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Article

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

Takehiro Jimbo,1 Yuka Sakuma,1 Naohito Urakami,2 Primo�z Ziherl,3,4 and Masayuki Imai1,*1Department of Physics, Tohoku University, Aoba, Sendai, Japan; 2Department of Physics and Information Sciences, Yamaguchi University,Yamaguchi, Japan; 3Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia; and 4Jo�zef Stefan Institute, Ljubljana,Slovenia

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

INTRODUCTION

Self-reproduction of vesicles by incorporating additionalmolecules leading to vesicle growth, deformation, and divi-sion into independent daughters is an indispensable featureof cellular life (1–3). One of the milestones in our under-standing of the role of molecular self-assembly in thisprocess is the development of artificial vesicles capable ofself-reproduction. In this context, self-reproduction hasbeen investigated using simple fatty-acid giant vesicles(4–7). For instance, upon addition of a droplet of oleic anhy-dride to oleic acid/oleate giant vesicle suspension, the anhy-dride molecules are hydrolyzed to oleic acid/oleate withinthe vesicle membrane. The vesicles supplied with the oleicacid/oleate molecules do self-reproduce by deforming toa 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 vesiclesystem by designing amphiphiles that transform from pre-cursors to membrane molecules by catalyst-assisted hydro-lysis. These novel (to our knowledge) observations prove

Submitted August 3, 2015, and accepted for publication February 19, 2016.

*Correspondence: [email protected]

Editor: Tobias Baumgart.

http://dx.doi.org/10.1016/j.bpj.2016.02.028

� 2016 Biophysical Society

that self-reproduction may be materialized by bilayer-form-ing molecules alone without relying on proteins, althoughthe physical mechanisms involved are not clear.

The above modes of vesicle self-reproduction are ofconsiderable interest although they are different from thoseseen in present-day cells. For instance, in bacteria the celldivision is conducted by a tubulin homolog, FtsZ, whichforms a ring (Z-ring) at the neck (11). The Z-ring constrictsin parallel with synthesis of a cross wall and completes thedivision. However, bacteria have the ability to switch into awall-free state called the ‘‘L-form’’. The proliferation of theL-form is independent of the FtsZ-based division and doesnot require the mechanisms that are pivotal for regulationof cell division, cell shape, elongation, coordinated chromo-some segregation, and balanced membrane lipid synthesisof walled cells, but it does requires excess membrane pro-duction to generate an imbalance between growth of cellsurface area and volume (12,13). These observations pro-vide direct support for the notion that purely biophysical ef-fects could have supported an efficient mode of proliferationin primitive cells.

When considering vesicle self-reproduction as a mechan-ical process controlled bymembrane elasticity, several issuesmust be addressed (14–16). One is the geometrical

Biophysical Journal 110, 1551–1562, April 12, 2016 1551

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Jimbo et al.

requirement to attain the deformation to the limiting shapeconsisting of a pair of spheres connected by a narrow neck.The pathway of this deformation depends on the vesiclearea and volume growth rates parameterized by the timeneeded for the membrane to double its area Td and the mem-brane hydraulic permeability Lp, respectively, as well as onthe spontaneous curvature C0 and bending rigidity k. Toensure that the daughters are identical in size and shape tothe mother, the product TdLpkC0

4 must be equal to 1.85(15).When the product is larger than 1.85, themother vesicleshow asymmetric division, whereas for mother vesicles withTdLpkC0

4 < 1.85, a growing vesicle is transformed intoshapes that cannot lead to self-reproduction. The secondissue concerns the mechanism of breaking the neck afterthe limiting shape has been reached. The breaking is not ex-pected 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 mech-anism of neck destabilization, e.g., mechanical agitation(7,19) or the coupling of local lipid composition in the multi-component vesicle to Gaussian curvature (20). In addition,after the neck has been broken, daughter vesicles shouldhave the same properties as the mother so that the self-repro-duction process can be repeated.

These questions are best studied experimentally using amodel system where self-reproduction can be easily trig-gered and controlled. To this end, Sakuma and Imai (21)developed a protocol where the mother produces twindaughters by cyclic heating and cooling. In this system,the membrane area does not grow by addition of moleculesor by in situ synthesis, and thus the number of the vesiclesincreases at fixed total area. This approach departs fromthe perfect replication strategy (15), because in each gener-ation the vesicle size is decreased; in this respect, it is some-what reminiscent of a reductive cleavage mode of earlyembryonic development where cells divide at fixed total vol-ume (22). The protocol relies on binary vesicles: those inSakuma and Imai (21) were composed of cylinder-shapedlipids with a high melting temperature Tm, DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine, Tm ¼ 41�C) andof inverse-cone-shape lipids with a low Tm, DLPE (1,2-dilauroyl-sn-glycero-3-phosphoethanolamine, Tm ¼ 29�C).By heating them above the Tm of DPPC, binary giant unila-mellar vesicles (GUVs) spontaneously deformed to abudded limiting shape using up the excess area producedby the chain melting of DPPC and then the neck wascompletely broken. After cooling back to the initial temper-ature, daughter vesicles recovered the spherical shape of themother through the main-chain phase transition in DPPCand the corresponding membrane area decrease. In thenext cycle, the process was repeated in both daughters andthen again, eventually yielding several generations of vesi-cles that captured the essence of self-reproduction.

