane and nanoparticles on the time scale of tens µs and the length scale of tens nanometers meaningful 4


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for the membrane vesiculation.23,25,28,32,33-35 To gain insight into the cellular internalization mechanism and the detailed kinetic pathway, we focus on the simulations of the interactions between a single GN of a certain oxidization degree and a 56×56nm2 planar membrane patch of 10,000 lipids and receptors over 60µs. The simulation includes a population of diffusible membrane-bound receptor molecules because experimental studies have proved that membrane receptors such as Fcγ receptor play a significant role in the transmembrane transport of GN.19 Further details on the simulation method and the molecular models of lipid, receptor and GN are given in Methods and Supplementary Information (Supplementary Fig.S1). Each GN is initially positioned above the membrane surface by about 10.0nm, with its basal plane parallel to the membrane. We examine the interaction states between lipid bilayer membrane and GN by systematically considering different conditions, such as receptor density, lateral size of nanoparticle, and surface tension of membrane, etc. For clarity, we summarize all the interaction states in Fig.1 at the beginning, and the detailed condition to each state is listed in the caption. In order to study endocytosis that is not receptor limited, we begin with a membrane of a high receptor density fR=0.5. Fig.2a presents the result of the simulation in which a GN with edge length lg=7nm interacts with a tensionless membrane. The receptors tend to aggregate around the GN owing to binding affinity, which pulls the membrane pieces to diffuse towards the both basal planes of the nanosheet. A partial wrapping state of GN is thereby induced where the GN-membrane complex remains uncapped at the top and bottom edges of the nanosheet. Recalling that three-dimensional (3D) nanospheres with a larger size are easier to be fully wrapped,36,37 we first enlarge the size of GN in order to reach a vesicle-enclosed structure that is 5


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an essential process in the endocytosis. The unique 2D geometry of graphene however makes this endeavor more difficult. Increasing lg to10.5nm and more never changes the partial wrapping state of such a 2D nanomaterial (Fig.2b).

a

b

c

d

e

f

g

h z x

Figure 1. a, Hemisphere vesicle formed (HS) at GN size lg=14nm, membrane tension σ =0, and receptor density fR=0. b, Grapheme-sandwiched structure (GS) at lg=10.5nm, σ =0.75 k BT / rc2 , and fR=0. c, Lying across membrane (LA) at lg=3.5nm, σ =0, and fR=0. d, Adhering to membrane surface (AM) at lg=7nm, σ =0.75 k BT / rc2 , and fR=0.5. e, Membrane rupture

(MR)

at lg=7nm, σ =2.09 k BT / rc2 , and fR=0.5. f, Incomplete flat vesicle (IFV) at lg=7nm, σ =0, and fR=0.5. g, Flat vesicle (FV) at lg=7nm, σ =-0.65 k BT / rc2 , and fR=0.5. h, The symbols and corresponding states. The colors of yellow, blue, and red indicate the beads of the unoxidized basal plane, the oxidized edge, and the oxidized basal plane of GN. The head beads of amphiphilic lipids are shown in pink, the tail beads in cyan, and receptor beads are green. Only the cross-sectional view of the lipid membrane around the GN is shown in each snapshot. Solvent beads are not shown for clarity.

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a

f

d

b

c z

e

y

g

h

x

Figure 2. a, At edge size lg=7nm, the GN is partially wrapped by the tensionless membrane of receptor density fR=0.5. b, At lg=10.5nm, the GN is also partially wrapped by the tensionless membrane with fR=0.5. c, At lg=7nm, the GN is fully wrapped by a tense membrane with negative surface tension, i.e., σ =-0.65 k BT / rc2 , and fR=0.5. d, An enlargement of the flat vesicle marked by the red square in c. e, Scheme showing the vertical and parallel cross-sectional views of the flat vesicle. f, Flat vesicles seen in the electron micrograph of the receptor-mediated cellular internalization of GNs (scale bar, 200nm. Reprinted from ref.19 with permission of authors and publishers; copyright 2012, Elsevier). g, The legend of h. The representative structure of each state can be found in Fig. 1. h, A two-dimensional state diagram characterizes the interrelated effects of GN size and membrane tension on the equilibrium states of the GN interacting with the bilayer membrane of fR=0.5. Data points are drawn as small symbol illustrated by g. Symbols are colored and grouped according to the states.

