Shape Transformations of Vesicles Self-Assembled from Amphiphilic

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Shape Transformations of Vesicles Self-Assembled from Amphiphilic Hyperbranched Multiarm Copolymers via Simulation Haina Tan, Shanlong Li, Ke Li, Chunyang Yu, Zhongyuan Lu, and Yongfeng Zhou Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b02206 • Publication Date (Web): 09 Aug 2018 Downloaded from http://pubs.acs.org on August 9, 2018

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Shape Transformations of Vesicles Self-Assembled from

Amphiphilic

Hyperbranched

Multiarm

Copolymers via Simulation Haina Tan,a Shanlong Li,a Ke Li,a Chunyang Yu*a, Zhongyuan Lub and Yongfeng Zhou*a a

School of Chemistry & Chemical Engineering, State Key Laboratory of Metal Matrix

Composites, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China, 200240. b

Institute of Theoretical Chemistry, State Key Laboratory of Supramolecular Structure and

Materials, Jilin University, Changchun, China, 130021. KEYWORDS: shape transformations, branched polymersomes, dissipative particle dynamics

ABSTRACT: The understanding of shape transformations of vesicles is of fundamental importance in biological and clinical sciences. Hyperbranched polymer vesicles (branched polymersomes) are newly emerging polymer vesicles with special structure and property. They have also been regarded as a good model for biomembranes. However, the shape transformations of hyperbranched polymer vesicles have not been studied both from experimental and theoretical level. Herein, the shape transformations of vesicles self-assembled from amphiphilic hyperbranched multiarm copolymers (HMCs) in response to the interaction parameters between hydrophobic core and hydrophilic arms and the polymer concentrations are investigated carefully through dissipative particle dynamics (DPD) simulations. In the morphological phase diagram,

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two types of vesicles are obtained: one type is the vesicles without holes formed at low concentrations including uni-lamellar vesicles, double-lamellar vesicles, discocyte-shaped vesicles and tubular vesicles; and the other type is the vesicles with holes formed at high concentrations including stomatocyte-shaped vesicles, toroidal vesicles, genus-3 (G-3) toroidal vesicles with three holes and genus-4 (G-4) toroidal vesicles with four holes. In addition, both the self-assembly mechanisms and the dynamics for the formation of these vesicles have been systematically studied. The current work will offer theoretical support for fabricating novel vesicles with various shapes from hyperbranched polymers.

1. INTRODUCTION

In living organism, cells exist in various shapes. For some cells, the changes of their shapes can cause severe diseases.1 As an example, human red blood cells display a biconcave shape in healthy environment. However, they will change shapes in blood diseases such as malaria, drepanocytosis, stomatocytosis, and hereditary spherocytosis.2-5 Therefore, understanding shape transformations of cells is not only biologically significant, but also helpful for disease diagnostics.6 However, due to the complexity in the composition and structure, it is very difficult to directly study cellular behaviors. To address this, artificial vesicles have been widely accepted as the model systems to mimic the cell shapes and shape transformations.7-9 Generally, liposomes self-assembled from phospholipids and polymersomes self-assembled from amphiphilic block copolymers are conventional model vesicles. Similar to human red blood cells, vesicles have shown a rich variety of shapes or shape changes in both experimental and theoretical simulation studies.6,10-31 For example, Michalet et al. observed equilibrium shapes of topological genus-2 (shapes with two holes) liposomes, which were found to be in agreement


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with theoretical predictions on the basis of a minimization of the elastic curvature energy for fluid membranes.10 Markvoort et al. studied the liposomes deformations on osmotic deflation using coarse grained molecular dynamics simulations, and prolate ellipsoid, pear-shaped, and budded vesicles were formed by changing pH or ion concentration.13 van Hest et al. reported a controllable shape transformation from polymersomes to stomatocytes by controlling kinetic manipulation of the phase behavior of the glassy hydrophobic segment in amphiphilic diblock copolymers.17 Liang and Karniadakis et al. used dissipative particle dynamics (DPD) approach to explore the shape transformations of vesicles formed from amphiphilic triblock copolymers, and a plethora of complex vesicle shapes, such as starfish-shaped, toroidal, long rod-like, and inverted vesicles, were obtained by regulating the repulsive parameters between the two hydrophilic blocks in the amphiphilic molecules.21 Nevertheless, researchers found that liposomes are of high membrane fluidity but are unstable due to the small molecular nature,7,14 while polymersomes are stable and designable but have lower fluidity.16,32 Compared with traditional liposomes and polymersomes, branched polymersomes (BPs) are a new type of polymer vesicles self-assembled from amphiphilic hyperbranched multiarm copolymers (HMCs).33,34 BPs have displayed the combined property advantages of strong stability like polymersomes and good membrane fluidity like liposomes.35 In addition, the size of BPs could be facilely adjusted to reach cell-like size and can be observed in real time under the optical microscope.33 Thus, BPs have shown great potentials to be the ideal model vesicles to mimic cellular morphologies and behaviors.34,36 For example, the membrane fusion and fission processes of individual BP were observed in real time, which have provided some new insights to the mechanism and dynamics inside the cellular behaviors. However, up to now, BPs only


