J. Phys. Chem. B 2007, 111, 5719-5725
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Lipid-Based Mechanisms for Vesicle Fission A. J. Markvoort,*,†,‡ A. F. Smeijers,† K. Pieterse,† R. A. van Santen,‡ and P. A. J. Hilbers† Departments of Biomedical Engineering and Chemical Engineering, TU EindhoVen, Postbus 513, 5600 MB EindhoVen, The Netherlands ReceiVed: December 1, 2006; In Final Form: February 27, 2007
Shape transformations and topological changes of lipid vesicles, such as fusion, budding, and fission, have important chemical physical and biological significance. In this paper, we study the fission process of lipid vesicles. Two distinct routes are considered that are both based on an asymmetry of the lipid distribution within the membrane. This asymmetry consists of a nonuniform distribution of two types of lipids. In the first mechanism, the two types of lipids are equally distributed over both leaflets of the membrane. Phase separation of the lipids within both leaflets, however, results in the formation of rafts, which form buds that can split off. In the second mechanism, the asymmetry consists of a difference in composition between the two monolayers of the membrane. This difference in composition yields a spontaneous curvature, reshaping the vesicle into a dumbbell such that it can split. Both pathways are studied with molecular dynamics simulations using a coarse-grained lipid model. For each of the pathways, the conditions required to obtain complete fission are investigated, and it is shown that for the second pathway, much smaller differences between the lipids are needed to obtain fission than for the first pathway. Furthermore, the lipid composition of the resulting split vesicles is shown to be completely different for both pathways, and essential differences between the fission pathway and the pathway of the inverse process, i.e., fusion, are shown to exist.
1. Introduction To achieve basic cellular functions, such as growth and division, primitive cells have to rely on self-organizing properties of their components or on specific interactions with their environment. For vesicles to divide (fission), membranes should not only grow, but also bend. This is usually assumed to be achieved by proteins that can either function as a scaffold or deform the membrane by penetrating the outer membrane monolayer. Interestingly, however, experiments such as those described by Luigi Luisi et al.1 and Szostak et al.2 show that vesicles can also reproduce in the absence of proteins, but because such experiments only show the fission indirectly, no insight into the mechanism is provided. In this paper, we focus on such possible fission mechanisms in the absence of proteins. Two different mechanisms by which membranes can bend in the absence of proteins are examined using coarse-grained molecular dynamics simulations. The first mechanism is based on the idea of minimization of line tension between domains with different lipid compositions. When more than one lipid type is present per monolayer, the lipid types can phase-separate under certain conditions. This results in domains differing in lipid composition from the rest of the membrane. The basic idea of vesicle fission from rafts is the existence of line tension at the interface between two different domains. According to the theory of Ju¨licher and Lipowsky,3,4 the borderline around a domain tends to become shorter due to minimization of this line tension, making the domain bulge out and finally bud off. An important point is that the process is postulated to be controlled purely by the line * To whom correspondence should
[email protected]. † Department of Biomedical Engineering. ‡ Department of Chemical Engineering.
be
addressed.
E-mail:
tension and not by the specific properties of the two phases. Although the existence of lipid rafts in biological membranes is still debated, the formation of domains has been well demonstrated for model systems. Elegant experimental visualization of this budding and fission process is given by Baumgart et al.5 and Bacia et al.,6 in which phase separation is obtained by the addition of different sterols. In the absence of rafts, a completely different mechanism is needed to obtain fission. Various experiments show that a variety of shape changes, including budding, can result from osmotically induced changes in the surface/volume ratio, thermally induced changes in relative leaflet area, or membrane growth.7 In addition, an area difference between the two monolayers, which can be obtained by a difference in the number of lipids in both monolayers, results in bending of the membrane and, as such, in a transformation of the vesicle shape. The geometrical shape of the lipids also can cause spontaneous curvature of the membrane. This spontaneous curvature can furthermore change with varying pH8 or ion concentrations9-12 such that a difference in pH value or ion concentration between the inner and outer environments of the vesicle can cause a change in the vesicle shape. For example, Sano et al.11 found that giant unilamellar vesicles (GUVs) of dipalmitoylphosphatidylcholine/cholesterol membranes undergo shape changes when La3+ ions are added to the aqueous solution. A discocyte GUV changed into a stomatocyte and subsequently into an inwardly budded shape after the addition of the ions. Similarly, a GUV shaped as a string of pearls transformed into a cylinder. Both shape changes appeared to be reversible by decreasing the ion concentration, indicating that no fission occurred. The proposed mechanism is that the ions direct the dipoles of the neutral lipids, increasing the lateral compression pressure of the membrane. This decreases the area of the outer membrane monolayer, which accounts for the shape change. Tanaka et al.12 found the same
