fcs was used to determine the 
 relative affinity of -syn100 for large unilamellar 
 vesicles ( luvs ) composed of 100% 
 popg or 1:1 ( mol / mol ) pg : pc under dilute conditions .
binding of fluorescently 
 labeled protein to unlabeled vesicles results in a shift in the autocorrelation 
 curves to the right ( longer diffusion times ) ( figure 1a ) ; the autocorrelation curves can then be fit to extract 
 the fraction of bound protein and to determine an apparent binding 
 affinity , kd ( see materials and methods 
 in the si for details ) .
these measurements 
 found that -syn100 binds to 100% popg vesicles with 
 60 times greater affinity than to 1:1 pg : pc vesicles ( kd = 2.25 and 136.9 m , respectively ) under 
 our buffer conditions .
this result agrees with previous studies showing 
 that -syn100 binding to lipids is driven primarily 
 by electrostatic interactions between anionic lipid headgroups and 
 positively charged lysine residues in the membrane - binding region 
 of the protein , although the 
 complex roles of hydrophobic lipid  protein interactions and 
 entropy can not be ruled out .
( a ) fcs traces for -syn100 in the absence ( black ) 
 or presence of equal concentrations of 1:1 pg : pc ( blue ) or 100% popg 
 ( red ) luvs .
the greater shift to the right in the 100% popg curve 
 reflects a larger fraction of -syn100 bound relative 
 to the 1:1 pg : pc curve .
( b ) -syn100 tubulation capacities 
 for 1:1 pg : pc and 100% popg at equal bound density , compared with 
 buffer .
the inset shows the corresponding absorbance traces for systems 
 with 1:1 pg : pc or 100% popg and buffer or -syn100 . in order to test the effect of 
 headgroup charge on -syn100-induced tubulation at 
 equal bound - protein density , we adjusted 
 the added protein concentration on the basis of the measured kd value . again , because of our previous measurements 
 under saturating conditions , this ensured equal density of bound protein . the ability of -syn100 to 
 tubulate liposomes was assayed by monitoring the change in the amount 
 of scattered light from a liposome solution in the presence of -syn100 .
we quantified -syn100 s tubulation capacity by determining the ratio of 
 the initial scattering intensity before addition of protein to the 
 near - final scattering intensity ( t = 2400 to 2500 
 s ) for each absorbance trace .
figure 1b shows 
 the dramatic loss of -syn100-induced tubulation 
 in the 1:1 pg : pc mixture compared with the 100% popg vesicles . while 
 -syn100 causes a rapid decrease in the amount of 
 light scattered by 100% popg vesicles ( figure 1b inset ) , the signal change for the 1:1 pg : pc vesicles is equivalent 
 to that of the control .
thus , we have 
 confirmed that previous reports of reduced tubulation in 1:1 mixtures 
 hold under conditions of equally bound protein . as 
 we will explore in depth below
, this does not necessarily mean that 
 the difference in binding energy does not dominate the biophysics 
 of tubulation . in order to begin to understand the remodeling 
 phenomena that take 
 place in 100% popg
time - averaged height surfaces , h(x ,  y) , 
 reflect the spontaneous curvature of a system by removing long - wavelength 
 temporal fluctuations of the membrane .
h(x ,  y) was determined using the method of our previous -syn 
 study ( see the si ) .
figure 2a presents h(x ,  y) for -syn100 bound to pure popg and 1:1 pg : pc bilayers determined over 
 the last 5 s of the simulations .
we quantified h(x ,  y) 
 by determining the percent excess area for each system as ( 1  ah(x , y)/axy )  
 100% , where ah(x , y ) is the area along the height surface and axy is the projected area ( see 
 the si ) .
there 
 is a significant increase in the percent excess area ( figure 2b , blue ) in the popg system ( 0.51% ) compared with 
 the 1:1 mixture ( 0.30% ) ( see supplemental table 
 1 ) . on a per - protein basis
, the magnitude of the induced spontaneous 
 curvature appears to be small on the scale of global membrane remodeling . 