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show regular spherical shape, and the shape transformations of BPs have not been disclosed by experiments or by theoretical works. Thus, the basic question is: can BPs have shape changes like liposomes or polymersomes? To address it, herein, we hope to disclose the shape transformations of BPs with the aid of computer simulation technique. Recently, our group has reported the formation mechanisms of the selfassembly of micelles and vesicles from HMCs,37,38 and disclosed the effects of degree of branching (DB), pH, and different solvents on the self-assembly of HMCs by using DPD simulation.39-41 These studies indicate that DPD simulation is an effective tool to investigate the self-assembly behaviors of HMCs. In this work, we also want to use DPD simulations to study the shape transformations of BPs. In the simulation, a HMC model with one hyperbranched core and many linear arms has been constructed. By regulating the polymer concentrations and the interaction parameters between hydrophobic core and linear arms, the morphological phase diagram of BPs has been built and various BPs with different shapes have been found. Through the phase diagram, we can visually see the formation conditions of each kind of vesicle and the phase region in which it is located, as well as the transition conditions between different shapes of vesicles. These simulation results are expected to provide theoretical guidance to some extent for the preparation of vesicles with different shapes in experiments. 2. SIMULATION METHOD AND MODEL A. DPD Method. DPD method is a mesoscopic simulation technique, which was first proposed by Hoogerbrugge and Koelman in 1992,42 and further improved by Español and Warren.43 In DPD model, each bead represents a cluster of atoms or molecules. The time evolution of the interacting beads is governed by Newton’s law of motion.44 The total force Fi exerted on bead i


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by bead j consists of a conservative force FijC, a dissipative force FijD, and a random force FijR , each of which is pairwise additive: Fi = ∑ (FijC + FijD + FijR )

(1)

j ≠i

where the sum runs over all neighboring beads within a certain cutoff radius rc. The conservative force is a soft repulsion with the form

α ij (1- rij / rc )rîj (rij < rc ) (2) FijC =  ( rij ≥ rc ) 0 where αij is the maximum repulsion between beads i and j, rij = ri − rj, rij = |rij|, rîj = rij/rij. The dissipative force and random force, acting together as a thermostat, are given by

FijD = −γω D (rij )(rîj ⋅ v ij )rîj

(3)

FijR = σω R (rij )ξij ∆t −1/ 2rîj

(4)

where vij is the relative velocity between beads i and j. γ and σ are the friction coefficient and noise amplitude, respectively. ωD(rij) and ωR(rij) are the distance-dependent weight functions for the dissipative force and random force, respectively. ξij is a random number with zero average and unit variance. Moreover, in order to generate a correct equilibrium Gibbs–Boltzmann distribution, the dissipative and random forces have to satisfy the following relations:

ω D (rij ) = [ω R (rij )]2 , σ 2 = 2γ k BT

(5)

where kB is the Boltzmann constant. According to Groot and Warren, we choose a simple form of ωD(rij) and ωR(rij) as follows:44 2  (1 − rij / rc ) (rij < rc ) (rij ≥ rc ) 0

ω D (rij ) = [ω R (rij )]2 = 

(6)

In the simulation, a modified version of the velocity–Verlet algorithm is used to integrate the equations of motion with a time step of ∆t = 0.02τ. For simplicity, the cut-off radius rc, the bead mass m, and the temperature kBT are taken as the reduced units, i.e., rc = m = kBT = 1, and thus the time unit τ = (mrc2/kBT)1/2 = 1. The number density ρ is set to 3. The interaction parameter αij


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can be mapped to Flory-Huggins parameter χ at ρ = 3 as αij = αii + 3.27χij, where αii = 25 is used for the same type of bead and to correctly describe the compressibility of water. To keep the S adjacent beads connected together along the polymer, a harmonic spring force Fij = Crij (C = 4.0)

is adopted between bonded i-th and j-th beads.45 B. Model and Condition. In this study, a typically vesicle-forming amphiphilic HMC (Figure