10.1021/jp068277u CCC: $37.00 © 2007 American Chemical Society Published on Web 04/11/2007
5720 J. Phys. Chem. B, Vol. 111, No. 20, 2007 shape changes in dioleoylphosphatidylcholine GUVs under the addition of either La3+ or Gd3+ ions. Furthermore, Furuike et al.8 found that spontaneous curvature can also change with varying pH. A theoretical explanation of the mechanism involved in such a budding/fission process is given by the spontaneous curvature model.13 This model can explain the occurrence of budding for a certain parameter regime.14-16 The fission process is divided into two phases. In the first phase, the vesicle transforms to a shape in which two vesicles are connected with a neck (budding). In the second phase, the neck ruptures, and two vesicles of similar composition are formed, although they might be of different size. In the literature, various experimental studies, mathematical models, and simulation studies on such vesicle budding and vesicle fission have been described. The mathematical models describe membranes as a continuum.17 In the experimental studies, giant unilamellar vesicles are examined using different microscopic approaches. New microscopic approaches, such as two-photon microscopy, result in increasingly better visualization of the process; however, the membranes are still viewed as a continuous medium. In contrast, using molecular dynamics computer simulations, the process can be studied at a molecular level for smaller vesicles (SUVs). For our molecular dynamics simulations, we use the same coarse-grained lipid model that we have used before to study the spontaneous formation of vesicles and the bilayer-vesicle transition18 as well as the fusion of such vesicles19 and the deformation due to spontaneous curvature.20 Although in this coarse-grained lipid model, some detail of the lipids is lost, these prior studies have shown that the bilayer properties and behavior compare well with the behavior in experiments and other simulations, whereas this simplification makes the simulations computationally tractable. In this paper, we thus discriminate between two distinct fission mechanisms: (1) via raft formation, in which the driving force is minimization of line tension, and (2) via changing lipidenvironment interactions resulting in spontaneous curvature of the membrane. The structure of this manscript is as follows: after a description of the simulation method, simulations of both fission mechanisms are described, the results of these simulations are discussed and compared with other simulations and theoretical models, and finally, the obtained fission pathway is compared with that of the inverse process, that is, fusion. 2. Method 2.1. Lipid Model. The coarse grained lipid model that we use here to study lipid-based fission mechanisms is based on previous studies.18,19 Its derivation and parameters are described in detail in ref 18. The lipid consists of 12 particles: 2 tails consisting of 4 hydrophobic tail (T) particles each connected to four hydrophilic headgroup (H) particles (Figure 1b). A third particle type, namely, water (W), is present as solvent. Three types of nonbonded interactions are present: the first is the interaction between two hydrophilic (H and W) particles, the second is the interaction between two hydrophobic (T) particles, and the third is for the hydrophilic-hydrophobic interaction. To introduce distinct types of lipids, we generalize the headgroup and tail particles in the original model to Hx and Ty, respectively, and allow distinct interactions for every pair of particle types. Although different headgroup and tail particle types are available, within one lipid type, all four headgroup particles still have the same type, as do the eight tail particles. We will refer to such a lipid built of four headgroup particles of type Hx and eight tail particles of type Ty as an HxTy-lipid.
Markvoort et al.
Figure 1. Van der Waals representation of (a) dipalmitoylphosphatidylcholine (DPPC), (b) our original coarse-grained lipid, (c) an example of a second type of lipid consisting of different headgroup and tail particles, and (d) water. All particles are colored corresponding to their type using a color scheme that is employed throughout the article.
TABLE 1: The Stiffer the Lipids, the Larger the Minimal Bilayer Size to Form Vesiclesa N k
256
512
1024
0.0 4.0 16.0 64.0 256.0
v v b b b
v v v b b
v v v v b
a N is the number of lipids in the bilayer, k is the bending parameter, and b and v indicate whether the bilayer remained flat or curled into a vesicle, respectively.
