they are involved , for example , in vesicular trafficking , 
 which requires the selective loading of cargo molecules into the vesicles , 
 or in endo- and exocytosis , where the membrane invaginates inward 
 or outward . in giant vesicles , model membrane systems with cell - size 
 dimensions , budding may be induced by 
 a number of possible mechanisms . for example , a slight area difference 
 between the two monolayer leaflets of the membrane or a change in 
 the vesicle area - to - volume ratio may lead to budding . in homogeneous membranes , budding is driven by the minimization 
 of the bending energy . in multicomponent membranes containing phase separated domains , budding is governed by the interplay of bending 
 rigidity and line tension of these domains . in the aforementioned studies , 
 the membrane properties play a crucial 
 role , whereas the enclosed homogeneous fluid is an inert  spectator  
 phase . however , when two ( or more ) liquid phases are in contact with 
 the membrane , their interactions with the bilayer become relevant 
 for the vesicle morphology . recently , such novel soft matter systems 
 were realized and phase separation inside vesicles was reported to lead to protein 
 partitioning in one of the liquid phases . budding has also been observed , but the underlying mechanism remains 
 to be elucidated . to shed light on this problem , we use giant 
 unilamellar vesicles 
 loaded with homogeneous aqueous solutions of water - soluble polymers . 
 osmotic deflation of the vesicle induces phase separation in the interior 
 solution and , at the same time , creates excess membrane area . depending 
 on membrane properties such as the membrane tension and spontaneous 
 curvature , the area created during deflation may be stored in membrane 
 nanotubes and/or may lead to vesicle 
 budding as shown in this paper . the budding direction can be reversed 
 if the phase separation occurs in the vesicle exterior . a systematic 
 study of the budding process reveals that it requires the wetting 
 of the membrane by both liquid phases . this wetting - induced budding 
 provides a possible mechanism for the selective loading of cargo molecules 
 into transport vesicles in cells . to prepare vesicles 
 encapsulating two phases we used a homogeneous 
 aqueous solution composed of 4.05 wt % poly(ethylene glycol ) ( peg , 
 8 kg / mol ) and 2.22 wt % dextran ( 400500 kg / mol ) ; see the supporting information . the membrane consists 
 of 95.9 mol % dioleoylphosphatidylcholine , 4.0 mol % gm1 ganglioside and 0.1 mol % fluorescent lipid marker ; see the supporting information . after formation , the 
 vesicles are diluted in an isotonic solution containing 4.41 wt % 
 peg and 1.45 wt % dextran . the osmolarity of the external medium is 
 then increased by adding a hypertonic solution of 3.92 wt % peg , 2.14 
 wt % dextran , and 3.27 wt % sucrose . this composition in the exterior 
 solution implies that its density is between those of the peg - rich 
 and dextran - rich phases , but smaller than the overall density of the 
 solution inside the vesicles . these conditions ensure that the vesicles 
 sediment to the chamber bottom and that the symmetry axis of the budded 
 vesicles is vertically oriented ; see figure 1a  f . in this way , the vesicles can be observed from the side 
 using a horizontally aligned microscope . the vesicle axial symmetry 
 allows for quantitative analysis of their shapes in contrast to the 
 systems explored previously . outward ( a  g ) 
 and inward ( h  q ) budding of vesicles 
 in contact with several aqueous solutions . ( a  f ) side - view 
 phase contrast images and ( g ) a cartoon of a vesicle sitting on a 
 glass substrate and subjected to osmotic deflation . after phase separation 
 ( b ) , the heavier and denser dextran - rich phase is located at the vesicle 
 bottom . further deflation causes the dextran - rich phase to wet the 
 membrane ( c ) , and then to bud out ( d  f ) . the osmolarity ratio r from ( a ) to ( f ) is 1.0 , 1.14 , 1.32 , 1.46 , 1.65 , and 1.76 , 
 respectively . the system was left to equilibrate for at least 2 h 
 after each consecutive deflation step . ( h  p ) xz - confocal scans and ( q ) a cartoon of vesicles in contact with fluorescently 
 labeled droplets of dextran - rich phase ( green ) . the confocal images in the rows ( h  j ) , 
 ( k  m ) , and ( n  p ) show the mixed fluorescence signal , 
 and the red and green channels separately . inspection of ( i , l ) shows 
 that the interface between the dextran - rich droplets and the peg - rich 
 background contains essentially no lipid . in order to induce the phase separation outside 
 the vesicles as 
 in figure 1h  q , we prepared a polymer 
 solution composed of 6.87 wt % peg and 2.86 wt % dextran . a small 
 fraction of dextran ( 1.25 wt % of the total dextran ) was labeled with 
 fluorescein isothiocyanate . the polymer solution was left at room 
 temperature ( 23 c ) for 2.5 days after which complete phase separation 
