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Oct 26, 2009 - The spontaneous fusion between the vesicles is studied, whose mechanism is as follows: first, a stalk is formed between the vesicles; t...
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Spontaneous Fusion between the Vesicles Formed by A2n(B2)n Type Comb-Like Block Copolymers with a Semiflexible Hydrophobic Backbone Ying-Tao Liu, Ying Zhao, Hong Liu, Yu-Hua Liu, and Zhong-Yuan Lu* Institute of Theoretical Chemistry, State Key Laboratory of Theoretical and Computational Chemistry, Jilin UniVersity, Changchun 130023, China ReceiVed: April 18, 2009; ReVised Manuscript ReceiVed: October 5, 2009

The spontaneous vesicle formation and fusion of A2n(B2)n (n ) 2-10) type comb-like block copolymers with semiflexible hydrophobic backbone are studied via dissipative particle dynamics (DPD) simulations. By systemically varying the solvent condition, we construct a phase diagram to indicate the thermodynamically stable region for vesicles. The spontaneous fusion between the vesicles is studied, whose mechanism is as follows: first, a stalk is formed between the vesicles; then, the holes appear in both vesicles near the feet of the stalk; finally, the stalk bends to circle the holes and the fusion process is completed. This fusion pathway is similar to that observed in Monte Carlo simulations and dynamic self-consistent filed theory but different from those reported in coarse-grained molecular dynamics and DPD simulations. The main reason for the difference may be attributed to the molecular structures used in different simulation techniques. 1. Introduction Vesicles are important three-dimensional assemblies. Their structural characteristics of the hollow sphere have attracted much attention for a variety of studies ranging from drug and gene delivery to chemical storage and waste transport. Vesicles with various sizes and functions can be spontaneously formed by amphiphilic polymers,1-6 which offer a rich diversity in chemical and material properties. A lot of functions of vesicles are related to their fusion behavior. In this aspect, understanding the vesicle fusion is of great importance. However, it is not easy to elucidate the vesicle fusion process on microscopic time and length scales in experiments due to the limitation of typical apparatus resolutions. In theoretical treatments of vesicle fusion, the most popular model is based on the phenomenological expression in terms of the elastic moduli,7 and the assumption of a particular fusion pathway has to be made.8 This, lacking enough microscopic details, hinders the pursuing of possible fusion pathways and the understanding of the molecular mechanism of vesicle fusion. Now the computer simulation techniques can serve as satisfactory tools to build up microscopic vesicle models and study their fusion behaviors. Atomistic molecular dynamics (MD) can be used to study vesicle fusion over short times and for small systems, but coarse-grained simulation techniques are needed to study realistic system sizes and times. With the assistance of coarse-grained MD simulations, Knecht and Marrink constructed the initial state, and studied the fusion of a spherical vesicle on the atomistic level.9 Two typical fusion pathways were found. In the first one, a stalk appears quickly in between the vesicles; subsequently, a hemifusion diaphragm (HD) is formed which is quite stable for a while; a crack-like pore is then induced by the defect, and the pore expends quickly and the fusion is completed. Another fusion pathway is similar to the first one, except that a hole near the HD appears for facilitating the solvent leakage and the exchange of lipid molecules between the inner and outer leaflets. Noguchi and * To whom correspondence should be addressed. E-mail: luzhy@ mail.jlu.edu.cn. Phone: 0086 431 88498017. Fax: 0086 431 88498026.