It is surprising that the recursive vesicle division is real-ized by simply mixing the inverse-cone-shape lipids into

1552 Biophysical Journal 110, 1551–1562, April 12, 2016

the GUV composed of the cylinder-shaped lipids. To iden-tify the role of PE lipids in the cyclic deformation-divisionprocess, it is important to quantitatively understand thephysical mechanics of vesicle deformation and division.Here we report a detailed three-dimensional (3D) imaginganalysis of the process using a fast confocal microscope.We use the images to measure two key geometrical param-eters that characterize vesicle shape, finding that theshape deformation trajectories in the phase space (23) areextremely reproducible from generation to generation. Thetrajectories are interpreted using the area-difference elastic-ity (ADE) theory and the main qualitative conclusion of ouranalysis is that the distribution of the inverted-cone compo-nent within the membrane is asymmetric. A tiny asymmetryof the area change between the inner and the outer mono-layer in the GUV causes an enormous effect of themorphology (24,25). Another interesting conclusion is thatthe membrane composition is relaxed at the end of each cy-cle. Relaxation by lipid traffic coupled with the lipid geom-etry most likely takes place during pore formation driven bymembrane shrinking so that, in this respect, the state of ves-icles is reset by the cooling stage of the cycle. The detailedquantitative analysis of the topological transition observedin our vesicles reveals the physical basis of self-reproduc-tion; the geometrical requirements for the recursive vesicledivision should also apply to perfect self-reproduction ofvesicles where the sizes of the daughter and the mother ves-icles 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

(Tm¼�2�C) and cholesterol. These lipidswere purchased fromAvanti Polar

Lipids (Alabaster, AL) and used without further purification. For 3D imag-

ing, fluorescent lipids, 18:1 Liss Rhod PE (Rhodamine 1,2-dioleoyl-sn-glyc-

ero-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]do-

decanoyl}-sn-glycero-3-phosphoethanolamine) were obtained fromMolec-

ular 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 mL 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 ob-

tained 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. Duringhydration, the lipid films spontaneously formedGUVs of diameters between

10 and 50 mm.

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,

Self-Reproduction of Binary Vesicles

Epsom, Tadworth, UK). During this manipulation, we maintained the sam-

ple suspension temperature above TDPPCm at z50�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

TDPPCm but above TDLPE

m , 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 trans-

formed into two daughter vesicles (step 3). Thereafter we decreased tem-

perature 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 Apochro-

mat 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 im-

ages consist of ~50 two-dimensional xy slices of frame size 160 � 160 mm

separated by 0.5 or 1 mm.

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

DA ¼ 2h#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 ¼ 6ffiffiffip

pV=A3=2 and reduced monolayer area difference Da ¼

DA=ð4 ffiffiffip

phA1=2Þ, we used the Surface Evolver to compute the relaxed

vesicle shape by minimizing the Helfrich energy (28),

Wb ¼ k

2#ð2HÞ2dA; (1)

where k 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 ¼ 8:2) during the heating-cooling cycle isshown in Fig. 1 (see Movie S1 in the Supporting Material).First the binary vesicle at 30�C (i.e., < TDPPC

m ¼ 41�C but> TDLPE

m ¼ 29�C) exhibited a spherical shape without do-mains (Fig. 1 A), although the binary vesicle is composedof a majority phase in the solid state and a minority phasein the liquid state. By heating to 50�C, chain melting ofDPPC in the solid state produces an excess area becausethe cross-section area of a DPPC molecule increases from0.48 nm2 in the solid phase to 0.64 nm2 in the liquid phase,i.e., by ~34% (29). By using this excess area, the binaryGUV started to transform to an oblate shape (Fig. 1 B),through faceted shapes (Movie S1), and then to a prolateshape (Fig. 1 C). At a certain point the prolate vesiclequickly deformed to the budded limiting shape (Fig. 1 E)via the pear shape (Fig. 1 D). After the neck was broken,

FIGURE 1 Sequence of z-projection of 3D im-

ages of a DPPC/DLPE binary GUV in the vesicle

division process driven by the heating-cooling cy-

cle between 30 and 50�C. (A–E) Deformations of

the first-generation vesicle (G1), where the mother

produced daughters. (F–J) Second-generation de-

formations (G2), where the daughters produced

granddaughter vesicles. Scale bar in (A) represents

10 mm. The extracted shapes obtained by relaxing

the bending energy at fixed v and Da are shown

in (A0)–(J0).


Jimbo et al.

the limiting shape vesicle was finally divided into two inde-pendent vesicles. After cooling to 30�C, DPPC chains reor-dered, which led to a decrease of the area of the daughtersand to an increase of their surface tension. To release thetension, pores were opened in the daughters and excess wa-ter was expelled through the pores as shown in Fig. 2 (seeMovie S2). The pore was opened at t ¼ 8.8 s (T ¼ 32�C)and closed at t ¼ 9.72 s in Movie S2. Thus the lifetime ofthe pore is ~1 s; its diameter is ~10 mm (i.e., considerablysmaller than the vesicle diameter of ~50 mm). After theheating-cooling cycle, the initial spherical mother vesiclewas transformed into two spherical daughter vesicles.When the cycle was repeated, the daughters produced thenext generation of vesicles, i.e., the granddaughters. MovieS1 shows three consecutive cyclic vesicle deformations. Wenote that such vesicle division was observed for most of theexamined GUVs and was stable against the heating andcooling rate (1�C/min–12�C/min). This repeatable vesicledivision is realized by mixing PE lipids into a DPPC vesicle.In a similar heating-cooling cycle, a pure DPPC vesicle iscrumpled due to the solidification.

