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Flow-Induced Shape Reconfiguration, Phase Separation and Rupture of Bio-Inspired Vesicles Xiaolei Chu, Xiang Yu, Joseph Greenstein, Fikret Aydin, Geetartha Uppaladadium, and Meenakshi Dutt ACS Nano, Just Accepted Manuscript • Publication Date (Web): 05 Jun 2017 Downloaded from http://pubs.acs.org on June 6, 2017

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Flow-Induced Shape Reconfiguration, Phase Separation and Rupture of Bio-Inspired Vesicles Xiaolei Chu, Xiang Yu, Joseph Greenstein, Fikret Aydin, Geetartha Uppaladadium and Meenakshi Dutt* Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854 ABSTRACT The structural integrity of red blood cells and drug delivery carriers through blood vessels is dependent upon their ability to adapt their shape during their transportation. Our goal is to examine the role of the composition of bioinspired multicomponent and hairy vesicles on their shape during their transport through in a channel. Via the Dissipative Particle Dynamics simulation technique, we apply Poiseuille flow in a cylindrical channel. We investigate the effect of flow conditions and concentration of key molecular components on the shape, phase separation and structural integrity of the bioinspired multicomponent and hairy vesicles. Our results show the Reynolds number and molecular composition of the vesicles to impact their flow-induced deformation, phase separation on the outer monolayer due to the Marangoni effect and rupture. The findings from this study could be used to enhance the design of drug delivery and tissue engineering systems. Keyword: Dissipative Particle Dynamics, bio-inspired vesicles, shape recognition, Poiseuille flow, hairy lipids, rupture

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Nanoparticles play a critical role in the encapsulation, storage and transport of therapeutic agents in a wide range of applications including drug delivery. The circulation time and bio-distribution of the nanoparticles is critically dependent upon their characteristics. The characteristics include the nanoparticle size,1-5 shape6-10 and response to various flow conditions11 (e.g., the Reynolds number in the human circulatory system can range from 1 in capillaries to 4000 aortas12). Hence, the successful delivery of therapeutic agents hinges upon the ability of the nanoparticles to maintain their structural stability under diverse flow conditions. The response of the nanoparticles to flow-induced stimuli is controlled by the architecture and concentrations of the constituent molecules. 13 Therefore, suitable molecular compositions can be selected to design nanoparticles which are structurally resilient under a range of flow conditions. The selection of molecular compositions can be inspired by biological particles such as red blood cells (RBCs) and bacterial cells. RBCs possess high deformability that allows for their transit through vasculature such as lung capillaries without rupturing.13-15 Similarly, bacterial cells such as E. coli have attachment pili or fimbriae which help them withstand shear forces.16 This study focuses on the response of cell- and bacteria mimetic nanoparticles to diverse flow conditions during transport in a channel. The investigation examines the role of the architecture and relative concentration of the molecular species constituting the nanoparticles on their response to various flow conditions. Of specific interest are nanoparticles with dynamic textured surfaces. Due to the challenges in resolving physical phenomena across a range of spatiotemporal scales through experimental approaches, a mesoscopic computational technique has been adopted for the study. Existing computational studies have investigated the behavior of different nanoparticles 2


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in microvascular flow, via techniques such as the boundary integral method,17 multiparticle collision dynamics18-20 and the lattice Boltzmann method.21 For example, elastic vertex networks have been used to model fluid vesicles to observe their shape transition in a capillary under different flow conditions.19 In addition, particle-based models have been used to study RBCs (modeled as single component liposomes) to demonstrated different kinds of shape deformations, as well as clustering and tumbling in response to various flow rates, viscosities and confinements.22-24 This study examines the behavior of multicomponent vesicles under Poiseuille flow in a channel and the role of specific molecular species on the response of the vesicles to different flow conditions. In this study, we have adopted a mesoscopic simulation technique entitled Dissipative Particle Dynamics (DPD) to examine the flow-induced response of two types of nanoparticles, namely bioinspired multicomponent and hairy vesicles. The multicomponent vesicles encompass representative amphiphilic molecular species present in biological cell membranes.25 Whereas the hairy vesicles are composed of amphiphilic molecular species, some of which are bearing water-soluble functional groups, or tethers, to mimic the fimbriae. The selection of the tethers was determined from earlier studies which showed that tether-bearing vesicles have extended in-vivo circulation half time and enhanced biodistribution. We examine the impact of the Reynolds number and the relative concentration of the key molecular components on the response of the two nanoparticles to the flow in a channel. We observe the vesicles to resist deformation with increasing Reynolds number, relative concentrations of cholesterol, molecules grafted with tethers and the tether length. For sufficiently high concentrations of the molecules bearing long tethers and 3