Takasu used Brownian dynamics (BD) simulations with the implicit solvent model to study the fusion between two vesicles, and a different fusion pathway was found10 at high temperature; i.e., the stalk is formed first; subsequently, two holes appear in both vesicles near the foot of the stalk; then, the stalk bends to circle the holes and the fusion is completed. This vesicle fusion dynamic pathway is further verified by Monte Carlo (MC) simulations,11 in which two parallel membranes are put in proximity to induce the formation of a stalk. In the research based on the dynamic self-consistent field theory (SCFT), Sevink and Zvelindovsky also favored this fusion pathway.12 In their research, the vesicles are formed by A2B2 type block copolymers and the fusion between the vesicles takes place without any manipulation. Besides the above mesoscopic simulation techniques, the dissipative particle dynamics (DPD) method had also been successfully applied to study the formation, budding, and fusion behaviors of vesicles.13-18 In comparison to SCFT, the chain molecules are not restricted to Gaussian and the chain dynamics can be illustrated vividly during the simulations in DPD. Moreover, the three governing forces between interacting DPD particles are pairwise additive and constructed to conserve the momentum, and correct hydrodynamic modes are included in the fluids. This is important to establish correct dynamic behavior for the evolution of complex assemblies in dilute solution. The main advantage of using DPD in the above studies resides in the high computation speed and the soft nature of the interactions between the DPD particles; thus, a larger time step can be used and a much longer time scale can be reached than typical coarse-grained MD. In a series of studies, Shillcock and Lipowsky and co-workers used DPD to study the fusion between a vesicle and a membrane or between vesicles under tension.18-20 They found that different fusion pathways can be realized by adjusting the membrane tension. At high membrane tension, the vesicle fusion pathway is characterized by stalk formation but without hemifusion. At low membrane tension, a new fusion dynamic pathway without stalk formation is proposed: one of the two contacting vesicles ruptures first so that a hemifusion diaphragm (mainly composed

10.1021/jp903570w CCC: $40.75  2009 American Chemical Society Published on Web 10/26/2009

Spontaneous Fusion between Vesicles of the lipids from the unruptured vesicle) is formed; then, a defect near the edge of the contact zone results in the rupture of the hemifused single bilayer and the fusion process is completed. Recently, Wu and Guo also used DPD to study the vesicle fusion induced by transmembrane proteins.14 The fusion dynamic pathway is fairly similar to that reported in ref 9, and the influence of transmembrane segments on accelerating the fusion is emphasized. The existence of transmembrane protein in vesicle models was also considered by Shillcock and Lipowsky in their DPD simulations,19 in which, however, the influence of the transmembrane protein is purely imposing a tension on the membrane. Other than the biological vesicles made of lipid molecules, the vesicles made of synthetic block copolymers (also called polymersomes) are also of great interest, because the use of synthetic polymers enables the designers to manipulate the characteristics of the vesicles in a wide parameter space. In simulation studies, the lipid molecules are always modeled as a big hydrophilic head connected with two hydrophobic tails, whereas various block copolymer architectures, for example, the diblock, the triblock, and the comb-like block copolymers,21 are designed to form vesicles. In a density functional theory (DFT) study with Gaussian chain model,21 the comb-like block copolymers with a hydrophilic backbone connected with hydrophobic side chains were found to form vesicles. Here, we show that, by using DPD simulations, somewhat trivially, the comb-like block copolymers A2n(B2)n (n ) 2-10) with both hydrophilic backbone/hydrophobic side chain and hydrophobic backbone/hydrophilic side chain can form vesicles. However, it is nontrivial that, in our DPD simulations, the backbones of the comb-like copolymers are semiflexible, controlled by adopting a bond angle potential between the backbone beads. This allows for more robust synthetic vesicles whose dynamical behaviors can therefore be compared to biovesicles. We then exclusively focus on the fusion between the vesicles formed by the comb-like copolymers. Since there are several different fusion pathways reported in the literature, especially the results obtained by using DPD simulations are not totally in agreement with those with MC and SCFT methods; we thus try to find whether these different fusion pathways are due to the simulation model or other factors. Moreover, simulating the fusion dynamics in most of the literature started with artificially placing the vesicles or membranes in close proximity. We notice that, to our knowledge, there was only one spontaneous vesicle fusion dynamics reported by using SCFT with the Gaussian chain model.12 Therefore, in the present DPD simulation study, we especially focus on the spontaneous fusion between the vesicles which may avoid possible biasing due to artificial manipulation on the evolution of the fusion processes. The paper is organized as follows: Section 2 exhibits the simulation details, section 3 shows the results and the corresponding discussion, and finally section 4 presents the concluding remarks. 2. Models and Simulation Details In the DPD method, a coarse-grained particle represents a group of molecular entities. For simplicity, the particles representing the block copolymers and the solvents in our simulations are coarse-grained so that they possess the same mass and size. Their mass m, maximum interaction radius rc, and the temperature kBT are taken as the units of the simulations, i.e., m ) rc ) kBT ) 1; thus, the time unit τ ) (mrc2/kBT)1/2 ) 1. The force acting on a particle contains three parts, each of which is pairwise additive and whose maximum interaction radius is rc ) 1:

