Membrane Wrapping Pathway of Injectable Hydrogels: From Vertical

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Biological and Environmental Phenomena at the Interface

Membrane Endocytosis Pathway of Injectable Hydrogels: from Vertically Capillary Adhesion to Laterally Compressed Wrapping Xianyu Song, Chongzhi QIAO, Teng Zhao, Bo Bao, Shuangliang Zhao, Jing Xu, and Honglai Liu Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b01395 • Publication Date (Web): 11 Jul 2019 Downloaded from pubs.acs.org on July 17, 2019

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Graphic abstract

By means of large-scale computational simulations, the membrane internalization of injectable hydrogels was studied, and this complicated process transforms from vertically capillary adhesion to laterally compressed wrapping.

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1

Membrane Wrapping Pathway of Injectable Hydrogels: from Vertical Capillary

2

Adhesion to Lateral Compressed Wrapping

3

Xianyu Song1, Chongzhi Qiao1, Teng Zhao1, Bo Bao1, Shuangliang Zhao1,*, Jing Xu1, and

4

Honglai Liu2,*

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1

State Key Laboratory of Chemical Engineering and School of Chemical Engineering, East

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China University of Science and Technology, Shanghai, 200237, China

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2

8

Engineering, East China University of Science and Technology, Shanghai, 200237, China

State Key Laboratory of Chemical Engineering and School of Chemistry and Molecular

9 10 To whom correspondence should be addressed. Email: [email protected] (SZ) or

11

*

12

[email protected] (HL)

13 14 15 16 17 18 19 20 21

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Abstract

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Membrane wrapping pathway of injectable hydrogels (IHs) plays a vital role in the

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nanocarrier effectiveness and biomedical safety. Whereas considerable progress in

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understanding this complicated process has been made, the mechanism behind this process

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has remained elusive. Herein, with the help of large-scale dissipative particle dynamics

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simulations, we explore the molecular mechanism of membrane wrapping by systematically

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examining the IH architectures and hydrogel-lipid binding strengths. To the best of our

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knowledge, this is the first report on the membrane wrapping pathway on which IHs

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transform from vertical capillary adhesion to lateral compressed wrapping. This

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transformation results from the elastocapillary deformation of networked gels and nanoscale

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confinement of bilayer membrane, and it takes long time for the IHs to be fully wrapped

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owing to the high energy barriers and wrapping-induced shape deformation. A collapsed

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morphologies and small compressed angles are identified in the IHs with thick shell or strong

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binding strength to lipids. In addition, the IHs binding intensively to membrane exhibit

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special nanoscale mixing and favorable deformability during the wrapping process. Our study

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provides a detailed mechanistic understanding of the influence of architecture and binding

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strength on the IHs’ membrane wrapping efficiency. This work may serve as rational

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guidance for the design and fabrication of IH-based drug carriers and tissue engineering.

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Keywords: membrane wrapping; injectable hydrogels; lipid membrane; computational

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simulations; elastocapillary deformation

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1. Introduction

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Cell-based therapy is considered to be one of the most booming strategies for treating

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various diseases.1-2 The major challenge in cell-based therapy lies in designing ideal

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nanocarriers to minimize the cytotoxic side effects and deliver the therapeutic cells to target

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sites efficiently and precisely.3 The diverse chemical compositions and elastic network

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structure endow injectable hydrogels (IHs) with unique properties, such as deformability,

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reversibility, self-healing, and stimuli responsiveness, when compared to ordinary rigid

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nanomaterials.

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capable of gelling in situ, and thus they readily integrate with the cell membrane and provide

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a local therapeutic opportunity at the targeted sites. Due to their great value and huge

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potential in application, such as biocompatibility, ease of systemic administration, and

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minimal invasion,6-7 previous studies have demonstrated that IHs could provide a versatile

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platform for biomedical applications, especially for the cell-based therapy.8

4-5

Once penetrating successfully into the cell membrane, the hydrogels are

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By introducing the chemophotothermal agents9-10 and advanced nanomaterials (i.e.,

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nanoparticles,11-12 carbon nanotubes,13 graphene oxide nanosheets14), various synergistic

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therapy strategies were proposed. Notably, there has been inspiring achievements in

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developing IHs for facile cellular encapsulation and controlled delivery toward smart control

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and scalable engineering.5, 15-16 Moreover, these cell-based therapy systems exhibit excellent

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multi-function and high drug loading as well as prolonged drug retention. Nevertheless, there

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is still a lack of molecular understanding of the elastocapillary deformation of the IH systems.

