ABSTRACT A two-dimensional (2D) model of lipid bilayers was developed and used to investigate a possible role of membrane lateral tension in membrane fusion. We found that an increase of lateral tension in contacting monolayers of 2D analogs of liposomes and planar membranes could cause not only hemifusion, but also complete fusion when internal pressure is introduced in the model. With a certain set of model parameters it was possible to induce hemifusion-like structural changes by a tension increase in only one of the two contacting bilayers. The effect of lysolipids was modeled as an insertion of a small number of extra molecules into the cis or trans side of the interacting bilayers at different stages of simulation. It was found that cis insertion arrests fusion and trans insertion has no inhibitory effect on fusion. The possibility of protein participation in tension-driven fusion was tested in simulation, with one of two model liposomes containing a number of structures capable of reducing the area occupied by them in the outer monolayer. It was found that condensation of these structures was sufficient to produce membrane reorganization similar to that observed in simulations with "proteinfree" bilayers. These data support the hypothesis that changes in membrane lateral tension may be responsible for fusion in both model phospholipid membranes and in biological protein-mediated fusion.
INTRODUCTION
Despite significant progress in the identification of fusion proteins and understanding the details of their function, an understanding of the mechanism of biological membrane fusion is still far from complete. A number of different hypotheses have focused on the question of how conformational changes in proteins are coupled to the profound rearrangement of lipid molecules associated with the formation of the initial fusion pore (reviewed in Bonnafous and Stegmann, 2000; Lentz and Lee, 2000; Ruysschaert and Epand, 1999; Zimmerberg and Chernomordik, 1999). Computer simulations of fusion seem to be useful tools to study lipid and protein rearrangements at the molecular level, but even a nanosecond-long atomic resolution simulation of a lipid bilayer with 50-100 lipid molecules requires several months of supercomputer time (Pastor, 1994). A two-dimensional model of lipid bilayers developed several years ago (Chanturiya, 1997) still remains the only computer model suitable for practical experimentation on the possible mechanisms of a large-scale bilayer rearrangement during membrane fusion. Although this model is schematic and does not allow direct extrapolation to measurable macroscopic parameters of real lipid bilayers, it is still useful for the rough evaluation of different fusion mechanisms. The majority of theoretical works on membrane fusion are focused on bilayer curvature-related effects in the immediate vicinity of the point of fusion (Kozlov and Markin, 1983; Siegel, 1999; Kozlov and Chernomordik, 1998). However, the possibility of the involvement of distant lipid molecules in the unification of the membrane in the contact area is now receiving more attention (Safran et al, 2001; Garcia et al, 2001). In the present work we use a twodimensional (21) model, with minor modifications, to study several aspects of purely lipidic fusion that were not tested in previous studies, and thus confirm the viability of this approach for fusion studies. We also modified the model to test the hypothesis that changes in protein conformation may be coupled to fusion via the membrane lateral tension mechanism that has been suggested to explain calcium-- induced fusion in different systems (Chanturiya et al., 2000).
MODEL DESCRIPTION
General principles of the 2D bilayer model
Protein-mediated fusion
It has been suggested (Pantazatos and MacDonald, 1999; Chanturiya et al., 2000) that certain conformational changes in fusion proteins may lead to protein removal from the outer monolayer of fusing membranes or a reduction in their area of occupation in the outer monolayer. When this happens, voids are generated that must be filled by lipid molecules. This results in an increase in the area per lipid in that monolayer of the membrane, and thus an increase in the membrane lateral tension. This may lead to fusion by a mechanism that is similar to calcium-induced fusion of purely lipidic molecules, but with a sensitivity to a stimulus determined by the nature of the protein. This hypothesis was tested using the simulation model described here. Parameters used for the lipid molecules were the same as the ones used in simulations of purely lipidic bilayers. Protein molecules capable of reducing the area occupied by them in the outer monolayer were represented by structures (referred to hereafter as proteins) having a length equal to that of the lipid and width equal to the width of two lipid molecules. These proteins were actually homologous to lipid dimers, and like regular lipids have three points of interactions (in the headgroup region, tail region, and 1/4 deep from the headgroup region) with neighboring lipid molecules on each side (e.g., 6 points total). Interactions of these points with neighboring Lipid molecules were described by the same set of equations as interactions between lipid molecules. Parameters of these "lipid/protein" interactions and of interactions between lipid molecules were unchanged in the course of simulations. Condensation of proteins was induced at some point during simulations by increasing attraction forces between three pairs of points on opposite sides of the protein molecule.