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∑ (FbijC + bFijD + bFijR)

bf i )

j*i

b FijC )

{

aij(1 - rij)rˆij (rij < 1) (rij g 1) 0

b V ij)rˆij FijD ) -γωD(rij)(rˆij · b b FijR ) σωR(rij)θijrˆij The conservative force b FijC is a soft repulsion acting along the line of particle centers, aij is a maximum repulsion between ri - b rj, rij ) |r bij|, and rˆij ) b rij/|r bij|. particle i and particle j, b rij ) b FijR act as a heat The dissipative force b FijD and random force b sink and source, respectively. ωD and ωR are r-dependent weight Vij ) b Vi - b Vj, and θij is a functions vanishing for r > rc ) 1. b Gaussian distributed random variable with unit variance. Espan˜ol and Warren22 showed that the dissipative force and the random force must obey the fluctuation-dissipation theorem. That is, ωD(r) ) [ωR(r)]2 and σ2 ) 2γkBT, so that the system has a canonical equilibrium distribution. Here, we select γ ) 3.67.23 In the DPD method, the time evolution of interacting particles is governed by Newton’s equations of motion24

db ri )b Vi dt dV bi ) bf i dt A modified version of the velocity-Verlet algorithm24,25 is used here to integrate the equations of motion. The time step is ∆t ) 5.0 × 10-2τ for the temperature control at kBT ) 1. A special property of comb-like block copolymers is that they can bend spontaneously by the uneven distribution of side chains around the backbone in bad solvents.26,27 It is naturally expected that the self-assembled membranes of the comb-like block copolymers, if possible, may possess spontaneous curvatures. Therefore, in this research, we mainly consider the comb-like block copolymer A2n(B2)n (n ) 2-10) with a structure as illustrated in Figure 1, in which A denotes the backbone particles and B the side chain particles, and study their self-assembly in dilute solutions. We use a harmonic spring with force Fs ) -krij (k ) 4) to connect the adjacent particles belonging to a polymer. A three-body potential is added on the consecutive triplets of the backbone to control the main chain rigidity,28 Uθ ) kθ(1 cos(θ - θ0)), where kθ is the bond angle potential strength, θ is the bond angle between the two bonds connecting particles (i - 1, i) and (i, i + 1), and θ0 ) 0 the equilibrium bond angle. We conduct the simulations in a cubic box with a side length equal to 40 at density F ) 3, so the particle number is 1.92 × 105. The repulsive strength between the same type of particle is RAA ) RBB ) RSS ) 25 (S denotes solvent), accounting for the compressibility of typical fluids.24 Groot and Warren had shown that the DPD interaction parameters between unlike species can be proportionally mapped onto Flory-Huggins χ parameters.24 Therefore, it is possible to tune the amphiphilicity of the block copolymer by varying the DPD interaction parameters between unlike species. It should be noted that, by systematically coarse-graining from experimental data, it is

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Figure 1. Model of comb-like block copolymer. Hydrophobic backbone, red beads; hydrophilic side chains, green beads.

