Role of Inverse-Cone-Shape Lipids in Temperature-Controlled Self-Reproduction of Binary Vesicles

Abstract

We investigate a temperature-driven recursive division of binary giant unilamellar vesicles (GUVs). During the heating step of the heating-cooling cycle, the spherical mother vesicle deforms to a budded limiting shape using up the excess area produced by the chain melting of the lipids and then splits off into two daughter vesicles. Upon cooling, the daughter vesicle opens a pore and recovers the spherical shape of the mother vesicle. Our GUVs are composed of DLPE (1,2-dilauroyl-sn-glycero-3-phosphoethanolamine) and DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine). During each cycle, vesicle deformation is monitored by a fast confocal microscope and the images are analyzed to obtain the time evolution of reduced volume and reduced monolayer area difference as the key geometric parameters that quantify vesicle shape. By interpreting the deformation pathway using the area-difference elasticity theory, we conclude that vesicle division relies on (1) a tiny asymmetric distribution of DLPE within the bilayer, which controls the observed deformation from the sphere to the budded shape; and (2) redistribution of DLPE during the deformation-division stage, which ensures that the process is recursive. The spontaneous coupling between membrane curvature and PE lipid distribution is responsible for the observed recursive division of GUVs. These results shed light on the mechanisms of vesicle self-reproduction.

Introduction

Self-reproduction of vesicles by incorporating additional molecules leading to vesicle growth, deformation, and division into independent daughters is an indispensable feature of cellular life (1, 2, 3). One of the milestones in our understanding of the role of molecular self-assembly in this process is the development of artificial vesicles capable of self-reproduction. In this context, self-reproduction has been investigated using simple fatty-acid giant vesicles (4, 5, 6, 7). For instance, upon addition of a droplet of oleic anhydride to oleic acid/oleate giant vesicle suspension, the anhydride molecules are hydrolyzed to oleic acid/oleate within the vesicle membrane. The vesicles supplied with the oleic acid/oleate molecules do self-reproduce by deforming to a pearlike shape and then dividing into two daughters. Recently Takakura et al. (8), Takakura and Sugawara (9), and Kurihara et al. (10) devised a self-reproducing vesicle system by designing amphiphiles that transform from precursors to membrane molecules by catalyst-assisted hydrolysis. These novel (to our knowledge) observations prove that self-reproduction may be materialized by bilayer-forming molecules alone without relying on proteins, although the physical mechanisms involved are not clear.

The above modes of vesicle self-reproduction are of considerable interest although they are different from those seen in present-day cells. For instance, in bacteria the cell division is conducted by a tubulin homolog, FtsZ, which forms a ring (Z-ring) at the neck (11). The Z-ring constricts in parallel with synthesis of a cross wall and completes the division. However, bacteria have the ability to switch into a wall-free state called the “L-form”. The proliferation of the L-form is independent of the FtsZ-based division and does not require the mechanisms that are pivotal for regulation of cell division, cell shape, elongation, coordinated chromosome segregation, and balanced membrane lipid synthesis of walled cells, but it does requires excess membrane production to generate an imbalance between growth of cell surface area and volume (12, 13). These observations provide direct support for the notion that purely biophysical effects could have supported an efficient mode of proliferation in primitive cells.

When considering vesicle self-reproduction as a mechanical process controlled by membrane elasticity, several issues must be addressed (14, 15, 16). One is the geometrical requirement to attain the deformation to the limiting shape consisting of a pair of spheres connected by a narrow neck. The pathway of this deformation depends on the vesicle area and volume growth rates parameterized by the time needed for the membrane to double its area T_d and the membrane hydraulic permeability L_p, respectively, as well as on the spontaneous curvature C₀ and bending rigidity κ. To ensure that the daughters are identical in size and shape to the mother, the product T_dL_pκC₀⁴ must be equal to 1.85 (15). When the product is larger than 1.85, the mother vesicle show asymmetric division, whereas for mother vesicles with T_dL_pκC₀⁴ < 1.85, a growing vesicle is transformed into shapes that cannot lead to self-reproduction. The second issue concerns the mechanism of breaking the neck after the limiting shape has been reached. The breaking is not expected to take place spontaneously in most vesicles (17) because the neck is stabilized by the spontaneous curvature (18). In such a case, self-reproduction must involve a mechanism of neck destabilization, e.g., mechanical agitation (7, 19) or the coupling of local lipid composition in the multicomponent vesicle to Gaussian curvature (20). In addition, after the neck has been broken, daughter vesicles should have the same properties as the mother so that the self-reproduction process can be repeated.

These questions are best studied experimentally using a model system where self-reproduction can be easily triggered and controlled. To this end, Sakuma and Imai (21) developed a protocol where the mother produces twin daughters by cyclic heating and cooling. In this system, the membrane area does not grow by addition of molecules or by in situ synthesis, and thus the number of the vesicles increases at fixed total area. This approach departs from the perfect replication strategy (15), because in each generation the vesicle size is decreased; in this respect, it is somewhat reminiscent of a reductive cleavage mode of early embryonic development where cells divide at fixed total volume (22). The protocol relies on binary vesicles: those in Sakuma and Imai (21) were composed of cylinder-shaped lipids with a high melting temperature T_m, DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine, T_m = 41°C) and of inverse-cone-shape lipids with a low T_m, DLPE (1,2-dilauroyl-sn-glycero-3-phosphoethanolamine, T_m = 29°C). By heating them above the T_m of DPPC, binary giant unilamellar vesicles (GUVs) spontaneously deformed to a budded limiting shape using up the excess area produced by the chain melting of DPPC and then the neck was completely broken. After cooling back to the initial temperature, daughter vesicles recovered the spherical shape of the mother through the main-chain phase transition in DPPC and the corresponding membrane area decrease. In the next cycle, the process was repeated in both daughters and then again, eventually yielding several generations of vesicles that captured the essence of self-reproduction.