Living cells can regulate their membrane area through active mechanisms,38 such as the contraction of the membrane-associated actomyosin cytoskeleton,39,40 which often leads to the contracted membrane with negative surface tension prompting the endocytosis process. Indeed, the GN with lg=7nm becomes fully wrapped when the surface tension of the membrane, σ, is reduced to -0.65 kBT/rc2 (Fig.2c). A close examination of the vesicle-enclosed structure reveals that the vesicle presents unique flat shape, as highlighted by the enlarged structure in Fig.2d and 7


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the schematic diagram in Fig.2e. To the best of our knowledge, such a flat vesicle-enclosed structure has not been reported in previous simulation studies of the transmembrane transport of 0-dimensional (0D),41 one-dimensional (1D),42 and 3D32 nanoparticles, and may be a characteristic structure in the endocytosis of 2D nanomaterials. Indeed, in light of the simulation results the similar structure can be identified from some previous experimental results yet this important structure has not been paid attention and its role in the cellular internalization of 2D nanoparticles has not been elucidated.19,21 As an example, Fig.2f shows the flat-vesicle like structure in the endocytosis of GN mediated by the Fcγ receptor, where the membrane tightly adheres to the both lateral sides of the wrinkled GN.19 We expect the flat vesicle to become further experimentally refined as additional characterizations advance. We systematically compute the receptor-mediated interaction states between GN and membrane as a function of lg and σ, allowing us to construct a diagram of the interaction states related to these both parameters (Fig.2h). As ultra-small sizes of nano-graphene (down to 10nm and below) may offer interesting behaviors in biological systems,6,10 small GNs with size near 10nm are focused in the present work. The representative states indicated by the symbols in Fig.2h are listed in Fig.1, and the shaded regions in the state diagram approximately discriminate the characteristic regions. The incomplete flat vesicle as demonstrated by Fig.2a occurs when σ is reduced to 0.75 kBT/rc2 whereas the critical σ for the formation of the complete flat vesicle needs to be further decreased to -0.56 kBT/rc2. Clearly, small surface tension is prone to induce vesicle-like structures.

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b

a

r1

Figure 3. Energy analysis for the capping process from an incomplete flat vesicle to a complete flat vesicle. a, The local structure of the incomplete flat vesicle. Here the GN is partially wrapped by a tensionless membrane. b, The local structure of the flat vesicle, where the GN is fully wrapped by a tense membrane with negative surface tension. r1 is the curvature radius of the semicylindrical cap.

To clarify the effect of membrane tension on the capping process from an incomplete flat vesicle to a complete flat vesicle, we provide an energy analysis for the wrapping states in the flat vesiculation of the GN. The local capping process is driven by the tension energy but however is opposed by the bending energy of the membrane. According to the classical Canham-Helfrich theory, the bending energy per unit area can be described by43

1 2 ebend = κ ( c1 + c2 − c0 ) + κ ′c1c2 2 where κ and

(1)

κ ′ are the bending modulus with units of energy, kBT. c1 and c2 are the local

principal curvatures of the two-dimensional membrane surface. c0 is the spontaneous curvature of the membrane. Here c0=0 is assumed for a symmetric membrane44 and the second term in Eq.(1) is dropped because no topological changes will be considered.45 As shown in Fig.3, the

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local cap caused by membrane deformation is taken as a semicylindrical structure in our energy analysis. Therefore the local principal curvatures and the bending energy per unit area of the semicylindrical cap, ecb , can be given by

c1 =

1 , c2 = 0 . r1

(2)

1 1 κ ecb = κ ( + 0)2 = 2 2 r1 2r1

(3)

where r1 is the curvature radius of the semicylindrical cap. Thus we can get the bending energy Ecb of the two semicylindrical caps of one vesicle as follow

Ecb = 2(

κ 2 1

2r

) S semi =

κ Ssemi r12

.