possible to build up a DPD model quantitatively in accordance with a specific block copolymer system.29 However, in this research, we have not systematically coarse-grained the model from a specific polymer system, since we are trying to focus on the general behavior of vesicle formation and fusion in dilute solutions. The block copolymer concentrations, which are defined by the volume fractions of the block copolymer beads in the systems (since all kinds of beads possess the same volume), range from 0.04 to 0.12. 3. Results and Discussion To reduce the parameter space of this system, we fix the repulsive strength RBS ) 27 (the value is similar to that between two solvent particles) and RAB ) 70. Therefore, the factors influencing the self-assembly of the comb-like block copolymers mainly include the hydrophobicity of the backbone (RAS), the concentration of the block copolymer, the molecular weights of the block copolymer, and the rigidity of the backbone. In DPD simulations of membranes, the importance of the bending potential had been emphasized. Without the rigidity of the molecules that form the internal structure of the membrane, a very large incompatibility between the hydrophilic and hydrophobic parts is required to generate a membrane structure comparable to a biological one.28,30 Here, we have also studied the influence of kθ on the vesicle formation and found that increasing kθ results in a membrane with larger bending modulus and a bigger RAS is required to form a vesicle. Thus, in the following studies, we have chosen a moderate value of kθ with kθ ) 4 to ensure that the vesicle can be formed under suitable thermodynamic conditions. To check the side chain length on the vesicle formation and fusion processes, we constructed a series of comb-like block copolymers with structures A6(B3)3, A6(B4)3, and A6(B6)3, each of which consists of four parallel samples. These three models possess the same backbone but different side chain lengths as compared to A6(B2)3. In the simulations, we directly take the simulation parameters that were used in the A6(B2)3 system. For model A6(B3)3, we do obtain larger vesicles with diameters ranging from 19 to 27; an example is illustrated in the Supporting Information. However, for the A6(B4)3 model, we only find worm-like micelles; for the A6(B6)3 model, we only find lots of spherical micelles. This may be because longer hydrophilic side chains will stabilize the micelle structures and consequently prevent them from further assembling. To further study the possible fusion between larger vesicles formed by A6(B3)3 comb-like block copolymers, we increase the simulation box length to 64. After about 34 000 DPD time units, we observe three well-generated vesicles, whose diameters are about 19, 21, and 23, respectively. However, we have not observed fusion between them, even after long simulation times (see the Supporting Information). It may be because, for the A6(B3)3

Figure 2. Conservative energy between the backbone beads and the solvents, EAS, versus simulation time. Also shown is the typical morphology evolution during vesicle formation for A6(B2)3 comb-like block copolymer in dilute solution at a concentration of φ ) 0.08. Here, we only show the iso-density surface between components A and B. The chain structures and solvent beads are ignored for clarity.

model, long side chains will prevent cohesion due to the steric hindrance. This result implies that we can only study the vesicle fusion for comb-like block copolymers with short side chain lengths. To check the influences of the block copolymer molecular weights on the vesicle formation, we have simulated a series of comb-like block copolymers with various molecular weights (A2n(B2)n with n ) 2-10), and always observed spontaneous vesicle formations under suitable thermodynamic conditions. Since there is no difference in the vesicle formation process for the comb-like block copolymers with different molecular weights, we will mainly take the results obtained for A6(B2)3 as examples in the following discussion. A typical vesicle formation process for A6(B2)3 in dilute solution is illustrated in Figure 2, in which the iso-density surfaces between components A and B at different times are plotted. In this simulation, RAS ) 150 and the concentration is 0.08. We have also shown in Figure 2 the time evolution of an energy index, EAS, to characterize the self-assembly process. EAS is defined as the per particle conservative energy between the comb-like block copolymer backbone (A) and the solvent (S):

EAS )

∑

monomer

{ 21 R (1 - r ) }/N 2

ij

ij

monomer

In the simulations, the initial setup configuration is always randomly distributed comb-like block copolymers in dilute solution. As shown in Figure 2, in the beginning of the simulations, these block polymers start to self-assemble into small micelles (see the iso-density surface in Figure 2, for example, at t ) 1000). Then, these platelets continue to merge together and form a membrane-like structure (for example, at t ) 9000). This membrane-like structure undulates, and suddenly bends to form a vesicle structure (see the iso-density surface at t ) 14 000). During the process of vesicle formation, EAS decreases, since the self-assembly will minimize the interaction energy between the hydrophobic backbone and the solvents. As shown in Figure 2, the vesicle formation process can be characterized by four stages: first, randomly distributed block copolymers form micelles in a short time, as demonstrated by a steep decrease of EAS in Figure 2; second, a membrane-like structure is formed, which is stable for a long simulation time, as shown by the first plateau in Figure 2; third, when the

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Figure 3. Phase diagram obtained for comb-like block copolymer A6(B2)3 in different concentrations (φ) with various repulsive strengths between backbone monomer and solvent (RAS). The data points are the simulation results, and the phase regions are drawn with different colors to guide the eyes.