S1 in Supporting Information) was considered as the prototype for DPD simulations.29 Accordingly, as illustrated in Figure 1, a coarse-grained model of the HMC molecule has been constructed. Considering the volume of the arm monomer is smaller than that of the core monomer, one repeat unit in the hyperbranched core was coarse-grained into one A bead (the pink bead), while three repeat units in the linear arms was coarse-grained into one B bead (the cyan bead).38,41 The model is denoted as A30B18, where the hydrophobic hyperbranched core is composed of 30 pink beads (A type) and the hydrophilic linear arms are composed of 18 cyan beads (B type). In addition, S type beads represent water molecules. As shown in Figure 1, there are seven dendritic (D) beads and fourteen linear (L) beads in the hyperbranched cores, and thus the DB of the model is DB = 2D/(2D + L) = 2 × 7/(2 × 7 + 14) = 0.5.46,47

Figure 1. Schematic structure for the HMC model A30B18. Pink beads represent hydrophobic

core, and cyan beads represent hydrophilic arms.


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As mentioned above, there are three types of beads (A, B, and S) in our simulation box. For the interaction between the same type of beads, αii = 25 is set to reflect the correct compressibility of the dilute solution.44 Empirically, the interaction parameter between the linear arms and water is set as αBS = 27, which implies that the arms are hydrophilic.48-50 The interaction parameter between the hyperbranched core and water is set as αAS = 80, which implies that the core is hydrophobic.22,51,52 In order to systematically investigate the effects of compatibility (αAB) between hyperbranched core and linear arms and the polymer concentrations (f), we construct a morphological phase diagram, i.e., the variation of self-assembly structures with αAB and f.53 In addition, the interaction parameter between the hyperbranched core and the linear arms is changed from 40 to 80, which means the increase of the incompatibility between hyperbranched core and linear arms. The bead concentration, which is defined by the volume fraction of the solute, is used to characterize the concentration of HMCs and is varied from 0.02 to 0.20. All simulations are performed in a cubic box of 60 × 60 × 60rc3 with periodic boundary conditions applied in all three dimensions. The bead number density is kept at ρ = 3, so there are a total of 6.48 × 105 DPD beads in each simulation. For each simulation, we started from randomly distributed HMCs in dilute solution, and a total of 8.00 × 106 time steps were carried out to attain the final equilibration. Meanwhile, we also calculated the time evolution of three energy indexes, EAS, EAB, and EBS, respectively, which are defined as per particle conservative energy between the hydrophobic hyperbranched core (A) and water (S), hydrophobic hyperbranched core (A) and hydrophilic linear arms (B), and hydrophilic linear arms (B) and water (S), respectively, to characterize the self-assembly equilibration process of BPs with different shapes.41,48 All DPD simulations were performed with HOOMD package54-57 on NVIDIA GTX 780Ti GPU processor.


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3. RESULTS AND DISCUSSIONS

The shape of reported BPs has been limited to be spherical in experiments. To systematically investigate the shape transformations of BPs, the morphological phase diagram constructed by DPD simulations is presented in the following sections. The morphological phase diagram is displayed in terms of the interaction parameters αAB and the polymer concentrations f for the HMC model, which possess one hydrophobic hyperbranched core and many hydrophilic linear arms. The detailed self-assembly mechanisms and the dynamic processes for the formation of different shapes of vesicles are also been discussed. A. Phase diagram of different shapes of vesicles. Figure 2 displays the morphological phase

diagram of different shapes of vesicles self-assembled from A30B18 as a function of αAB and f, and the corresponding characteristic snapshots of the self-assembly structures. In summary, eight different shapes of vesicles are observed, and the corresponding phase regions are shown in Figure 2a. According to whether these vesicles have holes, they can be divided into two categories (Figure 2b). Type I refers to vesicles without holes, including uni-lamellar vesicle, double-lamellar vesicle, discocyte-shaped vesicle, and tubular vesicle. Type II refers to vesicles with holes, including stomatocyte-shaped vesicle, toroidal vesicle, genus-3 (G-3, shapes with three holes) toroidal vesicle, and genus-4 (G-4, shapes with four holes) toroidal vesicle. In addition, the phase region of G-3 and G-4 toroidal vesicles is a mixed region of both. As displayed in Figure 2a, the type I vesicles are formed at lower concentrations, while the type II vesicles are formed at higher concentrations. In the phase region of type I vesicles, for f = 0.02, only uni-lamellar vesicle can be observed no matter what αAB is; when f = 0.04, 0.06, and 0.08, as αAB increases, the self-assembled structures are double-lamellar vesicle, discocyteshaped vesicle, tubular vesicle, and uni-lamellar vesicle in turn; for f = 0.10 and 0.12, discocyte-


