Mechanisms of Vesicle Spreading on Surfaces: Coarse-Grained

Mechanisms of Vesicle Spreading on Surfaces: Coarse-Grained...

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Mechanisms of Vesicle Spreading on Surfaces: Coarse-Grained Simulations Marc Fuhrmans* and Marcus Müller Institute for Theoretical Physics, Georg-August-Universität, 37077 Göttingen, Germany S Supporting Information *

ABSTRACT: Exposition of unilamellar vesicles to attractive surfaces is a frequently used way to create supported lipid bilayers. Although this approach is known to produce continuous supported bilayer coatings, the mechanism of their formation and its dependence on factors like surface interaction and roughness or membrane tension as well as the interplay between neighboring vesicles or the involvement of preadsorbed bilayer patches are not well understood. Using dissipative particle dynamics simulations, we assess diﬀerent mechanisms of vesicle spreading on attractive surfaces, placing special emphasis on the orientation of the resulting bilayer. Making use of the universality of collective phenomena in lipid membranes, we employed a solvent-free coarse-grained model, enabling us to cover the relatively large system sizes and time scales required. Our results indicate that one can control the mechanism of vesicle spreading by tuning the strength and range of the interactions with the substrate as well as the surface’s roughness, resulting in a switch from a predominant inside-up to an outside-up orientation of the created supported bilayer.

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INTRODUCTION The deposition of phospholipid bilayers on solid supports is crucial for a number of analytical techniques as well as for technical applications.1 It allows to study (bio)membranes using, e.g., atomic force microscopy,2 surface plasmon resonance,3 or ﬂuorescence correlation spectroscopy,4 and it is a promising tool in the design of diagnostic biosensors.5 Apart from the Langmuir−Blodgett technique,6 adsorption of unilamellar vesicles to an attractive surface is a frequently used method to fabricate supported lipid bilayers (SLB).7 In this technique, a solution of vesicles is brought into contact with a suitable substrate. Given suﬃciently favorable conditions, the vesicles will then adsorb to the surface, rupture, and spontaneously condense into a continuous bilayer covering the substrate. Although frequently used, the exact mechanism in which this process occurs is not understood very well,8 and even basic properties like the orientation of the resulting SLB are often not resolved with certainty. Theoretical considerations based on elastic theory9−11 discuss the process in terms of competing energy contributions due to the attraction between the adsorbed bottom of the vesicle and the surface, the adsorption-induced curvature of the vesicle’s top, and the membrane stretching. They predict that the adsorbed vesicle ruptures somewhere on its curved nonadsorbed top, resulting in an inside-up orientation of the created SLB.11 These considerations do not take into account the potential role of neighboring vesicles or free bilayer edges stemming from vesicles already ruptured, which have been demonstrated to be important factors.12,13 Additionally, it is not straightforward to © 2013 American Chemical Society

capture the eﬀect of the range of surface interactions or surface roughness on the formation of the initial rupture event because the lipid membrane is described by an inﬁnitely thin elastic sheet. Experimentally, the process has been observed using combinations of atomic force microscopy (AFM14,15), surface plasmon resonance,13 quartz crystal microbalance with dissipation,15,16 and ellipsometry.15,17 In most cases, these methods do not reveal the orientation of the SLB. For that reason studies using either oriented peptides as labels18,19 or selectively labeling the lipids in one monolayer20 have been performed. The latter study, using vesicles with biotinylated lipids in the outer monolayer, reports a predominant inside-up orientation of the resulting SLB and is in qualitative agreement with the predictions from elastic theory. The two studies relying on enzymes, on the other hand, report an outside-up orientation of the formed SLB based on observed enzyme activity. A recent publication,20 however, has suggested alternative interpretations of the data reported in these two articles, pointing out that the ﬁndings reported in ref 18 would also be compatible with unruptured vesicles adsorbing to the substrate, whereas the results reported in ref 19 might be an artifact of too strong interactions between the modiﬁed photosynthetic reaction centers used as label and the substrate, casting doubts on the reported bilayer orientation in both cases. Received: January 10, 2013 Revised: March 5, 2013 Published: March 11, 2013 4335

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chosen so that randomly placed lipids spontaneously self-assemble into a bilayer. The dimensionless ratio dHG/(2a)1/2 ≈ 4.3 of the membrane thickness, dHG, and the area per lipid, a, compares well with typical experimental values of 4−5 for typical lipids.30 The additional factor of 2 accounts for the fact that the lipids in our model possess only a single tail, whereas biological lipids are typically two-tailed. A detailed description of the interactions and a list of the parameters is provided in the Supporting Information. The thermal energy kBT serves as unit of energy in our model. The unit of length is chosen as the range of the nonbonded interactions σ, and the unit of time is denominated τ. Comparing the average distance of the head beads of the two leaﬂets in our simulation, dHG ≈ 4.30 σ, to the experimental value of 3.8 nm for the phosphate−peak distance,30 we establish the relation 1 σ ≈ 0.9 nm. In a similar fashion, we can compare the experimental value of the diﬀusion coeﬃcient of lipids, D = 5 μm2/s,31 to the value D = 0.013 σ2/τ in our simulations and obtain 1 τ ≈ 2 ns. The rate of lipid ﬂip-ﬂops from one side of a tensionless bilayer to the other occurred with a frequency of ∼4 × 10−6τ−1 per lipid. This value is larger than the value in the earlier model28 because of the smaller number of beads per lipid and lower bead density in the present model. Compared to the time scale of the processes under investigation, 1000 τ, however, the ﬂip-ﬂop frequency remains still low and is not expected to aﬀect our results. Simulation Method. We use molecular dynamics simulations with a dissipative particle dynamics (DPD) thermostat.28,32,33 If not explicitly stated otherwise, simulations were conducted at constant volume (NVT). In addition, for some bilayer simulations we used an ensemble in which the tangential pressure was held constant at zero (NPtT). The details of the implementation have been reported previously.28 We used an integration step of 0.005τ and a friction coeﬃcient of 0.5 for the DPD thermostat. In simulations in the NPtT ensemble, we assigned a mass of 0.0001 and a friction coeﬃcient of 0.1 to the additional degree of freedom corresponding to area ﬂuctuations. Lipid Vesicles. We simulated vesicles with a size of 9800 lipids corresponding to a diameter of 28 σ or ∼26 nm. The vesicles were formed spontaneously in simulations starting from free bilayer disks. With this approach, the system is free to adopt a suitable lipid distribution between inner and outer monolayer. After equilibration, no net current of lipids between the two leaﬂets was detected. On average, 5616 lipids reside in the outer and 4184 in the inner monolayers. Cargo and Volume Constraint. Since our membrane model is solvent-free, we were able to simulate empty vesicles with no volume constraint. This scenario corresponds to long experimental time scales where leakage of the vesicle’s content occurs before spreading. In fact, available data from AFM scans14 as well as from ﬂuorescence measurements12 indicate that the volume of adsorbed vesicles can shrink without permanent rupture and spreading of the vesicle. Alternatively, we have ﬁlled vesicles with 80 220 “cargo” beads, which mimic the volume constraint due to solvent inside the vesicle. These cargo beads possess purely repulsive interactions with the lipid beads. Their self-interactions is similar to those of the lipid tails, i.e., a slightly compressible liquid with low vapor pressure. The exact interaction parameters are listed in the Supporting Information. The area of the ﬁlled vesicle increased by a factor of 1.3, and the deformation of the vesicle upon adsorption results in an additional increase of the membrane tension because the adsorbed shape deviates from the minimal surface-to-volume ratio of a spherical unadsorbed vesicle. Substrate. The substrate is represented by a 9−3 Lennard-Jones potential in the normal z-direction

A rare occasion where the orientation was reported without using labels is an AFM study by Puu and co-workers.14 In this study, the vesicles were found to adsorb to the substrate and ﬂatten until a two bilayer thick disk is visible in the AFM scans. The situation at the edges of this disk could not be directly observed but was deduced indirectly by the development inbetween subsequent scans. The authors inferred two pathways: a rolling mechanism and a sliding mechanism. In the rolling mechanism, the upper and lower bilayer stay connected throughout the whole process. Only on one side a pore is formed, which allows the upper bilayer to roll down onto the substrate in a treadmill-like fashion, resulting in an inside-up orientation of the SLB. In the sliding mechanism, the upper and lower bilayer ﬁrst become completely detached, and only then the upper bilayer slides down onto the surface resulting in a roughly 50% mixture of orientations in the SLB. Because of these experimental diﬃculties, computer simulations that provide direct insights into the spreading dynamics with molecular resolution are greatly beneﬁcial to explore diﬀerent spreading mechanisms and allow for a systematic variation of the diﬀerent interaction parameters. To the authors’ knowledge, at present, simulations of vesicle rupture and spreading on surfaces are limited to two studies using Monte Carlo simulations to study adsorption and condensation21 and adsorption and rupture22 of vesicles and one molecular dynamics study.23 The former studies reduce the process to two dimensions and do not take into account explicit lipids. Instead, strongly simpliﬁed phenomenological membrane models are used, which in the latter study represent the vesicle as a circular chain of interaction centers characterized by a certain bending and stretching energy. In this model, rupture occurs at a critical bending angle motivated by fracture theory.24 However, while a certain degree of coarse-graining is needed to reach the necessary system size and time scale required to simulate collective phenomena in lipid membranes25 like vesicle spreading, a representation that retains the molecular character of the lipids is desirable. Most recently, Wu et al.23 have simulated the spreading of vesicles using a coarse-grained model.26 This study highlights the importance of the hydrophobicity of the lipid tails and membrane tension and distinguishes three possible outcomes: (i) intact vesicles, (ii) partial desintegration of the vesicles, or (iii) SLB formation, which are discussed in their dependence on factors favoring rupture and healing of the vesicle membrane. Molecular details of the rupture process, as well as the possibility of conditions favoring diﬀerent rupture locations and, in consequence, SLB orientations, however, are not addressed.