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It has been reported that polymer capsules with weak stiffness were efficiently wrapped by 3 / 31


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the cell membrane,17 and during this process, the membrane perturbation or fluctuation may

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be significantly affected.18 This special membrane wrapping pathway impedes possible

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transmembrane translocation because the energy barriers to be overcome during the

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membrane wrappings is smaller.19

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Besides, the adhesive stability and structure-property relationship of the IHs-membrane

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remain unclear in their apllications. For example, the inability to retain the structural integrity

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after injection limits their applications in the cell-based therapy.20 Recently, Yang et al.4

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found that the morphologies of IHs play a significant role in the invasive process.

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Specifically, the thinning IHs with two-dimensional geometry facilitates its encapsulation by

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a membrane, thereby greatly improving the efficacy of cell-based therapy.21-23 In addition, it

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is helpful to monitor the noninvasive pathway of IHs over time for optimizing the therapeutic

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efficacy and safety,21 and it’s of particular interest to understand the interaction between the

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IHs and membranes, e.g., how the IHs adapt to the surrounding heterogeneous matrix of a

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bilayer membrane, and whether this environment affects the IHs’ targeting and function.

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Though the incorporation of fluorescence dyes into IHs21-22 and in-situ imaging

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technologies23 have been developed to monitor the in-vivo membrane wrapping of IHs, the

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underlying mechanism still remains elusive, which is of great importance towards the

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highly-efficient design of IHs-based drug carriers and tissue engineering.24

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To tackle these problems, large-scale dissipative particle dynamics (DPD) simulations

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are performed to investigate the membrane wrapping pathway of the IHs. With the aid of

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coarse-graining, the specific information regarding the membrane wrapping dynamics of the 4 / 31


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IHs can be obtained over large time scale.25-26 Furthermore, by varying the morphological

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characteristics and hydrogel-lipid binding strength, the membrane wrapping pathway and

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corresponding membrane perturbation are examined.

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2. Simulation method and computational details

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2.1 Coarse-grained models

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DPD method represents a classical coarse-grained simulation, in which a cluster of

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atoms is grouped as one single DPD bead. Specifically, the lipid molecule is coarse-grained

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by simplifying the lipid heads (H bead) and tails (T bead) into hydrophilic and hydrophobic

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beads, respectively. There are different ways of coarse-graining in the existing literature to

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construct lipid membranes including the double-tail model and linear chain model.27-30 Each

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model has its own merits. For example, the linear lipid model was employed to study the

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bilayer properties, vesicle structure, and the drug delivery processes, which showed good

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agreements with experimental observations.31-33 However, Shillcock et al.31 argued that the

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lamellar phase composed of linear chain lipids is highly dependent on the tail stiffness of

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lipid, which may affect the equilibrium structure. Nevertheless, here we adopt the linear chain

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model HT3 in our simulations for reducing the computational cost. Furthermore, the

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employment of this model allows us to describe the experimental process,34 in which the size

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of a single injectable hydrogel ranges typically between 50 nm and 5 m.35 The

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coarse-grained model of lipid and the construction of bilayer membrane are presented in

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Figure 1A. One of the major advantages of the present simulations lies in that a large-scale

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membrane with 114.0×114.0 nm2 should be constructed with sufficient lipid molecules, 5 / 31


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which allows for mimicking the dynamical process of membrane wrapping.

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Figure 1. Schematic representation of computational models for bilayer membrane and IH:

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(A) coarse-grained models of bilayer membrane and single lipid molecule, (B) lateral view

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and (C) half-sectional view of the coarse-grained models of spherical hydrogel capsule. The

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bilayer membrane consists of 28800 lipids. Red beads signify the lipid heads, yellow beads

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represent the lipid tails, and the cyan beads indicate the hydrogel components.

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The hydrogel is coarse-grained by simplifying each polymer monomer into one single

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DPD bead (HY bead) with uniform size  , and these beads are internally connected by

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tetra-functional cross-linkers.36-37 Herein, the bead size  equals to the characteristic length

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scale rc as discussed below. In order to examine the influence of hydrogel architecture on

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the membrane wrapping, two types of hydrogels are designed, namely, the spherical stuffed

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hydrogel and spherical hydrogel capsules with different shell thicknesses.