To quantify the deformation-division process, we recon-structed 3D vesicle shapes from the images (Fig. 1, A0–J0)and extracted vesicle area and volume. Fig. 3 shows the ob-tained time dependence of vesicle area A (top panel) andvolume V (middle panel) as well as the temperature chart(bottom panel). The initial spherical GUV had A z 840mm2 and V z 2300 mm3, where the relative error of bothquantities is ~10%. Upon heating, the vesicle increased itsarea at almost constant volume and deformed to the buddedlimiting shape with Az 1060 mm2 and Vz 2400 mm3. Thisvesicle then divided into unequal daughters: the larger oneof A z 710 mm2 and V z 1800 mm3 and the smaller ofA z 310 mm2 and V z 510 mm3. Thus, the total vesiclearea and volume were conserved during division. On cool-ing, DPPC chain ordering caused the shrinkage of thedaughters, their final areas and volumes being z580 mm2

and z1300 mm3 (large daughter) and z240 mm2 andz360 mm3 (small daughter), respectively. Thus, duringthe cycle the total membrane area is almost conserved,whereas the volume is decreased by ~28% as the fluid isexpelled from the daughters to satisfy the geometricalrequirement 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 isessentially the same across all generations, i.e., mother/largedaughter/small daughter ¼ 1:0.70:0.30 for the first genera-tion and 1:0.70:0.30 and 1:0.73:0.27 for the two branchesof the second generation (Fig. 3). The geometry of thevesicle is governed by the reduced volume and the preferredmonolayer area difference in ADE theory (20), whichis determined by the composition of the vesicle. Thisgeometrical equivalence in the vesicle division supportsthe assumption that the offspring vesicles have almost thesame composition as the mother vesicles. In this sense,vesicle division is geometrically recursive.

From the 3D images, we extracted the time dependence ofthe reduced volume v and monolayer area difference Da.The deformation-division pathways of three vesicles (V1–V3) in the (v, Da) plane are presented in Fig. 4. For vesicleV3 (also shown in snapshots in Fig. 1), we show pathways ofthe first, second, and third divisions (G1, G2a and G2b, andG3, respectively; in the third generation, we were only ableto accurately analyze the deformation of the largest grand-daughter). 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 minimizingthe ADE energy (11,30), given by

WADE ¼ k

�1

2#ð2HÞ2dAþ 1

2Ah2kr

kðDA� DA0Þ2

�; (2)

where kr is the nonlocal bending modulus. The second term
is the nonlocal elastic energy due to the deviation of themonolayer area difference from the preferred value DA0
given by

DA0 ¼ Nþ�aPEfþ þ aPC�1� fþ�� N��aPEf�

þ aPC�1� f��; (3)

where Nþ and N� are the number of lipid molecules of theþ �
outer and the inner leaflet, and f and f are the corre-
sponding mole fractions of DLPE, whereas aPE and aPCare the cross-section areas of DLPE and DPPC, respectively.For all pathways, the spherical GUVs are initially deformedby following the stable oblate branch (line O). At v z 0.9,

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).

FIGURE 3 Time dependence of surface area (top panel), volume (middle

panel), and temperature (bottom panel) of a binary GUV in the cyclic defor-

mation-division process. (A–J) Top and middle panels correspond to vesi-

cles shown in (A)–(J) in Fig. 1. (Solid and open symbols) Large and the

small daughter formed after the first division, respectively, and their daugh-

ters; relative area and volume changes on heating and cooling are indicated

in the top and middle panels.

FIGURE 4 Deformation pathways of three DPPC/DLPE GUVs (V1, V2,

and V3) in the (v,Da) 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), grand-

daughter (G2a), and great-granddaughter (G3) of vesicle V3; scale bars,

10 mm. To see this figure in color, go online.


they hopped to the prolate branch (line P); within the ADEtheory, this transition is discontinuous but in a given realvesicle it is inevitably smeared across a narrow but finite vrange from 0.90 to 0.85 through intermediate shapes thatsmoothly mediate the deformation. After the oblate-prolatetransition, GUVs stayed on the stable prolate branch untilthe reduced volume approached the smallest value possiblein a budded shape, which is 1=

ffiffiffi2

p. Typically, the transition

to the budded limiting shape took place at a reduced volumev a little larger than 1=

ffiffiffi2

p, leading to daughters of unequal

sizes. This transition is essentially discontinuous too and ittakes place via a pearlike intermediate shape. All observedpathways including second and third generation lie ona well-defined single master curve at reduced volumes>~0.75, but the final transformation to the budded limitingshape was a little different in each individual vesicle.