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shaped vesicle, tubular vesicle, and uni-lamellar vesicle can be successively obtained with increasing αAB; note that only discocyte-shaped vesicle formation occurred at f = 0.14. In the phase region of type II vesicles, only G-3 and G-4 toroidal vesicles are observed when f = 0.10 and 0.12; for f = 0.14 and 0.16, G-3 and G-4 toroidal vesicles and toroidal vesicles are formed as αAB grows; for f = 0.18, the self-assembly structures are G-3 and G-4 toroidal vesicles, toroidal vesicles, and stomatocyte-shaped vesicle in turn; moreover, when f = 0.20, G-3 and G-4 toroidal vesicles can be obtain at lower αAB, while stomatocyte-shaped vesicle can be observed at higher αAB. As can be seen from the time evolution curves of EAS (Figure S2 in Supporting Information), all the eight BPs with different shapes remain unchanged for a long simulation time, which demonstrate that they indeed reach the final equilibration state.

Figure 2. (a) Phase diagram of different shapes of vesicles formed from A30B18 in solution as a

function of the interaction parameters αAB and the polymer concentrations f. Each point in the phase diagram is obtained by calculating at least five parallel samples. The region on the left side of the solid blue line belongs to type I vesicles while the region on the right side of the solid blue line belongs to type II vesicles. (b) Characteristic morphological snapshots corresponding to the vesicles in the phase diagram. Hydrophobic hyperbranched core is composed of pink beads, while hydrophilic linear arms are composed of cyan beads.


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B. Self-assembly behaviors of vesicles without holes. The self-assembly mechanism and the

dynamic process for the formation of uni-lamellar vesicle have been reported in our previous simulation work,39 and thus are not shown here again. We find the uni-lamellar vesicle grows larger as αAB increases, indicating the fusion of small uni-lamellar vesicles.38 In order to compare the size of different uni-lamellar vesicles and characterize the molecular packing model of the uni-lamellar vesicle, the radial density distributions from the center of mass to the outside of the uni-lamellar vesicles at αAB = 40 and αAB = 80, and one labelled molecule in the cross-section were given in Figure S3. From the density distribution profile, we can also calculate the radius r of the uni-lamellar vesicle, which are r = 8.3 at αAB = 80 and r = 4.9 at αAB = 40, respectively. From the packing model, each HMC undergoes a cylindrical “A-B-A” type micro-phase separation to form the monolayer membrane. Moreover, in order to characterize the size change of the uni-lamellar vesicle quantificationally, the r curve of the uni-lamellar vesicle is calculated

Figure 3. The relationships between uni-lamellar vesicle radius r and αAB (f = 0.02). Error bars

are obtained by averaging five parallel samples.


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with the increase of αAB. As illustrated in Figure 3, the value of r first increases and then tends to level off. This result indicates that the size of the uni-lamellar vesicle would not always increase as αAB increases, but would gradually tend to be steady. Figure 4 shows the characteristic snapshots in the formation process of double-lamellar vesicle self-assembled from A30B18 in solution. At the beginning, A30B18 molecules are randomly distributed in solution (Figure 4a), and then they aggregate into a mixture of small membranes and micelles within a short time (Figure 4b). Afterwards, the small membranes bend and close to form some small uni-lamellar vesicles and the other small micelles grow into worm-like micelles and larger membranes (Figure 4c). Then, the uni-lamellar vesicles gradually transform into small

Figure 4. Sequential snapshots of the formation of double-lamellar vesicle from A30B18 at the

initial state (a), 2.00 × 104 steps (b), 1.00 × 105 steps (c), 3.70 × 105 steps (d), 1.35 × 106 steps (e), 2.36 × 106 steps (f), 2.80 × 106 steps (g), and 4.00 × 106 steps (h). For each image, the upper one is the 3D view, while the lower one is the iso-surface view of type A. Water beads are omitted for clarity.