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By tailoring an ideal diamond cubic crystal structure, a spherical networked hydrogel with the radius Rgel  20 is firstly obtained. Then, the inner core with radius Rs  5 is 6 / 31


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eliminated. The obtained hydrogel capsule is shown in Figure 1B and 1C. The detailed

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fabrication method of hydrogel models can be found in previous studies.36-37 We note that

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this model presents a comparable size with practical hydrogel as stated below. In our

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simulations, the moderate crosslinked hydrogel with the crosslink density  =0.0217 is used,

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where 

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polymer particle and crosslinker particle, respectively.

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2.2 Simulation methodology

is defined as  = N p (N p +N c ) 34 with N p and N c being the numbers of

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Based on the dynamics of soft particles interacting with each other through conservative

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force FijC , dissipative force FijD , and random forces FijR , the time evolution of each DPD

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bead i subject to the total forces Fi follows the standard Newtonian equation of motion:38

Fi  mi

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dvi dr   FijC  FijD FijR , vi  i , dt i  j dt

(1)

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where vi , ri , and mi are the velocity, position, and mass of the 𝑖-th bead, respectively. The

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conservative force is soft-repulsive, and it reads:

FijC  aij (1  rij )rîj ,

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(2)

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where aij is the maximum repulsion force between the bead i and j, rij  ( ri  rj ) rc ,

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rij  rij , and rîj  rij rij . The dissipative force FijD is given as:

FijD  D ( rij )( rîj  vij )rîj ,

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(3)

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where  corresponds to the strength of friction, D ( rij )  (1  rij )2 , and vij = vi - v j . The

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random force is taken as:

FijR  R ( rij )ij rîj ,

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where ij

(4)

represents a zero-mean Gaussian random variable of unit variance, 7 / 31


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2k BT  , where  is the friction

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R ( rij )  1  rij , and  is a noise amplitude and equals to

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factor.39 In addition, the corresponding harmonic force U ijS on the bead pair i and j is given

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as:

U ijS  Cb ( r0  rij )rij ,

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(5)

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where Cb and r0 are the force constant and equilibrium distance, respectively. Herein, Cb =

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50 k BT rc 2 and r0 = 0.7 rc .27

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Meanwhile, the equation of the bond angle potential is given by

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U ijA =Ca (ij  0 )2

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where Ca and 0 are the bending stiffness and equilibrium angle, respectively. Here Ca =

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3.0 k BT and 0 = 180°.27

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2.3 Simulation details

(6)

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Thermoresponsive microgels are among the most investigated stimuli-responsive

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systems in drug delivery applications.40 Poly(N-isopropylacrylamide) (PNIPAM) represents

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one of the thermally sensitive polymers and displays a significant volumetric change at an

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LCST (about 32 ℃ ). With the aids of thermoresponsive hydrogels, drug agents can be

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effectively shielded and protected until reaching a treatment site due to the microgels’

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swelling properties below the LCST, and then release a predefined dosage of the drug within

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a locally heated tumour (about 40~42 ℃ ) because of the collapsed behavior of PNIPAM

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hydrogels above the LCST.41 We have investigated the swelling/deswelling behavior of

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PNIPAM microgels.36-37 Previous studies have demonstrated that PNIPAM chains become

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insoluble in aqueous solutions and tend to aggregate above LCST.42 Thus, the 8 / 31


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PNIPAM-based hydrogels are the hydrophobic state when they locate at the heated tumor and

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penetrate into the membrane. For any two beads of the same type, we adopt the conservative

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parameter aii =25 k BT rc .43 For any two beads of different types in lipid models, the

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conservative parameter aW -H is 25 k BT rc , and aW -T  aT -H is 100 k BT rc ,44-45 where W, H,

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T signify the water bead, the lipid head bead, and lipid tail bead, respectively. The DPD

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interaction parameter aW -H = 25 k BT rc indicates that water bead and lipid head bead are

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miscible and belongs to the same group of DPD component. To represent the hydrophobic

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state of PNIPAM-based hydrogels, we take a conservative parameter aT -HY =25 k BT rc .

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Meanwhile, binding = aH  HY  aW  HY vary from 30 to 85 k BT rc to describe the different

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hydrogel-lipid binding strengths, which is aroused from the certain surface or composition

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modifications of PNIPAM-based hydrogels, such as block polymer grafting with different

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types of polymer monomers or grafting ratios.46-48 The conservative parameters are listed in

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Table 1.