 was achieved . vesicles with gm1-doped membranes were prepared in the peg - rich phase at room 
 temperature using electroformation . approximately 2 l dextran - rich 
 phase was mixed with 200 l vesicle solution in the microscopy 
 chamber ( occasionally a mixture of 100 l peg - rich phase and 
 100 l vesicle solution was used ) . the chamber was shaken gently 
 in order to break the dextran - rich phase into tiny droplets , and to 
 increase the possibility for contact between the vesicles and the 
 dextran - rich droplets . the vesicles with dextran - rich droplets were 
 imaged after 2 h or on the next day . for the micropipet aspiration 
 experiments , performed only on vesicles 
 encapsulating two phases , the vesicles are predeflated with the hypertonic 
 solution , increasing the external osmolarity by 32% , and then , left 
 to equilibrate for one day . aspiration is realized by means of a glass 
 capillary , approximately 20 m in diameter , connected to a home - built 
 hydrostatic pressure system . after each consecutive pressure change the interfacial 
 tension of the phase separated polymer solution 
 is independently measured in bulk using spinning drop tensiometer ; 
 see the supporting information . figure 1a  g shows 
 side - view images and a cartoon of a vesicle at different degrees of 
 deflation described by the osmolarity ratio r , which 
 we define to be the ratio rex / rin,0 between the deflation - dependent osmolarity rex within the exterior compartment and the initial 
 osmolarity rin,0 within the interior compartment . the phase separation within the vesicle is induced 
 via osmotic deflation by adding the hypertonic solution to the external 
 medium . the resulting osmotic unbalance forces water out of the vesicle . since the polymers can not permeate the membrane , their concentration 
 in the vesicle increases . once it is above the binodal ( see figure 
 s1 in the supporting information ) , the 
 enclosed solution separates into peg - rich and dextran - rich phases ; 
 see figure 1b . the dextran - rich droplet is 
 always located at the bottom of the vesicle because of its higher 
 density compared to the peg - rich phase . when the vesicle is further 
 deflated with r > 1.3 , the dextran - rich phase 
 starts 
 to wet the membrane ; see figure 1c . the change 
 in the morphology of the dextran - rich droplet indicates a wetting 
 transition from complete wetting of the peg - rich phase in figure 1b to partial wetting in figure 1c as previously described in ref ( 12 ) . after the dextran droplet starts wetting 
 the membrane , the radius rc of the three - phase 
 contact line , where the external medium ( e ) , the 
 peg - rich phase ( p ) and the dextran - rich phase ( d ) are in close proximity , increases at first ; see figures 1c and 2a , b . at the same time , 
 the interfacial tension pd between 
 the liquid phases pulls on the membrane along this contact line and 
 leads to budding and a decrease in rc at 
 higher polymer concentrations ; see figure 2b . the budding process from the spherical vesicle shape in figure 1c to the pair of two spherical caps in figure 1d should be regarded as a strongly concentration - dependent 
 but smooth crossover rather than as a sharp transition . this crossover 
 behavior is most clearly seen in the behavior of the contact line 
 radius rc ; see figure 2b . as the osmolarity is increased further , the dextran - rich 
 phase protrudes further out ; see figure 1e , f . finally , the dextran - rich phase may form a completely spherical bud 
 whereby the area of the pd interface is close to 
 zero . ( a ) schematic illustration of the contact angles and the tensions 
 at the three - phase contact line (  ) with radius rc . when the dextran - rich 
 phase starts wetting the membrane , rc first 
 increases , but then decreases during the budding process . ( c ) evolution 
 of the three tensions with increasing polymer concentrations . the 
 weight ratio of dextran and peg is 0.55 . the 1st , 3rd , 
 5th , and 6th points from these data sets for the membrane tensions 
 correspond to the images ( c  f ) in figure 1 . thus , vesicles with different initial area adopt diverse shapes upon 
 deflation ; see the supporting information . wetting - induced budding can also occur toward the vesicle interior ; 
 see figure 1h  q , when the exterior solution 
 undergoes phase separation . the observations in these samples show 
 analogous vesicle morphologies . for low excess membrane area , the 
 dextran - rich droplets wet the membrane but deform the vesicle only 
 slightly ; see figure 1h  j , while strongly 
 deflated vesicles may engulf the dextran - rich droplets completely ; 
 see figure 1n  p . after 
 the wetting transition , the surface of the dextran - rich droplet exhibits 
 a  kink  at the three - phase contact line ; see figure 1c  h , j , k , m , q . this contact line divides the 
 vesicle membrane into pe and de segments . 