It is surprising that the recursive vesicle division is realized by simply mixing the inverse-cone-shape lipids into the GUV composed of the cylinder-shaped lipids. To identify the role of PE lipids in the cyclic deformation-division process, it is important to quantitatively understand the physical mechanics of vesicle deformation and division. Here we report a detailed three-dimensional (3D) imaging analysis of the process using a fast confocal microscope. We use the images to measure two key geometrical parameters that characterize vesicle shape, finding that the shape deformation trajectories in the phase space (23) are extremely reproducible from generation to generation. The trajectories are interpreted using the area-difference elasticity (ADE) theory and the main qualitative conclusion of our analysis is that the distribution of the inverted-cone component within the membrane is asymmetric. A tiny asymmetry of the area change between the inner and the outer monolayer in the GUV causes an enormous effect of the morphology (24, 25). Another interesting conclusion is that the membrane composition is relaxed at the end of each cycle. Relaxation by lipid traffic coupled with the lipid geometry most likely takes place during pore formation driven by membrane shrinking so that, in this respect, the state of vesicles is reset by the cooling stage of the cycle. The detailed quantitative analysis of the topological transition observed in our vesicles reveals the physical basis of self-reproduction; the geometrical requirements for the recursive vesicle division should also apply to perfect self-reproduction of vesicles where the sizes of the daughter and the mother vesicles are the same.

Materials and Methods

Sample preparation

Phospholipids used in this study were DPPC and DLPE. In addition, to examine the effect of the lipids having the phosphoethanolamine headgroup (PE lipids), we used DLPC (1,2-dilauroyl-sn-glycero-3-phosphocholine (T_m = −2°C) and cholesterol. These lipids were purchased from Avanti Polar Lipids (Alabaster, AL) and used without further purification. For 3D imaging, fluorescent lipids, 18:1 Liss Rhod PE (Rhodamine 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-n-(lissamine rhodamine B sulfonyl)) and Acyl 12:0 NBD PE (1-acyl-2-{12-[(7-nitro-2-1,3- benzoxadiazol-4-yl)amino]dodecanoyl}-sn-glycero-3-phosphoethanolamine) were obtained from Molecular Probes (Eugene, OR). Binary GUVs composed of DPPC and DLPE (mixed in the mole ratio of 8:2) were prepared using the gentle hydration method (26). First we dissolved the phospholipid mixture (DPPC/DLPE) in 10 μL of chloroform (10 mM). To dye the GUVs, 18:1 Liss Rhod PE was added to the solution at a molar concentration of 0.70% to the lipid solution. The solvent was evaporated in a stream of nitrogen gas and the obtained lipid film was kept under vacuum for one night to completely remove the remaining solvent. The dried lipid film was hydrated with 1 mL of pure water (Direct-Q 3 UV System; Millipore, Billerica, MA) at 60°C. During hydration, the lipid films spontaneously formed GUVs of diameters between 10 and 50 μm.

Microscopy

The vesicle suspension was transferred to the sample cell on a glass slide. This sample cell was set on a temperature-controlled stage for microscopic observation (model No. PE120; Linkam Scientific Instruments, Waterfield, Epsom, Tadworth, UK). During this manipulation, we maintained the sample suspension temperature above $T_m^{\text{DPPC}}$ at ≈50°C, at which the spherical vesicles exhibited a homogeneous single-phase appearance. Then we decreased the temperature from 50 to 30°C (step 1), which is below $T_m^{\text{DPPC}}$ but above $T_m^{\text{DLPE}}$, at a rate of 20°C/min. After 5 min equilibration, we heated the suspension to 50°C at a rate of 6°C/min, where binary GUVs first deformed to a budded limiting shape (step 2) and then transformed into two daughter vesicles (step 3). Thereafter we decreased temperature to 30°C at a rate of 12°C/min, which ensured that the daughter vesicles had a taut spherical shape (step 4). The GUV deformation caused by heating and cooling from 30 and 50°C and back was monitored by a high-speed confocal laser scanning microscope supported by a piezoelectric drive (LSM 5Live; Carl Zeiss, Jena, Germany; and objective Plan Apochromat 40x/0.95 or C-Apochromat 63x/1.20 W; Carl Zeiss). With our setup, a vesicle can be scanned within a period of 1–2 s and the obtained vesicle images consist of ∼50 two-dimensional xy slices of frame size 160 × 160 μm separated by 0.5 or 1 μm.

3D image analysis

To extract the shape of the target vesicle, we used our custom image-processing program where the surface is obtained by optimization of the fluorescence intensity distribution at the membrane (20). The surface image data were transferred to the Surface Evolver package (27), which was employed to evaluate the geometrical parameters of the vesicle including volume V; area A; and the monolayer area difference defined by $\Delta A=2h\oint HdA$, where h is the distance between the neutral planes of the monolayers and H is the local mean curvature. At fixed reduced volume v = $6\sqrt{\pi }V/A^{3/2}$ and reduced monolayer area difference Δa = $\Delta A/\left(4\sqrt{\pi }h{A}^{1/2}\right)$, we used the Surface Evolver to compute the relaxed vesicle shape by minimizing the Helfrich energy (28),

$$W_b=\frac{\kappa }{2}\oint {\left(2H\right)}^{2}dA,$$ (1)

where κ is the local bending constant. In all vesicles, the experimentally observed shape remained unaltered by numerical relaxation, suggesting that the deformations take place in a quasi-stationary fashion.

Results and Discussion

3D analysis of shape deformation

The observed shape deformation of one of our binary GUVs (DPPC/DLPE = 8:2) during the heating-cooling cycle is shown in Fig. 1 (see Movie S1 in the Supporting Material). First the binary vesicle at 30°C (i.e., < $T_m^{\text{DPPC}}$ = 41°C but > $T_{\text{m}}^{\text{DLPE}}$ = 29°C) exhibited a spherical shape without domains (Fig. 1 A), although the binary vesicle is composed of a majority phase in the solid state and a minority phase in the liquid state. By heating to 50°C, chain melting of DPPC in the solid state produces an excess area because the cross-section area of a DPPC molecule increases from 0.48 nm² in the solid phase to 0.64 nm² in the liquid phase, i.e., by ∼34% (29). By using this excess area, the binary GUV started to transform to an oblate shape (Fig. 1 B), through faceted shapes (Movie S1), and then to a prolate shape (Fig. 1 C). At a certain point the prolate vesicle quickly deformed to the budded limiting shape (Fig. 1 E) via the pear shape (Fig. 1 D). After the neck was broken, the limiting shape vesicle was finally divided into two independent vesicles. After cooling to 30°C, DPPC chains reordered, which led to a decrease of the area of the daughters and to an increase of their surface tension. To release the tension, pores were opened in the daughters and excess water was expelled through the pores as shown in Fig. 2 (see Movie S2). The pore was opened at t = 8.8 s (T = 32°C) and closed at t = 9.72 s in Movie S2. Thus the lifetime of the pore is ∼1 s; its diameter is ∼10 μm (i.e., considerably smaller than the vesicle diameter of ∼50 μm). After the heating-cooling cycle, the initial spherical mother vesicle was transformed into two spherical daughter vesicles. When the cycle was repeated, the daughters produced the next generation of vesicles, i.e., the granddaughters. Movie S1 shows three consecutive cyclic vesicle deformations. We note that such vesicle division was observed for most of the examined GUVs and was stable against the heating and cooling rate (1°C/min–12°C/min). This repeatable vesicle division is realized by mixing PE lipids into a DPPC vesicle. In a similar heating-cooling cycle, a pure DPPC vesicle is crumpled due to the solidification.