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In the DPD simulations, we take rc as the characteristic length scale and k BT as the

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characteristic energy scale, and the characteristic time scale is defined as  = mrc 2 k BT .49

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The velocity-Verlet integration algorithm is adopted with t  0.04 ,50 and a total of 6 × 105

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DPD simulation steps are performed to obtain the equilibrium state. On comparing a

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reasonable estimation for lipid bilayer thickness of 4 nm in experimental results, the thickness of

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the linear lipid molecule is around 3.5 rc .27 Thereby, the basic unit length in DPD simulations is

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about rc =1.14 nm. Mapping the diffusion coefficient of around 5 μm2s−1 of the POPC

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bilayer, the simulation time-scale is about 0.032 ns/step.51 Therefore the IH with a radius of 9 / 31


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20  corresponds a real size of 45.6 nm, comparable with practical hydrogels. For instance,

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the PNIPAM-based hydrogels, displaying a significant volumetric change at a lower critical

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solution temperature (LCST, 32℃), is of about 55nm above LCST.52-54 In our study, all

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simulations are accomplished in a cubic box with a size of 100 × 100 × 80 rc with periodic

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boundary conditions applied in all three directions, where the reduced particle density of

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simulation system is 3.0. All simulations are conducted in the NVT ensembles using

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LAMMPS package.55

3

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Table 1. Conservative parameters expressed in k BT rc units W (water) H (lipid head) T (lipid tail) HY (hydrogels) W

25

H

25

25

T

100

100

25

HY

30~85

30~85

25

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3. Results and discussion

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3.1 Membrane wrapping mechanism of IHs

25

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Here, we first investigate the membrane wrapping behavior of spherical stuffed IH. The

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resultant morphological evolution of membrane wrapping is shown in Figure 2A. Figure

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2A1-A3 show that the spherical IH is partially engulfed by the membrane and forms a

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gyro-shaped morphology. Specifically, we observe a sharpened adhesion area at the wrapping

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position due to the vertical structural elongation of the polymeric matrix. In this case, the

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generated geometry allows a comprehensive wrapping with a lower energy barrier. The

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subtle observation in Figure 2A1-A3 demonstrates that the membrane forms small

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undulations and then buckles. This result manifests a typical capillary phenomenon. Herein, 10 / 31


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we define the initial wrapping process (t≤0.32µs) as vertical capillary adhesion stage.

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Likewise, experimental and theoretical observations have reported the capillary adhesion

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phenomenon in the rigid nanoparticle-membrane systems.56-57 Originating from the van der

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Waals attractions between the IH and membrane, the formation of vertical capillary adhesion

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provides a driving force for the membrane to wrap the corner of IHs. As increasing the

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simulation time (t>0.32µs), the membrane progressively engulfs the IH, and a rugby-shaped

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morphology is observed, as shown in Figure 2A4-A6. In this stage, the sharpened adhesion

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area disappears, and the lateral compressed state is generated in the middle of the bilayer

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membrane. The comprehensive balance between membrane tension and hydrogel

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deformability plays a significant role in this stage. We identify the following process as

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lateral compressed wrapping stage. In generally, all these stages are controlled by the

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elastocapillary deformation of networked gels and nanoscale confinement of bilayer

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membrane.

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The density profiles over simulation time are computed. Figure 2B1-B6 show that the

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density distribution of the IH at the Z direction becomes more concentrated as increasing

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the simulation time. Ultimately, the density distributions of the IH and membrane coincide at

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the latter simulation time. In summary, all these results endorse a unique membrane wrapping

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pathway that the IHs transform from vertical capillary adhesion to lateral compressed

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wrapping during the wrapping process. Similar observations can be found in the IHs with

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different architecture characteristics, as included in the Supplementary Information (SI).

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Importantly, this exclusive membrane wrapping pathway is just identified in the soft IHs 11 / 31


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rather than in ordinary rigid nanomaterials.11-12 13 14 Besides, the designed IHs finally embed

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into the lipid membrane, rather than penetrating through the membrane, which is also

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different from the membrane endocytosis of rigid nanoparticles. Though affected by the

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bending modulus of the membrane,58 the membrane translocation induced by the IHs is

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majorly determined by the shape deformability of the IHs, which is not favorable for

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membrane rupture. Conversely, the intrinsic rotation of rigid nanoparticles offers a strong

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driving force for membrane rupture.59-60 The dynamical properties of this structural transition

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would be further discussed below.