RESULTS
Effect of internal pressure on fusion
While previous experiments successfully demonstrated the applicability of 2D simulation to model hemifusion of bilayers (Chanturiya, 1997), the question about the ability of this model to simulate complete fusion was left open. A number of experimental results on liposome/BLM fusion point out that vesicle internal pressure may be responsible for the conversion of hemifusion into complete fusion (Cohen et al., 1984; Chanturiya et al., 1997). Here we tested this hypothesis using the model modified to permit the introduction of internal pressure as described above. When we introduced vesicle internal pressure into the model, breaking of the outer monolayer occurred, followed by breaking of the inner monolayer in the same region (Fig. 2 B). This effect was observed in a relatively narrow range of K^sub p^ (2-3). Higher values resulted in breaking of both monolayers in several places, different from the region of contact and/or complete destruction of the bilayer in the region of contact.
Corresponding changes in head-head distances for molecules in different locations and changes in system energy are presented in Fig. 3. For molecules far from the contact region in both monolayers, internal pressure effectively reduces or even reverses reduction in head-head distances (Fig. 3, A and B), resulting in higher lateral tension in the bilayer compared to simulations without internal pressure (Fig. 2 A). In contrast, molecules close to the breakpoint of the membrane undergo transient ups and downs in head-head distances, but eventually condense to approximately the same head-head distances unrelated to the value of the pressure parameter.
Effect of incorporation of additional molecules into membranes
Additional molecules were inserted either into the contacting monolayers or the distal monolayers of two interacting bilayers. These additional molecules were assigned the same parameters as other molecules in the bilayers, and hence no shape-related effects were present. Results from this simulation are shown in Fig. 2 C. No signs of monolayer breaking were seen during 4000 cycles of computation, giving a similar effect on fusion as the experimental incorporation of lysolipids (Chernomordik et al., 1995). In a control experiment carried out with the same parameters but without the introduction of extra molecules, both contacting monolayers broke at cycle 1150 and an expanded zone of hemifusion was formed at cycle 3500 (Fig. 2 A). Similar results were observed even with a lower fraction of extra molecules than was used in Fig. 2 C. Having extra lipids at a ratio of ~1/9 to 1/8 to original lipids resulted in complete inhibition of hemifusion, whereas with extra lipids at a ratio of 1/11 to 1/10 contacting monolayers broke, but molecules on the edges were separated by only three to four times the initial distance at cycle 5500.
Corresponding changes in system energy and intermolecular distance are shown in Fig. 3 C. Incorporation of additional molecules caused an initial increase in system energy, led to a reduction of head-head distance, and eventually led to a reduction of both energy (compare Fig. 3, A and C) and lateral tension in the outer monolayer, inhibiting hemifusion. Insertion of the same number of extra molecules into distal monolayers did not result in any inhibition of bilayer fusion (data not shown).
Insertion of additional molecules into circular bilayers under the conditions used to simulate an internal hydrostatic pressure gave significantly different results. Outer monolayer insertion prevented normal hemifusion and fusion, but did not block the process completely. Breakage of monolayer continuity and connection (while distorted) of the internal contents of vesicles (data not shown) was observed even in the presence of extra molecules.
Fusion induced by increased tension in only one of two contacting bilayers
In these simulations we used the same protocol (with K^sub p^ = 0) as used previously for both structures, but limited the increase in K^sub hh^ to only one. As in all other simulations, head-head attraction parameters (K^sub hh^ and/or W^sub hh^) for the molecules in the area of contact were set lower than outside of this area. With K^sub hh^ and W^sub hh^ in the contact area set to one-half of the respective values outside the region of contact, it was possible to get breaking of both monolayers. The monolayer with an increased K^sub hh^ always broke first. The structure of bilayers in the region of contact was different from that observed for bilayers with tension in both monolayers. As a result of breaking in several points within the region of contact, an analog of an "inverted micelle" (Rand, 1981; Siegel, 1993) was formed (Fig. 4 A).
When a planar bilayer under tension was placed in contact with liposomes, no breakage of the contacting monolayer was observed unless K^sub hh^ was increased for the liposome. If the internal pressure of the liposomes is increased along with an increase in K^sub hh^, breakage of both bilayers in the area of contact, i.e. fusion, was observed (Fig. 4 B). Similar simulation results were also obtained for two liposomes when K^sub hh^ was increased in only one of them (data not shown).
The model is not sufficiently sophisticated to correctly reorient the lipids on the edges of pores upon breakage of a monolayer or to provide for an accurate simulation of the pore size. It loses connection with physical realities when the lipid molecules are separated by distances that exceed L^sub max^.