Figure 1.

Sequence of z-projection of 3D images of a DPPC/DLPE binary GUV in the vesicle division process driven by the heating-cooling cycle between 30 and 50°C. (A–E) Deformations of the first-generation vesicle (G1), where the mother produced daughters. (F–J) Second-generation deformations (G2), where the daughters produced granddaughter vesicles. Scale bar in (A) represents 10 μm. The extracted shapes obtained by relaxing the bending energy at fixed v and Δa are shown in (A′)–(J′).

Figure 2.

Pore formation of divided daughter GUV during the cooling process (another daughter vesicle is indicated by a triangle). The arrow in the 9.040 s frame indicates the pore (see also Movie S2).

To quantify the deformation-division process, we reconstructed 3D vesicle shapes from the images (Fig. 1, A′–J′) and extracted vesicle area and volume. Fig. 3 shows the obtained time dependence of vesicle area A (top panel) and volume V (middle panel) as well as the temperature chart (bottom panel). The initial spherical GUV had A ≈ 840 μm² and V ≈ 2300 μm³, where the relative error of both quantities is ∼10%. Upon heating, the vesicle increased its area at almost constant volume and deformed to the budded limiting shape with A ≈ 1060 μm² and V ≈ 2400 μm³. This vesicle then divided into unequal daughters: the larger one of A ≈ 710 μm² and V ≈ 1800 μm³ and the smaller of A ≈ 310 μm² and V ≈ 510 μm³. Thus, the total vesicle area and volume were conserved during division. On cooling, DPPC chain ordering caused the shrinkage of the daughters, their final areas and volumes being ≈580 μm² and ≈1300 μm³ (large daughter) and ≈240 μm² and ≈360 μm³ (small daughter), respectively. Thus, during the cycle the total membrane area is almost conserved, whereas the volume is decreased by ∼28% as the fluid is expelled from the daughters to satisfy the geometrical requirement for the topological transition of one sphere to two unequal spheres with same total area. Interestingly, the membrane area ratio of mother to daughter vesicles is essentially the same across all generations, i.e., mother/large daughter/small daughter = 1:0.70:0.30 for the first generation and 1:0.70:0.30 and 1:0.73:0.27 for the two branches of the second generation (Fig. 3). The geometry of the vesicle is governed by the reduced volume and the preferred monolayer area difference in ADE theory (20), which is determined by the composition of the vesicle. This geometrical equivalence in the vesicle division supports the assumption that the offspring vesicles have almost the same composition as the mother vesicles. In this sense, vesicle division is geometrically recursive.

Figure 3.

Time dependence of surface area (top panel), volume (middle panel), and temperature (bottom panel) of a binary GUV in the cyclic deformation-division process. (A–J) Top and middle panels correspond to vesicles shown in (A)–(J) in Fig. 1. (Solid and open symbols) Large and the small daughter formed after the first division, respectively, and their daughters; relative area and volume changes on heating and cooling are indicated in the top and middle panels.

From the 3D images, we extracted the time dependence of the reduced volume v and monolayer area difference Δa. The deformation-division pathways of three vesicles (V1–V3) in the (v, Δa) plane are presented in Fig. 4. For vesicle V3 (also shown in snapshots in Fig. 1), we show pathways of the first, second, and third divisions (G1, G2a and G2b, and G3, respectively; in the third generation, we were only able to accurately analyze the deformation of the largest granddaughter). Lines O, P, and L in Fig. 4 represent the oblate, prolate, and budded limiting shape branch, respectively. The location of each branch is determined by minimizing the ADE energy (11, 30), given by

$$W_{\text{ADE}}=\kappa \left[\frac{1}{2}\oint {\left(2H\right)}^{2}dA+\frac{1}{2A{h}^2}\frac{{\kappa }_r}{\kappa }{\left(\Delta A-\Delta A_0\right)}^2\right],$$ (2)

where κ_r is the nonlocal bending modulus. The second term is the nonlocal elastic energy due to the deviation of the monolayer area difference from the preferred value ΔA₀ given by

$$\Delta A_0=N^{+}\left[a_{\text{PE}}{\varphi }^{+}+a_{\text{PC}}\left(1-{\varphi }^{+}\right)\right]-N^{-}\left[a_{\text{PE}}{\varphi }^{-}+a_{\text{PC}}\left(1-{\varphi }^{-}\right)\right],$$ (3)

where N⁺ and N⁻ are the number of lipid molecules of the outer and the inner leaflet, and ϕ⁺ and ϕ⁻ are the corresponding mole fractions of DLPE, whereas a_PE and a_PC are the cross-section areas of DLPE and DPPC, respectively. For all pathways, the spherical GUVs are initially deformed by following the stable oblate branch (line O). At v ≈ 0.9, they hopped to the prolate branch (line P); within the ADE theory, this transition is discontinuous but in a given real vesicle it is inevitably smeared across a narrow but finite v range from 0.90 to 0.85 through intermediate shapes that smoothly mediate the deformation. After the oblate-prolate transition, GUVs stayed on the stable prolate branch until the reduced volume approached the smallest value possible in a budded shape, which is $1/\sqrt{2}$. Typically, the transition to the budded limiting shape took place at a reduced volume v a little larger than $1/\sqrt{2}$, leading to daughters of unequal sizes. This transition is essentially discontinuous too and it takes place via a pearlike intermediate shape. All observed pathways including second and third generation lie on a well-defined single master curve at reduced volumes >∼0.75, but the final transformation to the budded limiting shape was a little different in each individual vesicle.

Figure 4.

Deformation pathways of three DPPC/DLPE GUVs (V1, V2, and V3) in the (v, Δa) plane (middle panel). For vesicle V3, pathways for the first (G1), the second (G2a and G2b), and the third division (G3) are shown. Lines O, P, and L represent the oblate, prolate, and budded limiting shape branches, respectively. (Top panel) Micrographs of daughter (G1), granddaughter (G2a), and great-granddaughter (G3) of vesicle V3; scale bars, 10 μm. To see this figure in color, go online.