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Reynolds number, the molecules are observed to phase separate in the outer monolayer of the vesicles due to the Marangoni effect. In addition, the vesicles are unable to preserve their structural integrity and rupture at high Reynolds number, lower concentrations of the tether-bearing molecules and tether length. The results from this study could guide the design of nanoparticles with molecular compositions optimized for desired flow-induced response characteristics for applications in drug delivery, tissue engineering and bio-sensing.26-32 RESULTS AND DISCUSSION

Figure 1. Image of (a) DPPC, (b) PEGylated DPPC, (c) a HV with 50% of PEGylated DPPC and 50% of DPPC, (d) DPPC, (e) DMPC, (f) cholesterol, (g) glycolipid, and (h) a BMV with 32.5% of DPPC, 32.5% of DMPC, 30% cholesterol and 5% glycolipid. (i) An image of a HV flowing through in a cylindrical channel. The solvent particles are not shown. The image on the left shows the channel wall to encompass particles organized on a lattice.

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We used a mesoscopic simulation technique entitled DPD which simultaneously resolves the molecular and continuum properties, and reproduces hydrodynamic behavior.33-37 The distinct molecular species, as shown in Fig. 1, are represented by established coarse-grained models.25,38 In this study, we investigate two biologically inspired yet distinct types of vesicles: hairy vesicles (HVs) and bioinspired multicomponent vesicles (BMVs). The HVs encompass a mixture of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and Poly Ethylene Glycol-grafted, or PEGylated DPPC, as shown in Fig. 1 (a) - (c). The model for the PEGylated DPPC molecule (or hairy lipid) includes a hydrophilic tether (representing a PEG chain) grafted onto the head group of the lipid.38-40 We examine the impact of two tether lengths, encompassing 3 and 6 beads, which correspond respectively to degrees of polymerization 6 and 12 for PEG molecules.41 The BMVs are multi-component vesicles encompassing

two

distinct

phospholipid

species,

DPPC

and

1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), a glycolipid and cholesterol, as shown in Figs. 1 (d) - (g).

The effective chemistry of the amphiphilic molecules and their

interactions in both systems are captured through the soft repulsive interaction parameters between the different types of beads,25,38,42. In the cholesterol model, we introduce an additional bond between the pairs of diagonal beads (see Fig. 1 (f)) to represent the steroid ring. These additional bonds impart greater stiffness to the hydrophobic tail of cholesterol. As a result, the fluidity of the vesicle bilayer can be controlled by varying the concentration of cholesterol.43 To model the transport of the vesicles in a cylindrical channel under Poiseuille flow conditions, we create a cuboid-shaped simulation box of dimensions 40rc*40rc*60rc. The 5


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simulation box has a periodic boundary condition in the direction of the flow (z-axis). The particle density is set at ρ = 3 so that the total number of particles is given by 288,000. The channel is represented by a cylinder spanning the box with its cylindrical axis parallel to the z direction. The diameter of the channel is set to be 32 rc, corresponding to 25nm. The particles constituting the channel wall are organized on a lattice and kept frozen during the entire duration of the simulations. The solvent particles are located both inside and outside the channel. The soft repulsive interaction parameter between the particles encompassing the channel wall and all the other particles is set to be aij = 25.44 The number of solvent particles depends upon the composition of the vesicles so that the total number of particles in the system is conserved. Fig. 1 (i) shows a HV flowing through a cylindrical channel. To drive the flow through the channel, we implement an effective pressure gradient across the channel by adding a constant body force to all solvent particles outside the vesicles.44-48 The flow rate can therefore be tuned by varying the body force. The soft repulsion interaction parameter between the channel wall and solvent particles imposes a no-slip boundary condition which enables an equilibrium Poiseuille flow through the channel. We measure the time average of the z-component of the velocity of the solvent particles with respect to the radial distance from the channel cylindrical axis, as shown in Fig. SI1. The velocity at the solvent-channel interface is significantly small (factor of 10-4) compared to the magnitude of the mean flow velocity. Upon fitting the velocity to a parabolic line, we find that the transport of the solvent through the channel closely approximates Poiseuille flow. We characterize the flow via the Reynold’s number (Re) which encompasses both inertial and viscous contributions from the solvent flow. The Reynolds number is given by the equation Re =