Two distinct lipid types can thus have different headgroups (e.g., an HRTR-lipid versus an HβTR-lipid), different tails (e.g., an HRTR-lipid versus an HRTβ-lipid), or both (e.g., an HRTRlipid versus an HβTβ-lipid, Figure 1c). Unless stated otherwise, all interactions between particle types remain identical to the original model; however, per study, certain parameters are changed. For example, phase separation can be obtained in a membrane consisting of two types of lipids with different headgroup and tail types (i.e., HRTR-lipids and HβTβ-lipids) by decreasing the interaction of HR with Hβ, TR with Tβ, or both. Alternatively, spontaneous curvature can be obtained in a membrane with HRTR-lipids in one leaflet and HβTR-lipids in the other by changing the interaction of headgroup particles with water or with themselves. This was demonstrated in ref 20, in which an originally flat bilayer membrane was bent in this fashion. One more difference with our original lipid model used before to study vesicle formation18 is the omission of a bending potential. The reason for this is a previous finding that for smaller values of the bending constant, the mechanism of vesicle formation remains similar, but the minimum size of the bilayer necessary for the transition to a vesicle decreases. The smaller the bending constant, the more flexible the membrane, and as a result, the smaller the bilayer needs to be before vesiculation occurs. This is shown in Table 1. As we also expect the fission mechanisms to be equivalent for different values of the bending constant, we chose to omit the bending potential in this study to keep the simulations computationally tractable, since smaller vesicles can be used. 2.2. Initial Configuration. The initial configurations for our simulations are all derived from the final configuration of one prior simulation of vesicle fusion19 and are shown in the top row of Figure 2. Instead of using such an elongated vesicle, a spherical vesicle could have been used as the initial configuration. However, since
Lipid-Based Mechanisms for Vesicle Fission
J. Phys. Chem. B, Vol. 111, No. 20, 2007 5721
Figure 2. Configuration from which all initial configurations are derived by changing lipid types or removing some of the internal water particles. (a) Side view of the vesicle where water is not drawn, (b) cross section of the vesicle through its center, (c) vesicle with a surface fitted through the middle of the membrane, and (d) cross section of the vesicle with the fitted surface.
diffusion of water through the membrane is slow as compared to the simulation times reachable with our molecular dynamics simulations,21 the interior volume of a vesicle can hardly change during our simulations. For a sphere, hardly any shape changes are possible without changing the interior volume, hence, such a spherical vesicle will remain spherical and is, thus, incapable of fission. The starting configuration contains 2048 lipid molecules, of which 1289 are in the outer leaflet of the vesicle membrane and 759 are in its inner leaflet. The interior consists of 7009 water particles, whereas the vesicle is surrounded by 276 080 water particles. The volume fraction of this vesicle, that is, the volume of the vesicle divided by the volume of a spherical vesicle with the same membrane area, is approximately 0.80; hence, allowing shape changes.20 The volume fraction has been calculated using the area and volume of the bilayer center plane shown in Figure 2c. For all simulations, the initial configuration has been derived from this vesicle by reassigning lipid types. For some simulations, 7% of the interior water particles was also removed, resulting in a vesicle with a lower volume fraction, 0.77. Unless stated otherwise, all simulations have been performed in the isobaric-isothermal ensemble at atmospheric pressure and a temperature of 307 K. 3. Simulations 3.1. Fission via Raft Formation. The first fission mechanism that we study using our simulations is via raft formation. To obtain raft formation in our simulations, we use two types of lipids; namely, HRTR-lipids and HβTβ-lipids. Lipids of the same type interact with each other as before, but the attraction between lipids of different types is reduced. Because both the headgroup and tail particle types are different for the two lipid types, this reduced attraction can be applied for both the inter lipid type headgroup-headgroup interaction, that is, the headgroupheadgroup interaction between lipids of different type, and the inter lipid type tail-tail interaction. The initial configuration for these simulations is shown in Figure 3a. This initial configuration was obtained from the system in Figure 2 by assigning the 1024 left-most lipids to the HRTR-lipid type and the other 1024 to the HβTβ-lipid type. The results, after 5 000 000 iterations, of a series of simulations with varying inter lipid type interactions are summarized in Table 2.
Figure 3. A vesicle built of two components that phase-separate can undergo fission. The resulting vesicles have a lipid composition different from the original vesicle. Part (a) shows the initial configuration, (b) and (c) show subsequent intermediates, and (d) shows the completely separated final configuration.