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METHODS

Coarse-Grained Solvent-Free Model. We use a solvent-free, coarse-grained lipid model27,28 to study adsorption, fusion, rupture, and spreading of vesicles on attractive surfaces using dissipative particle dynamics. This model was shown to successfully reproduce key characteristics of lipid bilayers like area per lipid, bending rigidity, compressibility, and complex collective phenomena like the transition between gel and liquid phase, and also dynamic properties are well understood.29 Lipid molecules are represented by linearly connected interaction centers (beads). The amphiphiles are comprised of two bead species: 8 hydrophobic tail beads and 2 hydrophilic head beads. Nonbonded interactions are described by a weighted-density functional derived from expressing the nonbonded excess free energy as third-order expansion of the bead densities. The interaction parameters were

⎡⎛ ⎞9 ⎛ ⎞3⎤ S S V9 − 3(dz) = C ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎢⎣⎝ dz ⎠ ⎝ dz ⎠ ⎥⎦

(1)

representing the integrated van der Waals interactions between the solid surface and the lipid bilayer. The potential’s strength and range can be varied by the parameters C and S, respectively. The van der 4336

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Waals attraction is a power law and is not characterized by an intrinsic length scale; only the interplay between the van der Waals term that decays like dz−3 and the ad-hoc, repulsive contribution that decays like dz−9 deﬁnes a length scale. That length scale basically identiﬁes where the surface interaction switches from repulsive (at short distances) to attractive (at large distance). The strength of the van der Waals attraction (Hamaker constant) is proportional to the parameter combination CS3. A plot of the potential and the corresponding force is shown in Figure 1. The potential is truncated and shifted as detailed

model does not explicitly account for the speciﬁc interactions of diﬀerent lipid headgroups with diﬀerent kinds of substrates or any interactions due to the presence of ions, both of which are known to play a role in SLB formation. We rather assume that these eﬀects can be qualitatively captured by the strength and range of the surface potential (eq 1), and therefore, we do not associate any particular meaning with the power-law form of the surface potential. The strength and range are rather eﬀective parameters, whose values can be controlled, e.g., by a thin coating layer on the solid surface34,35 or electrostatic interactions. Another idealization of our surface model is absence of lateral structure or corrugations. Small scale corrugation has only a minor eﬀect on the equilibrium properties of SLB,36 but we expect it to exert a more pronounced eﬀect on the friction between surface and membrane. Since one particle of our coarse-grained model represents a collection of atoms, a faithful representation of surface friction is beyond the scope of the present model. In typical applications, there is a water cushion between the solid surface and the SLB that acts as lubrication layer, and one aims at minimizing the inﬂuence of the surface on the lipid dynamics in the SLB. Moreover, we note that the lack of explicit solvent in our model reduces friction in the nonadsorbed portion of the bilayer membrane. Thus, the in-plane dynamics of lipids in both the free and adsorbed bilayer is sped up.

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RESULTS General Eﬀects. Eﬀects on Bilayer Disks. The general eﬀects of the surface potentials on the lipid membranes were investigated using small bilayer disks (800 lipids, radius ≈6 σ) adsorbed to the surface as model for SLBs. This way we examine the surface’s inﬂuence on the bilayer thickness and the distribution of lipids between the proximal (facing toward the surface) and distal (facing away from the surface) leaﬂets. The free edge of the bilayer disks facilitates exchange of lipids between the monolayers and mitigates the long equilibration times due to the slow ﬂip-ﬂop rates in continuous bilayers. The line tension of the edges of the disks leads to a slight compression of the area per lipid and a concomitant increase of the bilayer thickness. However, these line eﬀects are small and not detrimental to our investigations because they aﬀect both leaﬂets in a similar way and are largely independent of the surface interaction parameters.

Figure 1. Surface potential and the corresponding force according to eq 1. The potential is cut oﬀ at a distance of 3.0 S using a shift function, and the increase of the force is additionally truncated for distances smaller than 1.11 S. in the Supporting Information. In addition, we implemented a cylindrical protrusion mimicking surface roughness. The potential is mapped around the protrusion so that the corresponding force always acts perpendicular to the surface as illustrated in Figure 2. While in principle all bead typeshydrophilic heads, hydrophobic tails, and cargo solventcan be aﬀected by the surface potential, we chose to only include interactions with the headgroup beads in most simulations; i.e., our simulations correspond to hydrophilic surfaces. Formally, the form of the surface potential is motivated by integrating the dispersion forces (van der Waals interactions) between a bead and the half-space occupied by the supporting surface. Our

Figure 2. Illustration of the protrusion of a “rough” surface. The potential is mapped around a cylindrical protrusion, so that the corresponding force acts perpendicular to the surface. The substrate is drawn in gray, and the cutoﬀ range of the potential is marked in red. Sketches of the force as a function of the distance r from the surface indicate the direction the force acts in in chosen regions. A two-dimensional cross section of the cylindrical protrusion is shown for sake of clarity. 4337

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Figures 3 and 4 show the density proﬁles perpendicular to the surface for the diﬀerent bead types as a function of the

Table 1. Headgroup Distance, dHG, and the Area Per Lipid, a, for the Proximal and Distal Leaﬂets of Bilayer Disks Adsorbed to Our Surface Potential; Ead Indicates the Potential Energy per Area Gained by Adhesion; Results Refer to Diﬀerent Values of the Strength, C, and Range, S, of the Surface Potentiala a [σ2] C [kBT]

S [σ]

prox

dist

dHG [σ]

Ead [kBTσ−2]

1.0 5.0 10.0 5.0

1.0

0.48(2) 0.46(2) 0.45(2) 0.46(2) 0.44(1) 0.43(1)

0.45(2) 0.50(2) 0.55(2) 0.50(2) 0.57(3) 0.71(4)

4.46(8) 4.48(8) 4.47(8) 4.48(8) 4.43(8) 4.17(8) 4.30

−0.39(7) −2.5(3) −5.8(5) −2.5(3) −3.4(3) −3.8(3)

1.0 2.0 3.0 free tensionless bilayer

0.50

a

Numbers in parentheses indicate the standard deviation of our data, and the values for a free continuous tensionless bilayer are given for comparison.