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tubular vesicles, and the larger membranes bend and close to form larger uni-lamellar vesicles, respectively (Figure 4d). Subsequently, the small tubular vesicles merge with the neighboring micelles to form disk-like vesicles (Figure 4e). After that, the two disk-like vesicles move closer to each other and then fuse into a larger double-lamellar membrane (Figure 4f). Finally, the larger double-lamellar membrane gradually bends and closes to form a double-lamellar vesicle (Figure 4g, 4h). Moreover, we study the real-time evolution of three eigenvalues (λ1, λ2, and λ3) of the squared radius of gyration tensor in three principal directions of the largest aggregate in the formation process of the double-lamellar vesicle. As we know, the final double-lamellar vesicle is formed through the combination of many component aggregates, and in each simulation step there would be one largest component aggregate. Thus, herein, the three eigenvalues of these largest component aggregates at different simulation time steps were tracked continuously, and the result is shown in Figure 5a. The detailed calculation method of the three eigenvalues can be found in Supporting Information.39,58-60 As illustrated in Figure 5, there are five stages in the selfassembly process. In the first stage, at the beginning, λ1 ≈ λ2 > λ3 at 2.0 × 104 steps (Figure 5a, inset), indicating the A30B18 molecules quickly aggregate into membrane, which is also proved by the direct morphology observation from aggregate I (Figure 5b). Then, λ1 ≈ λ2 ≈ λ3 at 8.0 × 104 steps, which suggests that the membrane gradually bends (aggregate II) and then closes to form uni-lamellar vesicle (aggregate III). Thus, stage 1 is featured as the formation of unilamellar vesicle. In the second stage, λ1 goes on increasing from 4.5 to 12.5, while λ2 and λ3 remain nearly constant, indicating the formation of anisotropic supramolecular structure. The direct morphology observation of aggregate IV (Figure 5b) indicates that it is small tubular vesicle, so stage 2 is featured as the transformation from uni-lamellar vesicle to tubular vesicle.


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Figure 5. (a) The time evolution of λl, λ2, and λ3 of the largest aggregates of a final double-

lamellar vesicle at different simulation steps. (b) The corresponding morphologies of the largest aggregates (I-XII). In the third stage, all the three values of λ1, λ2, and λ3 increase. The morphology observations indicate that the small tubular vesicle (aggregate IV) gradually transforms (aggregate V) to form a disk-like vesicle (aggregate VI) in this stage. Thus, stage 3 is featured as the transformation from tubular vesicle to disk-like vesicle. In the fourth stage, at the beginning, both λ1 and λ2 gradually decrease, while λ3 gradually increases, and then λ1 ≈ λ2 ≈ λ3. It is a stage for the bending (aggregates VIII-IX) and closing (aggregate X) of the double-lamellar membrane (aggregate VII). Finally, in the fifth stage, the three eigenvalues remain equal to each other again, and it is a stage attributed to the further closing (aggregate XI) of aggregate X to form the double-lamellar vesicle (aggregate XII) and the undulation of the double-lamellar vesicle. Correspondingly, the size and the shape of the largest aggregates as shown in Figure 5b were further quantified by the radius of gyration Rg and the asphericity δ, respectively (Table 1). The value of δ can vary from 0 to 1, where 0 and 1 correspond to a perfect spherical globule and a rod, respectively.61,62 As can be seen from Table 1, the values of Rg for aggregates I to III decrease from 8.39 to 6.89, indicating that the size of the aggregates gradually becomes smaller,


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while the values of δ decrease from 0.05 to 0.01, indicating that the morphologies of the aggregates change from small membrane to small spherical vesicle. For aggregates III and IV, the values of Rg increase from 6.89 to 13.74, and the corresponding values of δ increase from 0.01 to 0.58, which implies the transformation from spherical vesicle to tubular vesicle. Both Rg and δ for aggregates IV to VI decrease first and then increase, which indicates that the tubular vesicle turns into disk-like vesicle. The values of Rg from aggregates VII to XII decrease from 18.29 to 13.19, while the values of δ decrease from 0.096 to 0.003, implying that the large double-lamellar membrane formed from the disk-like vesicle membrane gradually bends and then closes to form a double-lamellar spherical vesicle. Moreover, in order to intuitively observe the complete self-assembly process of the resulting double-lamellar vesicle, a video clip was made and is shown in Video S1. Table 1. The radius of gyration Rg and the asphericity δ of the largest aggregates as indicated in

Figure 5b (I-XII).