ρU z DH , where ρ is µ 6


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particle density, U z is mean flow velocity and D H is the diameter of the channel. The dynamic viscosity ( µ = 1.60 ετσ -3 ) of the flow particles is derived by an established method through applying periodic Poiseuille flow in a rectangular simulation box.44 Using Re to characterize the flows will allow us to draw correspondence with biological systems involving flows of particles through confined volumes.49,50 We begin with an equilibrated vesicle in the cylindrical channel, surrounded by solvent particles. The simulations are run for a time t0 = 1000τ before a time dependent body force F = F0 (

t − 1) is applied to each solvent particle in the channel. This approach is t0

used to prevent the rupture of the vesicles caused by rapid solvent flow. After time t = 2t0 = 2000τ , the force F reaches the target value of F0 and remains constant for the

remaining duration of the simulation (namely, 18,000 τ). The equilibrium mean flow velocity has a linear dependence on F0 , as shown in Supporting Information (SI) Fig. SI1. Therefore, we tune the Re by varying the body force F0 from 0 to 0.008

k B T / σ . We study the shape

reconfiguration, phase separation and rupture of the vesicles under different flow conditions and examine the underlying mechanisms. Four random seeds were used to test the reproducibility of the measurements for each system. The HVs with tethers encompassing 3 and 6 beads will be referred respectively as HV-3 and HV-6.

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Figure 2. (a) Phase diagram of HV-6 for different concentrations of hairy lipids and Re. The relative length scale in the figure does not represent the real size of the vesicles. The flow is in -z direction. (b) Deformation index of HV-6 as a function of the concentration of hairy lipids and Re. All the measurements were performed using four random seeds.

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Flow-induced shape reconfiguration of HVs and BMVs. The shape of the HVs and BMVs are observed to undergo significant reconfiguration for a range of Re. Fig. 3 shows the characterization of the shape of HV-6 for different concentrations of the hairy lipids and Re. For small values of the mean flow velocity ( U z < 0.1 rc / τ) and Re (Re < 6 ), we do not find significant changes in the shape of the HVs. These results are observed for all concentrations of the hairy lipids. The HVs are observed to possess an approximately spherical shape when no flow is applied. As Re increases, the shape of the vesicles transitions from a sphere to a bullet with a slightly tapered head towards the direction of the flow. We note that at Re = 40, for a vesicle with 10% molar concentration of the hairy lipids, the shape of the vesicle undergoes a transition from a symmetric to an asymmetric bullet-like vesicle. This transition is significantly distinct from vesicles under the same flow conditions but with higher concentration of the hairy lipids. For higher concentrations of hairy lipids and Re, the hairy lipids are observed to phase separate on the surface of the HVs. This behavior will be discussed in the next section. To understand the role of the molecular composition and flow conditions on the deformation of the HVs, we perform quantitative measurements of the shape reconfiguration. The bullet-like shapes are approximately axially symmetric and therefore can be characterized through the Deformation Index (DI).51 The DI is defined as DI =

X − 1 , where Y

X and Y are respectively the long and short principal axes of the vesicles excluding the tethers. We measure the DI of the HV-6, for a range of concentrations of the hairy lipids (10% - 50%) and Re (0, 6, 12, 20, 25, 32, 38 and 45), as shown in Fig. 3(b). We would like to note that for solvent flows with Re > 45, the vesicles were observed to rupture under steady-state 9


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flow conditions and yield bicelles. Whereas for Re = 45, the HV-6 with lower concentration of hairy lipids (10 % - 30%) are observed to rupture. HV-6 with higher concentration of hairy lipids maintain their structural integrity and bullet-like shapes. Since DI measurement on compositions and flow conditions which yield bicelles cannot be compared with corresponding measurements for unruptured vesicles, those cases are excluded from Fig. 3. A movie of the rupture process is included in the supporting information. The shape transition of HV-6 from a sphere to a bullet is characterized by an increase of the DI, with Re > 6. At Re = 32, HV-6 with 10% and 20% concentrations of hairy lipids under go another transition from a bullet-like to a parachute-like shape which leads to rupture. This transition is captured by the sharp increase in DI. The DI measurements are found to support the phase diagram of HV-6 for different concentrations of hairy lipids and flow conditions. It is also observed that HV-6 maintains axial symmetry under different flow conditions, in comparison to HV-3 and BMV. The axial symmetry could be promoted by the spatial reorganization of the hairy lipids to enhance the resistance against the high flow-induced shear.

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Figure 3. (a) Phase diagram for the shapes of the HV-3 at different concentrations of the hairy lipids and Re. The relative length scale in the figure does not represent the real size of the vesicles. (b) Measurement of the deformation index of the HV-3 as a function of the concentration of hairy lipids and Re. All the measurements were performed using four random seeds.