however , the cumulative effect imparted by multiple proteins organizing 
 in a localized membrane region could induce enough curvature stress 
 to breach the energy threshold required for membrane remodeling . as 
 will be discussed below ,
recent work by the voth group shed light 
 on an important phenomenon where linear aggregation of n - bar domain 
 proteins occurs prior to macroscopic membrane remodeling . a similar mechanism for protein aggregation / alignment 
 may occur for -syn100 , acting as local nucleation 
 points for tubule formation . an additional set of simulations presented 
 below will expand on this point .
( a ) time - averaged height surfaces , h(x ,  y) , 
 for 1:1 pg : pc ( left ) 
 and popg ( right ) , determined over the last 5 s of the simulations
( b ) percent excess area per protein ( blue ) 
 and integrated total lipid order ( green ) for 1:1 pg : pc and popg .
pg : pc ( top ) and popg 
 ( bottom ) ( solvent , gray ; headgroup , cyan ; carbonyl - glycerol , green ; 
 acyl - chain , magenta ; -syn100 , black line ) .
( d ) local 
 total order parameter sz(x , y ) for the membrane 
 near the protein ( top ) and opposite the protein ( bottom ) in 1:1 pg : pc 
 ( left ) and popg ( right ) ( warm colors = more ordered , cool colors = 
 more disordered ) . the insets correspond to pure lipid sz(x , y ) for each lipid composition .
the location of the 
 n - terminus of -syn100 is indicated with  
 ( the protein itself is not shown ) .
it has been proposed that subtle changes in the depth of 
 partitioning 
 of an ah into the hydrophobic acyl - chain region can dramatically alter 
 the induced ( local ) curvature and that this curvature is dependent 
 on the membrane s hydrophobic thickness .
figure 2c shows that -syn100 partitions slightly deeper in the pg : pc mixture when the 
 depth is measured relative to the lipid component density ( zpep ) ( results for all of the other 1600:1 -syn100 systems are presented in supplemental 
 figure 2 ) .
however , zpep is not 
 the most relevant measure of partition depth in the context of curvature 
 induction . we define the hydrophobic 
 thickness of the membrane , 2dc , as the z distance between the points with equal probability for 
 acyl - chain or solvent densities .
there are two structural parameters 
 that dictate the magnitude and sign of the induced spontaneous curvature : 
 ( 1 ) the monolayer hydrophobic thickness dc and ( 2 ) the extent to which the protein partitions into dc .
interestingly , 
 for a given protein density ( 1600:1 or 400:1 ) , regardless of the pc 
 mole percent , the protein partitions to the same depth relative to dc ( see supplemental table 
 1 ) .
however , what does change with pc mole percent is the hydrophobic 
 thickness ( both in pure and protein systems ) , which increases by 0.16 
 nm in popg relative to the 1:1 pg : pc mixture ( see supplemental table 1 ) .
although this shift is quite small  below 
 the resolution of the martini cg beads 
current theory on ah 
 curvature suggests that with equal relative partition depth , changes 
 in hydrophobic thickness of 0.2 nm are capable of doubling the spontaneous 
 curvature .
thus , these data suggest a 
 strong correlation between hydrophobic thickness and curvature induction .
a shift in the membrane s hydrophobic thickness modulates 
 how other structural features of the membrane respond to -syn100 s relative partition depth , particularly the acyl - chain 
 order parameter .
we characterized the acyl - chain conformations around 
 -syn100 using a local total lipid order parameter , sz(x , y ) ( see the si for details of the method ) .
figure 2d illustrates sz(x , y ) for the region of the monolayer near 
 the protein ( top ) and opposite the protein ( bottom ) for the systems 
 with 1:1 pg : pc ( left ) and popg ( right ) , with the corresponding data 
 for protein - free bilayers given in the insets ( see supplemental figures 2 and 3 for complete results for other 
 1600:1 -syn100 systems ) .
the lipids near the protein 
 are equally disordered for both systems , but the change relative to 
 the bulk is much greater for popg .
when we quantified sz(x , y ) as a function 
 of distance from the protein , we observed an asymmetry across the 
 bilayer , sz = sz , opposite  sz , protein .
this asymmetry extends 
 out to distances of 5 nm ( supplemental figure 
 3e , f ) , with the largest asymmetry developing in the popg system . 