The key factor controlling the deformation-divisionpathway is the presence of the inverse-cone-shape PE lipids.In fact, the described pathway was observed only in binaryGUVs containing PE lipids and never in those without PE

lipids (18). Here we focus on the inverse-cone-shape geom-etry of DLPE. The spontaneous curvatures of PE lipids weremeasured using binary small unilamellar vesicles composedof egg-PC (egg-phosphatidylcholine) and a small mole frac-tion of NBD-labeled PE lipids (31). In two PE lipids with asomewhat longer chain length than DLPE, the obtainedspontaneous curvatures were �0.31 nm�1 (DMPE; 14:0PE) and �0.22 nm�1 (DPPE; 16:0 PE). Because novalue was reported for DLPE (12:0 PE), we use the abovemeasurements to estimate its spontaneous curvature to beHPE

sp ¼ �0:3 nm�1. This negative spontaneous curvaturecauses an asymmetric distribution of DLPE in the bilayer:the DLPE molecules preferentially partition into the innerleaflet of the spherical vesicle, resulting in a spontaneous cur-vature of the membraneC0. Because the shape of DPPCmol-ecules is cylindrical (their spontaneous curvature beingzero), we assume thatC0 is proportional toH

PEsp and to the dif-

ference of DLPE mole fractions in the two monolayersDf ¼ fþ � f�:

C0 ¼ aHPEsp Df; (4)

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


Jimbo et al.

WADE ¼ k

�1

2#ð2H � C0Þ2dAþ q

2Ah2ðDA� DA0Þ2

�þ kG#KdA; (5)

where

q ¼ kr

k(6)

is the ratio of nonlocal and local bending constants, kG is theGaussian bending modulus, and K is the Gaussian curvature.In the deformation to limiting shape before the neck isbroken, we can ignore the Gaussian curvature energy termdue to the Gauss-Bonnet theorem. For simplicity, weassume that the cross-section areas of DLPE and DPPCmol-ecules are the same aPE ¼ aPC ¼ a at T ¼ 30�C (aPE ¼0.512 nm2 at 35�C and aPC ¼ 0.479 nm2 at 20�C (29)).Then the renormalized preferred reduced monolayer areadifference at 30�C reads

D~a0 ¼ ðNþ � N�Þa8phR0

þ R0C0

2q¼ Da0 þ R0C0

2q; (7)

where R0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiNa=4p

p; N ¼ ðNþ þ N�Þ=2 is the radius of

the initial spherical vesicle (step 1). The shape deformationtrajectory is mapped on the phase diagram of stable vesicleshapes in the (v, D~a0 ) plane (Fig. 5 a) on the basis of theADE-SC model with the ratio of nonlocal and local bendingconstants q ¼ 3 (32,33). In the relevant range of v and D~a0,the theoretical phase diagram contains three discontinuoustransitions: the stomatocyte-oblate transition (Dsto/obl),the oblate-prolate transition (Dobl/pro), and the prolate-peartransition (Dpro/pea). These transitions take place when thetrajectory D~a0 (v) crosses the shape boundary lines. In ex-

FIGURE 5 (a) Phase diagram in the (v, D~a0 ) plane predicted by the ADE-SC m

lines) Discontinuous transitions between the stomatocyte and the oblate shape (

pear shape (Dpro/pea). The budded limiting shape line is labeled by L. The observe

the oblate-prolate transition and the budded limiting shape (open circles). The le

(Thick black line) Theoretical deformation trajectory obtained using our geometr

a symmetric bilayer. (b) Phase diagram in the (v2/3, D~a0 v) plane to emphasize t

online.


periments, the prolate-pear transition is difficult to pindown but the oblate-prolate transition at v x 0.9 and thepear-budded limiting shape transitions at v x 0.7–0.8 canbe located readily (Fig. 4). We indicate the observed shapetransition points in the phase diagram, Fig. 5 a. For example,the trajectory of V3-G1 in Fig. 4 exhibits the oblate to pro-late transition at vobl/pro x 0.88 and the pear to buddedlimiting shape transition at vLx 0.75. Using these tworeduced volumes we can mark the transition points at(v, D~a0 ) ¼ (0.88, 0.89) and (0.75, 1.8) on the shape transi-tion lines Dobl/pro and L in Fig. 5 a, respectively. By doingthis for all six deformation trajectories (V1, V2, V3-G1,V3-G2a, V3-G2b, and V3-G3 in Fig. 4) and connectingthe transition points by dashed lines, we obtain six D~a0ðvÞpathways that turn out to have very similar slopes.

The deformation from sphere to budded limiting shapeis caused by the increase of the cross-section area ofDPPC from a to (1þε)a (where ε > 0) due to the chainmelting. We assume that the cross-section area of DLPEremains unchanged during the deformation. It is reportedthat a tiny asymmetry of the lipid composition betweenthe inner and the outer monolayer coupled with the lipidgeometries causes an enormous effect of the morphology(21,22). To demonstrate the effect of the bilayer asymme-try, first we discuss the case of the symmetric bilayer, i.e.,C0 ¼ 0. After chain melting of the symmetric bilayer, thepreferred reduced monolayer area difference D~as0 ¼ Da0reads