The key factor controlling the deformation-division pathway is the presence of the inverse-cone-shape PE lipids. In fact, the described pathway was observed only in binary GUVs containing PE lipids and never in those without PE lipids (18). Here we focus on the inverse-cone-shape geometry of DLPE. The spontaneous curvatures of PE lipids were measured using binary small unilamellar vesicles composed of egg-PC (egg-phosphatidylcholine) and a small mole fraction of NBD-labeled PE lipids (31). In two PE lipids with a somewhat longer chain length than DLPE, the obtained spontaneous curvatures were −0.31 nm⁻¹ (DMPE; 14:0 PE) and −0.22 nm⁻¹ (DPPE; 16:0 PE). Because no value was reported for DLPE (12:0 PE), we use the above measurements to estimate its spontaneous curvature to be $H_{\text{sp}}^{\text{PE}}=-0.3$ nm⁻¹. This negative spontaneous curvature causes an asymmetric distribution of DLPE in the bilayer: the DLPE molecules preferentially partition into the inner leaflet of the spherical vesicle, resulting in a spontaneous curvature of the membrane C₀. Because the shape of DPPC molecules is cylindrical (their spontaneous curvature being zero), we assume that C₀ is proportional to $H_{\text{sp}}^{\text{PE}}$ and to the difference of DLPE mole fractions in the two monolayers $\Delta \varphi ={\varphi }^{+}-{\varphi }^{-}$:

$$C_0=\alpha H_{\text{sp}}^{\text{PE}}\Delta \varphi ,$$ (4)

where α is a dimensionless proportionality constant that accounts for the chain length difference between DPPC (16:0 PC) and DLPE (12:0 PE). As a result, the headgroup of the PE lipid is buried under the headgroup of DPPC, which modifies the spontaneous curvature imparted by DLPE, and the constant α describes this effect of the matrix. Here we explain the observed deformation pathway based on the area-difference-elasticity-spontaneous-curvature (ADE-SC) theory (11). The elastic energy of the ADE-SC model is given by

$$W_{\text{ADE}}=\kappa \left[\frac{1}{2}\oint {\left(2H-C_0\right)}^{2}dA+\frac{q}{2A{h}^2}{\left(\Delta A-\Delta A_0\right)}^2\right]+{\kappa }_{\text{G}}\oint KdA,$$ (5)

where

$$q=\frac{{\kappa }_r}{\kappa }$$ (6)

is the ratio of nonlocal and local bending constants, κ_G is the Gaussian bending modulus, and K is the Gaussian curvature. In the deformation to limiting shape before the neck is broken, we can ignore the Gaussian curvature energy term due to the Gauss-Bonnet theorem. For simplicity, we assume that the cross-section areas of DLPE and DPPC molecules are the same a_PE = a_PC = a at T = 30°C (a_PE = 0.512 nm² at 35°C and a_PC = 0.479 nm² at 20°C (29)). Then the renormalized preferred reduced monolayer area difference at 30°C reads

$$\Delta {\tilde{a}}_0=\frac{\left(N^{+}-N^{-}\right)a}{8\pi h{R}_0}+\frac{R_0{C}_0}{2q}=\Delta a_0+\frac{R_0{C}_0}{2q},$$ (7)

where $R_0=\sqrt{\overline{N}a/4\pi },\overline{N}=\left(N^{+}+N^{-}\right)/2$ is the radius of the initial spherical vesicle (step 1). The shape deformation trajectory is mapped on the phase diagram of stable vesicle shapes in the (v, $\Delta {\tilde{a}}_0$ ) plane (Fig. 5 a) on the basis of the ADE-SC model with the ratio of nonlocal and local bending constants q = 3 (32, 33). In the relevant range of v and $\Delta {\tilde{a}}_0$, the theoretical phase diagram contains three discontinuous transitions: the stomatocyte-oblate transition (D^sto/obl), the oblate-prolate transition (D^obl/pro), and the prolate-pear transition (D^pro/pea). These transitions take place when the trajectory $\Delta {\tilde{a}}_0$ (v) crosses the shape boundary lines. In experiments, the prolate-pear transition is difficult to pin down but the oblate-prolate transition at v $\simeq$ 0.9 and the pear-budded limiting shape transitions at v $\simeq$ 0.7–0.8 can be located readily (Fig. 4). We indicate the observed shape transition points in the phase diagram, Fig. 5 a. For example, the trajectory of V3-G1 in Fig. 4 exhibits the oblate to prolate transition at v^obl/pro $\simeq$ 0.88 and the pear to budded limiting shape transition at $v^{L\simeq }$ 0.75. Using these two reduced volumes we can mark the transition points at (v, $\Delta {\tilde{a}}_0$ ) = (0.88, 0.89) and (0.75, 1.8) on the shape transition lines D^obl/pro and L in Fig. 5 a, respectively. By doing this for all six deformation trajectories (V1, V2, V3-G1, V3-G2a, V3-G2b, and V3-G3 in Fig. 4) and connecting the transition points by dashed lines, we obtain six $\Delta {\tilde{a}}_0\left(v\right)$ pathways that turn out to have very similar slopes.

Figure 5.

(a) Phase diagram in the (v, $\Delta {\tilde{a}}_0$ ) plane predicted by the ADE-SC model with the ratio of nonlocal and local bending constants of q = 3. (Solid lines) Discontinuous transitions between the stomatocyte and the oblate shape (D^sto/obl), the oblate and the prolate shape (D^obl/pro), and the prolate and the pear shape (D^pro/pea). The budded limiting shape line is labeled by L. The observed six deformation trajectories in Fig. 4 are shown by dashed lines connecting the oblate-prolate transition and the budded limiting shape (open circles). The legend also contains the radii of the spherical vesicles at the initial stage, R₀. (Thick black line) Theoretical deformation trajectory obtained using our geometrical model. (Dotted line) Estimated deformation trajectory for a vesicle with a symmetric bilayer. (b) Phase diagram in the (v^2/3, $\Delta {\tilde{a}}_0$v) plane to emphasize the relationship between $\Delta {\tilde{a}}_0$ and v in Eq. 13. To see this figure in color, go online.