Protein-mediated fusion
Linear bilayers with "protein" molecules inserted in only one of the monolayers were found to reduce their overall length and bend in response to "condensation" of the protein molecules. However, when we placed two bilayers, one containing proteins, either as linear with circular or both circular in contact, and attempted to induce fusion by reducing the area occupied by protein, no fusion-like structural changes could be observed. Similar results were obtained on varying different model parameters, even when protein molecules were present in both structures. Condensed protein molecules become separated from adjacent lipid molecules and the protein-containing bilayer eventually disintegrated into a number of separate lipidic fragments and independent protein molecules (data not shown).
To achieve fusion induced by a conformational change of a protein it was necessary to introduce some modifications to the model. First, we increased the energy cost of monolayer stretching by replacing the energy functions described by Eq. 1 with others that provide a sharper increase in the system energy with changes in distance.
Second, to give lipid molecules more time to follow new lipid/protein boundaries, we increased the time during which the protein lateral dimension was reduced to new values. To achieve this, we substituted the instant increase of attraction forces within protein molecules, with a linear increase in these forces (determined by values of K^sub xx^ for protein) over the period of 300+ cycles. These two modifications resulted in a breakage of monolayers in the area of contact in response to "protein condensation" (Fig. 5). Corresponding changes in the protein area and distances between lipid molecules are shown in Fig. 6. The first transient increase in head-head distance between lipid molecules close to the monolayer break-point correlates with the beginning of the decrease in the size of protein molecules. The following decrease begins when the monolayer breaks and molecules close to the edge are getting freedom to condense. The reason for the second transient distance increase is less clear and is possibly related to the movement of the molecules out of the area of contact. In contrast to situations shown in Fig. 3, A and B, there was no reduction in head-head distances between molecules far from the contact area in this case. An opposite effect, an increase in head-head distances between lipid molecules in the outer monolayer in response to protein condensation, generates forces that pull lipids apart in the area of membrane contact.
DISCUSSION
Experiments with a simplified 2D model of a phospholipid bilayer presented here demonstrate the viability of this approach for studying the basic principles of the early stages of membrane fusion. We have demonstrated that two major experimental observations in fusion of protein-free membranes, hemifusion in the absence of internal pressure (Chanturiya et al., 1997) or complete fusion in the presence of internal pressure (Cohen et al., 1984), can be reproduced by this model.
We have also demonstrated that inhibition of fusion by lysolipids (which implies the insertion of extra molecules into the contacting monolayers) could be reproduced, but as a result of a mechanism completely insensitive to the shape of lysolipid molecules (Chernomordik et al., 1993). The universal inhibition of fusion in various systems by lysolipids is a well-known phenomenon. It is assumed that this effect is due to the specific molecular shape of lysolipid molecules. They have a relatively large polar headgroup area compared with the smaller hydrophobic area due to their having only one hydrophobic tail. The effect of this shape is to increase a preference for curvature toward a micelle, and for this reason the presence of lysolipids in a bilayer should increase the energy cost of the initial highly curved fusion intermediate, "stalk" (Kozlov and Markin, 1983) formation. However, our data indicate that lysolipids may inhibit fusion simply by insertion into the contacting monolayers, relaxing the tension required for fusion. Interestingly, the fraction of extra molecules required to inhibit hemifusion in simulation experiments (9-12%) is quite close to the fraction of lysolipids required to inhibit fusion in real membranes (13%, Chernomordik et al., 1995). These three results support the idea that tension increases in contacting phospholipid membranes is the primary reason for membrane breakage that leads to fusion.
The model also allowed us to investigate the possibility of tension-driven fusion in situations not as well-studied experimentally. It demonstrated the possibility of inducing breakage in both contacting monolayers even when an increase in lateral tension occurs only in one. Earlier it was shown that for vesicle/vesicle fusion, no aqueous content mixing or complete fusion was detected unless both membranes were perturbed in a way that increased tension (Lee and Lentz, 1997). However, when we performed experimental measurements on calcium-induced membrane mixing of vesicles, we observed fusion events similar to the results predicted by this computer model (Fig. 7). Our experimental design was based on the fact that at low concentrations (a few millimolar), calcium ions strongly interact with negatively charged phospholipid headgroups, but not with neutral phospholipids. If one of two contacting membranes bathed in a calcium-containing solution is charged and the other is not, then tension should develop in the first membrane only. With one of two membranes labeled with fluorescent lipid dye, fusion can be monitored by the established technique of fluorescent dye dequenching or by visual observation of dye redistribution.
The ability to induce fusion of two membranes by modification of only one of them is interesting for two reasons. First, it is important in the design of optimal systems for targeted drug delivery where the target, the cell membrane, obviously cannot be modified to fit optimal fusion requirements. Second, since some data suggest that even in many cellular systems all the necessary fusion machinery is located in only one membrane (Vogel et al., 1992; Chanturiya et al., 1999), an understanding of how this can occur is important to achieve an understanding of biological membrane fusion mechanisms.