TABLE 2: Overview of the Resulting Vesicle Shapes after 5 000 000 Iterations for Simulations with Different Inter Lipid Type Headgroup-Headgroup (HrHβ) or Tail-Tail (TrTβ) Interactions nr
HRHβ
T RT β
R-I R-II R-III R-IV R-V R-VI R-VII R-VIII R-IX R-X
-50% PR 0% -50% PR -50% -50% 0% -50% -50%
0% 0% PR PR PR 0% -50% PR PR PR
aP
note
resulta
NW ) 6509 NW ) 6509 NW ) 6509 NW ) 6509 T ) 318 K
P P B B B P B F F F
) prolate, B ) budded, F ) fission
In the first two simulations (R-I and R-II), only the strength of the inter type headgroup-headgroup interactions was decreased. In the case of a 50% decrease in this interaction and even in the case of a purely repulsive (PR) interaction between these headgroups, the vesicle reshaped only slightly. During these simulations, the contact area between the lipids of different types decreased by reducing the radius of the neck, but this neck remained filled with water, showing that for our vesicle, reducing the interaction strength of the headgroups only is not sufficient to obtain fission. In simulation R-III, the strength of the inter type tail-tail interaction was decreased instead of the inter type headgroupheadgroup interaction. This turned out to have a larger effect. The width of the neck decreased further such that the interior water was split in two parts, and thus, a budded vesicle was formed; however, full fission was not yet obtained. In simulations R-IV and R-V, in which the inter type headgroup-
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Markvoort et al. TABLE 3: Overview of the Resulting Vesicle Shapes after 5 000 000 Iterations for Simulations with Different Headgroup-Headgroup and Headgroup-Water Interaction for Lipids in the Outer (Hr-W and Hr-Hr) and Inner (Hβ-W and Hβ-Hβ) Monolayers nr
HR-W, %
HR-HR, %
Hβ-W, %
Hβ-Hβ, %
resulta
S-I S-II S-III S-IV S-V S-VI S-VII S-VIII S-IX S-X S-XI
2.5 5 10 10 15 20 20 25 30 35 25
-2.5 -5 -10 -10 -15 -20 0 0 0 0 -25
-2.5 -5 -10 0 0 0 0 0 0 0 5
2.5 5 10 0 0 0 0 0 0 0 0
P N N P F F P P F F F
a
Figure 4. With a proper spontaneous membrane curvature, vesicles can adopt a budded shape. This can be a prestage of fission. However, when the spontaneous curvature is created by changing both the inner and the outer lipids, complete fission does not occur in the time scale reachable with our simulations, because the neck is quite stable. Part (a) shows the initial configuration, (b) and (c) show subsequent intermediates, and (d) shows the final budded configuration.
headgroup interaction strength was also decreased, the budded state was stable as well. A reason that the vesicle does not split into two parts could be that the volume fraction of the initial vesicle is still too high. Since this volume fraction is 0.8, the membrane area has to increase approximately 10% to be able to envelop two vesicles with half of its interior each, or part of the interior volume should be segregated. A reduction of the volume fraction can be obtained in our simulations either by reducing the number of interior water particles in the initial configuration or by increasing the temperature. In the latter case, the membrane area is known to increase faster than the interior volume such that the volume fraction decreases. Increasing the temperature (T) from 307 to 318 K or reducing the number of interior water particles (NW) from 7009 to 6509 results in a volume fraction 0.77. Simulations R-VIII-IX, indeed, show full fission can be obtained for this lower volume fraction. Intermediate steps of one of these simulations (R-IX) are shown in Figure 3. 3.2. Fission via Spontaneous Curvature. The second fission mechanism that we study using our simulations is via spontaneous curvature. In our lipid model, changing ion concentrations or pH values that influence the packing of lipids in the bilayer and, thus, introduce spontaneous curvature can be incorporated by changing the headgroup-headgroup or headgroup-water interaction strengths or both. Spontaneous curvature is, thus, introduced by using two distinct lipid types: one for the lipids in the outer monolayer (HRTR-lipids) and one for the inner monolayer (HβTRlipids). The initial configuration is shown in Figure 4a. The tails of both lipid types are identical. By only changing the
P ) prolate/pear, N ) stable neck, F ) fission.