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Figure 2. Membrane wrapping pathway of IHs: (A1-A6) representative snapshots of

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membrane wrapping of spherical hydrogel with a radius Rgel  20 at different simulation

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time, (B1-B6) density profiles of the spherical hydrogel at the direction of simulation box-Z

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and (C1-C6) 2D density mappings of IHs corresponding to snapshot figures in (A1-A6). The

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color bar represents hydrogel density in the units of  2 . The solvent beads are not shown

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for clarity and the same as below. 13 / 31


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The two-dimensional (2D) density maps of the IHs are given in Figure 2C1-C6. The

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ring-like density distributions are obtained in the spherical stuffed IHs. This demonstrates a

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hollow structure is formed in the IH matrixes, which may result from strong hydrogel-lipid

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binding interactions and good deformability of the IHs. The chain configuration can be

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characterized by the radius-of-gyration paralleled to individual axes, which is defined as 61

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Rg 

1 n  ( Ri  Rc )2 n i 1

(7)

244

where  corresponds to each component (  being x, y, z), Ri is the position of the i-th

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polymer bead, and Rc is the position of the mass center of the polymer at the  direction,

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and

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radius-of-gyration for the IHs is observed at the directions of axis-X and axis-Y, while a

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decreased radius-of-gyration is obtained at the direction of axis-Z. This significant hydrogel

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deformation originates from the strong van der Waals attraction between the IH and

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membrane along the Z direction. Namely, once the hydrogels contact with the membrane,

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the vertical elongation of the IH is quickly identified. Consequently, at the initial wrapping

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process (t≤0.32µs), the radius-of-gyration for the IHs at the direction of axis-Z is larger than

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those at the direction of axis-X and axis-Y. The inverse variation trend is observed at the

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following wrapping process (t>0.32µs). Moreover, the total radius-of-gyration for the IHs

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also indicates a structural transition at 0.32µs, as shown in Figure 3B. The evolution of

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average height for the IHs slowly attenuates when t≤0.32µs, then rapidly decreases, and

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eventually reaches a platform. All these results confirm a structural transition in the wrapping

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dynamics as mentioned above.

denotes the ensemble average. As shown in Figure 3A, an increased

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(A)

R g /

2.8

2.6

2.4

Axis-X Axis-Y Axis-Z

0.1 259

1 Time/s

10

70

(B) 4.68

65 60

Total Rg/

4.64

55

4.6

50 45

4.56

40

Height/

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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4.52 0.1 260

1 Time/s

10

30

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Figure 3. Membrane wrapping dynamics of IHs: (A) radius-of-gyration of the spherical

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hydrogel at different directions of simulation box and (B) average height and total

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radius-of-gyration of the spherical hydrogel.

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3.2 Effects of hydrogel shell thickness on wrappings

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Microgel capsules have been utilized in various encapsulation and controlled release

266

applications.36, 62-63 By varying the hydrogel shell thickness ranging from Rs =8.5 to 20  ,

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the effect of hydrogel architectures on the membrane wrapping is studied. The membrane

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wrapping of the hydrogel capsule with different thickness is presented in Figure 4A1-A4. 15 / 31


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Similarly, the equilibrated morphologies of the IHs also demonstrate the lateral compression

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with different degrees. Compared with the spherical stuffed IHs, the hollow structure isn’t

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observed in the hydrogel capsules, as confirmed in Figure 4B1-B4. The high affinity

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between the IH and membrane induces the formation of hollow structure in the stuffed IHs,

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while the favorable lateral deformation makes the hollow IH tend to be collapsed state.

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Moreover, it seems that the hydrogel nanosheet is generated at the shell thickness Ds 

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8.5  , as illustrated in Figure 4A4 and 4B4. This is because the hydrogel capsules are

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favorable to be laterally compressed, as confirmed by the total radius-of-gyration for the IHs.

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Figure 4. Membrane wrapping pathway of the IHs with different shell thicknesses. (A1-A4)

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Representative snapshots of spherical hydrogel with different shell thicknesses Ds  20.0,

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15.0, 11.25, 8.5  , respectively. The hydrogel with a shell thickness of

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corresponds to the spherical stuffed hydrogel. (B1-B4) 2D density maps of the IHs

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correspond to the snapshot Figures A1-A4. The color bar indicates the hydrogel density in the 16 / 31


Ds  20.0 

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283

units of  2 . (C) The evolution of total radius-of-gyration for the IHs. (D) evolution of

284

contact angle for the IHs embedded in the bilayer membrane. The equilibrium simulation

285

time is 19.2 s.