undulation of the membrane-like structure is strong enough, the membrane-like structure starts to bend quickly and EAS decreases sharply (as shown in Figure 2); at last, a stable vesicle appears and EAS reaches the second plateau, as shown in Figure 2. It should be mentioned here that by simply exchanging A and B while keeping all of the simulation parameters intact, i.e., changing the comb-like block copolymer backbone hydrophilic and the side chains hydrophobic just as in ref 21, we can still observe vesicle formation. Other factors influencing the vesicle formation are the backbone hydrophobicity of the comb-like block copolymer and the concentration. By systemically varying the repulsion strength between the backbone monomer and the solvent (RAS) and the concentration (φ), we can construct a phase diagram indicating the thermodynamic region that stable vesicles can be found, as shown in Figure 3. It is clear that, in lower concentrations, much hydrophobic backbone is needed to form a vesicle. To clarify the phase boundary between the micelles and the vesicles, we have redone the simulations near the phase boundary with different initial configurations and with longer times; no shift of the boundary line is found. Therefore, we think in these cases the systems are in equilibrium. In order to interpret the phase diagram, we calculate the number of side chain B beads inside (Nin) and outside (Nout) the vesicles and the ratio (rB) between Nin and Nout. The ratio rB takes the values 0.11, 0.19, 0.22, 0.24, 0.30, 0.32, 0.33, 0.37, and 0.37 for the concentrations changing from 0.04 to 0.12 with 0.01 as the step. Actually, rB represents the curvature ratio between the outer and inner spheres of a vesicle. A smaller rB means a higher bending free energy.31 To compensate for it, more energy reduction due to vesicle formation is needed. That is why, in lower concentrations, much hydrophobic backbone is required to form a vesicle. We also find that for comb-like block copolymers with different molecular weights, rB always takes a value around 0.33 for φ ) 0.10; i.e., the molecular weight does not have an apparent influence on the vesicle structure and stability. Vesicle fusion is essential for cell viability. Different computer simulation models were applied to study the vesicle fusion dynamic pathways. The results from Brownian dynamics,10 Monte Carlo,11 and dynamic SCFT12 suggest a dominant fusion pathway that a stalk is formed first; then, holes in both vesicles appear near the root of the stalk; subsequently, the stalk bends to encircle the holes and the fusion is completed. However, the results from coarse-grained MD9,32-34 and DPD14,18-20 do not favor the above fusion pathway; instead, they suggest different fusion pathways. Especially, DPD simulations revealed two typical pathways describing vesicle fusion. One

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Figure 4. Spontaneous vesicle fusion process for the comb-like block copolymer A6(B2)3. Here, φ ) 0.10 and RAS ) 150. In the figure, we show the iso-density surface between components A and B. For clarity, the chain structures and the solvent beads are not shown. Since we are focusing on the vesicle fusion process, some small droplets formed by the block copolymers in the system are also omitted when preparing the iso-density surface.

is from a stalk, and the stalk expands radially to form a hemifused state, which then eventually ruptures to complete the fusion process. The other is also from a stalk; it is then followed quickly by the formation of transmembrane pores. It is interesting to find that the vesicle fusion pathway (stalk formationholes in both vesicles-stalk bends to encircle the holes) supported by one group of simulation techniques (BD, MC, and SCFT) is not supported by the other group of simulation techniques (coarse-grained MD and DPD). Is this difference originated from the simulation techniques used or different molecular structures considered in different models (in BD, MC, and SCFT simulations, the linear diblock copolymers were considered, whereas, in coarse-grained MD and DPD, lipid-like molecules were considered)? We then increase the concentration of the block copolymers in our DPD simulations to φ ) 0.10 and study the spontaneous fusion between the vesicles. It should be noted that, in these simulations, no artificial manipulation of the vesicles is needed, and the initial simulation setup is always randomly distributed comb-like block copolymers in dilute solution. We select the system with RAS ) 150 as an example in the following discussion. Ten independent simulations are conducted for better statistics. First, randomly distributed copolymers self-assemble into micelles; second, the micelles diffuse in the simulation box and form larger ones when they meet together; third, some of the large micelles may bend abruptly to form vesicles; then, the copolymers and/or the micelles may further join the vesicles if they are approaching to a short distance; at last, due to the growth of the vesicles, two large vesicles are finally formed. It should be noted that the final shapes and sizes of the two vesicles will vary with samples (but not much), but their fusion mechanism is consistent. Interestingly, we have observed only one fusion pathway in these independent simulations. It should be noted that, for RAS e 100, we have not observed spontaneous vesicle fusion in the simulation time span in this research. It can be attributed to the lower tension in the cases of smaller RAS;28 thus, very slow fusion may take place between the vesicles if possible, as denoted by pathway I in ref 18. A typical fusion process, as shown in Figure 4, can be depicted as follows: first, two vesicles with different sizes and shapes are spontaneously formed due to the self-assembly of comb-like block copolymers (see, for example, the iso-density surface at t ) 12 500). These vesicles move independently in