Da0 ¼�1þ ε

�1� f

��ðNþ � N�Þa8ph0

�1þ ε

�1� f

��1=2R0

¼ ðNþ � N�Þa8phR0

�1þ ε

�1� f

��3=2; (8)

odel with the ratio of nonlocal and local bending constants of q¼ 3. (Solid

Dsto/obl), the oblate and the prolate shape (Dobl/pro), and the prolate and the

d six deformation trajectories in Fig. 4 are shown by dashed lines connecting

gend also contains the radii of the spherical vesicles at the initial stage, R0.

ical model. (Dotted line) Estimated deformation trajectory for a vesicle with

he relationship between D~a0 and v in Eq. 13. To see this figure in color, go


where f ¼ ðfþ þ f�Þ=2. Here h0 is membrane thickness af-ter melting, which is generally smaller than the initial thick-ness because the membrane area is increased. To lowestorder, we may assume that the membrane volume isconserved, which gives h0 ¼ h=½1þ εð1� fÞ�. Becausethe vesicle volume itself is constant during the deformationfrom the sphere to the budded limiting shape, the reducedvolume after the chain melting is given by

v ¼ �1þ ε

�1� f

��3=2: (9)

By combining Eqs. 8 and 9, we find that the deformation tra-jectory in (v, Da0) plane reads

Da0 ¼ Daini0

v; (10)

where Daini0 ¼ ðNþ � N�Þa=ð8phR0Þ is the initial renormal-ized reduced monolayer area difference. When we increasetemperature from 30 to 50�C, which gives rise to a 30% in-crease of the area of DPPC, the reduced volume decreasesfrom 1 to 0.72 and the normalized preferred monolayerarea difference increases from Daini0 to Daini0 /0.72. Forexample, when the GUV has Daini0 ¼ 1, Da0 increases to1.39, which is too small to attain the deformation to thelimiting shape as shown by the dotted line in Fig. 5 a. Infact, GUVs with a symmetric bilayer membrane cannottransform to the limiting shape as shown in Appendix A.Thus we need a booster mechanism to explain the observeddeformation and the asymmetric area increase of the bilayeris a plausible candidate (21,22).

When DLPE lipids are distributed asymmetrically in thebilayer, D~a0 after chain melting is given by

D~a0 ¼ 1

8phR0

��Nþ � N��a1þ ε

�1� f

�3=2� εNaDf

1þ ε

�1� f

�3=2�þ R0C0

2qv�1=3; (11)

where the reduced volume is expressed by Eq. 9. By
combining Eqs. 9 and 11), we find that the deformation tra-jectory in (v, D~a0 ) plane reads
D~a0 ¼ 1

v

�Daini0 � R0

2h

Df

1� f

�1� v2=3

��þ R0C0

2qv�1=3:

(12)

For convenience, we also replot the phase diagram in the2/3
(v , D~a0 v) plane (Fig. 5 b), which emphasizes the relation-
ship between D~a0 and v:

D~a0v ¼ Daini0 � R0

2h

Df

1� fþ

1

2h�1� f

�þ aHPE

sp

2q

!R0Dfv

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 slopeof the broken lines that connect the oblate/prolate and pear/limiting shape transition points. This model trajectory withD~aini0 ¼ 0:5 and R0Df¼�2.7� 10�8 m (here h¼ 3� 10�9

m and f ¼ 0:2 are given parameters) describes well theobserved shape deformation from the sphere to the buddedlimiting shape. The discrepancy between the model andthe experimental trajectories mostly originates from the dif-ference in the initial renormalized preferred area differenceD~aini0 . To attain the deformation to the limiting shape, the re-normalized preferred reduced monolayer area differenceD~a0 has to increase from D~aini0 � 0:5 to a value on thelimiting shape line L ( D~a0 ~1.8). This requirement is satis-fied by the slope of the trajectories. According to our asym-metric model (Eq. 13), a similar slope indicates that theproduct R0Df should be the same in all vesicles. It shouldbe noted that the slope is very sensitive to Df becauseGUVs have a very large value of R0/2h x 1800 (21,22).Thus, a tiny asymmetric distribution of DLPE in the bilayeris sufficient to cause the deformation to the limiting shape.Because DLPE molecules prefer to partition into the innerleaflet of the initial spherical vesicle, the area of the outerleaflet is increased by DPPC chain melting more than thatof the inner leaflet, which results in a tiny asymmetry.From the constant slope of the model trajectory ofR0Df ¼ �2.7 � 10�8 m and R0 ¼ 10 � 10�6 m, we obtainDf¼�0.0027. Our asymmetric model analysis leads to twoimportant conclusions: 1) distribution of PE lipids in thebilayer is asymmetric, Dfs0; and 2) the model trajectoryhas D~aini0 ~ 0.5. This deformation mechanism well explainsobserved deformations where almost all vesicles exhibit thesame shape transition pathway from the sphere to thebudded limiting shape upon heating.

So far, the asymmetric lipid distribution coupled with thespontaneous curvature of the lipid, i.e., lipid sorting, hasbeen investigated extensively (31,34–36). These studiesindicate that the coupling between the membrane curvatureand the spontaneous curvature of lipid is weak and the lipidsorting is only observed in small unilamellar vesicles withradii of several tens of nanometers. Thus, the asymmetryof the lipid distribution in GUVs is very small. We showthat the very small asymmetric distribution of DLPE inGUV bilayer needed to interpret our experimental observa-tion, Df ¼ �0.0027, is consistent with the prediction of thelipid sorting model described in Appendix B. Unfortunately,this tiny change would be very difficult to measure.