The deformation from sphere to budded limiting shape is caused by the increase of the cross-section area of DPPC from a to (1+ε)a (where ε > 0) due to the chain melting. We assume that the cross-section area of DLPE remains unchanged during the deformation. It is reported that a tiny asymmetry of the lipid composition between the inner and the outer monolayer coupled with the lipid geometries causes an enormous effect of the morphology (21, 22). To demonstrate the effect of the bilayer asymmetry, first we discuss the case of the symmetric bilayer, i.e., $C_0=0$. After chain melting of the symmetric bilayer, the preferred reduced monolayer area difference $\Delta {\tilde{a}}_0^{\text{s}}=\Delta a_0$ reads

$$\Delta a_0=\frac{\left[1+\epsilon \left(1-\overline{\varphi }\right)\right]\left(N^{+}-N^{-}\right)a}{8\pi h^{\prime }{\left[1+\epsilon \left(1-\overline{\varphi }\right)\right]}^{1/2}{R}_0}=\frac{\left(N^{+}-N^{-}\right)a}{8\pi h{R}_0}{\left[1+\epsilon \left(1-\overline{\varphi }\right)\right]}^{3/2},$$ (8)

where $\overline{\varphi }=\left({\varphi }^{+}+{\varphi }^{-}\right)/2$. Here h′ is membrane thickness after melting, which is generally smaller than the initial thickness because the membrane area is increased. To lowest order, we may assume that the membrane volume is conserved, which gives $h^{\prime }=h/\left[1+\epsilon \left(1-\overline{\varphi }\right)\right]$. Because the vesicle volume itself is constant during the deformation from the sphere to the budded limiting shape, the reduced volume after the chain melting is given by

$$v={\left[1+\epsilon \left(1-\overline{\varphi }\right)\right]}^{-3/2}.$$ (9)

By combining Eqs. 8 and 9, we find that the deformation trajectory in (v, Δa₀) plane reads

$$\Delta a_0=\frac{\Delta a_0^{\text{ini}}}{v},$$ (10)

where $\Delta a_0^{\text{ini}}=\left(N^{+}-N^{-}\right)a/\left(8\pi h{R}_0\right)$ is the initial renormalized reduced monolayer area difference. When we increase temperature from 30 to 50°C, which gives rise to a 30% increase of the area of DPPC, the reduced volume decreases from 1 to 0.72 and the normalized preferred monolayer area difference increases from $\Delta a_0^{\text{ini}}$ to $\Delta a_0^{\text{ini}}$/0.72. For example, when the GUV has $\Delta a_0^{\text{ini}}=1$, Δa₀ increases to 1.39, which is too small to attain the deformation to the limiting shape as shown by the dotted line in Fig. 5 a. In fact, GUVs with a symmetric bilayer membrane cannot transform to the limiting shape as shown in Appendix A. Thus we need a booster mechanism to explain the observed deformation and the asymmetric area increase of the bilayer is a plausible candidate (21, 22).

When DLPE lipids are distributed asymmetrically in the bilayer, $\Delta {\tilde{a}}_0$ after chain melting is given by

$$\Delta {\tilde{a}}_0=\frac{1}{8\pi h{R}_0}\left[\left(N^{+}-N^{-}\right)a{\left\{1+\epsilon \left(1-\overline{\varphi }\right)\right\}}^{3/2}-\epsilon \overline{N}a\Delta \varphi {\left\{1+\epsilon \left(1-\overline{\varphi }\right)\right\}}^{3/2}\right]+\frac{R_0{C}_0}{2q}{v}^{-1/3},$$ (11)

where the reduced volume is expressed by Eq. 9. By combining Eqs. 9 and 11), we find that the deformation trajectory in (v, $\Delta {\tilde{a}}_0$ ) plane reads

$$\Delta {\tilde{a}}_0=\frac{1}{v}\left[\Delta a_0^{\text{ini}}-\frac{R_0}{2h}\frac{\Delta \varphi }{1-\overline{\varphi }}\left(1-v^{2/3}\right)\right]+\frac{R_0{C}_0}{2q}{v}^{-1/3}.$$ (12)

For convenience, we also replot the phase diagram in the (v^2/3, $\Delta {\tilde{a}}_0$ v) plane (Fig. 5 b), which emphasizes the relationship between $\Delta {\tilde{a}}_0$ and v:

$$\Delta {\tilde{a}}_{0}v=\Delta a_0^{\text{ini}}-\frac{R_0}{2h}\frac{\Delta \varphi }{1-\overline{\varphi }}+\left(\frac{1}{2h\left(1-\overline{\varphi }\right)}+\frac{\alpha H_{\text{sp}}^{\text{PE}}}{2q}\right)R_0\Delta \varphi v^{2/3}.$$ (13)

The model trajectory (thick black line in Fig. 5, a and b) based on Eq. 12 or 13 was determined to reproduce the slope of the broken lines that connect the oblate/prolate and pear/limiting shape transition points. This model trajectory with $\Delta {\tilde{a}}_0^{\text{ini}}=0.5$ and R₀Δϕ = −2.7 $\times$ 10⁻⁸ m (here h = 3 $\times$ 10⁻⁹ m and $\overline{\varphi }=0.2$ are given parameters) describes well the observed shape deformation from the sphere to the budded limiting shape. The discrepancy between the model and the experimental trajectories mostly originates from the difference in the initial renormalized preferred area difference $\Delta {\tilde{a}}_0^{\text{ini}}$. To attain the deformation to the limiting shape, the renormalized preferred reduced monolayer area difference $\Delta {\tilde{a}}_0$ has to increase from $\Delta {\tilde{a}}_0^{\text{ini}}\sim 0.5$ to a value on the limiting shape line L ( $\Delta {\tilde{a}}_0$ ∼1.8). This requirement is satisfied by the slope of the trajectories. According to our asymmetric model (Eq. 13), a similar slope indicates that the product R₀Δϕ should be the same in all vesicles. It should be noted that the slope is very sensitive to Δϕ because GUVs have a very large value of R₀/2h $\simeq$ 1800 (21, 22). Thus, a tiny asymmetric distribution of DLPE in the bilayer is sufficient to cause the deformation to the limiting shape. Because DLPE molecules prefer to partition into the inner leaflet of the initial spherical vesicle, the area of the outer leaflet is increased by DPPC chain melting more than that of the inner leaflet, which results in a tiny asymmetry. From the constant slope of the model trajectory of R₀Δϕ = −2.7 × 10⁻⁸ m and R₀ = 10 × 10⁻⁶ m, we obtain Δϕ = −0.0027. Our asymmetric model analysis leads to two important conclusions: 1) distribution of PE lipids in the bilayer is asymmetric, $\Delta \varphi \ne 0$; and 2) the model trajectory has $\Delta {\tilde{a}}_0^{\text{ini}}$ ∼ 0.5. This deformation mechanism well explains observed deformations where almost all vesicles exhibit the same shape transition pathway from the sphere to the budded limiting shape upon heating.