Figure 3. (top) Particle density proﬁles in the z-direction for diﬀerent strengths of the surface potential, eq 1, C/kBT = 1.0, 5.0, and 10.0, with ﬁxed range S = 1.0 σ. Note that the increased height of the proximal headgroup peak is mainly due to suppressed membrane ﬂuctuations at high interaction strength. To compare the actual particle numbers in the proximal and distal leaﬂets, one should therefore use the integrals of the headgroup peaks shown as dotted lines. (bottom) Plots of the surface potentials for comparison.

without correction. The latter eﬀect can, however, be avoided by dividing the continuous bilayer into smaller parts and separately obtaining the density proﬁle for each part. The full density proﬁle can then be reconstructed by aligning and averaging the partial proﬁles. Figure 3 compares the eﬀects of diﬀerent potential strengths, reﬂected by the C parameter, for an unscaled potential range (S = 1.0 σ). The area per lipid of the proximal leaﬂet is smaller and the thickness of the whole bilayer is larger than in the free bilayer, which partially results from the line tension of the edge of the disk. In addition, with increasing potential strength the area per lipid of the distal leaﬂet increases signiﬁcantly, while the area per lipid of the proximal leaﬂet decreases slightly (except for the weakest potential strength), creating an asymmetry between the two leaﬂets. This eﬀect goes hand in hand with an extension of the lipids in the proximal leaﬂet, causing the proximal leaﬂet to thicken while the distal leaﬂet becomes thinner. In addition, the total area of the adsorbed bilayer disks’ increases (data not shown). The potential energy of adsorption depends on the parameters used (cf. Table 1) but is in the order of magnitude of kBT/σ2 and thus agrees well with experimental estimates of 5.2 kBT per lipid.37 The lateral diﬀusion constant of lipids is reduced compared to a free, tensionless bilayer. For a potential strength of C = 10.0 kBT we ﬁnd diﬀusion constants of 0.012 σ2/τ in the distal and 0.010 σ2/τ in the proximal leaﬂet, corresponding to a reduction of 17%, which is comparable to the reduction of 30% measured in coarse-grained simulations by Faller and co-workers.38 The eﬀects of scaling the surface potential’s range are shown in Figure 4. We varied the parameter S from 1.0 σ to 3.0 σ while the potential strength was kept constant at C = 5.0 kBT. The potential’s eﬀects are ampliﬁed by the increased range. The area per lipid of the proximal leaﬂet is decreased further, and that of the distal leaﬂet is increased in turn. As a consequence, the asymmetry between the leaﬂets is also increased. The bilayer’s thickness decreases further with increasing range, and the total area of the bilayer disk increases. For all parameter combinations tested, the membranes remained in a liquid disordered state, and no gel-like regions were observed.

Figure 4. (top) Particle density proﬁles in the z-direction for diﬀerent ranges of the surface potential, characterized by the values S/σ = 1.0, 2.0, and 3.0. C = 5.0 kBT. To compare the particle numbers in the proximal and distal leaﬂets, integrals of the headgroup peaks are shown as dotted lines. Only headgroup beads are aﬀected by the potential. (bottom) Plots of the potentials for better comparability. All plots have been shifted along the z-axis so that the minima of the potentials coincide.

parameters of the surface potential. To eliminate the distortion at the bilayer edges, we only took into account lipids within a small cylindrical region around the disks’ centers. The distance of the headgroup peaks, dHG (computed as the diﬀerence of the z-coordinate of the leaﬂets’ headgroups’ centers of mass), and the area per lipid, a, for the bilayer disks subjected to the diﬀerent potentials are listed in Table 1. Corresponding values for a continuous tensionless bilayer are also given as reference. Because of undulations in the free bilayer, which are suppressed by the surface potential in the other data, the area per lipid of the continuous bilayer is slightly underestimated, and in addition, the headgroup distance would be overestimated 4338

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For considering the used interaction ranges, it should be noted that a simple comparison of the potential’s cutoﬀ range of 3.0 S to the bilayer thickness is misleading, since the surface of the substrate does not coincide with z = 0 σ, because the repulsive part of the potential lies “below” the represented surface. A better impression can be obtained from Figure 4, where one can see that even at the highest range used in our simulations (S = 3.0 σ) the range where the potential is signiﬁcant barely exceeds the thickness of a single adsorbed bilayer. Eﬀects on Vesicles. Next, we subjected vesicles to the surface potential. For low potential strengths (C < 10.0 kBT), vesicles were placed above the surface so that the vesicles’ bottoms were just within the potential’s range. For higher potential strengths, instead, we started with snapshots obtained from vesicles adsorbed at lower strength to avoid rupture due to the “collision” between vesicle and surface. We ﬁrst considered conditions, under which the adsorbed vesicles stayed intact. In this setup, the vesicle’s curvature together with the slow dynamics of lipid exchange between the inner and outer monolayer pose additional restrictions on the lipid distribution. As expected, the vesicles deform more at high potential strengths, and the cargo restricts the deformation. In addition, the contact area with the surface also increases with increasing potential strength, illustrating the driving force behind the deformation. Snapshots of the vesicles’ shape in molecular resolution are presented in Figure 5, illustrating how the

Figure 6. Particle density proﬁle for a vesicle ﬁlled with cargo adsorbed to a surface characterized by C = 15.0 kBT and S = 1.0 σ. The proﬁle takes into account only beads within a cylinder perpendicular to the surface potential with a radius of 1.0 σ around the vesicle’s center of mass. For comparison, dotted lines represent the integrals over the headgroup peaks corresponding to the diﬀerent leaﬂets.

monolayer. At the vesicle’s top, however, our ﬁndings are similar to the situation in a radial density proﬁle of a free vesicle, where the inner monolayer has a higher density due to the membrane’s curvature. As for the bilayer disks, the vesicles remained in a liquid disordered state, and no gel-like regions were observed. Rupture and Spreading Pathways. Isolated Vesicles. In order to assess which potential parameters were needed to induce rupture and spreading of the adsorbed vesicles, we systematically varied the potential’s strength and range. Table 2 shows an overview of the outcomes after 3000 τ long simulations. Table 2. Overview of States Assumed after 3000 τ Simulations of an Empty Vesicle Adsorbed to the Surface Potentiala

Figure 5. Snapshots showing cross sections through the center of adsorbed vesicles in molecular detail. Headgroups of the inner and outer leaﬂet are shown in red and green, respectively, and lipid tails in gray. The coordinates have been averaged over multiple frames to eliminate noise. As can be seen, the contact angle decreases, and the depth of the dip at the edge of the vesicle’s bottom increases with higher potential strength C and range S.

C [kBT]

S = 1.0 σ

S = 2.0 σ

S = 3.0 σ

1.0 5.0 10.0 16.0

V/V/V V/V/V V/V/V V/V/B1

V/V/V V/V/V B2/B2/B1 B2/B2/B3

V/V/V B2/B1/B1 B4/B1/B2 P/P/P

a

The entries indicate stable vesicles (V), vesicles that burst and form bilayer disks (B), and vesicles that spread via the parachute mechanism (P). Numbers in superscript indicate the number of pores formed simultaneously. For each combination of parameters three simulations were performed.

contact angle between vesicle and substrate decreases with rising potential strength and range and showing the packing frustration at the sharp kinks of the bilayer at the vesicle’s outer edge. The latter is accompanied by a pronounced dip of the inner bilayer at the outer edge of the vesicle’s bottom. Plots of the average position of the lipid headgroups for the inner and outer leaﬂets of empty vesicles and vesicles ﬁlled with cargo are shown in the Supporting Information. As for the bilayer disks, we also obtained density proﬁles perpendicular to the surface for the vesicles. For this we only took into account a cylindrical volume around the vesicle’s center of mass in the surface plane with a radius of 1.0 σ. For such small radius, the area of the ﬂat bottom and curved top of the vesicle within the cylinder can be considered approximately equal. The results for a vesicle ﬁlled with cargo adsorbed to a surface with potential strength C = 15.0 kBT and range S = 1.0 σ are displayed in Figure 6. At the vesicle’s bottom, we ﬁnd results similar to those for adsorbed bilayer disks. The vesicle’s outer monolayer has a higher lipid density than the inner

For the short potential range S = 1.0 σ, a potential strength of C = 16.0 kBT was needed before we observed pore formation and spreading of a vesicle without cargo within a time of 3000 τ. With this strength, the vesicles ﬁrst adsorbed and deformed. The deformed vesicles then remained stable for 700 τ and longer before a pore opened and quickly expanded until a bilayer disk was formed. As illustrated in Figure 7, these pores consistently formed in the vesicles’ side walls at a very low position close to the vesicles’ ﬂattened bottoms adsorbed to the surface. Once formed, the curved top of the vesicle drew back and shrank, thereby expanding the pore. At the same time the ﬂat bottom 4339

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Figure 7. Empty vesicle rupturing and spreading via the receding-top mechanism after adsorption to a short-ranged surface potential (C = 16.0 kBT, S = 1.0 σ). Depicted are isosurfaces marking the volume occupied by the hydrophobic tail beads. For clarity, each snapshot is rendered from a 3/4 view (top) and a side view (bottom). Shown are the initial pore (A: 740 τ), its rapid expansion via recession of the upper rim (B: 880 τ), and growth of the ﬂat bottom (C: 980 τ).

spread out on the surface, until a bilayer disk formed with an almost exclusive inside-up orientation. This “receding-top” mechanism did not change for stronger potentials up to the maximal tested strength of C = 40.0 kBT; the process merely took place faster. When increasing the surface potential’s range, we observed that the minimal strength to induce rupture of the adsorbed vesicles decreased, as shown in Table 2. In addition, with the stronger and longer-ranged potentials, frequently more than one pore opened simultaneously, giving rise to morphologies as those depicted in Figure 8. In these simulations, the pores expanded and the bottom of the vesicle spread just as described above. Only toward the end of the spreading process, an additional topological change was

required to absorb the archlike structure that remained of the vesicle’s top into the developing bilayer disk. This was achieved by fusing the arch’s inside to the bilayer disk, thereby closing the arch and creating an unporated bilayer protrusion that could subsequently be incorporated into the bilayer disk without further topological changes. Also for these simulations, the orientation of the created bilayer disk was almost exclusively inside-up except for a small number of lipids corresponding to the top of the arch that remained from the vesicle’s top. Additional snapshots from independent simulations showing similar morphologies are given in the Supporting Information. Using the number of tail beads found in a 1.0 σ thick volume slice parallel to the surface starting right above the vesicle’s adsorbed bottom, we can illustrate the time development of vesicles spreading via the receding-top mechanism as shown in Figure 9. The most striking feature of the plots for the diﬀerent

Figure 9. Time development of the vesicles spreading via the recedingtop mechanism. Shown is the normalized number of tail beads n found in a 1.0 σ thick volume slice above the vesicles’ bottom layers for diﬀerent potential strength and range. For each combination of parameters three simulations have been performed.