headgroup-headgroup and headgroup-water interaction parameters spontaneous curvature is obtained.20 In Table 3 an overview is given of the simulations with different interaction parameters, showing whether or not they resulted in complete fission. In the first simulation (S-I), the headgroup-headgroup interaction for the lipids in the outer monolayer (HR-HR) has been decreased by 2.5% as compared to the original parameters, and the headgroup-water (HR-W) interaction has been increased by 2.5%. Furthermore, for the lipids in the inner monolayer, the changes are the other way around, that is, a 2.5% increase in the headgroup-headgroup interaction (Hβ-Hβ) and a 2.5% decrease in the headgroup-water interaction (Hβ-W). The spontaneous curvature introduced in this way reshaped the prolate vesicle into a pear shape. When these changes are 5% (simulation S-II), vesicles undergo budding because of the resulting spontaneous curvature (Figure 4). Analogous to the experiments described above, two vesicles are formed that are still connected by a neck. In the time scale reachable by our molecular dynamics simulations, the formed neck (Figure 4d) remains stable (as also suggested in ref 15). For a 10% change (simulation S-III), a budded vesicle with a stable neck is formed as well. As suggested in ref 15, a way to destabilize the neck is the introduction of other membrane components that prefer to stay in regions with large positive Gaussian curvature. If the neck is the weakest point, another way to destabilize the neck could be to increase the temperature. The results of such a simulation at higher temperature (354 versus 307 K) show that this can, indeed, break the neck, resulting in complete fission. As described in ref 20, spontaneous curvature can also be introduced by changing only one lipid type. Because the spontaneous curvature of a bilayer is half of the difference of the spontaneous curvatures of the two separate leaflets,22 the change in the interactions for the one lipid should be roughly twice as large. Simulation S-IV shows, however, that for a 10% change, the vesicle remains prolate. But when we change the outer lipid type by 15% without changing the inner lipids (simulation S-V), a neck is formed that is less stable than the one in simulation S-II, and hence, this neck rapidly breaks, resulting in complete fission. Intermediates of this fission process are shown in Figure 5. First a neck is formed. Subsequently, hemifission is reached, that is, the state in which the inner monolayer is separated into two parts, whereas the outer monolayer is still intact (Figure 5e). This is rapidly followed by complete fission.
Lipid-Based Mechanisms for Vesicle Fission
J. Phys. Chem. B, Vol. 111, No. 20, 2007 5723 4. Discussion
Figure 5. When only the interaction strengths for the lipids in the outer monolayer are changed, complete fission is obtained. The resulting vesicles have the same relative lipid composition as the original vesicle. Part (a) shows the initial configuration, (b-f) show subsequent intermediates, and (g) shows the completely separated final configuration.
Simulations S-VII-X show that the dumbbell shape and successive fission can also be obtained by only changing the headgroup-water interaction of the lipids in the outer monolayer. So far, the strength of the headgroup-headgroup interaction for the lipids in the inner monolayer of the vesicles that reached fission has been equal to the headgroup-water interaction, just as in our original lipid model. But simulation S-XI shows that even when the headgroup-water interaction is stronger, resulting in a hydration shell around the headgroup and so driving the spontaneous curvature in the opposite direction, fission can still be obtained with a large enough hydration of the lipids in the outer monolayer.