 because of the compositional difference of the p and d phases , these two membrane segments experience two distinct 
 tensions , pe and de ; see figure 2a . by fitting the vesicle and the drop contours in the microscopy images 
 with circular arcs , we obtain the three contact angles e , p , and 
 d with e + p + d = 2 ; see figure 2a . 
 for outward budding , these contact angles are related to the membrane 
 tensions pe and de and the interfacial tension pd , via1 the case of inward budding is described 
 in the supporting information . these equations 
 are analogous to neumann s 
 triangle for capillary surfaces . from 
 the analysis of the vesicle images , we can calculate the total polymer 
 concentration within the vesicle at every osmolarity ratio r , assuming that the volume change corresponds to the loss 
 of water . the interfacial tension pd in eqs 1 is measured independently for bulk 
 polymer solutions ; see the supporting information . knowing pd , we can compute the 
 tensions pe and de from eqs 1 ; see figure 2c . the interfacial tension pd increases with the total polymer concentration because the 
 composition difference between the coexisting phases is enhanced . their nonmonotonic 
 dependence on the polymer concentration arises from two competing 
 effects of the deflation process . first , the total vesicle volume 
 is decreased , which in the absence of any other constraint , would 
 act to reduce the membrane tensions pe and de . however , 
 deflation also increases the interfacial tension pd ; see figure 2c , which may 
 be balanced in two ways following ( eqs 1 ) : ( i ) 
 by a reduction of the area of the pd interface , which 
 as a consequence leads to a reduction in the contact angle e , or ( ii ) by an increase in the membrane 
 tensions pe and/or de . inspection of figure 2c shows that pe and 
 de first decrease at low 
 polymer concentrations , which implies that the increased interfacial 
 tension pd can be balanced by a 
 reduction of the contact angle e alone . however , as the polymer concentration is further increased , 
 the tension de passes through 
 a minimum and starts to increase whereas the tension pe stays essentially constant . thus , in this 
 second concentration range , the increase in the interfacial tension 
 pd is primarily balanced by an 
 increase in the tension de . indeed , we will argue further below that the pe membrane segment can not pull  against  the pd interface . the two concentration ranges in which either 
 the membrane tensions or the interfacial tension dominate correspond 
 to two different vesicle morphologies as observed optically : sphere 
 or a pair of spherical caps ; see figure 1 . the crossover between these two morphologies marks the budding process . for a fixed composition 
 of the polymer phases , , we apply 
 suction pressure to a deflated dumbbell - like vesicle ; see figure 3a . the pressure produces mild membrane tensions 
 in the range 4383 n / m ; see the supporting information , which do not lead to membrane stretching . the angle e , which characterizes the degree of budding , increases with the applied 
 suction pressure , i.e. , the bud is retrieved and the budding process 
 is reversed . simultaneously , the excess area of the vesicle part outside 
 of the pipet is reduced , a reduction that could also be achieved by 
 vesicle inflation , i.e. , by the reverse of the process shown in figure 1 . ( a ) side - view phase contrast images of a vesicle under 
 different 
 suction pressures . the small dense droplet at the vesicle bottom is 
 the dextran - rich phase . ( b ) the tension ratios as a function 
 of the contact angle e describing 
 the degree of budding . the stars in the data correspond to the images 
 in ( a ) as indicated by the numbers . ( c ) wettabilities , as defined 
 in the text , as a function of the contact angle e . the upper set of data confirms eq 4 . the tension pe is imposed 
 by the micropipet ; see the supporting information , and the tension de can 
 be calculated from the measured contact angles via eqs 1 . the two tensions normalized by the interfacial 
 tension pd are shown in figure 3b as a function of the angle e . for small e or 
 high degree of budding , the tensions pe and de change only 