when only the first shell of lipids is considered ( by integration 
 out to 1 nm from the protein ) , the order asymmetry shows a strong 
 correlation with the excess area , where the popg system again experiences 
 twice the effect relative to the 1:1 mixture ( figure 2b , green bars ) .
we speculate that because of the increased dc in popg , there is a greater volume beneath 
 the protein that must be accommodated by the neighboring lipid s 
 acyl chains , leading to more disordering of the lipids and giving 
 rise to increased order asymmetry .
the simulation 
 data comparing -syn100 in 100% pg and the 1:1 pg : pc 
 mixture suggest , but in no way prove , a direct correlation between 
 the depth of partition relative to the hydrophobic thickness , the 
 order parameter asymmetry across the leaflets , the induced positive 
 curvature , and tubulation .
however , this correlation does not take 
 into account the difference between the binding affinities for 100% 
 popg and the 1:1 pg : pc mixture .
one explanation for the role of the 
 affinity difference relates to the electrostatic repulsion between 
 pg headgroups , which is lessened in the mixture . as a result ,
the 
 100% popg membrane is under greater lateral pressure than that of 
 the mixture .
binding of -syn can relieve this pressure by screening 
 lipid  lipid interactions through lys 
although current theory focuses on the 
 importance of protein partition depth relative to hydrophobic thickness , 
 it is possible that the protein inserts at the optimal zpep position ( figure 2c ) for tubulation 
 in the 100% pg bilayer .
parsing the relative contributions of 
 these driving forces  binding energy , partition depth , hydrophobic 
 thickness , and order perturbations  is far from trivial . in 
 an effort to isolate the binding - energy component , we engineered a 
 minimally altered variant of -syn100 that would 
 partition to the same depth in pure popg bilayers ( maintaining a constant dc and local curvature induction ) but have a 
 reduced kd .
s membrane 
 binding domain comprises seven imperfect heptad repeats with consensus 
 sequence xktkegvxxxx ( x = any residue ) .
we replaced the hydrophobic nac domain ( the sixth heptad ) 
 with a replicate of the fifth heptad ( gavvtgvtava  
 ektkeqvtnvg ) . the anticipated effect on kd and
the depth was uncertain , as the alteration reduces 
 the hydrophobicity while adding extra charged residues ( zero change 
 in net charge ) . because lys residues in -syn associate strongly 
 with pg headgroups , we suggest that any reduction in measured binding 
 affinity should be attributed to the loss in hydrophobicity .
we first tested the depth of partition and the order parameter 
 asymmetry of this nac - null protein using simulations , and figure 3a shows that indeed the engineered variant has nearly 
 identical binding depth and order parameter asymmetry as -syn100 .
the nac - null variant actually partitions slightly less 
 deeply , and this is manifested in a slightly greater curvature field 
 ( supplemental table 1 and supplemental figure 
 4a  c ) .
experimentally , we found that the binding affinity 
 of nac - null was reduced 6-fold , which is considerably less of an effect 
 than the lipid headgroup charge with the native -syn100 sequence but significant nonetheless .
we also found that at equal 
 bound protein density , the nac - null variant induced an approximately 
 50% reduction in tubulation ( figure 3b and supplemental figure 4d ) , also a smaller but significant 
 effect .
thus , on the basis of the similar partition depths and order 
 asymmetry along with the reduced kd , the 
 results for the engineered nac - null construct strongly suggest that 
 while there may be a range of partition depths over which tubulation 
 is possible , the binding energy is a major player in dictating whether 
 tubulation occurs . ( a ) comparison of protein partition depths and integrated 
 order 
 parameter asymmetries for -syn100 ( left ) and nac - null 
 ( right ) proteins .
( b ) experimental tubulation capacities at equal 
 bound protein density for popg + buffer ( black ) , popg + -syn100 ( blue ) , and popg + nac - null ( red ) .
( c ) comparison of excess 
 areas per protein for the low - density ( 1600:1 , blue ) and high - density 
 ( 400:1 , green ) systems for -syn100 ( left ) and nac - null 
 ( middle ) in popg and -syn100 in 1:3 pg : pc ( right ) . 