In the previous section, we have shown simulations of two distinct fission pathways. The simulations of the second mechanism have, to the best of our knowledge, not been studied before. The domain formation, budding, and subsequent fission of vesicles via the first mechanism, however, have been shown using other simulation techniques, as well. These techniques include DPD simulations,23-26 Brownian dynamics simulations,27 and a solvent-free method.28 Here, we study this budding and subsequent fission with molecular dynamics simulations that provide an accurate description of the molecular motion, which could be crucial for the process. Solvent-free methods are, of course, much faster, but as we have shown for the formation of vesicles,18 the solvent may play an important role in such processes. Just like Laradji in his DPD simulations, we need quite a large repulsion between the two lipid types to obtain fission; otherwise, buds remain stable, and fission does not occur. In agreement is also that less repulsion between the lipid types is needed when the volume fraction of the vesicle to be budded off is reduced. For the fission mechanism using spontaneous curvature, smaller differences between the lipids are necessary than for the mechanism with rafts: only headgroups had to change, and the required changes were smaller in magnitude. Moreover, where the spontaneous curvature mechanism can reach fission for our initial vesicle, fission via the raft mechanism is reached only for vesicles with a smaller volume-to-area ratio. That only smaller differences are necessary in the case of the spontaneous curvature mechanism can be explained by the fact that this mechanism comprises a “global” effect, that is, all lipids of a monolayer contribute. The raft mechanism, on the other hand, is a “local” effect, that is, only contributed by the lipids at the phase separation line. Furthermore, for the spontaneous curvature mechanism, the changes in the parameters can be even smaller to reach the same effect for larger vesicles; namely, the shape of a vesicle and, thus, the question whether a bud is formed depends on the product of the spontaneous curvature and the radius of a spherical vesicle with the same membrane area. Thus, if the diameter of the vesicle is doubled, only half the spontaneous curvature, and consequently, approximately half the difference in interaction strength, yields the same result. To keep our simulations computationally tractable, our vesicles are relatively small, but for larger vesicles, the changes in the parameters, thus, can be even smaller to achieve the same result. Typical for the fission mechanism via raft formation is that the resulting vesicles have a different lipid composition from the original vesicle. Whereas the original vesicle consisted of 50% HRTR-lipids and 50% HβTβ-lipids, one of the resulting vesicles consists of only HRTR-lipids and the other of only HβTβlipids. For a self-replicating system, such as the primitive cell, this can be undesirable, and hence, fission without raft formation seems more natural in that respect. The process of fission involves the evolution of an initially intact membrane into two separate membranes. This must proceed via a pathway of intermediate structures, requiring both membrane deformations and perturbations. A theoretical description of such fission pathways is given by Kozlovsky.17 First, deformations bring the membrane into a typical neck-like shape. Then two scenarios are possible. The neck may rupture and subsequently reseal into the new configuration of two separate membranes. Such fission would be expected to be leaky because the formation of large and long-living pores is necessary to disrupt the neck. This is not observed in our simulations. All
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Figure 6. Schematic representation of intermediates in the fusion and fission pathways of our simulations. The two different colors represent the inner and the outer monolayer.
our simulations seem to follow the second scenario of hemifission, in which the membrane remains impermeable throughout the whole process of fission. The neck undergoes hemifission: its internal monolayer self-fuses, whereas the outer monolayer maintains its integrity. Subsequently, self-fusion of the outer monolayer completes the fission. Furthermore, as predicted by Kozlovsky, the formation of the hemifission state seems to be the energetically most unfavorable state because in our simulations, all vesicles rapidly undergo complete fission once hemifission occurs. In addition, as predicted in the same work, increasing spontaneous curvature of the membrane favors the fission reaction. Kozlovsky also predicts that once the neck diameter is smaller than a certain threshold value, hemifission happens spontaneously. However, this is not always the case in our simulations. A reason for this can be found in the ratio between the headgroup-headgroup and the headgroup-water interaction strengths of the lipids in the inner monolayer. In our first simulations S-I-III, where this ratio was larger than one, the neck remained stable, even when the water was completely removed from the neck. But for the simulations in which this ratio was smaller than or equal to one, indeed, only equilibrium shapes were found with water in the neck or in which complete fission was