Parameters

I

II

III

IV

V

VI

Rg

8.39

7.54

6.89

13.74

13.66

21.18

δ

0.05

0.08

0.01

0.58

0.17

0.35

VII

VIII

IX

X

XI

XII

Rg

18.29

14.48

14.03

13.36

13.20

13.19

δ

0.096

0.066

0.031

0.005

0.004

0.003

Furthermore, we also investigated the self-assembly processes of discocyte-shaped and tubular vesicles, which are respectively given in Figure S4 and Figure S5. In addition, two video clips in Videos S2 and S3 provide the complete dynamic formation processes of discocyte-shaped and tubular vesicles, respectively. The obtained discocyte-shaped vesicle is consistent with that selfassembled from amphiphilic linear block copolymers.22,63 Meanwhile, the three eigenvalues λ1,


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Figure 6. The time evolution of λl, λ2, and λ3 of the largest aggregates of a final long tubular

vesicle at different simulation steps. λ2, and λ3 of the largest component aggregates in each simulation step of a final tubular vesicle are also calculated. As one can see from Figure 6, the self-assembly process can be classified into three stages. In stage 1, λ1, λ2, and λ3 are almost equal to each other at first, and then λ1 gradually increases while λ2 and λ3 remain nearly constant. Then, λ2 gradually increases but λ1 and λ3 are almost constant. Subsequently, λ1 and λ2 remain almost no change, while the value of λ3 goes on increasing to λ1 ≈ λ2 ≈ λ3. This is the characteristic of the formation and evolution of spherical vesicles. Thus, stage 1 is featured as the formation of spherical vesicles. In stage 2, the value of λ1 suddenly increases to about two times as much as before and then gradually level off, while λ2 and λ3 are nearly constant. So it is a stage featured as the formation of short tubular vesicle from the fusion of two spherical vesicles. In stage 3, λ1 further increases to a value around 16 with λ3 nearly constant, while λ2 increases and then decreases to the original value. It is the fusion process between short tubular vesicle and small spherical vesicle to form the resulting long tubular vesicle. Moreover, the largest component aggregates at the specific


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simulation steps are also indicated in Figure 6, which intuitively indicates the changes of aggregate size and morphology during the self-assembly process. As mentioned above, two fusion processes are included during the formation process of tubular vesicle. One involves the fusion of two small spherical vesicles, and the detailed pathway is provided in Figure 7. At the beginning, the two small spherical vesicles move closer to each other and are coalesced together (Figure 7a). Subsequently, the outer hydrophilic layers of the two vesicles laterally fuse, and then their hydrophobic layers gradually laterally fuse (Figure 7b). After the lateral fusion of the inner hydrophilic layers of the two vesicles, the short tubular vesicle is obtained (Figure 7c-7d). The other involves the transition from the short tubular vesicle to the long tubular vesicle, which is induced through the lateral fusion between a small spherical vesicle and a short tubular vesicle, as depicted in Figure 8. At first, the small spherical vesicle comes into contact with one end of the short tubular vesicle (Figure 8a). Then, the hydrophilic and hydrophobic layers of the contact surface fuse quickly (Figure 8b). Finally, after a gradual deformation, the final long tubular vesicle is formed (Figure 8c-8e). Therefore, the two kinds of lateral fusion processes are “sphere to sphere” fusion and “tube to sphere” fusion.

Figure 7. A real-time lateral fusion process from two small spherical vesicles into one short

tubular vesicle in the simulation at 2.13 × 106 steps (a), 3.06 × 106 steps (b), 3.07 × 106 steps (c), and 3.08 × 106 steps (d).


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Figure 8. A real-time lateral fusion process between a small spherical vesicle and a short tubular

vesicle to form a long tubular vesicle in the simulation at 4.37 × 106 steps (a), 4.78 × 106 steps (b), 4.84 × 106 steps (c), 4.89 × 106 steps (d), and 7.99 × 106 steps (e). C. Self-assembly behaviors of vesicles with holes. Stomatocyte-shaped vesicles are bowl-

shaped structures of nanosize dimensions, and its inner cavity can be used as a nanoreactor in

Figure 9. Sequential snapshots of the formation of stomatocyte-shaped vesicle from A30B18 at

the initial state (a), 2.00 × 104 steps (b), 9.00 × 104 steps (c), 1.50 × 105 steps (d), 3.00 × 105 steps (e), 8.00 × 105 steps (f), 8.50 × 105 steps (g), and 3.00 × 106 steps (h). For each image, the upper one is the 3D view, while the lower one is the cross-sectional view.