( d ) time - averaged height surfaces for high - density ( 400:1 ) -syn100 ( left ) and nac - null ( middle ) systems in popg and -syn100 in 1:3 pg : pc ( right ) .
the average protein position is indicated 
 with white spheres , and the n - terminus of the protein is indicated 
 with . because the nac - null 
 variant shows decreased affinity relative 
 to -syn100 in popg despite the presence of extra 
 lys residues , it is likely that binding of the native protein ( and 
 possibly the stability of the bound protein 
furthermore , 
 given the 60-fold reduction in affinity of -syn100 for 1:1 pg : pc versus popg , an effect that has previously 
 been shown to be electrostatically driven these findings strongly suggest at least 
 a two - stage binding process : ( 1 ) electrostatically driven adsorption 
 of the unfolded protein and ( 2 ) a combination of electrostatic and 
 hydrophobic stabilization of the -helical bound state .
we note that whereas our experiments capture 
 the full - binding process , the simulations probe only the second stage . 

binding energy not only dictates the equilibrium distribution of 
 bound and unbound protein but also reflects the strength ( stability ) 
 of the interaction between the protein and the lipids in its solvation 
 shell . a tighter coupling  be it between charged ( lys / pg ) or 
 hydrophobic groups  should be manifested as a larger , more stable 
 complex whose diffusion in the membrane will be slowed by size .
this 
 may increase the likelihood of stable , nucleating assemblies of proteins . 
 in an attempt to more deeply understand the binding energy difference 
 that dictates the reduced tubulation in the nac - null variant , we simulated 
 the two proteins ( -syn100 and nac - null ) at high 
 density on pure pg bilayers ( for details , see materials and methods 
 in the si ) .
figure 3d shows the calculated curvature 
 fields for -syn100 ( left ) and nac - null ( middle ) . 

the -syn100 system shows a broad area of positive 
 spontaneous curvature spanning well beyond the local region of a single 
 protein ( it should be noted that these images show a larger region 
 of membrane than those in figure 2a ) .
protein 
 alignment that reinforces the curvature fields between proteins . even 
 though nac - null induces a similar low - density curvature field and 

has the same depth and same order parameter asymmetry ( supplemental figure 4 ) , at high density it does 
 not display the same curvature - field reinforcement as -syn100 ( figure 3d , middle ) .
quantification 
 of these surfaces shows a 50% decrease in curvature capacity for high - density 
 nac - null ( figure 3c ) , matching the experimentally 
 observed decrease in tubulation ( figure 3b ) 
 remarkably well .
figure 3c shows that 
 in the case of the 
 native -syn100 sequence , the high - density per - protein 
 curvature field recovers that of the low - density ( single - protein ) 
 case .
this recovery is absent in the case of nac - null , suggesting 
 a loss of time - averaged helical alignment compared with the native 
 sequence .
we quantified this effect by time - averaged distance matrices 
 for amino acids in nearest - neighbor protein 
protein pairs ( supplemental figure 5 ) . by observing the temporal 
 stability within these distance matrices ( or lack thereof ) , we asked 
 the following question : does the stability of specific protein 
protein 
 alignment motifs ( which may correlate with binding energy ) correlate 
 with stabilization of long - range curvature fields ? despite limited 
 sampling , the data are consistent with the notion that the reinforcement 
 of the curvature fields in -syn100 correlates with 
 stabilization of protein  protein alignments . as hypothesized , 
 in the case of -syn100 the proteins sample a relatively 
 tight window of possible alignment states ( 25.2% unique states sampled ) . 

most interestingly , the nac - null results show a marked increase in 
 the transitions between states ( 50.4% ) .
the most recent theory for 
 ah - induced curvature induction suggests 
 a small range of depths over which positive curvature will be induced 
 for a given hydrophobic thickness . as proteins partition more deeply 
 into the bilayer , the effect is lost and can even be reversed to produce 
 negative curvature .
the data presented 
 thus far do not directly address this because relative to dc the simulated proteins all partitioned to 
 the same depth . in a purely computational experiment , we manipulated 
 this partitioning by artificially varying the charge of -syn100 ( via computational point mutations ) within the same lipid 
 mixture ( i.e. , the same dc ) .
indeed , the 
 results confirmed a high sensitivity of the curvature to subtle changes 
 in depth .
for example , we showed the ability to turn a 100% pc bilayer 
 with -syn100 ( deep partitioning , small dc , low curvature ) into a pg - like bilayer ( shallow partitioning , 
 small dc , high curvature ) . while -syn100 does not bind pure pc bilayers in the fluid phase , this 
 computational exercise is valuable in the context of understanding 
 the driving forces for curvature induction .
context , interpretation of the lost tubulation in the pg : pc mixture , 
 where the protein depth relative to dc is invariant , is complicated by the concomitant decreases in curvature 
 and affinity . in order to exaggerate the relationship among depth , 
 hydrophobicity , and curvature , we simulated a 400:1 system in a 1:3 
 pg : pc mixture . in this mixture ,
the protein again partitions to the 
 same position relative to dc as in popg . 