Figure 8. Typical mechanism of a vesicle spreading in simulations where multiple pores opened simultaneously upon adsorption (C = 16.0 kBT, S = 2.0 σ). As in the simulations in which only one pore had formed, the adsorbed bottom of the vesicle spreads outward from the pores while the upper rim of the pore recedes (A: 200 τ; B: 300 τ), depleting lipids from the vesicle’ top until all that remains of the top is a narrow arch (C: 400 τ). This arch shrinks until its opening closes by fusion of the arch’s inside to the bottom (D: 600 τ). The lipids in the remaining protrusion are then absorbed into the bilayer. The orientation of the created lipid bilayer is almost exclusively insideup, with only a small amount of lipids from the outer monolayer corresponding to the described arch found in the upper monolayer. The volume occupied by the lipid tails is represented as gray isosurface while red and green spheres mark the positions of headgroup beads originating from the inner and outer monolayer, respectively.

potential parameters at which this receding-top mechanism is observed is the large spread of rupture times observed at low potential strength (C = 5.0 kBT, S = 3.0 σ). This indicates a high nucleation barrier for the required poration of the vesicle at low potential strength despite the long-range used. At intermediate strength and range (C = 10.0 kBT, S = 2.0 σ), a much smaller spread of rupture times is found, characteristic of a signiﬁcantly lowered nucleation barrier. At high strength and short range (C = 16.0kBT, S = 1.0 σ; cf. Table 2), only one out of a total of three simulations spread within the simulated time, 4340

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of the vesicle and was gradually absorbed (rather than becoming a segment of the SLB in its original conﬁguration). However, if we started with a preadsorbed vesicle obtained at a lower potential strength (cf. Figure 11A), the process was

indicating again a very high nucleation barrier. When combining high strength with intermediate range (C = 16.0 kBT, S = 2.0 σ) or intermediate strength with long-range (C = 10.0 kBT, S = 3.0 σ), the spreading process virtually starts as soon as the vesicle makes contact with the potential with no noticeable spread between diﬀerent simulation runs, suggesting that with these parameters the process is a thermodynamically driven and not a nucleated process. Once one or several pores have been nucleated, the further development is very similar for all parameter combinations, illustrating the metastable nature of vesicles adsorbed to potentials of suﬃcient strength. The long tails and occasional bumps seen in some of the trajectories analyzed in Figure 9 correspond to bilayer “tongues” which can be temporarily trapped when the spreading vesicle edge meets its periodic image or the lipid arches described for trajectories with multiple pores. Both of these structures need relatively long times to be absorbed into the supported bilayer, but have little impact on the overall spreading process. In the simulations combining a range of S = 3.0 σ and a strength of C = 16.0 kBT, we observed a diﬀerent, “parachute”, mechanism as shown in Figure 10. Here, the vesicles did not

Figure 10. Vesicle spreading via the parachute mechanism upon exposition to a long-ranged surface potential (C = 20.0 kBT, S = 3.0 σ). After a slight deformation upon adsorption (A: 10 τ), pores open at the outer edge of the vesicle’s bottom. Through these pores, the vesicle’s inside makes contact with the potential and the vesicle’s top starts spreading out on the substrate (B: 50 τ). The vesicle’s bottom is gradually absorbed into the underside of the spreading bilayer, resulting in a SLB with an almost exclusive outside-up orientation (C: 230 τ). Lipid headgroups are shown in gray and lipid tails in red and green, indicating lipids originating from the vesicle’s inner and outer monolayer, respectively. In addition, a light green isosurface visualizes the volume occupied by the tail beads.

Figure 11. Typical mechanism of a vesicle spreading in simulations using a relatively strong, long-ranged surface potential (C = 16.0 kBT, S = 3.0 σ). See text for description (A: 10 τ; B: 37 τ; C: 77 τ; D: 160 τ; E: 199 τ). The graphical representation is the same as in Figure 8. On the left, a three-quarter view shows the adsorbed vesicle’s top; on the right a view of the vesicle’s bottom is given. For (C), an additional cross section through one of the pores is shown depicting the lipid tails as gray sticks.

rupture on the top, but multiple small pores formed at the outer edge of the bottom of the adsorbed vesicle. Through these pores, the vesicle’s inner monolayer made contact with the surface and spread outward with the vesicle’s outer monolayer facing upward. Depending on the initial conﬁguration, we observed two diﬀerent pathways. If we started with a free, spherical vesicle just within range of the potential, the pores in the vesicle’s bottom developed at an early stage of deformation as shown in Figure 10A, and the mechanism proceeded without rupture of the vesicle’s top, resulting in an upper monolayer of the SLB that was composed of lipids originating entirely from the vesicle’s outer monolayer, while the lower monolayer displayed a mixed composition. The part of the vesicle’s bottom that initially made contact with the surface (Figure 10B) stayed connected to the spreading inside

interrupted by rupture of the vesicle’s top, resulting in the vesicle’s bottom being incorporated into the created SLB as a central segment with an inside-up orientation. In this pathway, ﬁrst, a ring-shaped, one-bilayer-thick bulge developed around the vesicle’s base as depicted in Figure 11B. Subsequently, multiple small pores opened in the bottom at the inside of the three-bilayer junction (Figure 11B). Through these pores, lipids from the inner monolayer moved toward the surface potential and spread outward, as the bulge increased (panel C). After the bubble corresponding to the original vesicle’s interior had shrunk considerably, a pore in the upper part of the vesicle opens (panel D), and the vesicle’s top is adsorbed into the growing SLB. The orientation of the resulting bilayer shows a pattern corresponding to the diﬀerent stages of the spreading 4341

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Figure 12. Shape of the outer edge of absorbed vesicles prior to rupture. Shown are a vesicle spreading via the receding-top mechanism (C = 16.0 kBT, S = 1.0 σ, left) and a vesicle spreading via the parachute mechanism (C = 16.0 kBT, S = 3.0 σ, right). The points indicate the location of the midplane of the bilayer. In addition, vertical bars indicate the thickness of the hydrophobic core, and horizontal bars indicate the curvature found at the respective points.

potential strength of C = 5.0 kBT only in one out of a total of ﬁve simulations a stalk developed within a duration of 3000 τ. Below a potential strength of C = 5.0 kBT, the vesicles stayed stable for the entire duration of the simulations (3000 τ). At higher strength, a stalk formed between the outer monolayers at the vesicle’s bottom very close to the substrate, taking more than 2000 τ to appear at C = 5.0 kBT. The further fusion process took place via the stalk-hemifusion pathway, as shown in detail in the Supporting Information. Expansion of the stalk led to a hemifusion diaphragm, whose rupture concluded the fusion process. We did not observe further rupture and spreading of the adsorbed vesicles in these simulations, and the ﬁnal state was an “endless” membrane tube that spanned one of the periodic boundaries. At higher potential strength, fusion over the periodic boundary often occurred in both lateral directions. In addition, starting from C = 10.0 kBT, the fusion process was accompanied by a bilayer composed entirely of lipids from the outer monolayer spreading on the free surface area. Snapshots of this process are provided in the Supporting Information. In addition, pores frequently formed and stayed open in the vesicles sides above the connecting these bilayers to the vesicle. For long-ranged surface potentials (S = 3.0 σ), we observed a mechanism similar to the parachute mechanism described for isolated vesicles, where pores formed in the vesicle’s bottom. At a potential strength of C = 20.0 kBT, the spreading bilayer grew faster than the deformation of the vesicle, preventing contact of the vesicle and its periodic image and resulting in fusion of the spreading bilayer instead. Under continued ﬂow of lipids from the vesicle’s interior, the spreading went on until all available surface was covered, at which point the process was arrested. When continued in the NPtT ensemble, however, the process continued until the vesicle was completely absorbed into the bilayer via the parachute mechanism described above, without rupture of the vesicle’s top. Eﬀects of Preadsorbed Bilayer Disks. To test the selfsupporting aspect of vesicle spreading on solid supports, we simulated a vesicle adsorbing to our surface potential next to a preadsorbed bilayer disk (9800 lipids) using a relatively weak potential strength (C = 5.0 kBT, S = 1.0 σ). The vesicle