(4)

Here Ssemi is the area of one cap. The negative surface tension energy Ecs caused by the two excess caps can be described by

Ecs = 2σ S semi

(5)

where σ is the surface tension energy per unit area. The capping process can advance spontaneously only if the total energy Ect of the two semicylindrical caps is negative, which means the following equation must be satisfied:

Ect = Ecb + Ecs = (

κ r12

+ 2σ ) S semi < 0

(6)

namely

σ 0.6) turns to keep the GN adhering to the membrane surface owing to a strong binding affinity. For the membrane without receptor, reducing the surface tension can never lead to the flat vesicle-like structure (Fig.4b), revealing again the key role of membrane receptors in the endocytosis of 2D nanomaterials.

Kinetic pathways and complex rotation behaviors of the 2D nanomaterial To understand the kinetic mechanism of the receptor-mediated transmembrane transport of the 2D nanomaterial, we become interested in the fundamental question of what is the detailed pathway of a flat vesiculation event of a GN. A typical simulated event towards an incomplete flat vesicle is shown in Fig.5a1-a8, where a GN with lg=7nm interacts with a tensionless membrane of fR=0.5. More detailed process can be found in Supplementary Video S1. Further information about the GN orientation relative to the membrane during this process can be revealed by examining its entry angle, φ , defined as the dihedral angle between the GN surface and the surface parallel to membrane (Fig.5c). Combining Fig.5a1-a8 and c, we find that the GN orientation during the receptor-mediated translocation process can be divided into four characteristic stages as denoted by the dashed lines and schemed by the insetting diagrams in Fig.5c. In the first stage, the GN is not captured by the membrane and thereby does not take a predominant orientation. In the second stage, the GN pierces the membrane through one of its corner sites while its orientation spontaneously takes a predominant entry angle at about

φ ≈ 45o and keeps the pose during the piercing process (Fig.5a2 and a3). Previous simulation 13


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indicated that the orthogonal orientation with φ =90o exhibits the lowest energy when a GN pierces a model membrane without receptor.30 Our simulation demonstrates that the strong binding affinity from the membrane receptors can modify the entry angle towards a degree where the adhesion energy contributed by the receptors can be balanced by the energy arisen from the confinement on the thermal motions of both membrane and graphene (decreasing the entropy of the system). In the third stage shown by Fig.5a4, a rotation of GN is observed which pulls apart the membrane into two pieces moving to opposite directions as denoted by the red arrows. A local energy analysis reveals that the rotation of the GN in this stage can be fundamentally attributed to the hydrophobic attraction of lipid tails with the GN (Supplementary Information SI-3). Indeed, rotating GN from φ =45o to 40o leads to a significant decrease of energy with about 13 kBT at lg=7nm. However, the GN cannot rotate further along this direction, but rather turns to the reverse direction in the last stage (Fig.5a5-a8). One can find from the slices that the segregated membrane pieces respectively diffuse to the two basal planes of the GN along opposite directions, leading to a torture prompting the rotation of the GN towards almost vertical alignment. To clarify the role of the receptor in such a behavior of laying down to stand up, we calculated the coordination number, Nr, defined as the average number of lipid beads interacting with a graphene bead, and a smaller Nr corresponds to a lower covering degree of graphene nanosheet by lipid molecules but a higher by the receptors.47 The time-dependent plot of Nr in Fig.5d indicates that more and more receptors diffuse to the planes of the GN in the last stage, which spontaneously drives the membrane pieces to wrap the nanosheet. Despite the large membrane deformation owing to the negative membrane tension, these four characteristic stages can still be identified in the simulation event towards a complete flat vesicle where lg=7nm, σ=-0.65 kBT/rc2 and fR=0.5 (Fig.5b1-b8). Fig.5b1-b4 are representative 14


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snapshots presenting these four successive stages in the event. In addition, Fig.5b5-b8 shows the detailed pathway of the capping process from an incomplete flat vesicle to a complete flat vesicle (see Supplementary Video S2 for more details). The calculation for the time-dependence of Nr in this case demonstrates again that the driving force pulling the membrane pieces to wrap the GN is contributed by the in-plane diffusion of receptors (Supplementary Fig.S4).

b1

b2

b3

b6

b5

b4

c1

c2

c3

30

c6

c5

c4

20

z

a 100 Self-Rotation Angle, ω(°)