Another important result obtained by the model trajectoryanalysis is that the mother and the offspring spherical vesi-cles have D~aini0 ~ 0.5 and R0Df constant in their trajectories,which ensures the recursive nature of vesicles in the divisioncycle. To elucidate this recursive nature, we simulate D~a0 ofthe daughter vesicle after the heating-cooling cycle. Forsimplicity, we deal with a symmetric division process wherethe mother vesicle produces two identical daughters. The


Jimbo et al.

initial mother vesicle at T¼ 30�C (step 1) has a radius of R0,a preferred reduced monolayer area difference D~a

ð1Þ0 ¼ 0.5,

and the composition asymmetry of Df(1) ¼ �0.0027. Whenwe assume that the vesicle maintains the lipid compositionDf(1) through the division, i.e., no lipid exchangebetween the inner and the outer leaflet, the daughter vesicle(step 4) has Da

ð4Þnle0 ¼ Da

ð1Þ0 =

ffiffiffi2

p ¼ 0:35 and Df(4)nle ¼�0.0027. These values are in disagreement with theexperimental results of Da

ð4Þexp0 y0:5 and f(4)exp ¼ffiffiffi

2p

Dfð1Þexp ¼ �0.0038. This disagreement suggests a redis-tribution of lipids within the bilayer, which may take placeduring pore opening upon cooling (Fig. 6). At this stage, theouter and the inner monolayers are connected by pore rimand thus lipids can migrate between the leaflets to equili-brate the chemical potential of lipids between the innerand the outer leaflets. Lipid traffic through the rim of thepore has been observed in binary vesicles composed ofcone- and cylinder-shaped lipids (37). When this binaryvesicle was subjected to a similar heating and cooling cycle,the binary vesicle forms a single pore below the main-chaintransition temperature of DPPC. During pore formation,the binary GUVs showed a rolled membrane at the rim ofthe pore (torus rim), which implies the lipid traffic by achemical potential difference between the outer leaflet andthe inner leaflet due to the lipid geometry.

In the vesicle division cycle, the pore formation takesplace in the fluid-solid coexistence region, where most ofthe DPPC lipids are in the solid phase and most of theDLPE lipids are in the fluid phase. Thus DLPE (majority)and DPPC (minority) in the fluid phase can participate inthe lipid exchange through the rim to equilibrate the chemi-cal potential of lipids in the outer and the inner leaflet.However, when lipid traffic through the rim of the porecompletely equilibrates the chemical potential, the daughtervesicle should have D~a

ð4Þeq0 y1:0 and Df(4)eq ¼ �0.0047

(Appendix B). This discrepancy indicates that lipid trafficthrough the pore rim cannot attain the complete equilibriumdue to the finite lifetime of the pore. Thus, due to the poreclosing, the lipid exchange was terminated at ~20% of thelipid traffic toward equilibrium as estimated by comparingthe deviations of the experimental and the equilibriumpreferred monolayer area differences from that expected inabsence of lipid exchange: ðD~að4Þexp0 � D~a

ð4Þnle0 Þ=ðD~að4Þeq0 �

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.


D~að4Þnle0 Þ ¼ ð0:5� 0:35Þ=ð1:0� 0:35Þ ¼ 0:2. Here we esti-

mate the lipid exchange through the rim of the pore basedon the diffusion of lipids. Because the diffusion coefficientof phospholipid in the fluid phase is ~7 � 10�12 m2/s (38),the mean diffusion distance during the typical pore lifetimeof 1 s is ~5 mm. Then lipids located at a distance within5 mm from the rim may diffuse across the rim during thepore opening, which covers ~12% of the vesicle area. Thisfraction is roughly consistent with the estimated lipid ex-change of ~20%. The lipid exchange through the rim isdriven by the chemical potential difference, which acceler-ates the lipid flow compared to the simple diffusion process.By combining the experimentally determined value ofR0Df z �2.7 � 10�8 m and Eq. 13, we estimate the valueof the dimensionless constant introduced in Eq. 4: a ¼ 0.5(Appendix A). It is plausible that the short chain length ofDLPE (12:0 PE) and the matrix effect of DPPC (16:0 PC)reduces the spontaneous curvature compared with that ofDMPE having HDMPE

sp ¼ �0.3 nm�1.We note that the restricted lipid traffic discussed above

slightly modifies the deformation trajectories from theperfectly recursive trajectory, because the fraction of the lipidrelaxation area to the total vesicle area depends on the size ofvesicle. For the vesicles with the radius of ~10 mm, the lipidexchange is limited to ~20% of the complete exchange.This fraction should increase with decreasing vesicle sizeand finally reach 100%whereD~aini0 is 1.0 and the compositionasymmetry is determined by the equality in the chemical po-tential of the lipids (Appendix B). Thus, from generation togeneration, D~aini0 gradually approaches 1.0. In fact, D~aini0 in-creases with the decrease of R0 as shown in Fig. 7, which isconsistent with our model.