process (see Figure 11E). At the outer edge, a small area of lipid bilayer composed of lipids originating almost entirely from the outer monolayer corresponds to the ﬁrst bulge formed. Within this region, a ring-shaped bilayer area has a outside-up orientation, with the lipids at the bottom corresponding to the lipids from the vesicle’s inner monolayer that moved through the pores in the bottom. In the center, a bilayer region corresponds to the original bottom of the vesicle and shows an inside-up orientation. In order to better distinguish the factors that determine diﬀerent rupture location observed in the receding-top and the parachute mechanism, Figure 12 plots the average shape of the vesicles prior to rupture for two simulations performed at high potential strength (C = 16.0 kBT) but diﬀerent range (S = 1.0 σ versus S = 3.0 σ). To obtain the highest resolution, only the highly curved outer edge of the deformed vesicles is shown along with the curvature and bilayer thickness. Interestingly, the curvature at the potential rupture locations is almost zero, whereas the bilayer thickness is signiﬁcantly reduced. With cargo, the minimum potential strength needed to induce rupture of the vesicles without increased range of the surface potential, S = 1 σ, was found to be C = 20.0 kBT. At this strength, and also at C = 25.0 kBT, the mechanism is similar to that of empty vesicles. The vesicles adsorb to the surface, deform, but stay intact for considerable times of up to 3000 τ and more. After that time, a pore opens and expands in a fashion similar to the empty vesicle. The pores again form consistently at the vesicles’ side walls at a very low position, close to the vesicles’ ﬂattened bottoms. Only at much higher tension (area of unadsorbed vesicles stretched to 1.46 times the value of empty vesicles) we observed rupture at other, random locations in the vesicle’s top. Eﬀects of Neighbors. To investigate the eﬀects of crowding, we conducted simulations of an empty vesicle exposed to surfaces with strengths C ranging from 1.0 to 20.0 kBT (S = 1.0 σ). The simulation box was chosen smaller than in the simulations described above so that the vesicle’s deformation upon adsorption gave rise to a contact between the vesicle and its periodic image. The extent of the contact could be adjusted by varying the lateral box size and was chosen so that at a 4342

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vesicle’s receding top was completely absorbed into the bilayer disk. We found an inside-up orientation of the created SLB as in the standard pathway with rupture in the top. Eﬀects of Surface Protrusions. We also investigated vesicle spreading on a surface with a cylindrical protrusion. Using a moderate potential strength (C = 10.0 kBT), we subjected both empty vesicles and vesicles ﬁlled with cargo to surface potentials with a protrusion of 0.0 or 1.0 σ radius and a height of 10.0 σ. The setup used was similar to that used for the adsorption of single vesicles to ﬂat surfaces: the vesicles were placed with their center of mass above the protrusion and their bottom just within range of the potential at the tip of the protrusion. With empty vesicles and a short potential range, no rupture of the vesicles was observed. The vesicles adsorbed to the top of the protrusion and deformed, resulting in vesicles either engulﬁng the protrusion with their adsorbed bottoms or vesicles creeping down one side of the protrusion until they reached the ﬂat surface area. In both cases, the vesicles stayed intact. We did not observe a dependence on the radius of the protrusions. When using vesicles ﬁlled with cargo, we observed two pathways, depending on the protrusion radius. For a radius of 1.0 σ, the vesicles adsorbed to the protrusion’s top and simply stayed there with only minor deformation. For the sharper protrusion with a radius of 0.0 σ, the vesicles were pierced by the protrusion. In the latter pathway, a pore opened in the vesicle’s bottom when it adsorbed to the tip of the protrusion. Once opened, the pore slid down the protrusion until the vesicle reached the regular surface, to which it adsorbed causing a slight deformation of the vesicle. However, the pore did not expand, and the adsorbed vesicle stayed stable even though the membrane was pierced in the bottom. Rupture of the vesicle’s top, however, was still observed at suﬃcient potential strength. The results for empty vesicles with longer potential range of up to S values of 3.0 σ are presented in Table 3. Here we ﬁnd a gradual transition to the parachute mechanism. Figure 14 illustrates this mechanism, which in its full extent is only observed with the longest potential range (S = 3.0 σ). The vesicle ﬁrst adsorbed to the protrusion’s top and formed a dip as if to engulf the protrusion. This process, however, was interrupted by pores opening next to the indented part of the vesicle’s bottom. Through these pores, the vesicle’s inner monolayer became exposed to the protrusion’s surface and started creeping down the protrusion, keeping constant contact to the protrusion’s side from all directions. When the bilayer reached the protrusion’s bottom, it spread out on the regular surface, gradually depleting material from the vesicle’s body. During this process, the part of the vesicle’s bilayer that ﬁrst adsorbed to the protrusion’s tip remained at its location, at times becoming almost completely cut oﬀ except for a few stalks connecting it to the vesicle’s main body. Only toward the end of the process, this region was gradually absorbed until a continuous bilayer disk engulﬁng the protrusion was formed. However, this appeared to only be a metastable state, and in most simulations a pore formed above the protrusion’s tip and the bilayer almost completely receded from the curved region of the surface potential, resulting in a pierced planar bilayer around the protrusion. In addition, during the spreading process, transient pores opened and closed in the growing bilayer disk. These pores appear to always develop close to the protrusion and close relatively fast. Lipid transport through these pores is almost exclusively directed from the upper to the

spontaneously formed a stalk with the bilayer disk. This stalk quickly elongated until it spanned almost half of the vesicle’s base as shown in Figure 13. In this state, the vesicle stayed for a long time of over 9000 τ before a pore opened in the vesicle’s side directly above the elongated stalk. Through this pore, lipids from the vesicle moved to the adsorbed bilayer disk, gradually depleting the vesicle without expanding the pore. Only after the vesicle had shrunken considerably the pore enlarged until the

Figure 13. Vesicle spontaneously fused to a preadsorbed bilayer disk on a surface characterized by S = 1.0 σ, C = 5.0 kBT. Each snapshot is shown in two representations. On the left, a molecular view with gray tail beads and color-coded headgroups is given. Red headgroups identify lipids originating from the preadsorbed bilayer disk, while green headgroup indicate lipids stemming from the vesicle. On the right, the volume occupied by the hydrophobic tail beads is shown as green isosurfaces. For the ﬁrst snapshot, a cross section through the center of the vesicle and disk is shown on the left, illustrating the system’s topology. The initial stalk quickly expands until the bilayer disk is connected to the vesicle by an elongated stalk spanning almost half of the vesicle’s adsorbed base (A: 625 τ). A pore opens in the vesicle’s side above the stalk (B: 12 500 τ), allowing lipids to move from the vesicle’s top to the adsorbed bilayer disk (C: 15 625 τ). Up to a certain stage this shrinking of the vesicle proceeds without enlarging the pore. After that, the pore expands (D: 19 375 τ), until its receding rim is completely absorbed into the bilayer disk (E: 21 875 τ). 4343

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Table 3. Overview of the Behavior of Vesicles Adsorbing to a Surface with a Protrusion As a Function of Potential Strength, C, Range, S, and Protrusion Radius, ra S [σ] r [σ]

C [kBT]

1.0

2.0

2.25

2.5

2.75

3.0

0.0

5.0 7.5 10.0 20.0 5.0 7.5 10.0 20.0

0/0/0 0/0/0 0/0/0 E/E/E 0/0/0 0/0/0 0/0/E F/F/F

E/E/E F/F/F F/F/F F/F/M E/E/E F/F/F F/F/F M/M/M

F/F/F F/F/F F/F/F M/M/M E/E/E F/F/F F/F/F M/M/M

F/F/F F/F/M M/M/M P/P/P F/F/F F/F/F M/M/M P/P/P

F/F/F F/F/M M/M/M P/P/P F/F/F M/M/M M/M/M P/P/P

F/F/F M/M/M P/P/P P/P/P F/F/F M/M/M P/P/P P/P/P

1.0

a The entries indicate adsorption to the tip of the protrusion with very little deformation (0), vesicles engulﬁng or rolling down the protrusion without any topological changes (E), engulﬁng with additional fusion of the vesicle’s top to the vesicle’s bottom directly above the protrusion (F), rupture and spreading via the parachute mechanism (P), or an incomplete parachute mechanism, where a bubble corresponding to the vesicle’s original morphology remains, but a part of the vesicle’s membrane nevertheless spreads on the surface via the parachute mechanism (M). For each parameter combination three simulations have been performed.