obtained. To elucidate this discrepancy and to explore whether the monolayers not only undergo bending but also tilt the hydrocarbon chains with respect to the membrane surface, as predicted by Kozlovsky, as well, a more detailed analysis of fission on a more detailed lipid model should be performed. In this model, the bending potential should be reinstated, and a more detailed parametrization of the headgroups should be adopted. Such a parametrization of the headgroups would also enable the prediction of lipid types and pH values/ ion concentrations for which fission can be obtained experimentally. Finally, we compare the fission pathway from our simulations with the fusion pathway from our prior simulations.19 Some schematic drawings of important intermediates of both pathways are shown in Figure 6. Although our simulations are 3D, for clarity these drawings are 2D as all intermediates are almost axially symmetric. The symmetry axis has been drawn in every
Markvoort et al. intermediate as a dotted line. Furthermore, the two different colors represent the inner and the outer monolayer. Most importantly, although fission is the inverse process of fusion, the fission pathway is not simply the reverse of the fusion pathway. The most obvious distinction is visible on the second row of the Figure; namely, the last step of fusion usually comprises a hemifusion diaphragm that breaks and is subsequently incorporated into the inner monolayer. The first step of fission, on the other hand, comprises the formation of a narrow neck. However, both pathways also have some similarities. For example, both pathways share a “hemi” state, that is, a state in which the outer monolayer is intact as for the completely fused vesicle, but in which the inner monolayer can be divided into two parts, one for each of the subvesicles. An essential difference between the hemifusion and hemifission states, however, is that the line of contact between the selffusing monolayers is perpendicular to the symmetry axis in the case of fusion, whereas it is parallel in case of fission. This difference explains why fusion can be leaky, especially when it progresses via anisotropic stalk expansion where part of the external solution is enveloped by the fusing external monolayers, whereas for fission, this is not the case because the vesicle interior is kept separate from the exterior at all times. 5. Conclusion Two completely different mechanisms of lipid-based vesicle fission have been demonstrated using molecular dynamics computer simulations. In the raft-formation mechanism, a vesicle consisting of two lipid types splits into two vesicles that each consist of one of the two lipid types. In the spontaneous curvature mechanism, on the other hand, a vesicle consisting of two lipid types splits into two vesicles that both have the same lipid composition as the original vesicle. The latter mechanism is very interesting because smaller differences between the two types of lipids are required to obtain fission than in the former mechanism. Only changes to the headgroupheadgroup or headgroup-water interactions of one of the monolayers, which can be caused by changes in pH value or ion concentrations, suffice to split an initially stable vesicle into two stable, smaller vesicles. Acknowledgment. We thank Ben de Kruijff, Antoinette Killian, Peter Spijker, Mark Peletier, Remco van der Hofstad, and Maarten van Wieren for many fruitful discussions. References and Notes (1) Berclaz, N.; Mu¨ller, M.; Walde, P.; Luigi Luisi, P. J. Phys. Chem. B 2001, 105, 1056 -1064. (2) Hanczyc, M.; Fujikawa, S.; Szostak, J. Science 2003, 302, 618622. (3) Ju¨licher, F.; Lipowsky, R. Phys. ReV. Lett. 1993, 70, 2964-2967. (4) Ju¨licher, F.; Lipowsky, R. Phys. ReV. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1996, 53, 2670-2683. (5) Baumgart, T.; Hess, S.; Webb, W. Nature 2003, 425, 821-824. (6) Bacia, K.; Schwille, P.; Kurzchalia, T. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 3272-3277. (7) Ka¨s, J.; Sackmann, E. Biophys. J. 1991, 60, 825-844. (8) Furuike, S.; Levadny, V.; Li, S.; Yamazaki, M. Biophys. J. 1999, 77, 2015-2023. (9) Sasaki, D. Cell Biochem. Biophys. 2003, 39, 145-162. (10) Kooijman, E.; Chupin, V.; Fuller, N.; Kozlov, M.; de Kruijff, B.; Burger, K.; Rand, P. Biochemistry 2005, 44, 2097-2102. (11) Sano, R.; Masum, S.; Tanaka, T.; Yamashita, Y.; Levadny, V.; Yamazaki, M. J. Phys. Condens. Matter 2005, 17, S2979-S2989. (12) Tanaka, T.; Tamba, Y.; Masum, S.; Yamashita, Y.; Yamazaki, M. Biomed. Biochim. Acta 2002, 1564, 173-182. (13) Deuling, H.; Helfrich, W. J. Phys. France 1976, 37, 1335-1345. (14) Bozic, B.; Svetina, S. Eur. Biophys. J. 2004, 33, 565-571.
Lipid-Based Mechanisms for Vesicle Fission (15) Chen, C.; Higgs, P.; MacKintosh, F. Phys. ReV. Lett. 1997, 79, 1579-1582. (16) Svetina, S.; Zeks, B. Anat. Rec. 2002, 268, 215-225. (17) Kozlovsky, Y.; Kozlov, M. Biophys. J. 2003, 85, 85-96. (18) Markvoort, A.; Pieterse, K.; Steijaert, M.; Spijker, P.; Hilbers, P. J. Phys. Chem. B 2005, 109, 22649-22654. (19) Smeijers, A.; Markvoort, A.; Pieterse, K.; Hilbers, P. J. Phys. Chem. B 2006, 110, 13212-13219. (20) Markvoort, A.; van Santen, R.; Hilbers, P. J. Phys. Chem. B 2006, 110, 22780-22785. (21) Smeijers, A.; Pieterse, K.; Markvoort, A.; Hilbers, P. J. Phys. Chem. B 2006, 110, 13614-13623.
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