286 287

Figure 4C displays that the thicker capsule generates larger total radius-of-gyration for

288

the IHs. Meanwhile, the structural transition can be further confirmed by the evolution of

289

total radius-of-gyration. Furthermore, we introduce the compressed angle conception to

290

quantitatively interpret the observed relation between structural compression and IHs

291

architecture. The definition of compressed angle is illustrated in Figure 4D. The decrease of

292

the shell thickness results in a decreased compression angle. It is because it’s easier for a

293

thinner IH to generate shape deformation. The compressed angle of the spherical stuffed IHs

294

is smaller than that of the hydrogel capsule with a shell thickness Rs =15  . This result can

295

be interpreted by the fact that the spherical stuffed IHs form a hollow structure as confined at

296

the membrane (see Figure 4B1). In order to quantify the lateral compression strength, the

297

geometrical shape parameter  is introduced, which is defined as 64

298 299

1 2

 = g( Rgx2  Rgy2 ) Rgz2 .

(8)

Note that   1 indicates a vertical elongation at the axis-Z direction and   1

300

represents a spherical shape or isotropic object, while   1 suggests a lateral compression.

301

Figure 5A shows the dynamical shape variation of the IHs, which indicates the IHs undergo

302

structure transition over simulation time. Especially, the structure transition time depends on

303

the hydrogel shell thickness: ts  20.0 < ts 15.0 < ts 11.25 < ts 8.5 . The evolution of the 17 / 31


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wrapping ratio for each IH is recorded in Figure 5B. Here the wrapping ratio  H is defined

305

as the ratio of the instantaneous height variation of IHs to the maximal height variation of

306

IHs. It should be noted that the wrapping ratio defined here is different from the conventional

307

one,  S , defined by contacting surface conception.65-66 The relation and difference between

308

them are  S =f S ( H ,  )g H , where H is height variation of IHs, and  represents the

309

shape deformation parameter of IHs.

310

coefficient. We take f S ( H ,  ) as a constant for simplicity. Nevertheless, the wrapping ratio

311

introduced in this work can quantify the wrapping process, as confirmed by the scaling

312

factors. (see Figures 5B and 8B) As increasing the simulation time, the wrapping ratio for

313

each IH gradually increases, and then reaches a platform. At the monotonous increasing

314

region, the wrapping ratio shows approximate scaling from  ~ t 0.928 to  ~ t1.908 . It seems

315

that the hydrogel shell thickness has a weak influence on the wrapping time tw (defined as

316

the time required for a successful IH internalization). The lateral compression inhibits or

317

frustrates the wrapping process due to the wrapping-induced shape deformation, thus, the

318

wrapping time tw is dominated by the lateral compressed wrapping stage. The theoretical

319

computation of wrapping time is included in the SI.

f S ( H ,  ) is the H-dependent and  -dependent

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Langmuir

Structural compression

2 (A)1.8 1.6

Rs=20.0 Rs=15.0 Rs=11.25

1.4

Rs=8.5 laterally compressed wrapping

1.2 1

vertically capillary adhesion

0.8 0.1

320

1 Time/s

10 Rs=20.0

(B)

Rs=15.0 Rs=11.25

1

Rs=8.5

tio Wrapping ra

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

Page 20 of 32

0.1 Kslope2=0.928

0.01

321

Rs=8.5 Rs=11.25 Rs=15.0 Rs=20.0

Kslope1=1.908

10

T

1 /s ime

0.1

322

Figure 5. Membrane wrapping dynamics of different hydrogel shell thickness: (A) structural

323

compression of IHs and (B) wrapping ratio of IHs.