Figure 14. Cross sections through a vesicle spreading on a surface with a protrusion of 10.0 σ height and 1.0 σ radius via the parachute mechanism (S = 3.0 σ, C = 10.0 kBT). The graphical representation is the same as in Figure 10. The vesicle starts to engulf the protrusion (A: 70 τ), and pores open next to the indented part of the vesicle’s bottom (B: 100 τ). Through these pores, the inner monolayer gains contact with the surface potential and the bilayer creeps down the protrusion’s side and continues to spread onto the planar region with the inner monolayer still facing the substrate (C: 170 τ). The part of the vesicle’s bilayer that ﬁrst adsorbed to the protrusion’s tip remains at its location and at times is almost completely cut oﬀ except for a few stalks connecting it to the other lipids. Only after the vesicle’s main body has shrunk and starts to approach the detached region, the lipids on top of the protrusion get absorbed, resulting in a continuous bilayer covering the surface and protrusion (D: 290 τ).

surface, which is balanced by the costs for compression of the proximal and stretching of the distal monolayer. Only for the weakest potential used, the described asymmetry appears to be slightly reversed, possibly indicating a counteracting eﬀect due to larger monolayer undulations on the distal than on the proximal side. The extension of the lipids and the thickening of the proximal monolayer together with the decreased area per lipid can be seen as a ﬁrst step toward the gel phase formation observed experimentally, e.g. ref 42, but in our simulations the proximal monolayer remains in the liquid-disordered phase. Thus, our coarse-grained model captures the relevant eﬀects of adsorbed bilayer membranes and is a good starting point for studying the collective process of vesicle spreading. Stronger and longer-ranged potentials had a more pronounced eﬀect, with a signiﬁcant jump when the range was scaled with S = 3.0 σ. At this range, a small part of the distribution of the distal headgroup beads overlaps with the surface potential. As seen in Figure 4, the eﬀects of long potential range mainly manifest in the distal monolayer which becomes signiﬁcantly thinner, whereas the proximal monolayer turned out to be much less sensitive to the interaction range. For adsorbed vesicles, the distribution between inner and outer monolayer depends on the location. In the ﬂat, adsorbed bottoms, we observed a higher lipid density in the outer monolayers, similar to the ﬁndings for the bilayer disks. In the curved top, however, the situation was reversed like one would

lower leaﬂet of the bilayer, resulting in small islands of lipids stemming from the outer monolayer on the side facing the substrate (not shown in Figure 14). At shorter potential ranges, the parachute mechanism was not observed, S < 2.5 σ, or incomplete, S ≤ 2.75 σ. Figure 15 contains exemplary snapshots showing the distinguishing states for the diﬀerent pathways identiﬁed in Table 3. At S = 1.0 σ, the vesicles simply engulfed the protrusion. At S = 2.0 σ, the process was similar, except that the vesicles’ bottoms fused to the top above the protrusion. In addition, the vesicles rupture at the edge as already described at this range in the absence of protrusions. Starting from S = 2.5 σ the engulfment process was accompanied by pores next to the top of the bump, through which the inner monolayer can make contact with the surface. However, for S < 3.0 σ, this contact was only developed at one side, and the rest of the vesicles’ bodies still proceeded to engulf the protrusion with its outer monolayer.

■

DISCUSSION AND CONCLUSIONS Static Properties. Using adsorbed bilayer disks as model for SLBs, we found an overall increase of the disk radius and an asymmetry of the lipid density between the proximal and distal leaﬂets. Our ﬁndings are in accord with previous coarse-grained simulations of SLB with implicit36 and explicit solvent,39,40 but the asymmetry is slightly more pronounced than in atomistic models.41 The driving force behind this process is the adsorption energy gained by the lipids partitioning to the 4344

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would rather be under- than overestimated when using small vesicles. In addition, it is reasonable to assume that the behavior at the highly curved outer edge of adsorbed and ﬂattened vesicles is dominated by the size-independent high curvature component perpendicular to the surface shown in Figure 12, while the size-dependent curvature component around the perimeter of the contact zone is orders of magnitude lower and, in consequence, has less inﬂuence. Vesicle Spreading. Spatial Range of Surface Potential Dictates Spreading Mechanism and Orientation of SLB. At short potential range, the location of the pore initiating the vesicles’ rupture is at the vesicle’s side directly above the adsorbed bottom for both empty vesicles and vesicles subject to a volume constraint and moderate tension. This receding-top mechanism qualitatively agrees with recent coarse-grained simulations with explicit solvent.23 The location of the initial pore is not surprising because this is the location where the membrane curvature is highest and where one can expect the packing frustration to be maximal (Figure 5). Even though the creation of a pore in the adsorbed vesicle’s curved side appears to be more favorable than in any other area of the vesicle, the pore does not spontaneously elongate around the vesicle’s edge and separate the vesicle’s top from the adsorbed bottom in a zipper-like fashion. Instead, the vesicle follows the pathway that maximizes the contact area between the lipid bilayer and the substrate. The driving role of adhesion energy is also illustrated by the observation that, at low potential strength and range, the formation of the pore takes very long, but once it formed the remaining steps of the pathway proceed continuously without further arrest. Free energy contributions from unfavorable free bilayer edges (pore rim and edge of adsorbed bilayer disk) appear to be less important in comparison. The spreading process’s dependence on the potential parameters indicates that both interaction range and strength reduce the nucleation barrier of pores in the adsorbed vesicle (Table 2 and Figure 9). It is interesting to note that, although we ﬁnd the vesicle’s top and bottom to stay connected in all our simulations, we do observe morphologies that have a remarkable similarity to AFM images that have been interpreted as sliding.14 Considering that the connectivity of the top and bottom layer is impossible to deduce from AFM data, the simultaneous formation of multiple pores and the subsequent independent expansion of the pores and spreading of the adsorbed bottom (Figure 8) would result in AFM data indistinguishable from the reported results. An alternative interpretation of the data reported in ref 14 would therefore be a mechanism, in which multiple pores open and grow simultaneously in an adsorbed vesicle. This reinterpretation is especially noteworthy, since the resulting orientation of the SLB is inside-up in our simulations, but would be 50−50 in a sliding mechanism. At high potential range, we observe a parachute mechanism, in which pores open at the inner edge of the vesicle’s bottom. In this mechanism, the SLB develops as a ring-shaped bulge around the vesicle’s base and possesses an outside-up orientation. The simultaneous development of multiple tiny pores in the vesicle’s bottom (Figure 11 B) suggests a very low nucleation barrier, which can be rationalized by the pronounced dip of the inner monolayer at this location (Figures 5 and 16) which brings headgroups on the inside within the range of the surface potential. In addition, this interpretation agrees well with the apparent role of the potential range as the deciding factor in determining which pathway is taken.

Figure 15. Cross sections of distinguishing snapshots of vesicles adsorbing on a surface potential with a protrusion of 10.0 σ height and 1.0 σ radius via nonparachute mechanisms (S ≤ 2.75 σ, C = 10.0 kBT). The chosen visualization is identical to that described in Figure 14. At S = 1.0 σ the vesicles simply engulf the protrusion without rupture (top). At S = 2.0 σ, the process is similar, with the addition that the vesicles’ tops fuse to the vesicles’ bottoms above the protrusion (middle). At S = 2.5 σ, we observe an incomplete parachute mechanism. The inner monolayer only makes contact with the surface potential at one side (the right side in the snapshot shown at the bottom), while the rest of the vesicle simply engulfs the protrusion with its outer monolayer facing the substrate. Nevertheless, at the side where the inner monolayer made contact, it creeps down the protrusion and spreads on the surface as described in the parachute mechanism. Note that the snapshot shown at the bottom corresponds to an earlier time in the trajectory than the other two.

expect in a free vesicle. In addition, comparing the vesicle’s bottom to the top, the lipid density in the outer monolayer was higher at the bottom, whereas for the inner monolayer it was higher at the top. Taking curvature into account in the adsorbed vesicle, we can understand why the inner monolayer’s lipid density is decreased relatively to the curved top in the ﬂat bottom region. By the same argument the outer monolayer should have an increased lipid density at the bottom in agreement with our ﬁnding. In addition, the adhesion energy gained by headgroups in close vicinity to the surface can be expected to further increase the lipid density of the outer monolayer in the contact zone. Although our vesicles are at the lower end of vesicle sizes used in experiments, the amount of deformation observed 4345

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Figure 16. Snapshots illustrating the deciding role of interaction range in the determination of the pathway chosen and the corresponding orientation of the resulting SLB. Shown are rupture at the side of the vesicle’s top at short potential range (top, receding-top mechanism) and poration in the vesicles bottom at long potential range (bottom, parachute mechanism). The respective ranges of the potentials used are indicated by the dashed black lines. Gray circles represent lipid headgroups, and red and green lines represent lipid tails from the inner and outer monolayer, respectively.