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catalysis.64 The self-assembly process of stomatocyte-shaped vesicle is shown in Figure 9. A30B18 molecules are randomly distributed in solution at the beginning (Figure 9a). Then, these randomly distributed molecules quickly aggregate into some irregular aggregates with lamellar structure (Figure 9b), which gradually get together and then bend to form an ordered selfassembly structure with a membrane in the cavity (Figure 9c-9d). Subsequently, the membrane in the cavity slowly bends (Figure 9e,f), and then both ends of the membrane connect with the outer membrane (Figure 9g). Eventually, the shape of the membrane in the cavity transforms into stomatocyte structure, and the outer membrane forms bowl-shaped structure (Figure 9h). In addition, to further illustrate this process, a complete self-assembly trajectory of the stomatocyteshaped vesicle is shown in Video S4. Furthermore, a typical dynamic formation process of toroidal vesicle is presented in Figure S6 and the video clip S5. The formation process is similar to that of the toroidal structure from amphiphilic triblock copolymers.65 Moreover, the self-assembly process of G-3 toroidal vesicle with three holes is also shown in Figure S7 and Video S6. In addition, to clearly exhibit the morphology of G-3 toroidal vesicle, the snapshots from different views are displayed in Figure S8. It should be noted that from both the first hole in the left view and the second hole in the right view, a part of the third hole in the front view can be observed, which indicates that the three holes in the G-3 toroidal vesicle are interpenetrating. Furthermore, the rotation video clip of G-3 toroidal vesicle is shown in Video S7. So we can further conclude that the shape of the G-3 toroidal vesicle is close to axisymmetric with a three-dimensional structure. In order to further investigate the formation of G-3 toroidal vesicles, the evolutions of the inner membrane, the holes structure, and the total number of holes are tracked, as illustrated in Figure 10. As can be seen from the changes in the inner membrane shown in the first column, the


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Figure 10. The evolutions of the inner membrane, the holes structure, and the total number of

holes in the formation process of G-3 toroidal vesicle, respectively. (a) 1.50 × 105 steps, (b) 1.70 × 105 steps, (c) 2.20 × 105 steps, (d) 3.60 × 105 steps, and (e) 6.80 × 105 steps. For each image, the one in the first column is the 3D view, while the one in the rest columns is the iso-surface view of type A. molecules in the membrane undergo diffusion and rearrangement, and then gradually form three ordered cavities. Accordingly, the structures and numbers of the holes in the outer surface observed from the three visual angles I, II, and III are shown in the iso-surface views of type A. Taking the visual angle I in the second column as an example, the number of holes remains constant (Figure 10a-10c) then decreases (Figure 10d), and finally leaves only one (Figure 10e). The decrease in the number of holes is attributed to the closing of the holes as the molecules in the inner membrane rearrange. Similarly, the same is true for the holes shown from the visual angles II and III. Moreover, the total number of holes gradually decreases from seven to three. Therefore, the formation of G-3 toroidal vesicles is due to the rearrangement of molecules within the membrane and the consequent changes in the external holes. Note that the G-3 toroidal


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vesicle is formed at 6.80 × 105 steps (Figure 10e), and the self-assembly structure still keep constant at 8.00 × 106 steps, which indicates that the structure is stable. Likewise, the snapshots of the self-assembly process and the video clip of complete dynamic formation process of G-4 toroidal vesicle with four holes are shown in Figure S9 and Video S8, respectively. Moreover, in order to intuitively observe the morphology of G-4 toroidal vesicle, the snapshots from different views are displayed in Figure S10. From the front view, the left view, the right view, and the bottom view, a total of four holes can be observed, and they are interpenetrating. Furthermore, the rotation video clip of G-4 toroidal vesicle is shown in Video S9. Thus, it can be concluded that G-4 toroidal vesicle is also a three-dimensional structure close to axisymmetric structure. To further study the formation of G-4 toroidal vesicle, we track the evolutions of the inner membrane, the holes structure, and the total number of holes, as shown in Figure S11. 4. DISCUSSION

The above simulation results indicate that various BPs with different shapes can be found in the morphological phase diagram from the self-assembly of HMCs. In the phase diagram, the phase region occupied by the uni-lamellar vesicle is the largest, which implies the uni-lamellar vesicle is an easily formed self-assembled structure. In addition, the size of the uni-lamellar vesicle could be controlled by adjusting the interaction parameter αAB. That is to say, the higher is the incompatibility between the hydrophobic hyperbranched core and the hydrophilic linear arms, the larger are the uni-lamellar vesicles, and the vesicle size finally tends to level off. The double-lamellar vesicle is formed through the bending and closing of double-lamellar membrane, which needs high energy. Thus, the double-lamellar vesicle is relatively difficult to form, and its phase region is the smallest. The formations of long tubular vesicles or tubes involve the lateral