We examined the effect of tether length on the shape of the HVs under diverse flow conditions, as shown in Fig. 4. Similar to the results for HV-6, significant reconfiguration of 11


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the shape of the HV-3 is observed for Re > 10. For 10% concentration of hairy lipids and Re > 32, the vesicle undergoes a transition from a bullet-like to an unstable worm-like shape. However, for higher concentrations of the hairy lipids, the DI increases with Re but the shape of the HV-3 remains stable. The presence of 20% concentration of hairy lipids stabilizes the shape of HV-3 under strong perturbative flows (that is, Re ≥ 32). However, it is unclear whether higher concentrations of hairy lipids would reduce the shape reconfiguration of the HV-3 for high Re. We note that all the HV-3 rupture at Re = 45.

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Figure 4. (a) Phase diagram for the shapes of BMVs for different concentrations of cholesterol and Re. The relative length scale in the figure does not represent the real size of the vesicles. (b) Measurements of the deformation index of BMV as a function of the concentration of cholesterol and Re. All the measurements were performed using four random seeds. We examined the flow-induced shape reconfiguration of BMVs for different concentrations of cholesterol, as shown in Fig. 5. The shape of the BMVs are found to be impacted by the flow conditions. Also, BMVs with higher concentration of cholesterol are observed to resist shape reconfiguration for higher values of Re. We surmise that the presence of cholesterol in the bilayer increases its rigidity and enables the bilayer to resist shear-induced deformations caused by the solvent flow. Based on the DI measurements, a BMV encompassing 10% concentration of cholesterol could have 50% change in its shape compared with a BMV with 50% concentration of cholesterol at the highest Re.

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Figure 5. Measurements of the surface stress as a function of Re for (a) HV-6, (b) HV-3 and (c) BMV. The measurements for the HVs have varied the concentration of the hairy lipids. Similarly, the measurement of the BMVs have varied the concentration of cholesterol. All the measurements were performed using four random seeds.

The role of the concentration of molecular components on the deformation underlying the shape reconfiguration of the vesicles can be understood through the surface stress. The 14


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surface stress is defined as the reversible work needed per unit area to deform a surface. In this study, we use the surface stress to evaluate the ability of a vesicle surface to resist shear-induced deformation under flow. We evaluated the surface stress through the following equation: σ =

1 Fαβ ( yβ − yα ) .52 Where Ac is the surface area of the vesicle, N is ∑ ∑ 2 Ac N α β ≠α

the total number of particles involved in this calculation, Fαβ is the non-bonded force between particle α and β , and y is the position vector of a particle.

The surface area

of each vesicle is evaluated through Delaunay triangulation of a three dimensional point set of the lipid head beads. The surface stress is averaged over all the lipid head beads and measured as a function of the Re, as shown in Fig. 6. We observe a decrease in the surface stress for both BMVs and HVs with Re. This result indicates that the vesicles are less resistant to deformation at higher Re. This observation agrees well with the measurements of DI as it suggests the vesicles tend to deform at a higher rate for larger values of Re. The shape deformations of HVs depends on the concentration of hairy lipids and tether length, as shown in Figs. 3 and 4. Hence, it becomes important to understand the effect of tether length and concentration on the surface stress. This knowledge can link the resistance of HVs to flow-induced deformations and molecular compositions. Higher concentration of the hairy lipids does not appear to have a significant effect on the deformation resistance of the HVs. The surface stress is significantly lowered for shorter tether length, for 10% concentration of the hairy lipids. This effect becomes more pronounced at high Re. This result explains the sudden change in the deformation of the vesicle as characterized by the DI at the corresponding flow conditions. These results are consistent with the phase diagrams shown in Figs. 3 and 4, where large deformations are observed for 15


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HV-3 with 10% concentration of hairy lipids. For the BMVs, the concentration of the cholesterol is observed to influence the surface stress of the vesicles as demonstrated by the different levels of deformation, especially at high Re. The surface stress increases with the concentration of cholesterol, with the vesicles undergoing smaller deformations at certain values of the Re. These results are supported by experimental studies which reported that cholesterol-encompassing liposomes deformed less than their pure lipid counterparts under microstreaming flow.53 As the concentration of cholesterol in the bilayer increases, the bilayer will be more rigid. Hence, more work will be required to deform the surface of the vesicle. This will result in increasing surface stress and less shear-induced deformations in the bilayer.