324

3.3 Effects of hydrogel-lipid binding strength on wrappings

325

The conservative parameter aij between both beads of different types corresponds to

326

the mutual solubility, and herein the conservative parameter binding = aH  HY = aW  HY is used

327

to describe the hydrogel-lipid binding strength. The conservative parameter binding varies

328

from 30 to 85 k BT rc . A small conservative parameter suggests a strong hydrogel-lipid 19 / 31


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329

binding strength and vice versa. The bilayer membrane wrapping with different

330

hydrogel-lipid binding strengths is simulated, as depicted in Figure 6. The lateral

331

compression with different degrees of deformation is observed in the equilibrated

332

morphologies of the IHs. Intriguingly, Figure 6A1 reveals a collapsed structure under high

333

hydrogel-lipid binding strength (i.e., binding = 30k BT rc ). Comparatively, the 2D density map

334

shows an obvious corona at the edge of the spherical structure, as shown in Figure 6B1.

335

When at a moderated hydrogel-lipid binding strength (i.e., 45 k BT rc  binding  65 k BT rc ),

336

the hollow morphology is formed in the bilayer membrane (illustrated in Figure 6B2 and

337

B3). However, at a low hydrogel-lipid binding strength (i.e., binding =85k BT rc ), a spherical

338

encapsulated morphology is formed (illustrated in Figure 6A4), which can be confirmed by

339

the corresponding 2D density map of the IHs (illustrated in Figure 6B4). Compared with a

340

low hydrogel-lipid binding strength, the nanoscale mixing is identified under high

341

hydrogel-lipid binding strength. The sectional-view and top-view of the IHs are given in

342

Figure 7. From Figure 7A1-A2, we examine that the IH dissolves into the membrane

343

accompanying with special co-dissolution phenomena. However, in the case of medium

344

hydrogel-lipid binding strength, the deformable wrapping occurs, as depicted in Figure

345

7B1-B2.

20 / 31


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346 347

Figure 6. Membrane wrapping under different hydrogel-lipid binding strengths. (A1-A4)

348

binding =30, 45, 65, 85 kBT rc , respectively. (B1-B4) 2D density map of IHs corresponding

349

to snapshot figures in A1-A4. The color bar represents the hydrogel density in the units of

350

 2 . (C) The evolution of total radius-of-gyration for the IHs. (D) evolution of contact angle

351

for the IHs embedded in the bilayer membrane. The equilibrium simulation time is 19.2 s.

352

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353

Figure 7. Comparison of membrane wrapping morphologies under different hydrogel-lipid

354

binding strengths: (A1-A2) binding = 30 k BT rc and (B1-B2) the binding = 65 k BT rc .

355

Though different hydrogel-lipid binding strengths are simulated, an obvious structural

356

transition is also identified in Figure 6C. Moreover, high hydrogel-lipid binding strength

357

leads to an increased radius-of-gyration owing to the confined compressibility of the IHs. The

358

computed compression angle is displayed in Figure 6D, which indicates the IH morphology

359

transforms from the wetting compression state to adhesive encapsulation, as reflected in

360

Figure 6A1-A4. The phenomenon of the wetting compression state was also reported by

361

previous studies when the hydrogels are placed at the confinement space.67-69 Figure 8A

362

presents the evolution of structural compression of the IHs. We observe the large

363

hydrogel-lipid binding strength gives rise to short transition time. The evolution of wrapping

364

ratio for each IH is given in Figure 8B. It is demonstrated that the hydrogel-lipid binding

365

strength has a significant role in the wrapping time. However, the approximative scaling from

366

 ~ t1.294 to  ~ t1.819 is obtained at the monotonous increase region. Our simulation results

367

indicate that the hydrogel-lipid binding strength of binding  85k BT / rc could optimize the

368

wrapping time. With high hydrogel-lipid binding strength, a longer wrapping time is needed

369

because of the nanoscale mixing and favorable deformability during the wrapping process.

370

On comparison of different hydrogel-lipid binding strengths, severe structure compression

371

and deformation of IHs can be found at high hydrogel-lipid binding strength of

372

binding  30k BT / rc , as shown in Figure 8A. In fact, stronger deformability results in longer

373

wrapping time owing to higher energy barriers.18, 70 22 / 31


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Page 24 of 32

374

Satarifard and Zhang et al.18, 59 have studied the effect of surface tension on membrane

375

wrapping. Herein, the stress distribution for the IHs is computed, as shown in Figure S1. The

376

stress distribution with a surface normal in the Y-direction inside the membrane is

377

characterized via the equation of ( X , Z )  PZZ  0.5g( PXX  PYY ) , where the PXX , PYY , PZZ ,

378

are the pressure tensor at the X, Y, and Z directions.18,

379

tension at the contact site implies that the bilayer membrane experiences a severe