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90 80 70 ω

60 50 40

25 30 35 40 45 50 55 60 65

y

Time(µs)

Figure 6. a, The time dependence of self-rotation angle, ω , of the GN in the vesiculation event demonstrated by the snapshots of b1-b6 (red) and the vesiculation event demonstrated by the snapshots of c1-c6 (green). The inset is the scheme showing the definition of ω where the cyan cylinder denotes the direction along y-axis and the pink cylinder at the GN center the normal direction of the basal plane of GN. The red arrow indicates the self-rotation of GN around the pink cylinder. b1-b6, Successive stages of a vesiculation event where GN with lateral size lg=7nm is partially wrapped by a tensionless membrane. The times of the snapshots are: b1, 23.10µs; b2, 26.18µs; b3, 30.80µs; b4, 36.95µs; b5, 46.20µs; and b6, 53.90µs. c1-c6, Successive stages of a vesiculation event driven by the GN on a tense membrane with surface tension σ =-0.65 k BT / rc2 . The times are: b1, 26.18µs; b2, 30.80µs; b3, 38.50µs; b4, 40.80µs; b5, 44.65µs; and b6, 60.05µs. In

b1-b6 and c1-c6, the receptor density of the membrane is set as fR=0.5. Only the y-z cross section view of the lipid membrane around the GN is shown in each snapshot. The red arrows denote the self-rotation directions of GN. Solvent beads are not shown for clarity. 15


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Rotation towards vertical alignment has also been reported in simulations of the interactions

between

lipid

membrane

and

1D

nanomaterial42,48

or

anisotropic

3D

nanomaterials.32,49,50 In addition to such a revolution behavior (rotation relative to the membrane), it is interested to find that the 2D geometry can induce unique self-rotation of a 2D nanomaterial where the nanosheet rotates around the axis normal to the center of its basal plane. In Fig.6a we show the time-dependent behaviors of the self-rotation angle, ω, defined as the insetting scheme, for the two flat vesiculation events referred in Fig.5. The clockwise and anticlockwise self-rotational processes of the GN can be definitely identified from the plots as well as the snapshots in Fig.6b1-b6 and c1-c6. More detailed self-rotational pathways of GN in these both events can be seen in Supplementary Figs. S5, S6 and Videos S3, S4. Despite of the different rotational directions for these both events, all the self-rotation behaviors finally lead to the parallel orientation of one GN edge to the membrane plane. The localized corner piecing for entry initiation leads the GN diagonal to become the potential path for the membrane wrapping in the flat vesiculation. The self-rotation of GN can significantly reduce such a long path distance as the edge length of the square GN is shorter than its diagonal. It is not difficult to anticipate that the self-rotation is a crucial and indispensable behavior in the transmebrane transport of noncircular 2D nanomaterials. It has been demonstrated that the receptor density can greatly affect the rotation of 1D nanomaterials.42 To elucidate the effect of this factor on the rotation of 2D nanomaterials, the detailed kinetic pathway of the receptor-mediated translocation process is examined at various receptor densities. We find that the rotation behaviors of GN are very similar with those demonstrated in Figs. 5 and 6 when the receptor density is a bit smaller or larger. However, significantly changing the receptor density does lead to modified rotation behaviors (Supplementary Fig. S7). In particular, without receptor, the first three stages, i.e., capturing, piercing, and pulling apart, are the same with those at fR=0.5 (Fig. S7a1-a5). However, the reverse 16


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rotation at the last stage does not occur due to the lacking of the driven force originating from the receptor-GN binding. Instead, the GN inserts into the center of the bilayer membrane, causing the graphene-sandwiched superstructure (Fig. S7a6-a8). In sharp contrast, at a very high receptor density with fR=0.9, the GN is arrested by the receptors on the membrane at the initial piercing (Fig. S7b1-b3). The piercing and following stages are absolutely suppressed as the GN keeps a state adhering to the membrane surface (Fig. S7b5-b8).