Lastly, we discuss the mechanism of breaking the neck inthe budded limiting shape to produce daughter vesicles. It iswell known that single-component vesicles do deform to thebudded limiting shape in response to external stimuli (e.g., a

FIGURE 7 Relationship between the vesicle radius R0 and the initial re-

normalized, preferred, reduced monolayer area difference, D~aini0 . To see this

figure in color, go online.


change of temperature or osmotic pressure) but breakingthe narrow neck between the buds is harder (14) becausethe neck is stabilized by the spontaneous curvature (15).On the other hand, in multicomponent vesicles, division isobserved more readily (39,40). The free-energy analysisof binary vesicles shows that the coupling of the local lipidcomposition to the Gaussian curvature does destabilize thenarrow neck and encourages vesicle division if the minorcomponent lipids prefer to be located in regions with largepositive Gaussian curvature (17). In our system, by addingDLPE lipids, the binary vesicles show division. Thus, theneck should be destabilized by the presence of DLPE.

To examine the coupling between Gaussian curvatureand local PE lipid composition in DPPC/DLPE binary ves-icles, we used the fatty-acid-labeled PE lipid (Acyl 12:0NBD PE) which can be used to visualize the local compo-sition of PE lipids during division. DPPC/DLPE vesiclescontaining 1 mol % Acyl 12:0 NBD PE showed a similardeformation-division process during the heating-coolingcycle, but we could not detect a definite localization ofPE lipids at the spherical part. It is possible that this is amatter of the limited spatial and temporal resolution ofour experimental technique, which will be improved in afuture project.

CONCLUSIONS

By simply mixing inverse-cone-shaped DLPE moleculesinto cylinder-shaped DPPC molecules, the binary GUVsreadily produce daughter vesicles repeatedly during theheating-cooling cycle, thereby capturing the essence of thevesicle self-reproduction. To reveal the roles of PE lipids,we performed quantitative 3D analysis of shape deformationand division process and found that the process relies on twokey factors: 1) asymmetric distribution of DLPE in thebilayer and 2) redistribution of DLPE during the coolingstage.

The asymmetric distribution of DLPE is essential for thedeformation from the sphere to the limiting shape. Due totheir inverse-cone shape, DLPE molecules preferentiallypartition into the inner leaflet, which increases thepreferred area difference as the reduced volume isdecreased and drives the deformation of the vesicle to thebudded limiting shape. Although the asymmetric distribu-tion of DLPE in GUV bilayer, Df ¼ �0.0027, is verysmall, the asymmetry plays a significant role in the shapedeformation because it is enhanced by the ratio of vesiclesize and membrane thickness, typically several thousands.On the other hand, the redistribution of DLPE in the defor-mation-division process is needed to reset the vesicle state,and it most likely takes place during pore opening inducedby cooling. During pore formation, lipids can migratebetween the leaflets to minimize the elastic energy. Thisinitialization enables the vesicle to undergo recursivedivision. It is quite interesting to note that this recursive na-

ture is promoted by the free energy minimization coupledwith the lipid traffic between the outer and the innermonolayers.

It has been pointed out that a tiny asymmetry in bilayercauses an enormous influence on a shape deformation tra-jectory (21,22). So far, the asymmetric lipid distributioncoupled with the spontaneous curvature of the lipid, i.e.,lipid sorting, has been investigated extensively, becausethe sorting of both lipids and proteins in trafficking path-ways lie at the heart of cellular organelle homeostasis.These studies indicate that the coupling between the mem-brane curvature and the spontaneous curvature of lipid isweak and the lipid sorting is only observed in small unila-mellar vesicles with radii of several tens of nanometers.The lipid sorting model predicts the asymmetry of the orderof 10�3 in GUV, which is consistent with our observation,Df ¼ �0.0027. Here we show that such tiny compositionasymmetry ensures the observed shape deformation andthe recursive nature. Thus the spontaneous coupling be-tween membrane curvature and PE lipid distribution isresponsible for the observed deformation-division-initiali-zation process.

The heating-cooling protocol is advantageous as a wayto realize vesicle division for several reasons, primarilybecause of its speed, which allows us to produce one gener-ation within a few minutes and because it can be used tomanipulate a large number of vesicles at the same time.In addition, it is quite robust in the sense that self-reproduc-tion is not very sensitive to variations in the heating andcooling rates. If combined with a steady supply of lipidsto the membrane, the protocol could foreseeably be fine-tuned to produce daughters that would be just as big asthe mother. It is conceivable that, by adjusting these ratesand the overall temperature sequence, one could alsoenhance the symmetry of vesicle division, the goal beingthe identical-twin transformation. Another interesting chal-lenge is application of this technique to the reported self-reproduction systems (oleic acid/oleate vesicles (4) andmembrane molecule/catalyst vesicles (9,10)), which willreveal roles of supplied molecules in the self-reproductionof vesicles.

Of course we do not claim that the temperature changeand the pore formation were necessary for the proliferationof early cells. Yet our work shows that this process couldhave included a physical mechanism of the proliferation,and may be minimally helped by a primitive regulatorynetwork creating an asymmetric lipid distribution coupledwith the membrane curvature; this would give rise to therecursive cell division following the equilibrium ADE-SCmodel. Our model vesicle regulates a similar asymmetriclipid distribution using the order-disorder transition withinthe membrane and the pore formation. With the detailedquantitative insight into the physics of vesicle self-replica-tion reported here, these intriguing prospects may beexplored in a more systematic way.