The nucleation barrier for rupture can be lowered by increasing both strength and range of the potential, until the spreading process becomes spontaneous and no metastable adsorbed vesicles exist, as demonstrated for the receding-top mechanism in Table 2 and Figure 9. In the regime where the parachute mechanism is observed, the process is also spontaneous and begins immediately upon adsorption. The dips in the vesicle’s bottom continuously become more pronounced until many small pores develop in the bottom almost simultaneously and in a remarkably regular pattern (Figure 11 B), suggesting a thermodynamically driven process. The dependence on the interaction range is an interesting option for the design of surfaces that determine the orientation of SLBs by tuning the range of the surface interactions e.g., by surface coating or electrostatic interactions in an experiment. Cargo Tends To Slow Down Spreading. The fact that empty vesicles require a lower strength of surface potential to rupture than vesicles with cargo (16.0 versus 20.0 kBT) suggests that a curvature-driven rather than a tension-driven mechanism is energetically favorable. Moreover, the excessive adhesion strength required to rupture vesicles with a volume constraint due to solvent creates an interaction window, in which ﬁlled vesicles are stable but empty vesicles spread, allowing for a mechanism in which the vesicles stay intact while the solvent slowly leaks until enough deformation is achieved to form a curvature-induced pore at the outer edge of the adsorbed vesicle. This interpretation is in agreement with experimental ﬁndings, where vesicles condense into SLBs easier under hyperosmotic conditions than under hypoosmotic stress. Experiments indicate that contents leakage is feasible on the time scale of spreading.12,14 Thus, solvent molecules inside the vesicle might slow down the parachute mechanism but not block the process if the solvent can leak. A putative pathway for this leaking, in addition to direct permeation of the vesicle membrane, is partitioning to the solvent layer between substrate and vesicle via the pores formed in the vesicle’s bottom, from where the molecules could escape sideways. The slowing down of the spreading mechanism might be favorable

A similar morphology as the bulge around the vesicle’s perimeter has also been observed in AFM scans.14 However, in these experiments the bulge had a thickness of two bilayer widths. One of the key ﬁndings of our simulation study is that the orientation of the SLBs created by spreading of vesicles on solid supports critically depends on the range of the surface interactions. Short-ranged surface−lipid interactions favor vesicle rupture on the top creating SLBs with an inside-up orientation. For long-ranged interactions, however, we observe poration of the adsorbed bottom of the vesicles. Through these pores, the vesicle’s inside makes contact with the substrate and spreads outward with the vesicle’s outside facing upward. In both mechanisms, the location of rupture is close to the outer edge of the ﬂattened adsorbed vesicle, as one would expect due to the high curvature and packing frustration in this area. As Figure 12 reveals, however, the locations of rupture themselves display virtually zero curvature, and it is nonlocal eﬀects of the highly curved spreading outer vesicle edge that result in a thinning of the adjacent bilayer regions in the top and bottom of the adsorbed vesicle (similar to the thinning observed in the proximity of transmembrane peptides with positive hydrophobic mismatch43−46 or the thinning of block copolymer bilayers at kink grain boundaries47). At short potential range, the thinning is less pronounced at the bottom, which can be explained by the competing inﬂuence of adhesion energy gained by adsorbing lipids which favors a high lipid density at the vesicle’s bottom. It is therefore more likely for the vesicle’s side to rupture, unless an additional contribution favors poration in the vesicle’s bottom. Such contribution is the direct exposition of lipid headgroups from the inner monolayer to the surface potential at long potential range, which, as illustrated in Figure 16, is achieved with a scaling factor S = 3.0 σ in our simulations. (This inﬂuence of long-ranged substrate interactions is also visible in the density proﬁles of adsorbed bilayer disks (Figure 4); one can see that the main change occurs in the distal monolayer, directly reﬂecting the importance of the interaction range.) 4346

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pores at lower potential strength than in noncrowded vesicles). However, due to the limited available surface area in our setup, we could not observe the spreading process itself in these simulations. Surface Protrusions Facilitate Outside-Up Orientation. In the presence of a cylindrical protrusion, we observe a facilitation of the parachute mechanism, in the sense that it is (partially) observed at both lower range and weaker strength of the surface potential compared to ﬂat surfaces. This parachute mechanism results in an outside-up orientation of the SLB. Our results suggest that for the parachute mechanism to occur two conditions have to be met: (i) a pore has to open to give the inner monolayer access to the surface; (ii) this pore has to develop early in the process, as pores in an already adsorbed vesicle with its outer monolayer facing the substrate will not expand as would be required for reversing the SLB orientation. If the conditions are not met, the vesicle either engulfs the protrusion without poration or a mixed pathway is observed, in which one part of the vesicle adsorbs with its outside, and the other spreads on the surface with its inner monolayer facing the substrate. The transition between engulﬁng and parachute mechanism appears to be gradual, and the ratio between the area adsorbing in an inside-up and the outside-up orientation can be set by choosing the range and strength of the interactions with the surface. The engulfed state itself requires highly unfavorable curved bilayer regions to wrap the bottom of the vesicle around the protrusion, and has to be considered metastable, as a vesicle adsorbing to a ﬂat part of the surface clearly has a lower energy, and we indeed observed a number of simulations in which the vesicle only creeps down the protrusion’s side or engulfs the protrusion only partially and starts escaping sideways once it has reached the planar region of the surface. The balance of bending rigidity κ and adhesion energy W gives rise to the characteristic length scale Ra = (2κ/W)1/2, which is relevant both for adhesion of vesicles and wrapping. If the vesicle radius is large compared to Ra, the vesicle adsorbs and deforms.9,10 For the interaction parameters listed in Table 1, we ﬁnd characteristic length scales Ra in the order of magnitude of σ, which is small compared to our vesicle size and agrees with the adsorption and deformation observed in our simulations. The same length scale applies also to wrapping of bilayers around curved attractive surfaces.48 Here, however, the curvature radii of the protrusions (calculated as the radius of the protrusion increased by the distance at which the surface force switches from repulsive to attractive) are 1.2 and 2.2 σ, and thus very close to Ra, and indeed we see a transition from binding without deformation to engulﬁng in this parameter regime. In the regime where we observe spreading, however, the adhesion energy becomes the dominant contribution, as illustrated by the highly ﬂattened shape with very unfavorable curvature adopted by our vesicles even on perfectly ﬂat surfaces. We therefore focus our further discussion of curvature eﬀects on their inﬂuence on the rupture location and the observed spreading pathway. When using ﬁlled vesicles, the vesicles either stayed intact and adsorbed to the tip of the protrusion or, when the protrusion was very sharp, opened a pore and slid down the protrusion without the vesicle’s volume changing. In both cases, the cargo kept the vesicle from deforming suﬃciently to increase its contact area with the surface. Even though a pore formed when using sharp protrusions, no spreading on the surface was observed. This can be rationalized because