Flow-induced phase separation in HVs. The morphological transition of the HV-6 from a spherical to bullet-like shape is accompanied by a phase separation of the hairy lipids on the surface of the vesicle (see Fig. 3). An examination of the internal cavity of a HV-6 (see Fig. 7) shows the hairy lipids to be uniformly distributed in the inner monolayer. The PEGylated lipids in the outer monolayer are exposed to the solvent flow in the channel whereas those in the inner monolayer are not. We surmise that the phase separation is promoted by the solvent particles impinging on the tethers emanating from the outer monolayer of the HV-6. The solvent particles in the center of the channel move faster than those closer to the channel wall, as shown in Fig. 2. Averaged over a long time scale, the vesicle under steady state moves as a single entity with particles possessing uniform velocity. This uniform velocity is approximately the mean flow velocity. Therefore, the velocity 16


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gradient of the flow acts as an effective pulling shear force in the direction of the flow and as a drag shear force in a direction opposite to the flow, sweeping the hairy lipids to the front end and the rear part of the vesicle. This phenomenon is known as the Marangoni effect which was earlier used to explain the influence of surfactants on the rising velocity of a gas bubble in solution.54 Another study reported gathering of surfactants molecules in the liquid-liquid interface on a deformed liquid droplet in shear flow.55 Our observation demonstrates stable surface phase separation due to the Marangoni effect in Poiseuille flow. In addition, the impact of the velocity gradient (in terms of the effective pulling and drag forces) on the vesicle increases with the length and concentration of the tethers. Therefore, the degree of phase separation in HV-6 increases with the concentration of the hairy lipids. Hence, the phase separation on the outer monolayer of the HV-6s is induced by the solvent flow, and not promoted by the phase behavior of the surfactants. We note that HV-3 and BMV do not demonstrate flow-induced phase separation.

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Figure 6. Measurement of the line tension as a function of Re for (a) HV-6, (b) HV-3 and (c) BMV. The inset in (a) shows the inner cavity of a HV-6 with 30 % hairy lipids. All the measurements were performed using particle trajectories generated from simulations with four different random seeds. We examine the correlation between the degree of phase segregation and Re by measuring the interfacial line tension under different flow conditions, as shown in Fig. 7. The measurements are performed on equilibrium configurations of the HVs and BMVs, for a range of concentrations of hairy lipids and cholesterol. The line tension of an interface 18


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between two segregated phases can be measured through the excess free energy per unit contact length along the interface. We estimate the line tension λ of the domain boundary

1  through the following equation λ =  (U AA +U BB ) − U AB  / lmo for a binary system (e.g., 2  HV).56 Similarly, the line tension for a quaternary system (e.g., BMV) can be written as a superposition

of

six

binary

terms

and

3 2

is

given

by

 

λ =  (U AA + U BB + U CC + U DD ) − (U AB + U AC + U AD + U BC + U BD + U CD  / lmo . Uij are the pair interaction energies between two like (i = j) or unlike components (i ≠ j), and ɭmo is given by 1.1rc which is the lateral size of the lipid molecules determined from the area per lipid.56 Our results show that under equilibrium conditions, the line tension decreases with increasing concentration of the hairy lipids in the HVs, as shown in Fig. 7. This result is in good agreement with an earlier study which demonstrated that the increasing excluded volume of the tethers reduces the interactions between the hairy lipids.38 For BMVs under equilibrium conditions, the line tension is observed to increase with the concentration of cholesterol (see Fig. 7). We believe that this result arises from the formation and growth of cholesterol-enriched domains which increases the interaction between the cholesterol molecules, as illustrated in Fig. SI2. We find the line tension for both BMV and HV-3 to remain independent of Re. Whereas for HV-6, the line tension is influenced by both Re and the concentration of the hairy lipids. These results show that phase segregation does not occur in HV-3, which agrees with the phase diagram in Fig. 4. For HV-6 with hairy lipid concentrations higher than 10%, we observe the line tension to rapidly increase for Re > 6. This trend continues until the line tension reaches a value where the phase segregated state is 19


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unable to be sustained due to the perturbative effect of the solvent particles at a critical Re (namely, Rec). For higher Re (Re ≥ 45 and Re ≥ 52 for respectively 10% - 30% and 40% - 50% concentration of hairy lipids), the line tension drops and the vesicle ruptures. The relation between the line tension and Re demonstrates that the phase segregation on the outer monolayer of HV-6 is induced by flow. In addition, the degree of the phase segregation is dependent on Re. We also conclude that Rec tends to increase with the concentration of the hairy lipids.