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Figure 5. Spontaneous vesicle fusion process for the comb-like block copolymer A6(B2)3. Here, we focus on the region that the fusion takes place and present the chain structures during the fusion process. In the figure for one vesicle: hydrophobic backbone, red beads; hydrophilic side chains, green beads. For the other vesicle: hydrophobic backbone, purple beads; hydrophilic side chains, light blue beads. Water beads are not shown for clarity.

the simulation box, without any artificial manipulations. When the vesicles come into close contact, a thin stalk is formed. The stalk is stable for a comparatively long time; then, a hole appears in a vesicle near the foot of the stalk, which can be clearly observed at t ) 18 700. Quickly, the second hole emerges in the other vesicle near the foot of the stalk (see t ) 18 800). Then, the vesicles start to fuse together by stalk bending and circling the two holes (t ) 18 900). The stalk finally closes, and a tubular vesicle appears. To rule out the possibility that the system size may influence the fusion pathway, we have conducted simulations in a box with side length equal to 80 at lower concentrations (ranging from φ ) 0.01 to φ ) 0.05), and found that the vesicles can also fuse with the same pathway that was described above (please see the Supporting Information for details). Thus, the box with a side length of 40 in our simulations is big enough to demonstrate the vesicle fusion kinetics, and the initial state is not influencing the fusion

pathway. Although in the literature about DPD simulations of vesicle fusion, various time steps (ranging from 0.02 to 0.05) were adopted; there is also research showing that a larger time step may lead to artifacts on membrane properties.35 We thus redo the simulations related to vesicle formation and fusion processes with a smaller time step (0.02), but no difference about the vesicle formation and fusion dynamics is found. An example is shown in the Supporting Information. Thus, we conclude that our results shown in the present research are independent of the time step in the range we have selected. For a better illustration of the vesicle fusion dynamic pathway, we focus on the region in which the vesicle fusion takes place, and draw the molecular structures during the fusion in Figure 5. We can clearly see that these vesicles are close to each other in Figure 5a; then, a thin stalk is formed, as shown in Figure 5b. The holes appear in both vesicles near the feet of the stalk, as shown in Figure 5c and d, respectively. Finally, the stalk

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Figure 6. Spontaneous vesicle fusion process for the lipid-like molecule B3(A4)2. Here, we present the chain structures during the fusion process. In the figure for one vesicle: hydrophobic tails, red beads; hydrophilic head chains, green beads. For the other vesicle: hydrophobic tails, purple beads; hydrophilic head chains, light blue beads. Water beads are not shown for clarity. Parts a, b, and c correspond to t ) 6500, 6600, and 6650, respectively.

bends and encircles the two holes and the fusion process is completed, corresponding to the snapshots shown in Figure 5e and f, respectively. Similar results of vesicle fusion are obtained for the comblike block copolymers A2n(B2)n with various molecular weights (n ) 2, 3, 4, and 5). We observe that the fusion process is accomplished in a shorter time when n is smaller. This may be determined by the structure of the comb-like block copolymer, because a shorter chain can reorder easily. The vesicle fusion process in our DPD simulations is different from that reported in other DPD simulations14,18 and coarsegrained MD9 but similar to that observed in BD, MC, and dynamic SCFT simulations.10-12 We note that, interestingly, in these BD, MC, and SCFT simulations, the linear diblock copolymers were modeled, whereas, in these DPD and coarsegrained MD simulations, lipid-like molecules with one head connected to two tails were modeled. Thus, the question is as follows: is this difference on the fusion pathway originated from the simulation techniques used or different molecular structures considered in different models? To check this, we further construct a lipid-like molecule model with structure B3(A4)2, in which three linearly connected B beads denote the hydrophilic head with two hydrophobic tails, as denoted by four A attached. This lipid model structure is totally the same as that used in ref 18. For this lipid model, we adopt simulation parameters purely the same as those used in our comb-like block copolymer simulations. Thus, the only difference in this comparative simulation is the molecular structure. We find that the B3(A4)2 system with φ ) 0.10 does self-assemble into vesicles, which then spontaneously fuse together to form a larger one. Four independent simulations are conducted for better statistics. In each of the simulations, the fusion process is highly reproducible; an example is illustrated in Figure 6, in which parts a, b, and c correspond to t ) 6500, 6600, and 6650, respectively. In the beginning of the fusion, two vesicles touch each other; then, a stalk is formed between them. This stalk connection will evolve into an HD structure. As shown in Figure 6a, a hole shortly appears in one of the vesicles near the HD, connecting the regions inside and outside the vesicle. Figure 7a and b shows that the two vesicles are approaching each other, and Figure 7c is the iso-density surface version of Figure 6a, clearly showing the hole. This hole is transient, only for facilitating the solvent leakage and