to the parachute mechanism, as the initial restriction to a round shape would limit contact between vesicle and surface to a small area, preventing other parts of the vesicle from making contact with the surface. This would allow the vesicle’s inner monolayer to spread out on the surface while the solvent slowly leaks, and avoid the vesicle from ﬂattening (which would favor rupture of the top) or, if protrusions are involved, keep the vesicle from merely engulﬁng the protrusion as observed in our simulations displaying a mixed pathway. While the presence of solvent had no inﬂuence on the rupture location for the receding-top mechanism at the tension level used in most of our simulations, at even higher tension (bilayer stretched to 1.46 in place of 1.3 times its tensionless area), the adsorbed vesicles ruptured at random locations in the vesicle’s top, indicating an alternative tension-driven mechanism at very high tension. Vesicle Crowding and Preadsorbed Bilayers Accelerate Spreading. At low potential strength and range, crowding of vesicles led to fusion via the stalk−hemifusion pathway. This is probably owed to the low headgroup density at the outer edge of the ﬂattened vesicles which facilitates the contact between the hydrophobic cores required for stalk formation. At higher potential strength, we ﬁnd lipids from the outer monolayer moving toward the surface to form a one bilayer thick bulge spreading on the surface until all available space was covered. This behavior can be rationalized by to the altered ratio of surface between the inside and outside of the structure, which increases in the fused topology. As a consequence, lipid material from the outside becomes available to spread on the surface. In addition, if several vesicles fuse to form a ringlike topology, the line tension of the bulge’s edge will create a force supporting growth of the bulge by trying to minimize the circumference of the enclosed empty surface area. With our observation that for strongly ﬂattened vesicles only an incomplete parachute mechanism is observed due to rupture of the vesicle’s top, the restricted deformation due to high vesicle concentration on the surface can be considered a favorable factor for the parachute mechanism. Preadsorbed bilayer disks readily fuse to vesicles adsorbing in their vicinity. This process occurs even more readily than the fusion between neighboring vesicles. This is not unexpected, since, in addition to the unfavorable curvature and low headgroup density at the outer edge of the adsorbed vesicle, the free edge of the bilayer disk itself is an energetically costly structure. The spontaneous expansion of the formed stalk to an elongated T-junction spanning almost half of the vesicle’s perimeter proves the stalk’s favorable free energy balance relative to the unconnected structures. While the result of the fusion appears to be metastable, judging by its long observed lifetime, we observe pore formation in the vesicle’s side above the elongated stalk at a potential strength signiﬁcantly lower than that required for the rupture of isolated vesicles. This observation can be rationalized by the free energy cost of the pore rim that is partially oﬀset by the creation of a ﬂat membrane patch at the bottom of the pore and it is in agreement with the self-promoting aspect of vesicle spreading observed in experiments.12,13 The formation of similar elongated T-junctions (see Supporting Information) along with pores in the vesicles’ sides above them in our simulations mimicking vesicle crowding suggests that high vesicle concentrations can also be expected to facilitate fusion in a similar fashion as preadsorbed bilayer disks (as indicated by the observation of 4347

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substrates monitored by surface plasmon resonance spectroscopy. Biochim. Biophys. Acta 1994, 1195, 267−275. (4) Benda, A.; Beneš, M.; Marecek, V.; Lhotskỳ, A.; Hermens, W. T.; Hof, M. How to determine diffusion coefficients in planar phospholipid systems by confocal fluorescence correlation spectroscopy. Langmuir 2003, 19, 4120−4126. (5) Tampé, R.; Dietrich, C.; Gritsch, S.; Elender, G.; Schmitt, L. In Nanofabrication and Biosystems: Integrating Materials Science, Engineering, and Biology; Hoch, H. C., Jelinski, L. W., Craighead, H. G., Eds.; Cambridge University Press: New York, 1996. (6) Tamm, L. K.; McConnell, H. M. Supported phospholipid bilayers. Biophys. J. 1985, 47, 105−113. (7) Brian, A. A.; McConnell, H. M. Allogeneic stimulation of cytotoxic T cells by supported planar membranes. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 6159−6163. (8) Anderson, T. H.; Min, Y.; Weirich, K. L.; Zeng, H.; Fygenson, D.; Israelachvili, J. N. Formation of supported bilayers on silica substrates. Langmuir 2009, 25, 6997−7005. (9) Seifert, U.; Lipowsky, R. Adhesion of vesicles. Phys. Rev. A 1990, 42, 4768−4771. (10) Lipowsky, R.; Seifert, U. Adhesion of vesicles and membranes. Mol. Cryst. Liq. Cryst. 1991, 202, 17−25. (11) Seifert, U. Configurations of fluid membranes and vesicles. Adv. Phys. 1997, 46, 13−137. (12) Johnson, J. M.; Ha, T.; Chu, S.; Boxer, S. G. Early steps of supported bilayer formation probed by single vesicle fluorescence assays. Biophys. J. 2002, 83, 3371−3379. (13) Reimhult, E.; Zäch, M.; Höök, F.; Kasemo, B. A multitechnique study of liposome adsorption on Au and lipid bilayer formation on SiO2. Langmuir 2006, 22, 3313−3319. (14) Jass, J.; Tjärnhage, T.; Puu, G. From liposomes to supported, planar bilayer structures on hydrophilic and hydrophobic surfaces: An atomic force microscopy study. Biophys. J. 2000, 79, 3153−3163. (15) Richter, R. P.; Brisson, A. R. Following the formation of supported lipid bilayers on mica: A study combining AFM, QCM-D, and ellipsometry. Biophys. J. 2005, 88, 3422−3433. (16) Reimhult, E.; Höök, F.; Kasemo, B. Intact vesicle adsorption and supported biomembrane formation from vesicles in solution: Influence of surface chemistry, vesicle size, temperature, and osmotic pressure. Langmuir 2003, 19, 1681−1691. (17) Beneš, M.; Billy, D.; Benda, A.; Speijer, H.; Hof, M.; Hermens, W. T. Surface-dependent transitions during self-assembly of phospholipid membranes on mica, silica, and glass. Langmuir 2004, 20, 10129−10137. (18) Contino, P. B.; Hasselbacher, C. A.; Ross, J. B.; Nemerson, Y. Use of an oriented transmembrane protein to probe the assembly of a supported phospholipid bilayer. Biophys. J. 1994, 67, 1113−1116. (19) Salafsky, J.; Groves, J. T.; Boxer, S. G. Architecture and function of membrane proteins in planar supported bilayers: A study with photosynthetic reaction centers. Biochemistry 1996, 35, 14773−14781. (20) Reimhult, E.; Kasemo, B.; Höök, F. Rupture pathway of phosphatidylcholine liposomes on silicon dioxide. Int. J. Mol. Sci. 2009, 10, 1683−1696. (21) Dimitrievski, K.; Reimhult, E.; Kasemo, B.; Zhdanov, V. P. Simulations of temperature dependence of the formation of a supported lipid bilayer via vesicle adsorption. Colloids Surf., B 2004, 39, 77−86. (22) Dimitrievski, K.; Kasemo, B. Simulations of lipid vesicle adsorption for different lipid mixtures. Langmuir 2008, 24, 4077− 4091. (23) Wu, H. L.; Chen, P. Y.; Chi, C. L.; Tsao, H. K.; Sheng, Y. J. Vesicle deposition on hydrophilic solid surfaces. Soft Matter 2013, 9, 1908−1919. (24) Zhdanov, V. P.; Kasemo, B. Comments on rupture of adsorbed vesicles. Langmuir 2001, 17, 3518−3521. (25) Müller, M.; Katsov, K.; Schick, M. Coarse-grained models and collective phenomena in membranes: Computer simulation of membrane fusion. J. Polym. Sci., Part B: Polym. Phys. 2003, 41, 1441−1450.

expansion of the pore would not result in an increased contact area with the surface. While the pore slides down the protrusion, expansion would reduce the contact. Later in the process, when the pierced vesicle has reached and adsorbed onto the regular ﬂat part of the surface, the lipids in the vesicle’s bottom that would be directly aﬀected by an expansion are already adsorbed and therefore do not gain contact free energy. In fact, the lipids at the outer edge of the contact zone would have to move to the unadsorbed and therefore unfavorable top of the vesicle to expand the circumference of the adsorbed area. In addition, the lipids at the pore’s rim experience an attractive force from the protrusion’s edge, which also contributes to keeping the pore from expanding. While our model of protrusions, implemented as a single cylindrical bump on an otherwise ﬂat surface, cannot be seen as a faithful representation of a rough surface, it can nevertheless be used to test the salient eﬀects of protrusions. In addition, we argue that on an actual rough surface only the largest protrusions will matter, the density of which can be so low that an approaching vesicle would only experience eﬀects from a small number of them at a time. An interesting avenue would be to speciﬁcally engineer surfaces with protrusions that force vesicle spreading via the parachute mechanism and thereby experimentally control the orientation of the SLB. An exciting extension of this inhomogeneous vesicle spreading at surface protrusions is the investigation of the chemical surface patterns on vesicle spreading. Recent experiments indicate that the interface between two domains of the surface pattern inﬂuences the spreading mechanism.49

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ASSOCIATED CONTENT

S Supporting Information *

Technical details of the coarse-grained solvent-free model, plots of the average headgroup positions of adsorbed vesicles, additional snapshots of conﬁgurations in which multiple simultaneous pores opened and that resemble AFM data interpreted as sliding mechanism, as well as snapshots illustrating the fusion between adsorbed vesicles. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing ﬁnancial interest.

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ACKNOWLEDGMENTS It is a great pleasure to thank Kostas Ch. Daoulas, Martin Hof, Martin Hömberg, Giovanni Marelli, Ilya Reviakine, and Yuliya Smirnova for helpful discussions. The simulations have been performed at the HLRN Hannover/Berlin, Jülich Supercomputer Center, and the GWDG, Göttingen, Germany. Financial support has been provided by the Volkswagen Foundation and the DFG within the SFB 803/B3.

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REFERENCES

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Mechanisms of Vesicle Spreading on Surfaces: Coarse-Grained

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