A possible explanation for this trend could be that solvent particles with

increasing momentum and kinetic energy are required to disrupt or prevent the phase separation of higher concentrations of hairy lipids. Hence, the HV-6 are able to increasingly resist flows that reduce the degree of phase separation on the surface of the vesicle with higher concentrations of the hairy lipids. It is worthwhile to point out that for hairy lipids concentration of 10%, we do not observe a significant variation in the line tension for different values of the Re in comparison to the other concentrations. The value of Rec for this systems is 20, which is the smallest among all the concentrations of hairy lipids.

Role of solvent on shape reconfiguration and phase separation in HVs. To understand the role of the solvent on the shape reconfiguration and phase separation, we examine the shear force acting on the vesicles. The shear force is defined as the force between solvent and tether beads in the direction of flow (that is, the z direction). The shear force on the HV is measured during the transient and equilibrium phases of the flow. These measurements were performed for Fo = 0.0004, 0.0008, 0.002, 0.003, 0.004, 0.005, and 0.006 k B T / σ which corresponds to Re = 2.6, 5.3, 12, 20, 26, 32 and 40. Fig. 8 shows the shear 20


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force on the tethers for 10% and 50% concentration of hairy lipids, for both HVs at Fo = 0.0004, 0.002, and 0.005 k B T / σ .

Fig. SI3 shows similar measurements for the remaining

concentrations of the hairy lipids and Fo.

Figure 7. Measurements of the shear force as a function of time, for 10% (left) and 50% (right) concentration of the hairy lipids, at Fo = 0.0004, 0.002 and 0.005 k B T / σ . For low Re or applied force (~ 0.0004 k B T / σ ), the shear force on the tethers is relatively constant. As the Re increases, the fluctuations in the shear force captures the response of the tethers on HV-6 to the impinging solvent (see Figs. 8 (c), (d)). Yet the shear 21


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force on the tethers is insufficient to induce a large degree of phase separation. In addition, the larger spacing between the hairy lipids and conformational configurations of the longer tethers introduces greater variability in the number of solvent beads trapped between the tethers. This results in greater fluctuation in the shear force for 10% concentration of hairy lipids due to the larger separation between neighboring tethers. When Re increases further, the hairy lipids completely phase separate on the surface of the HV-6 (see Fig. 2). For 10% concentration of hairy lipids, the time evolution of the shear force shows the phase separation to minimize the opposition to the flow of the solvent beads and reduce the shear force on HV-6 (see Fig. 8 (e)). Hence, the shape reconfiguration and phase separation processes preserve the structural integrity of HV-6 under flow. However, for 50% concentration of hairy lipids, their complete phase separation is accompanied by the shear force attaining an equilibrium value higher than its initial value (see Fig. 8(f)). We surmise that after the hairy lipids have redistributed to the extreme ends of the vesicle (see Fig. 2), the concentration of hairy lipids is sufficiently high that the tethers continue to encounter a large number of impinging solvent beads. We would like to point out that HVs with shorter tethers are determined to be significantly less responsive to increasing Re. Comparison of the shear force for different tether lengths, concentrations and Re can be obtained by comparing the average equilibrium shear force, as shown in Fig. 9 (a). For HVs with shorter tethers, the shear force increases with the concentration of hairy lipids but remains primarily unresponsive to changes in Re. One possible hypothesis for this observation is that there are fewer solvent beads interacting with the shorter tethers than there are with the longer tethers. 22


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We test this hypothesis by computing the solvent frequency which is the number of solvent particles at a given distance from the outer monolayer of a HV divided by the total number of solvent beads (see Fig. 9 (b)). The solvent frequency between distances 0 to 0.899 rc (length of short tether) is the same for both tether lengths. For larger distances, the long tether continues to be exposed to the solvent, as captured by the solvent frequency. Hence, the response of HV-6 to variations in Re is due to the solvent beads trapped between the longer tethers at a distance ranging from 0.899 rc to 1.838 rc (namely, the tether length). These results support our proposed hypothesis of more solvents beads interacting with longer tethers. The shear force on the tethers of HV-6 at 10% and 20% concentration of the hairy lipids increases with Re but is not accompanied by any phase separation. For Re > 20, the shear force begins to decrease. The higher values of Re are accompanied by movement of the hairy lipids towards the extremities of the vesicle to reduce opposition of the tethers to the solvent flow. For higher concentrations of hairy lipids, the shear forces are observed to increase until Re = Rec before attaining an equilibrium value. This behavior at higher Re is attributed to the limited space at the extremities of the vesicle which is unable to accommodate all the hairy lipids. Whereas phase separation is observed to occur at higher Re and concentrations of the hairy lipids, some of these lipids will drift away from the extremities and oppose the solvent flow. The distribution of hairy lipids at the two extremes implies that the vesicles experience shear forces in two opposite directions (along and against the flow direction) due to the Marangoni effect. However, we record significantly positive net shear force for HV-6 at nontrivial values of Re. This explains why we observe majority of the hairy lipids to gather at 23