4

h (nm)

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6

8

lg (nm)

10

12

14

0

5

2

-150

4

-300 (kBT )

6 8

a1

φ

a2 h

hH 2hT

10

Figure 7. GN-bilayer interaction energy versus GN size and piercing distance. The inset is the scheme showing the initial state (a1) and the final state (a2) of the whole piercing process. hH and

hT are the thicknesses of the head and the tail groups in the lipid monolayer respectively. h is the piercing distance of the GN tip and φ represents the revolution angle relative to the membrane plane.

Energy analyses reveal the fundamental mechanism To gain a refined picture of the fundamental mechanism of the flat vesiculation, we next perform energy analyses for the piercing and wrapping stages in this event. A key issue dominating the piercing of a 2D nanomaterial is the origin of such a passive process. To address this issue, the interaction energy change is calculated when a square GN with entry angle φ =45o 17


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inserts into a membrane through its corner site, as schemed by the insetting diagrams of Fig.7. By combining a series of piecewise functions, we develop the numerical model accounting for all the possible regimes in the piercing process (see Supplementary Information SI-4). Fig.7 presents the interaction energy landscape, plotted by the colored contour map, with respect to lg and the piercing distance, h. An energy barrier of about 5.6kBT can be identified from the figure at the initial corner piecing, in excellent agreement with 5kBT from the all-atom molecular dynamics simulations.30 Our analysis further indicates that such an energy barrier remains with respect to various lg. The blue region at the right bottom clarifies that at the very last regime a larger GN induces a deep energy valley with negative values (even -300 kBT) owing to the hydrophobic attraction between lipid tails and the plane of GN, which accounts for the necessary driving force for the insertion of the 2D nanomaterial. Fig.7 also implies that the insertion of a larger GN may be easier than a smaller one in view of the deeper energy valley of the larger GN. We also develop an analytical model based on local energy to complement the simulations of the wrapping process in the flat vesiculation event and to determine the critical condition for the formation of an incomplete flat vesicle as shown in Fig.2a, because the incomplete flat vesicle is the indispensable precursor of a complete wrapping state. The kinetic pathway in Fig.5a1-a4 has demonstrated that the hydrophobic attraction between lipid tails and the unoxidized basal plane of GN drives the piercing and rotating of the GN. The unwrapping structure then evolves into an incomplete flat vesicle with the diffusion of the membrane pieces towards both sides of the GN, which is pulled by the strong binding affinity of the membrane receptors to the GN. However, such diffusion will induce membrane deformation near the GN, generating bending energy gain that opposes the wrapping process. Clearly, the wrapping process 18


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in the flat vesiculation event is dominated by three energy contributions: the GN-bilayer interaction energy, the receptor-GN adhesion energy and the bending energy of the deformed membrane. To elucidate the details about how these energy items contribute to the event, a theoretical model is developed to analyze the energy difference from unwrapping state to the incomplete flat vesicle shown in Fig.8.

b

a

φ

θ

r

Figure 8. The 3D schematic illustrations of the unwrapping state and the incomplete flat vesicle in the flat vesiculation event. a, The schematic diagram of the unwrapping state where the pink arrows indicate the diffusion directions of the membrane pieces because of the strong receptor-GN binding affinity. b, The schematic diagram of the incomplete flat vesicle. φ denotes the GN entry angle. θ indicates the arc of the curved membrane near GN and r is the local curvature radius.

According to the energy analysis in SI-3, the GN-bilayer interaction energy of the unwrapping state can be calculated by

Eui = −8hH kT (1 − 2ϕ )

1 sin 2 φu

(

)

2lg sin φu − hH .

(8)

where kT is the interaction energy density of lipid tails with unoxidized basal plane of GN ( kT < 0 ) and φu represents the entry angle of the unwrapping state. As displayed in Fig.8b, the membrane pieces deform along a cylindrical trajectory when they diffuse onto the surfaces of the GN. For the incomplete flat vesicle, based on Eq. (3), the bending energy per unit area of the

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curved membrane near GN is κ 2r 2 where r is the local curvature radius. The area of the curved membrane can be given by

Scur = rφv l g

(9)

where φv and θ v represent the GN entry angle and the arc of the curved membrane near the GN respectively. It can be not difficult to find that φv is equal to θ v in view of the dashed lines in Figure 8. Combining the equations (3) and (9), we can thereby get the bending energy of the two membrane pieces, Evb, as follow

Evb = 2(

κ 2r

2

) Scur = 2(

κ 2r

2

)(rφvlg ) =

κφv lg

(10)

r

The adhesion energy Eva between GN and receptors can be described by

Eva = 2k R lg 2 .