surprisingly , when we calculated the distance matrix for interacting 
 proteins in pg : pc mixtures , we found similar ( or even reduced ) mobility 
 as in the wild type ( supplemental figure 5d ) .
similar to the 400:1 popg system , this reduced mobility is accompanied 
 by a reinforcement of local curvature fields ( figure 3c , d ) , although the stabilized curvature field is less than 
 half as intense .
we can explain the reduced curvature intensity as 
 a result of a 0.14 nm reduction in dc in 
 going from the 400:1 popg system to the 1:3 pg : pc system .
however , in view of 
 the dramatically reduced binding affinity that we measured experimentally , 
 along with the observation of increased mobility of nac - null , the 
 reduced mobility of the protein was perplexing .
however , in the context 
 of a two - stage binding process and the fact that our experiments were 
 performed at equal bound protein density , interpretation of the data 
 becomes possible .
the loss in binding affinity likely reflects a loss 
 in electrostatic attraction between the unfolded , soluble protein 
 and the lipid headgroups .
however , once adsorbed , the folded and bound 
 protein is stabilized by a solvating lipid shell , primarily through 
 lys  pg contacts . in 100% pg ,
the lipids are free to bind and 
 unbind the protein without great penalty , as the lys groups can be 
 immediately stabilized by another pg . on the other hand , in the pg : pc 
 mixture , lipid exchange is likely slowed by the penalty of replacing 
 a lys  pg contact with a lys  pc contact . thus , lipid 
 diffusion ( binding / unbinding ) could be expected to be slowed in the 
 pg : pc mixture . on average this
may slow protein diffusion because 
 the time - averaged lipid  protein complex will be more stable . 

our simulations are not sampled well enough to test this long - time - scale 
 phenomenon with statistical certainty .
figure 4 summarizes much of the relevant 
 data presented thus far . as stated above
, there is a systematic increase 
 in hydrophobic thickness of native -syn100-containing 
 bilayers as the pg density increases ( figure 4 , black dashed line ) . as the hydrophobic thickness decreases from 
 2.0 to 1.9 nm ,
there is reduced lipid order asymmetry 
 that correlates with a reduction in curvature and is consistent with 
 loss of tubulation capacity .
when we incorporate the data for the 
 nac - null systems , in particular the result at high density , this correlation 
 fails .
the nac - null protein partitions less shallow than -syn100 , inducing an even greater hydrophobic thickness and lipid 
 order asymmetry ( curvature ) ( figure 4 , black 
  ) ; experimentally , however , nac - null has a reduced tubulation 
 capacity . for these reasons ,
we conclude that lipid order asymmetry 
 ( lost in the native sequence at 1:3 pg : pc ) is necessary but not sufficient 
 ( present in nac - null ) for tubulation .
colors demarcate 
 low - density ( 1600:1 , black ) vs high - density ( 400:1 , blue ) .
figure 4 also reiterates the point 
 that 
 at high density ( 400:1 ) , pg : nac - null and 1:3 pg : pc + -syn100 induce approximately the same amount of per - protein curvature . 

this shows that these induced curvature fields alone do not directly 
 correlate with tubulation , as the nac - null variant does tubulate vesicles 
 ( albeit 50% less than pure pg ) .
the data suggest 
 that even if a protein partitions to the appropriate depth in a membrane 
 with sufficient hydrophobic thickness ( and therefore imparts sufficient 
 lipid order asymmetry ) , the tubulation capacity is reduced if stable 
 protein  lipid complex interactions are not established ( as 
 in nac - null ) . however , in the 400:1 1:3 pg : pc + -syn100 system , stable protein 
lipid complex interactions are formed , 
 as evidenced by the stabilized curvature field ( figure 3d ) and the reduced protein mobility ( supplemental 
 figure 5d ) , yet reduced lipid order asymmetry reduces the stress 
 on the membrane below the tubulation threshold .
therefore , we conclude 
 that stability of the protein in the bound state ( lost in nac - null ) 
 is a necessary but not sufficient ( present in the native sequence 
 at 1:3 pg : pc ) component of the tubulation mechanism .
thus , it 
 appears that two constraints must be met in order for 
 -syn100 to tubulate a vesicle : ( 1 ) it must bind 
 with sufficient energy to slow the protein / lipid dynamics and allow 
 for nucleation of pretubule assemblies and ( 2 ) it must bind in a narrow window of depths , inducing a particular 
 hydrophobic thickness that can promote sufficient per - protein curvature . 