380

heterogeneous deformation and favorable mechanical rupture.55 As shown in Figure S1, the

381

scattered distribution of stress demonstrates the interaction between the membrane and IHs

382

doesn’t readily make membrane rupture, and thus the membrane endocytosis induced by the

383

IHs has not been found.71 In addition, the affluence of surface tension on the membrane

384

wrapping is quantified through theoretical calculation, in which the relationship between the

385

surface tension and lateral compressed wrapping time tlcw is identified. The computation

386

details are presented in the SI. As a result, the lateral compressed wrapping time tlcw is

387

mainly dependent on the surface tension: tlcw ∼ 2 IH  IH , where  are the characteristic

388

radii of IHs,  IH is the viscosity of the IHs, and  IH is the surface tension of IHs. Moreover,

389

the surface tension also determines the adhesive morphology of polymer matrix. Generally, a

390

large membrane tension triggers an axisymmetric morphology in a polymer matrix, while a

391

small membrane tension induces a non-axisymmetric shape.18

59

392

23 / 31


A dramatic change of surface

Page 25 of 32

2 (A) 1.8

binding=30kBT/rc binding=45kBT/rc

1.6

binding=65kBT/rc binding=85kBT/rc

1.4 1.2

laterally compressed wrapping

1

0.1

393

1 Time/s

10 (B)

binding=30kBT/rc binding=45kBT/rc binding=65kBT/rc

1

Kslope1=1.294

binding=85kBT/rc

tio

0.8

vertically capillary adhesion

Wrapping ra

Structural compression

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

Langmuir

0.1 Kslope2=1.819

0.01

394

0.1 Time 1 /s

30kBT/rc 45kBT/rc 65kBT/rc 10

85kBT/rc

395

Figure 8. Membrane wrapping dynamics of the IHs with different hydrogel-lipid binding

396

strengths: (A) structural compression of IHs and (B) wrapping ratio of IHs.

397 398

Figure 9. Membrane wrapping pathway of IHs.  HS ,  MS ,  HM correspond to the surface 24 / 31


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399

stress tensors of the biphasic interface, VHS , VMS , VHM indicate the tangent vectors of the

400

biphasic interface, and the subscript H , S , M represent hydrogel, solvent, membrane,

401

respectively.

402

4. Conclusions

403

With the help of large-scale DPD simulations, we have systematically investigated the

404

membrane wrapping process of IHs by considering different IH architectures and

405

hydrogel-lipid binding strengths. A theatrical structure transition from vertical capillary

406

adhesion to lateral compressed wrapping is discovered, which is significantly different from

407

the situation with non-elastic nanomaterials. Originating from the van der Waals attraction of

408

hydrogel-lipid, the formation of vertical capillary adhesion offers a driving force for the

409

membrane to wrap the corners of IHs (see Figure 9A). The conformational variation of the

410

IHs at the boundary of the membrane is mainly determined by a vector balance of the surface

411

stresses,72 as illustrated in Figure 9B. Correspondingly, the IHs gradually embed into the

412

membrane (see Figure 9C). However, the lateral compression inhibits the membrane

413

wrapping process due to the wrapping-induced shape deformation, and thus, the wrapping

414

time for vertical capillary adhesion stage is much shorter than that for lateral compressed

415

wrapping stage. All these results can be explained by the unique collaboration of

416

lastocapillary deformation of networked gels and nanoscale confinement of bilayer

417

membrane. Moreover, our results demonstrate the stuffed IH forms a hollow structure during

418

the wrapping process. Conversely, a collapsed architecture is discovered in the IH capsules

419

because of their strong compressibility and deformability compared with stuffed IH. In 25 / 31


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420

addition, when at large hydrogel-lipid binding strength, the special nano-mixing occurs, and

421

this would result in a long wrapping time. We are currently extending our computational

422

approach to address these mechanistic membrane wrappings of IHs in a systematic manner as

423

will be discussed in subsequent work.

424

Conflicts of interest

425

The authors have no conflicts of interest to declare.

426

Acknowledgments

427

This work is supported by National Natural Science Foundation of China (Nos. 21878078,

428

and 21808056), by National Natural Science Foundation of China for Innovative Research

429

Groups (No. 51621002), and by the Shanghai Science and Technology Innovation Action

430

Plan (18160743700).

431 432

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Membrane Wrapping Pathway of Injectable Hydrogels: From Vertical

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