(11)

Here kR is the interaction energy density of the GN with the receptors (kR 0 in Eq. (13), meaning that, if ∆E . kT l g 2 sin 2 φu

(14) 20


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This leads to a critical point of kR/kT,η0 , as follow

η0 =

4hH (1 − 2ϕ )

(

2lg sin φu − hH

)

(15)

lg sin φu 2

2

where η0 is a dimensionless parameter. For k R kT < η0 , the energy difference is ∆E > 0 , indicating that the flat vesiculation will never occur because the driving force from the receptor-GN binding affinity is too low to overcome the hydrophobic attraction between lipid tails and the unoxidized basal plane of GN. For k R kT > η0 , the flat vesiculation can advance which however is opposed by the bending energy from the curved membrane near the GN. In this case, if ∆E

κφv

2lg kT ( k R kT ) − η0 )

.

(16)

This gives the following boundary condition between the regions of the unwrapping state and the incomplete vesicle at k R kT > η0 ,

r (k R kT ) =

κφv

2l g kT ( k R kT − η0 )

(17)

The plots in Fig.9 are obtained based on this r-kR/kT relation andη0 . Our analysis reveals that the receptor-mediated flat vesiculation is dominated by the ratio kR/kT where kR is the receptor-GN adhesion energy density and kT is the energy density of the interactions between lipid tails and the unoxidized basal plane of GN. Interestingly, the dependence of the flat vesiculation on kR/kT can be separated into three characteristics regions based on a dimensionless parameter η0 defined as Eq.(15) (Fig.9). Below η0, the flat vesiculation will never occur because the driving force from the receptor binding is too low to overcome the hydrophobic attraction between lipid tails and GN. Beyond η0, the flat vesiculation can advance which however is opposed by the bending 21


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energy from the curved membrane near the GN. This leads to a critical relationship between kR/kT and the local curvature radius of the membrane, r, as defined by Eq.(17). The red plot in Fig.9 presents this r-kR/kT relation consisting of the transition boundary between regions II and III. The flat vesiculation can only occur in region III because additional energy barrier from the curved membrane can be effectively overcome by the receptor-GN adhesion energy. The dimensionless parameter η0 and the defined r-kR/kT relation allow effective approaches to control the flat vesiculation in the endocytosis of 2D nanomaterials.

r

r

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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I

0

II

η0

III

kR/kT

Figure 9. Flat vesiculation is dominated by a dimensionless parameter and a defined relationship determined by complicated energy contributions. kR is the receptor-GN adhesion energy density and kT is the interaction energy density of lipid tails with unoxidized basal plane of GN. η0 is the critical point of kR/kT below which the formation of flat vesicle is impossible. r is the local curvature radius of the membrane, as indicated by the insetting scheme. The red line represents the bound beyond which the formation of flat vesicle is possible. The blue dot line at kR/kT=η0 and the red line separate the phase diagram into three regions, as marked by different colors and I, II and III. For the present simulations, we take typical parameter values lg=7nm, ϕ =0.3,

kT = −7 k BT / nm 2 , and hH =0.5nm. As shown in Fig.5a5-a8, φu and φv can be taken 22


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as 40° and 50° respectively. Thus we can getη0 = 0.23 and

r (k R kT ) = 0.18 ( k R kT − η0 )

(18)

where r has the same unit with lg. Eqs. (15) and (17) indicate that the three regions in Fig.9 can be modified by changing the parameters in them such as lg. Indeed, as demonstrated in Fig.10, reducing lg from 7nm to 3.5nm can increase the value of η0 from 0.23 to 0.42 but evidently decrease the area of region III, demonstrating the robustness of η0 and the r-kR/kT relation in the control of the vesiculation event.