So far, the asymmetric lipid distribution coupled with the spontaneous curvature of the lipid, i.e., lipid sorting, has been investigated extensively (31, 34, 35, 36). These studies indicate that the coupling between the membrane curvature and the spontaneous curvature of lipid is weak and the lipid sorting is only observed in small unilamellar vesicles with radii of several tens of nanometers. Thus, the asymmetry of the lipid distribution in GUVs is very small. We show that the very small asymmetric distribution of DLPE in GUV bilayer needed to interpret our experimental observation, Δϕ = −0.0027, is consistent with the prediction of the lipid sorting model described in Appendix B. Unfortunately, this tiny change would be very difficult to measure.

Another important result obtained by the model trajectory analysis is that the mother and the offspring spherical vesicles have $\Delta {\tilde{a}}_0^{\text{ini}}$ ∼ 0.5 and R₀Δϕ constant in their trajectories, which ensures the recursive nature of vesicles in the division cycle. To elucidate this recursive nature, we simulate $\Delta {\tilde{a}}_0$ of the daughter vesicle after the heating-cooling cycle. For simplicity, we deal with a symmetric division process where the mother vesicle produces two identical daughters. The initial mother vesicle at T = 30°C (step 1) has a radius of R₀, a preferred reduced monolayer area difference $\Delta {\tilde{a}}_0^{\left(1\right)}$ = 0.5, and the composition asymmetry of Δϕ⁽¹⁾ = −0.0027. When we assume that the vesicle maintains the lipid composition Δϕ⁽¹⁾ through the division, i.e., no lipid exchange between the inner and the outer leaflet, the daughter vesicle (step 4) has $\Delta a_0^{\left(4\right)\text{nle}}=\Delta a_0^{\left(1\right)}/\sqrt{2}=0.35$ and Δϕ^(4)nle = −0.0027. These values are in disagreement with the experimental results of $\Delta a_0^{\left(4\right)\text{exp}}\cong 0.5$ and ϕ^(4)exp = $\sqrt{2}\Delta {\varphi }^{\left(1\right)\text{exp}}$ = −0.0038. This disagreement suggests a redistribution of lipids within the bilayer, which may take place during pore opening upon cooling (Fig. 6). At this stage, the outer and the inner monolayers are connected by pore rim and thus lipids can migrate between the leaflets to equilibrate the chemical potential of lipids between the inner and the outer leaflets. Lipid traffic through the rim of the pore has been observed in binary vesicles composed of cone- and cylinder-shaped lipids (37). When this binary vesicle was subjected to a similar heating and cooling cycle, the binary vesicle forms a single pore below the main-chain transition temperature of DPPC. During pore formation, the binary GUVs showed a rolled membrane at the rim of the pore (torus rim), which implies the lipid traffic by a chemical potential difference between the outer leaflet and the inner leaflet due to the lipid geometry.

Figure 6.

Schematic representation of vesicle morphology changes from steps 1 to 4 including pore formation. During pore formation, lipids redistribute through the rim of pore. To see this figure in color, go online.

In the vesicle division cycle, the pore formation takes place in the fluid-solid coexistence region, where most of the DPPC lipids are in the solid phase and most of the DLPE lipids are in the fluid phase. Thus DLPE (majority) and DPPC (minority) in the fluid phase can participate in the lipid exchange through the rim to equilibrate the chemical potential of lipids in the outer and the inner leaflet. However, when lipid traffic through the rim of the pore completely equilibrates the chemical potential, the daughter vesicle should have $\Delta {\tilde{a}}_0^{\left(4\right)\text{eq}}\cong 1.0$ and Δϕ^(4)eq = −0.0047 (Appendix B). This discrepancy indicates that lipid traffic through the pore rim cannot attain the complete equilibrium due to the finite lifetime of the pore. Thus, due to the pore closing, the lipid exchange was terminated at ∼20% of the lipid traffic toward equilibrium as estimated by comparing the deviations of the experimental and the equilibrium preferred monolayer area differences from that expected in absence of lipid exchange: $\left(\Delta {\tilde{a}}_0^{\left(4\right)\text{exp}}-\Delta {\tilde{a}}_0^{\left(4\right)\text{nle}}\right)/\left(\Delta {\tilde{a}}_0^{\left(4\right)\text{eq}}-\Delta {\tilde{a}}_0^{\left(4\right)\text{nle}}\right)=\left(0.5-0.35\right)/\left(1.0-0.35\right)=0.2$. Here we estimate the lipid exchange through the rim of the pore based on the diffusion of lipids. Because the diffusion coefficient of phospholipid in the fluid phase is ∼7 $\times$ 10⁻¹² m²/s (38), the mean diffusion distance during the typical pore lifetime of 1 s is ∼5 μm. Then lipids located at a distance within 5 μm from the rim may diffuse across the rim during the pore opening, which covers ∼12% of the vesicle area. This fraction is roughly consistent with the estimated lipid exchange of ∼20%. The lipid exchange through the rim is driven by the chemical potential difference, which accelerates the lipid flow compared to the simple diffusion process. By combining the experimentally determined value of R₀Δϕ ≈ −2.7 × 10⁻⁸ m and Eq. 13, we estimate the value of the dimensionless constant introduced in Eq. 4: α = 0.5 (Appendix A). It is plausible that the short chain length of DLPE (12:0 PE) and the matrix effect of DPPC (16:0 PC) reduces the spontaneous curvature compared with that of DMPE having $H_{\text{sp}}^{\text{DMPE}}$ = −0.3 nm⁻¹.

We note that the restricted lipid traffic discussed above slightly modifies the deformation trajectories from the perfectly recursive trajectory, because the fraction of the lipid relaxation area to the total vesicle area depends on the size of vesicle. For the vesicles with the radius of ∼10 μm, the lipid exchange is limited to ∼20% of the complete exchange. This fraction should increase with decreasing vesicle size and finally reach 100% where $\Delta {\tilde{a}}_0^{\text{ini}}$ is 1.0 and the composition asymmetry is determined by the equality in the chemical potential of the lipids (Appendix B). Thus, from generation to generation, $\Delta {\tilde{a}}_0^{\text{ini}}$ gradually approaches 1.0. In fact, $\Delta {\tilde{a}}_0^{\text{ini}}$ increases with the decrease of R₀ as shown in Fig. 7, which is consistent with our model.

Figure 7.

Relationship between the vesicle radius R₀ and the initial renormalized, preferred, reduced monolayer area difference, $\Delta {\tilde{a}}_0^{\text{ini}}$. To see this figure in color, go online.