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fusion between spherical vesicles or between spherical vesicles and small tubular vesicles. There are some similarities in the formation processes of discocyte-shaped vesicles, stomatocyteshaped vesicles, toroidal vesicles, G-3 toroidal vesicles, and G-4 toroidal vesicles, which refer to the molecular rearrangement from irregularly lamellar aggregates to ordered aggregates. As mentioned above, all the lamellar vesicles are monolayer (Figure S3c) and all single HMC molecule presents a cylindrical micro-phase separation. Herein, both the variation of αAB and the polymer concentration f play important roles in changing the cylinder shape. We had taken the HMC molecule from the vesicles to show the cylindrical micro-phase separation process, and the corresponding cartoons for the cylinder structure were also provided and summarized in Figure S12. With the increase of αAB, the HMC molecule stretched more, and thus the cylinder became more stretched and much thinner, leading to the decrease of the curvature of the vesicle. The increase of curvature will increase the vesicle size and change the vesicle morphology. In addition, with the increase of concentration f, the self-assembled intermediates tend to aggregate and fuse together, and then form the more complex lamellar structures. Thus, different vesicle shapes were obtained with the change of αAB and f as shown in the phase diagram (Figure 2). This work also manifests that like liposomes or polymersomes, BPs have abundant of shapes and shape transformations. They even show G-3 and G-4 toroidal vesicles which have not been found in polymersomes. It should be attributed to the special properties of BPs. Although belonging to polymer vesicles, BPs have thinner vesicle membranes and better membrane flexibility and fluidity when compared with the conventional polymersomes.32 Thus, BPs have good membrane deformability to support many shapes. 5. CONCLUSIONS


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In summary, we have systematically investigated the shape transformations of vesicles selfassembled from amphiphilic hyperbranched multiarm copolymers by using DPD simulations. Through controlling the hydrophobic-hydrophilic interaction parameters αAB and the polymer concentrations f, the phase diagram of the BPs with different shapes has been predicted theoretically. Eight different shapes of vesicles, including the ones without holes, such as unilamellar, double-lamellar, discocyte-shaped and tubular vesicles, as well as the ones with holes, such as stomatocyte-shaped, toroidal, G-3 toroidal and G-4 toroidal vesicles, are obtained from the simulations. Meanwhile, the shape transformation dynamics of these vesicles have been disclosed in detail. Although, most of the experimental works on hyperbranched polymer vesicles are limited to simple spherical shape, the present simulation results demonstrate they can have various shapes and shape transformations if the polymers or experimental conditions could be properly designed and controlled. We believe this theoretical work could guide scientist to design novel vesicles through the self-assembly of hyperbranched polymers.

ASSOCIATED CONTENT Supporting Information. This material is available free of charge via the Internet at

http://pubs.acs.org. Molecular structure of HBPO-star-PEOs; Curves of the conservative energy between the core beads and arm beads (EAB), the arm beads and water (EBS), and the core beads and water (EAS), respectively; Radial density distributions of A and B segments across the membrane of the unilamellar vesicles and the molecular packing model of the uni-lamellar vesicle; The detailed calculation method of the three eigenvalues of the squared radius of gyration tensor; Sequential snapshots of the formation of discocyte-shaped vesicle, tubular vesicle, toroidal vesicle, G-3


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toroidal vesicle with three holes, G-4 toroidal vesicle; Snapshots of G-3 and G-4 toroidal vesicle from different views; The evolutions of the inner membrane, the holes structure, and the total number of holes in the formation process of G-4 toroidal vesicle; Schematic representation of the micro-phase separated single molecules in different shapes of vesicles.

AUTHOR INFORMATION Corresponding Author

E-mail: [email protected]; [email protected] Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported by the Center for High-Performance Computing, Shanghai Jiao Tong University. We thank the National Natural Science Foundation of China (21774077, 51773115, 21474062, 21404070 and 91527304), and the Program for Basic Research of Shanghai Science and Technology Commission (17JC1403400) for financial support.

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2014, 10, 2245-2252.

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Insert Table of Contents Graphic and Synopsis Here.

This work investigates for the first time on the shape transformations of vesicles self-assembled from amphiphilic hyperbranched multiarm copolymers by dissipative particle dynamics simulations.


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Shape Transformations of Vesicles Self-Assembled from Amphiphilic

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