8

6

r (nm)

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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4

2

0 0.0

0.5

1.0

kR/kT

1.5

2.0

Figure 10. The effect of the GN edge length on the dimensionless parameter η0 and the boundary condition of r. The dot and solid lines indicate the point of η0 and the boundary condition of r respectively. The GN edge length lg=7nm (red), lg=5nm (green), and lg=3.5nm (blue).

Conclusions In summary, by combining CG simulations and systematic energy analysis, we have established the essential mechanism and detailed kinetics for the receptor-mediated 23


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transmembrane transport of the graphene nanosheet. Considering the universal capabilities of the simulation models and the theoretical approaches, the results could be generalized to all the 2D nanomaterials. Thus, this information points towards the possible nature of the endocytosis of 2D nanomaterials: a flat vesiculation process governed by both the receptor density and the membrane tension that is regulated by living cells through active mechanisms. The detailed pathway of a flat vesiculation event presents a delicate cooperation between lipid membrane and the 2D nanomaterial, and is characterized by a revolution of the nanosheet relative to the membrane and, particularly, by a unique self-rotation around its normal during membrane wrapping. Energy analyses reveal that the flat vesiculation event can be fundamentally dominated by a dimensionless parameter η0 and a defined relationship determined by complex energy contributions as stated in the text. Such a η0–dependent flat vesiculation behavior is ubiquitous in the receptor-mediated transmembrane transport of 2D nanomaterials, and could suggest a useful guideline for controlled cell delivery of these nanomaterials. The universal nature of the findings provides fundamental insights into the transmembrane transport and cytotoxicity of 2D nanomaterials, and may serve as a foundation for the future development of such emerging nanomaterials for widespread nanomedical applications.

Methods Coarse-grained molecular simulations in this paper are on the basis of DPD.31 The model of the amphiphilic lipid is constructed by a head group with three hydrophilic beads and two tails consisting of three hydrophobic beads. The receptors are modeled as the same as the lipids except having a different GN-receptor attractive head group.42 Before contact with nanomaterials, the receptors are distributed uniformly, with a low density, on the cell membrane. Once the 24


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interaction starts, the local reduction in free energy caused by the nanomaterial-receptor binding drives receptors towards the contact zone by diffusion. 36 This finally results in a high level of receptors in the contact site and the vicinity of the nanomaterials. Hence, we focus on the case where the number of receptors is relatively high in order to study endocytosis that is not receptor limited.26,42 Initially, 10,000 lipids and receptors with various densities self-assemble into a lipid bilayer membrane spanning the simulation box. As the present work focuses on the kinetics and endocytic pathways of receptor-mediated endocytosis for 2D nanomaterials, a sparsely oxidized GN is used as an example in the present simulations, which is constructed based on the typical structure model representing outcomes from standard oxidization processes.51,52 In this oxidized GN model, there are high correlations in oxidation sites due to the fact that a carbon atom on some broken π bond may be oxidized with much higher probability than its counterpart with an intact π bond. Actually, the oxidized degree of GN may affect the interaction behaviors, and the theoretical analysis and our previous work47 can provide useful insight into this aspect. The modulus of the GN model is calibrated according to the experimentally found elasticity of graphene.47,53 To prevent the passage of fluid beads through the GN, an additional bounce-back boundary condition is imposed on the GN surfaces.54 Surface tension of the membrane is controlled by a widely used approach, that is, N-varied DPD method.33,48,55 The size of our simulation box is 80 × 80 × 40rc3 and periodic boundary condition in all directions is taken into account, where rc=0.7 nm is the cutoff distance. The total physical time of each simulation is over 60µs (4 × 105 time steps). More details on the simulation method and the molecular models of lipid, receptor and GN are given in Supplementary Information. 25


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Supporting Information Available: The additional simulation results and videos. This material is available free of charge via the Internet at http://pubs.acs.org.

Acknowledgements The authors thank Guanghui Ma and Hua Yue for proving the original image of the experimental observation, and Bojun Dong, Zihan Huang, Ye Yang and Guolong Zhu for helpful discussions. This work is supported by the National Natural Science Foundation of China under grant nos.51273105, 21422403, and 21174080.

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Graphic Abstract

33


Receptor-Mediated Endocytosis of Two-Dimensional Nanomaterials

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