Lastly, we discuss the mechanism of breaking the neck in the budded limiting shape to produce daughter vesicles. It is well known that single-component vesicles do deform to the budded limiting shape in response to external stimuli (e.g., a change of temperature or osmotic pressure) but breaking the narrow neck between the buds is harder (14) because the neck is stabilized by the spontaneous curvature (15). On the other hand, in multicomponent vesicles, division is observed more readily (39, 40). The free-energy analysis of binary vesicles shows that the coupling of the local lipid composition to the Gaussian curvature does destabilize the narrow neck and encourages vesicle division if the minor component lipids prefer to be located in regions with large positive Gaussian curvature (17). In our system, by adding DLPE lipids, the binary vesicles show division. Thus, the neck should be destabilized by the presence of DLPE.

To examine the coupling between Gaussian curvature and local PE lipid composition in DPPC/DLPE binary vesicles, we used the fatty-acid-labeled PE lipid (Acyl 12:0 NBD PE) which can be used to visualize the local composition of PE lipids during division. DPPC/DLPE vesicles containing 1 mol % Acyl 12:0 NBD PE showed a similar deformation-division process during the heating-cooling cycle, but we could not detect a definite localization of PE lipids at the spherical part. It is possible that this is a matter of the limited spatial and temporal resolution of our experimental technique, which will be improved in a future project.

Conclusions

By simply mixing inverse-cone-shaped DLPE molecules into cylinder-shaped DPPC molecules, the binary GUVs readily produce daughter vesicles repeatedly during the heating-cooling cycle, thereby capturing the essence of the vesicle self-reproduction. To reveal the roles of PE lipids, we performed quantitative 3D analysis of shape deformation and division process and found that the process relies on two key factors: 1) asymmetric distribution of DLPE in the bilayer and 2) redistribution of DLPE during the cooling stage.

The asymmetric distribution of DLPE is essential for the deformation from the sphere to the limiting shape. Due to their inverse-cone shape, DLPE molecules preferentially partition into the inner leaflet, which increases the preferred area difference as the reduced volume is decreased and drives the deformation of the vesicle to the budded limiting shape. Although the asymmetric distribution of DLPE in GUV bilayer, Δϕ = −0.0027, is very small, the asymmetry plays a significant role in the shape deformation because it is enhanced by the ratio of vesicle size and membrane thickness, typically several thousands. On the other hand, the redistribution of DLPE in the deformation-division process is needed to reset the vesicle state, and it most likely takes place during pore opening induced by cooling. During pore formation, lipids can migrate between the leaflets to minimize the elastic energy. This initialization enables the vesicle to undergo recursive division. It is quite interesting to note that this recursive nature is promoted by the free energy minimization coupled with the lipid traffic between the outer and the inner monolayers.

It has been pointed out that a tiny asymmetry in bilayer causes an enormous influence on a shape deformation trajectory (21, 22). So far, the asymmetric lipid distribution coupled with the spontaneous curvature of the lipid, i.e., lipid sorting, has been investigated extensively, because the sorting of both lipids and proteins in trafficking pathways lie at the heart of cellular organelle homeostasis. These studies indicate that the coupling between the membrane curvature and the spontaneous curvature of lipid is weak and the lipid sorting is only observed in small unilamellar vesicles with radii of several tens of nanometers. The lipid sorting model predicts the asymmetry of the order of 10⁻³ in GUV, which is consistent with our observation, Δϕ = −0.0027. Here we show that such tiny composition asymmetry ensures the observed shape deformation and the recursive nature. Thus the spontaneous coupling between membrane curvature and PE lipid distribution is responsible for the observed deformation-division-initialization process.

The heating-cooling protocol is advantageous as a way to realize vesicle division for several reasons, primarily because of its speed, which allows us to produce one generation within a few minutes and because it can be used to manipulate a large number of vesicles at the same time. In addition, it is quite robust in the sense that self-reproduction is not very sensitive to variations in the heating and cooling rates. If combined with a steady supply of lipids to the membrane, the protocol could foreseeably be fine-tuned to produce daughters that would be just as big as the mother. It is conceivable that, by adjusting these rates and the overall temperature sequence, one could also enhance the symmetry of vesicle division, the goal being the identical-twin transformation. Another interesting challenge is application of this technique to the reported self-reproduction systems (oleic acid/oleate vesicles (4) and membrane molecule/catalyst vesicles (9, 10)), which will reveal roles of supplied molecules in the self-reproduction of vesicles.

Of course we do not claim that the temperature change and the pore formation were necessary for the proliferation of early cells. Yet our work shows that this process could have included a physical mechanism of the proliferation, and may be minimally helped by a primitive regulatory network creating an asymmetric lipid distribution coupled with the membrane curvature; this would give rise to the recursive cell division following the equilibrium ADE-SC model. Our model vesicle regulates a similar asymmetric lipid distribution using the order-disorder transition within the membrane and the pore formation. With the detailed quantitative insight into the physics of vesicle self-replication reported here, these intriguing prospects may be explored in a more systematic way.

Author Contributions

T.J., Y.S., P.Z., and M.I. designed the research; T.J. and Y.S. developed the experiment system; T.J., N.U., and P.Z. developed the 3D analysis software; and T.J. performed experiments and data analysis. The obtained results were discussed by all authors, and T.J., P.Z., and M.I. wrote the article.

Editor: Tobias Baumgart.

Appendix A

Shape deformation of vesicle with symmetric bilayer

To demonstrate shape deformation of GUVs with the symmetric bilayer, we replaced DLPE by DLPC $\left(T_m^{\text{DLPC}}=-2°\text{C}\right)$. As both DPPC and DLPC lipids are of cylindrical shape, they are symmetrically distributed in the bilayer. We prepared a ternary DPPC/DLPC/cholesterol vesicle. Here we added cholesterol to prevent DPPC-DLPC phase separation at 30°C, because the deformation from the phase-separated spherical vesicle produced a vesicle with multiple buds (41). It should be noted that cholesterol does not affect the distribution of phospholipids in bilayers (42). In fact, ternary GUVs composed of DPPC/DLPE/cholesterol = 8:2:2 show a similar vesicle division pathway to that of the binary GUVs composed of DPPC/DLPE = 8:2 (see Movie S3). Fig. 8 shows the deformation of a ternary vesicle composed of DPPC/DLPC/cholesterol = 8:2:2 induced by heating from 30 to 50°C. The spherical ternary GUV first deformed to the prolate shape and then to the oblate shape, but no transformation to the budded limiting shape was observed, i.e., no vesicle division. This confirms that the asymmetric distribution of lipids in the bilayer is responsible for the observed shape deformation to the budded limiting shape.