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the rear extremes of the vesicle upon phase separation. For increasing concentrations of hairy lipids at a given Re, the shear force on the tethers in HV-6 increases due to higher number of the solvent beads impinging upon the tethers and occupying the space between the tethers. With increasing concentration, the shear forces reach a maximum at 30% concentration of the hairy lipids before decreasing due to the limited volume between the tethers available for the solvent beads to occupy. These results support the hypothesis that phase segregation in the outer monolayer of the vesicle is flow induced. At 30% concentration of hairy lipids, the shear force increases after it reaches a minimum at Re=32. At Re=32 the hairy lipids reorganize themselves to the extremities of the vesicles so as to minimize the opposition of the tethers to the solvent flow. When Re increases to 40, the hairy lipids are unable to move to the extremities of the vesicles. This causes the tethers to oppose the flow of the solvent, thereby increasing the shear force.

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Figure 8. Measurements of the (a) average shear force experienced by the hair groups of HV-3 and HV-6 for different concentrations of the hairy lipids and Re, and (b) the normalized solvent frequency outside the vesicle as a function of the distance from the outer monolayer of the vesicle.

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Figure 9. Images of HV-6 with 50% hairy lipids during rupture process: time (a) t’ = 0 τ, (b) t’ = 200 τ, (c) t’ = 260 τ, (d) t’ = 360 τ. Flow-induced rupture of HVs and BMVs. The vesicles are unable to maintain their structural integrity beyond a specific Re. We observe BMV and HV-3 to rupture at Re ≥ 45, for all concentrations of cholesterol and hairy lipids respectively. Similarly, HV-6 with hairy lipids at concentrations given by 10 - 30% and 40 - 50% rupture respectively at Re = 48 and Re = 52. These observations indicate that the concentration of cholesterol does not have a significant effect on preserving the integrity of the vesicles under flow. However, longer tethers and higher concentrations of hairy lipids enhance the structural integrity of the vesicles at a higher Re. The rupture mechanism is induced by the spatial reorganization of the molecular components in the outer monolayer, as shown in Fig. 10. Due to the strong flow-induced shear force, a few molecules are pushed out from the bilayer and form a tail. These molecules can disaggregate from the vesicle and re-aggregate to form a micelle (Fig. 10 (a)). As the vesicle continues to lose molecules, the molecular population in the outer monolayer reduces. The molecules in the inner monolayer reorganize to shield the hydrophobic region of the 26


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bilayer from exposure to the solvent. This process leads to the formation of a transient pore in the bilayer, as shown in Fig. 10 (b). The size of the transient pore increases due to the extensional shear applied on the bilayer by the flow, fully exposing the aqueous interior region of the vesicle and eventually leading to its rupture. The mechanism underlying the rupture process is similar for all the vesicles. Distortion of the vesicles due to flow-induced extensional shear could also induce their rupture. The molecules in the bilayer will lose their tight packing as the vesicle elongates and deviates from a spherical shape. This process will increase the exposure of the hydrophobic tails of the molecules to the aqueous environment. The molecules will reorient their head groups to prevent energetically unfavorable interactions between the hydrophobic tails and the solvent, which would cause the formation of transient holes, and eventually rupture the vesicle. This mechanism is pertinent for BMVs, where we do not observe disaggregation of the molecules from the vesicle and their re-aggregation to form micelles.

CONCLUSION

Via DPD, we examined the transport of cell-mimicking and bacteria-mimicking vesicles in a cylindrical channel under Poiseuille flow conditions. Our results demonstrate the concentration of cholesterol, hairy lipids, the length of the tethers and Re to influence the shape, phase separation and structural integrity of the vesicles. The concentration of cholesterol is observed to impact the mechanical stiffness of the bilayer. Hence, higher concentrations of cholesterol impart greater resistance to shear-induced deformations. Cholesterol-rich domain formation is observed for higher concentrations. However, no large-scale phase separation of cholesterol is observed. The structural integrity 27