 weakly . in the regime of large e or low degree of budding , the crossover between these two regimes indicates the budding ( or 
 bud retrieval ) process , which is continuous . the sharp increase 
 in pe and de at high aspiration 
 pressures or large e can be understood 
 by considering the force balance at the three - phase contact line as 
 in ( 1 ) , which imply pe / sin 
 d = de / sin p = pd / sin e . as the contact angle e approaches 
  , small changes in e lead 
 to significant changes in pe and de . for the regime 
 of lower aspiration pressures ( smaller e ) , where the changes in the tensions pe and de are insignificant ; see figure 3b , the vesicle 
 shape is governed primarily by the minimization of the interfacial 
 area apd ; see the sequence 
 of images 3 to 1 in figure 3a and figure s4 
 in the supporting information . in 
 these experiments , thus , the wettability of one of the phases , 
 for example the peg - rich phase , on the membrane should be constant . if we consider a planar membrane , i.e. , e =  , this wettability will be characterized by cos p . to examine the limit of a planar membrane , 
 we plot cos p as a function of 
 the angle e in figure 3c . the planar membrane limit is described by the angle p *  p ( e   ) . e < 178 leads to cos p *  0.87 or an angle of 30. 
 for such a planar surface , the wettability is defined as ( de  pe)/pd . following eqs 1 , one obtains2 we will now consider the limit of a 
 planar membrane in which the 
 contact angle e approaches . 
 we expand the right - hand side of eq 2 with respect 
 to (   e ) , see the supporting information , which leads to3where o( e ) indicates terms of order  
  e . furthermore , 
 from the experimental data we find that ( de  pe)/pd is approximately constant 
 over the whole e range with an 
 average value of 0.86  0.02 ; see figure 3c , which implies the relation4 this observation can be understood 
 if one considers the membrane 
 shape on different length scales . when viewed with optical resolution 
 as in figures 1 and 3 however , this kink can not persist 
 to small scales since the membrane has a finite bending rigidity and 
 a sharp kink would imply an infinite bending energy . therefore , the 
 membrane should be smoothly curved on small scales and its contact 
 with the pd interface should be characterized by 
 an intrinsic contact angle in , 
 which represents the angle between the pd interface 
 and the plane tangent to the membrane along the contact line . the relations 2 and 4 then imply that the angle p * is identical with the intrinsic contact angle in as introduced in ref ( 16 ) . it represents the actual 
 contact angle between the membrane and the pd interface 
 at the nanometer scale . for the polymer composition as studied in 
 the aspiration experiments , we obtain cos p *  0.87 from linear extrapolation of cos p as in figure 3c and 
 cos p * = 0.86  0.02 from 
 relation 4 . thus , both estimates lead to in = p * 
  0.53 or 30 providing us with two methods to determine 
 the intrinsic contact angle . since in is smaller than 90 , 
 the pe membrane segment and the pd interface pull roughly in the same direction . an increase in the 
 interfacial tension arising , e.g. , from an increase in the polymer 
 concentrations , must then be primarily balanced by an increase in 
 the mechanical tension de of the de membrane segment , which agrees with the 
 data in figure 2c for high polymer concentrations . above , the budding process 
 was analyzed using the force balance 
 relations in eqs 1 , which can be directly applied 
 to the images as obtained by optical microscopy . as explained in ref ( 16 ) , these force balance relations 
 are valid in the tension - dominated regime , i.e. , on length scales 
 that exceed the characteristic scale pd/  100 nm , where  is the bending rigidity 
 of the membrane . on smaller scales , one obtains more complex force 
 and torque balance equations , which also depend on the bending rigidity 
 . however , the bending rigidity 
 does not affect the intrinsic contact angle . indeed , as shown here , 
 we are able to deduce the existence of this contact angle from the 
 coarse - grained force balance eqs 1 alone by 
 considering the limit of a planar membrane , for which the effective 
 contact angle e approaches the 
 limiting value e =  ; see 