Figure 8.

Deformation of a DPPC/DLPC/cholesterol = 8:2:2 ternary GUV caused by heating from 30 to 50°C. Scale bar, 10 μm. The extracted relaxed shapes obtained by 3D analysis are shown.

Appendix B

Lipid sorting of binary vesicle in the solid-liquid coexisting phase

For convenience, we consider a binary GUV composed of DLPE (inverse-cone-shaped lipids) and DPPC (cylinder-shaped lipids) with the inner radius (neutral plane) of R − h/2 and the outer radius (neutral plane) of R + h/2. A DLPE molecule is characterized by a molecular cross-section area a_PE and a spontaneous curvature $H_{\text{sp}}^{\text{PE}}$, and a DPPC molecule has a_PC and $H_{\text{sp}}^{\text{PC}}=0$. The relaxation of the lipid distribution takes place during the pore opening upon cooling, where the membrane is composed of the solid phase rich in DPPC and the liquid phase rich in DLPE. As shown in Fig. 1, we could not observe solid domains at 30°C by a confocal microscope, suggesting the submicroscopic size of domains, although the main-chain transition temperature of the DPPC/DLPE = 8/2 binary vesicle is 39°C (21). Because the membrane thickness is 3 nm, here we assume that the submicroscopic solid domains cannot transverse through the edge of pore. Then, while the pore is opening, lipids in the liquid phase are redistributed in the bilayer to decrease the total free energy of the vesicle. Thus, a small amount of DPPC can move in the fluid phase. For simplicity, we assume that DPPC and DLPE in the liquid phase have the same cross-section area, a. The lipid flux between the inner and the outer monolayer is governed by the difference of chemical potentials. Then the entropy of DPPC molecules is given by

$$S=N_{\text{PC}}^{\text{liq}}{k}_{\text{B}}\left(\text{ln}\frac{A(1-\psi )}{a}-\text{ln}{N}_{\text{PC}}^{\text{liq}}-1\right),$$ (B1)

where A is the membrane area, $N_{\text{PC}}^{\text{liq}}$ is the number of DPPC molecules in the liquid phase, and ψ is the area fraction of the solid phase. The chemical potentials of DPPC molecules $\left({\mu }_{\text{PC,liquid}}\right)$ in outer (+) and inner (−) monolayer read

$$\begin{array}{l}{\mu }_{\text{PC,liquid}}^{\pm }\cong {\mu }_{\text{0,liquid}}^{\pm }+\text{ln}\frac{A^{\pm }\left(1-\psi \right)}{a}\\ \left(k_{\text{B}}T=1\right),\end{array}$$ (B2)

where ${\mu }_0$ is the interaction energy of a single DPPC including the bending energy. In equilibrium, the balance of the chemical potentials reads

$$\Delta {\mu }_{\text{PC,liquid}}={\mu }_{\text{PC,liquid}}^{+}-{\mu }_{\text{PC,liquid}}^{-}=0.$$ (B3)

The bending energy of a single molecule in outer and inner leaflet is given by

$$w_b^{\pm }=\frac{\tilde{\kappa }}{2}{\left(2H^{\pm }-C_0^{\pm }\right)}^{2}a,$$ (B4)

where $\tilde{\kappa }=\kappa /2k_{\text{B}}T$ is the bending modulus of monolayer assumed to be the same in both monolayers (which is supported a posteriori by the small concentration difference), $H^{\pm }=1/\left(R\pm h/2\right)$ is the mean curvature of each monolayer, and $C_0^{\pm }=\pm \alpha H_{\text{sp}}^{\text{PE}}{\varphi }^{\pm }$ is the spontaneous curvatures of each monolayer. Because the difference in ${\mu }_0$ between the two monolayers is the bending energy, $\Delta {\mu }_{\text{PC},\text{liquid}}$ is described by

$$\begin{array}{c}\Delta {\mu }_{\text{PC,liquid}}=\frac{\tilde{\kappa }}{2}{\left(\frac{2}{R+h/2}-\alpha H_{\text{sp}}^{\text{PE}}{\varphi }^{+}\right)}^{2}a-\frac{\tilde{\kappa }}{2}{\left(\frac{2}{R-h/2}+\alpha H_{\text{sp}}^{\text{PE}}{\varphi }^{-}\right)}^{2}a+\text{ln}\frac{A^{+}}{A^{-}}\\ \approx \tilde{\kappa }a\left(\frac{h}{R^3}+\frac{\alpha H_{\text{sp}}^{\text{PE}}}{R}\overline{\varphi }\right)\left(4+\alpha H_{\text{sp}}^{\text{PE}}R\Delta \varphi \right)+\text{ln}\frac{A^{+}}{A^{-}}=0.\end{array}$$ (B5)

Taking into account $H_{\text{sp}}^{\text{PE}}\left(=-0.3{\text{nm}}^{-1}\right)\approx 1/h$, the lipid composition difference, Δϕ, in the second bracket is $R{H}_{\text{sp}}^{\text{PE}}\sim R/h\sim 3600$. Thus, the flux of lipids between the outer and inner leaflet is governed by the lipid asymmetry in the bilayer. Using $\tilde{\kappa }=135$ (bilayer bending modulus of DPPC is ∼270 k_BT at 30°C (43)), R =10 μm, h = 3 nm, $\left({\varphi }^{+}+{\varphi }^{-}\right)/2=0.2$, and $a=0.48{\text{nm}}^{-1}$, we obtained Δϕ = −0.0018 for α = 1 and −0.0047 for α = 0.5. These values are close to the estimate extracted from the experimental data $\Delta \varphi =-0.0027$. Thus, the asymmetric distribution of DLPE in the GUV bilayer obtained in this study is consistent with the lipid sorting model. Because the lipid exchange in the vesicle with R = 10 μm is limited to 20% of the complete exchange, the experimental value of $\Delta \varphi =-0.0027$ suggests that a plausible value of the dimensionless proportionality constant α is 0.5.

Supporting Material

Movie S1. Division of a DPPC/DLPE = 8:2 Binary GUV Driven by the Three Consecutive Heating-Cooling Cycles between 30 and 50°C

The start temperature was 30°C and the thermal history is presented in Fig. 2. Scale bar is 10 μm.

Movie S2. Pore Formation of Divided Daughter GUV during the Cooling Process

Another daughter vesicle is indicated by a triangle. The pore was opened at t = 8.8 s (T = 32°C) and closed at t = 9.72 s.