Jimbo et al.

APPENDIX A

Shape deformation of vesicle with symmetricbilayer

To demonstrate shape deformation of GUVs with the symmetric bilayer,

we replaced DLPE by DLPC ðTDLPCm ¼ �2 �CÞ. 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 choles-

terol does not affect the distribution of phospholipids in bilayers (42). In

fact, ternary GUVs composed of DPPC/DLPE/cholesterol ¼ 8:2:2 show a

similar vesicle division pathway to that of the binary GUVs composed of

DPPC/DLPE ¼ 8:2 (see Movie S3). Fig. 8 shows the deformation of a

ternary vesicle composed of DPPC/DLPC/cholesterol ¼ 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.

APPENDIX B

Lipid sorting of binary vesicle in the solid-liquidcoexisting 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 þ h/2. A DLPE molecule is characterized by a molecular cross-section

area aPE and a spontaneous curvature HPEsp , and a DPPC molecule has aPC

and HPCsp ¼ 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 micro-

scope, suggesting the submicroscopic size of domains, although the main-

chain transition temperature of the DPPC/DLPE ¼ 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 redis-

tributed 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 as-

sume 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 gov-


erned by the difference of chemical potentials. Then the entropy of

DPPC molecules is given by

S ¼ NliqPCkB

�lnAð1� jÞ

a� ln Nliq

PC � 1

�; (B1)

where A is the membrane area, NliqPC is the number of DPPC molecules in

the liquid phase, and j is the area fraction of the solid phase. The chemical

potentials of DPPC molecules ðmPC;liquidÞ in outer (þ) and inner (�) mono-

layer read

m5PC;liquidym5

0;liquid þ lnA5 ð1� jÞ

a

ðkBT ¼ 1Þ;(B2)

where m0 is the interaction energy of a single DPPC including the bending

energy. In equilibrium, the balance of the chemical potentials reads

DmPC;liquid ¼ mþPC;liquid � m�

PC;liquid ¼ 0: (B3)

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

given by

w5b ¼ ~k

2

�2H5 � C5

0

�2a; (B4)

where ~k ¼ k=2kBT is the bending modulus of monolayer assumed to be the

same in both monolayers (which is supported a posteriori by the small con-

centration difference), H5 ¼ 1=ðR5h=2Þ is the mean curvature of each

monolayer, and C50 ¼ 5aHPE

sp f5 is the spontaneous curvatures of each

monolayer. Because the difference in m0 between the two monolayers is

the bending energy, DmPC; liquid is described by

DmPC;liquid ¼ ~k

2

�2

Rþ h=2� aHPE

sp fþ�2

a� ~k

2

�2

R� h=2

þ aHPEsp f

��2

aþ lnAþ

A�

z~ka

h

R3þ aHPE

sp

Rf

! 4þ aHPE

sp RDf�þ ln

Aþ

A� ¼ 0:

(B5)

FIGURE 8 Deformation of a DPPC/DLPC/

cholesterol ¼ 8:2:2 ternary GUV caused by heat-

ing from 30 to 50�C. Scale bar, 10 mm. The ex-

tracted relaxed shapes obtained by 3D analysis

are shown.


Taking into account HPEsp ð¼ �0:3 nm�1Þz1=h, the lipid composition dif-

ference, Df, in the second bracket is RHPEsp � R=h � 3600. Thus, the flux

of lipids between the outer and inner leaflet is governed by the lipid asym-

metry in the bilayer. Using ~k ¼ 135 (bilayer bending modulus of DPPC is

~270 kBT at 30�C (43)), R ¼10 mm, h ¼ 3 nm, ðfþ þ f�Þ=2 ¼ 0:2, and

a ¼ 0:48 nm�1, we obtained Df ¼ �0.0018 for a ¼ 1 and �0.0047 for

a ¼ 0.5. These values are close to the estimate extracted from the experi-

mental data Df ¼ �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 ¼ 10 mm is limited

to 20% of the complete exchange, the experimental value of Df ¼ �0:0027

suggests that a plausible value of the dimensionless proportionality constant

a is 0.5.

SUPPORTING MATERIAL

Three movies are available at http://www.biophysj.org/biophysj/

supplemental/S0006-3495(16)00216-2.

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.

ACKNOWLEDGMENTS

We thank Professor Toshihiro Kawakatsu (Tohoku University) and Profes-

sor Sa�sa Svetina (University of Ljubljana) for helpful discussions.

This work was in part supported by Grant-in-Aid for Scientific Research

(A) (Nos. 22244053 and 25247070), Grant-in-Aid for Scientific Research

on Innovative Areas ‘‘Fluctuation and Structure’’ (No. 25103009), by

Grant-in-Aid of Tohoku University Institute for Promoting Graduate De-

gree Programs Division for Interdisciplinary Advanced Research and

Education, by Marie-Sk1odowska-Curie European Training Network

COLLDENSE (H2020-MSCA-ITN-2014 grant No. 642774), by the Slove-

nian Research Agency (grant No. P1-0055), and by the European Science

Foundation Research Networking Programme QuanTissue.

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