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of the BMV is determined to be independent of the concentration of cholesterol. The tether length is found to impact the interactions between the solvent and tether beads. Increasing the tether length results in greater excluded volume which in turn traps solvent beads at the bilayer solvent interface, and shields it from rapidly moving solvent beads. The population of the solvent beads occupying the region between the bilayer-solvent interface and the length of the short tethers is the same for both tether lengths. However, the short tethers are unable to trap the solvent beads between the tethers and protect the bilayer-solvent interface from flow-induced shear. Hence, the vesicle becomes increasingly resistant to flow-induced deformation with tether length. This effect is enhanced for increasing tether concentrations. Similarly, the structural stability of the vesicle increases with tether length and concentration. In addition, the shape of the vesicles is observed to remain symmetric along the channel cylindrical axis for higher tether length and concentrations. The velocity gradient in the channel applies an effective pulling and dragging force on the tethers, thereby sweeping the hairy lipids to the extremities of the vesicle. This effect is enhanced by high Re, tether length and concentration, and results in the phase separation of the hairy lipids on the surface of the vesicle due to the Marangoni effect in Poiseuille flow. The phase separation of the hairy lipids prevents the opposition to the flow of the solvent, thereby aiding the preservation of the structural integrity of the vesicle. The predictions from our investigation can be tested via some experimental techniques. Techniques such as electron microscopy can be used to visualize lipid vesicles at nanometer resolutions.57 The electron microscopy technique can be combined with immuno-gold 28


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staining to investigate specific molecules on the vesicle surface, and hence be used to test some of our predictions.58 Since the vesicles are flowing in the fluid in our study, an alternative method to test our predictions is flow cytometry. The sensitivity of this method has been recently improved to enable the detection of biological particles whose diameters are less than 100 nm.59 For example, in a recent investigation,60 a miniaturized nano flow cytometer was used to analyze single vesicles with diameters in the range of 100 nm. This investigation demonstrated fluorescent labelling of single vesicles and multi-color detection of specific molecules on the surface of vesicles within this size range. Although the vesicles in our study are smaller than this range (30-40 nm), we would expect similar observations as reported for the size range of 100 nm as the vesicles would approximately be in same scale. To test our predictions, we can label one of our lipid species (such as the PEGylated lipids). Using this approach, we can track the locations of the PEG groups as a function of the flow rate. The results from this study can potentially aid the design of drug delivery vehicles which can sustain transport through confined volumes such as blood capillaries, or microfluidic devices in tissue engineering for enhanced in vivo transport efficiency. For example, our results provide insight on the organization of PEG groups on the surface of the vesicle as function of the concentration and length of the PEG chains, and the flow rate of the solution. We observed phase separation of the PEG chains at certain concentrations of the PEG chains and flow rates. The phase separation results in the formation of non-PEG bearing patches on the vesicle surface, which can enable the binding of these vesicles to immune cell surfaces. Thus, the design parameters can be selected based on the blood flow rate in the 29


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targeted region of the body. In addition, the shape and elastic properties of the drug delivery vehicles can influence their circulation time and biodistribution profile.61,62 Our results can provide insight on suitable cholesterol concentrations for BMVs or PEG concentrations for HVs at various flow rates to obtain a specific shape for the vesicles. In addition, it has been shown that deformable particles with shapes and elastic properties similar to red blood cells have longer circulation time and improved biodistribution profiles.61 Thus, although our vesicles do not have underlying cytoskeleton encompassing spectrin, they can be designed to mimic the shape and elastic properties of red blood cells.

METHODS The details of the DPD simulation technique33,38,42 along with the pair and non-pair interactions25,42 used in this study can be obtained from our previous investigations. Physical correspondence of the model was obtained by an established approach.25,38,42

Supporting Information

The Supporting Information is available free of charge on the ACS Publications website at DOI:.

One figure of velocity profile of the flow in the cylindrical channel in the simulations; One figure of mean flow velocity in the channel depending on the body force imposed on the flow particles; one figure of per-bead cholesterol-cholesterol interaction energy increases linearly as the concentration of cholesterol increases in the BMVs; one figure of shear force measurement for HVs at different flow rates. (PDF) 30


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One movie of a HV-6 vesicle with 50% hairy lipids rupturing at Reynolds number equals to 50. (AVI) Corresponding Author * [email protected]

ACKNOWLEDGEMENTS This research has been supported by RDI2 through its ELF initiative. The authors also acknowledge the use of computational resources at Texas Advanced Computing Center and San Diego Supercomputer Center through XSEDE allocation TG-DMR1400125. We would like to thank Dr. Charles M. Roth and Dr. Stavroula Sofou for insightful discussions on transport of nanoparticles in the circulatory system.

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