Figure 7. The iso-density surfaces between components A and B are shown here. Parts a, b, c, and d correspond to t ) 6200, 6250, 6500, and 6650, respectively. A transient hole can be clearly seen in part c.

the exchange of lipid molecules between the inner and outer leaflets of the vesicle.9 It is closed again in a short time, as illustrated in Figure 6b. The HD structure is recovered soon, as shown in Figure 6b, and the transmembrane fusion pore is formed clearly, as shown in Figure 6c (and in Figure 7d the iso-density surface version). This fusion process is very similar to that reported in the literature, as denoted by pathway II, with both DPD18 and coarse-grained MD simulations.9 Actually, the membrane tension will strongly influence the fusion pathways. The membrane tension itself is related to several molecular factors such as the molecule structure, the interactions between different species, the rigidity of the molecules, and so on. In this research, the short side chain length and the rigidity of the backbone of the comb-like block copolymers may yield higher membrane tension. This will further determine the vesicle fusion mechanism which is accompanied by holes appearing in the vesicles. Therefore, the difference between the molecular structures yields different membrane tension, and finally results in different fusion pathways. However, in our simulations, we have not started with a well-prepared membrane; instead, we start from a randomly distributed copolymer dilute solution and trace the steps of vesicle formation and spontaneous fusion. Therefore, it is basically impossible for us to obtain a quantitative membrane tension in the simulations. In this simple comparison, we find that the molecular structure is a very important factor influencing the vesicle fusion dynamic process. Thus, a polymersome may not possess the function of a biovesicle formed by lipids. It seems that the fusion between the former is likely accompanied with holes in the vesicles, so the leakage of the solvents is inevitable. This phenomenon may not be good for biovesicles, but it may open a new way for the design of vesicles for other usages.

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4. Conclusions In summary, the spontaneous vesicle formation and fusion of A2n(B2)n (n ) 2-10) type comb-like block copolymers with a semiflexible hydrophobic backbone are studied via DPD simulations. The spontaneous fusion between the vesicles is studied, whose mechanism is similar to that observed in BD, MC, and dynamic SCFT simulations but different from those reported in coarse-grained MD and DPD simulations. The main reason for the difference may be attributed to the molecular structures used in different simulation techniques. Further studies along this line are ongoing. Acknowledgment. This work is supported by NSFC (20774036, 20974040, 50930001) and Graduate Innovation Fund of Jilin University (20091009). Supporting Information Available: Figures showing the iso-density surfaces for a system with a simulation box size of 80 × 80 × 80 and with a concentration of 0.01, the iso-density surfaces focusing on the two vesicles during fusion, an example of the vesicle formed for the A6(B3)3 model, three vesicles formed for the A6(B3)3 model in a larger box with a size of 64 × 64 × 64, and the vesicle fusion process simulated with a time step of 0.02. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Discher, D. E.; Eisenberg, A. Science 2002, 297, 967. (2) Allen, T. M.; Cullis, P. R. Science 2004, 303, 1818. (3) Hillmyer, M. A. Science 2007, 317, 604. (4) Hamley, I. W.; Castelletto, V. Angew. Chem., Int. Ed. 2007, 46, 4442. (5) Morishima, Y. Angew. Chem., Int. Ed. 2007, 46, 1370. (6) Blumenthal, R.; Clague, M. J.; Durell, S. R.; Epand, R. M. Chem. ReV. 2003, 103, 53.

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