 the line of arguments after eq 2 . wetting - induced 
 budding requires contact of the membrane with both 
 phases , whereby the budding direction depends on whether the two phases 
 are inside or outside the vesicle ; see figure 1 . if the membrane is wetted completely by one of them , wetting - induced 
 budding can not occur . instead , the excess area created during deflation 
 is stored in nanotubes stabilized by the membrane spontaneous curvature . therefore , the wetting transition as in figure 1b , c precedes the budding process . more generally , 
 the degree of budding and tubular formation results 
 from the competition between the spontaneous curvature of the membrane 
 and the wetting properties of the aqueous phases on the membrane . budding , on 
 the other hand , is favored when neither one of the aqueous phases 
 dominantly wets the membrane ( i.e. , partial wetting ) . since the membrane 
 must be wetted by both aqueous phases during the budding process , 
 it can not occur if the system exhibits complete wetting . after 
 the wetting transition , one has pd = ( de  pe)/cos in > de  pe corresponding to partial wetting with intrinsic 
 contact angle in . the energy cost 
 of increasing the contact area between the membrane and the dextran - rich 
 phase is smaller than the energy gain of decreasing the pd interfacial area . with deflation , the tensions pe and pe decrease and budding occurs spontaneously provided excess 
 membrane area is available . upon further deflation , the tension pe , which is dominated by the membrane spontaneous 
 curvature saturates ; see figure 2c . this behavior reflects the fact that at high 
 polymer concentration the fraction of dextran in the peg - rich phase 
 becomes negligible ; see the supporting information . it can also occur during the phase separation process if the transient 
 tensions satisfy pd > de  pe and there is excess membrane area . more than one bud can form 
 in a metastable state , as observed in our own experiments and in ref ( 11 ) . vesicles in contact with 
 two phases in the interior or exterior 
 can undergo budding , provided the membrane is partially wetted by 
 both phases and excess area is available . if one of the phases does 
 not wet the membrane , it will exist as a small droplet inside or outside 
 the vesicle . the budding process is governed by the interplay between 
 the membrane tensions pe and de and the interfacial 
 tension pd . we demonstrated that 
 for a fixed composition of the liquid phases the budding process can 
 be reversed by applying tension to the membrane . the process 
 of wetting - induced budding provides a possible mechanism 
 for the selective vesicular transport in cells . molecular crowding 
 widely exists in the interior of cells and can lead to microcompartmentation . the membrane prefers to enclose macromolecular solutions , to which 
 it has higher affinity , thus loading the appropriate molecules in 
 transport vesicles . wetting of a membrane by a liquid droplet creates 
 a contact line , which may enhance endocytotic or exocytotic processes . wetting - induced budding of vesicles in cells could be used to locally 
 regulate and compartmentalize cellular processes such as protein synthesis , 
 to restrict chemical reactions to particular segments of the membrane 
 surface or parts of the cell , or to terminate such reactions by dewetting 
 or bud retraction . wetting - induced budding may also provide simple 
 physical mechanism for vesicle shedding , involved in membrane traffic and molecule transfer among neighboring 
 cells or to the cell exterior .
osmotic deflation of vesicles enclosing two liquid phases 
 can lead 
 to bulging of one of the phases from the vesicle body . 
 this budding 
 process is preceded by a complete to partial wetting transition of 
 one of the liquid phases on the membrane and depends on the membrane 
 tensions and the tension of the interface between the enclosed liquid 
 phases . 
 these tensions dominate in different morphology regimes , the 
 crossover of which initiates the budding process . in addition , the 
 degree of budding can be controlled by aspiration via micropipets . 
 we also demonstrate that the budding direction can be reversed if 
 there are two external phases in contact with the vesicle .