Our experiments with modeling tension-driven, protein-- mediated fusion demonstrated that this mechanism is, in principle, possible. Lateral condensation of a limited number of specific molecules in the outer monolayer was sufficient to break both contacting monolayers (Fig. 5), which is a necessary precondition for membrane fusion to occur. However, it was also found that to get to this point, our model needed to be significantly more fine-tuned than in a seemingly similar case when tension was increased purely with packing changes in the lipidic monolayer, as occurs with calcium ion binding. While an exact analysis of differences in bilayer reorganization for lipid- and protein-- induced tension is not possible, an approximate analysis of these two situations might be helpful. For purely lipidic bilayers we modeled the induction of fusion very similar to that by the binding of divalent ions to a negatively charged membrane. The increase in head-head attraction force (K^sub hh^) between lipid molecules outside of the area of contact is greater than that between the molecules within the area of contact. This leads to a differential change in the head-head distance for molecules in these two areas. Such differential changes in attraction forces are justified by the assumption that ionic charges in the area of membrane contact are distributed between two membranes, and thus have lesser effect on counter charges in the membrane compared to ions located outside of this area of contact. This assumption is yet to be tested in real systems, but modeling experiments have not resulted in fusion when forces in the contact region, determined by the K^sub hh^ value, were the same as forces outside the region. This means that the increase in system energy by itself is not sufficient to cause breakage of a bilayer. Only when a gradient of energy is present can lipid molecules flow out of the contact region and initiate fusion (Chanturiya, 1997; Safran et al., 2001). With increased separation, attraction forces finally become insufficient to hold molecules together and monolayers break. There is a difference between this situation and the situation when tension is induced by condensation of a limited number of molecules located outside of the area of membrane contact. In the latter case we do not have an increase in K^sub hh^ for lipid molecules next to the area of contact. These molecules are not active participants in tension development, but rather mediators of energy delivery to this area. As shown in Fig. 6, protein condensation increases the separation between lipid molecules in contrast to the decrease in interlipid distance when K^sub hh^ is increased (Fig. 3). It still produces forces that attempt to pull apart molecules in the area of contact, but these forces are weaker than the forces that result from the increase of head-head attraction energy. They were not sufficient to break monolayers when a simple linear dependence of attraction energy versus distance was used in the original model. Only when we replaced it with Eq. 5, producing a nonlinear dependence of energy on distance, does it become possible to overcome the sum of reaction forces and break the monolayer in the area of contact.
Taken together with results of model simulations, the analysis indicates that while tension-driven fusion may be induced by protein condensation, this mechanism is not as effective as one that involves condensation of the whole lipid monolayer. It seems likely that tension development due to protein condensation may work in tandem with other protein mediated effects) in fusion, such as creation of a hydrophobic defect in the area of contact (Bentz, 2000) or destabilization of the target membrane by a fusion peptide.
It is important to remember that the behavior of a 3D system should certainly be different from the 2D model used here. It is possible that tension-driven fusion can be completed in a 3D system without additional assumptions. There are two major differences between 2D and 3D model bilayers that can make formation of the initial 3D pore easier. First, in a 3D model system more than two molecules will participate in the delivery of energy to the break point in the monolayer. Second, molecules in a 3D system have more freedom to move in the monolayer, and this may also change the results significantly. A 3D model based on similar principles as described above is currently under development. Because both the number of molecules and the number of interactions calculated would be higher in a 3D system, we expect about a two-order increase in computational time will be required. However, even 200-500 h of desktop computer time per experiment is still acceptable, and may be reduced with the use of more powerful machines.
The authors are grateful to Dr. Tim Whalley for help in the preparation of this publication.
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[Author Affiliation]
Alexandr Chanturiya,* Puthurapamil Scaria,* Oleksandr Kuksenok,^ and Martin C. Woodle*
*Genetic Therapy Inc., Gaithersburg, Maryland 20878 USA, and ^lnstitute of Biochemistry, Kiev, Ukraine
[Author Affiliation]
Submitted June 4, 2001 and accepted for publication March 1, 2002.
Address reprint requests to Alexandr Chanturiya, LCMB, NICHD, NIH, Bldg. 10, Rm. 10D04, 10 Center Drive, MSC, Bethesda, MD 20892. Tel.: 301-594-1108; Fax: 301-594-0813; E-mail: chanturia@nih.gov.
P. Scaria's and M. C. Woodle's present address is Intradigm Corporation, 12115K Parklawn Drive, Rockville, MD 20852.
O. Kuksenok's present address is Department of Chemical Engineering, 1249 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261.