furthermore , because the nac - null variant still maintains some tubulation 
 activity , there must be a driving force present in the nac - null and 
 popg -syn100 systems but not in 1:3 pg : pc , one that 
 is not dependent on strong binding affinity and drives the formation 
 of a tubule .
we propose that this driving force is the energetic penalty 
 of induced lipid order asymmetry across the leaflets . for -syn100 to induce 
 tubulation of a large vesicle
we speculate that there exists a reinforced / nucleating -syn100 structure with high order asymmetry and that resolution 
 of this asymmetry may drive tubulation .
no experimental information 
 is available to suggest that such structures exist or to provide hints 
 concerning what those structures might look like . in a modest effort 
 to gain insight into how large - scale assemblies may promote tubulation , 
 we ran three simulations with hand - built assemblies ( consisting of 
 48 proteins ) embedded in a popg membrane .
we recognize that these 
 tubule simulations sample only three possible nucleating structures 
 and acknowledge that other computational techniques ( including more 
 aggressive coarse graining and mesoscopic 
 modeling ) may be better - suited for such investigations . 

nonetheless , this approach has allowed us to investigate the possible 
 behaviors of acyl chains in the remodeling process .
each system contained 
 85  296 lipids ( 5  200  608 total cg beads ) and 
 48 proteins arranged in one of three unique conformations ( spoke , 
 circumferential , and carpet ) .
the local protein density for each system 
 ( defined as the protein : lipid ratio within 1 nm of the protein ) was 
 set at 1:50 , just below the experimental saturation density 
 observed with anionic and zwitterionic / anionic lipid mixtures .
figure 5 displays the initial starting configuration 
 and the final snapshot for the spoke conformation .
for all three protein conformations , membrane remodeling 
 occurred very rapidly . during the first 40 ns ,
an initial 
 invagination spanned the central ring of the membrane encompassing 
 the inner 5 nm of the protein spokes . by 100 ns ,
by 300 
 ns there was a fully formed nascent tubule ( 25 nm in height ) 
 surrounded by undulating popg bilayer .
it is possible that if these simulations 
 were allowed to run for much longer times , the highly ordered protein 
 conformation might diffuse apart .
while we can not rule this out , we 
 do note that after 300 ns the carpet conformation began to realign 
 into radial ( spoke ) and circumferential orientations to orient -syn 
 to the tubule s curvature field ( supplemental 
 figure 9d ) .
the system 
 includes 48 -syn100 proteins ( yellow ) and 85  296 
 popg lipids ( blue ) .
the n - terminus 
 of each protein is indicated by . ( b ) snapshot at 300 ns simulation 
 time .
figure 6a shows the total lipid order parameter sz(x , y ) for the protein monolayer ( top ) and 
 the opposite monolayer ( bottom ) calculated over the first 20 ns ( left ) 
 and the last 20 ns ( right ) of the simulation of the spoke conformation 
 ( results for the circumferential and carpet conformations are presented 
 in supplemental figures 8 and 9 , respectively ) . 
 in all three systems , there is a large shift in the total lipid order 
 toward greater disorder and eventually the formation of antialigned 
 chains [ i.e. , negative sz(x , y ) ] . as the tubule 
 forms , this shift in order is accompanied by a transition toward a 
 symmetric sz(x , y ) profile across the 
 bilayer ( figure 6b , c and supplemental figures 8 and 9 ) . by the end of the tubulation 
 event ,
the two monolayers have similar sz(x , y ) profiles [ see supplemental figure 10 for the detailed time course of sz(x , y ) for 
 the spoke conformation ] .
this change is different than the changes 
 observed for the low - density -syn100 systems ( figure 2d and supplemental figure 3 ) where a stable asymmetry is established . because of the high protein 
 density
, the limited numbers of lipids near the protein are forced 
 to accommodate the void volume beneath each protein , inducing increased 
 splay away from the local normal .
( a ) sz(x , y ) for 
 the protein - containing leaflet ( top ) 
 and opposite leaflet ( bottom ) at the early stage ( 0 to 20 ns , left ) 
 and the late tubule stage ( 830 to 850 ns , right ) .
the color map reference 
 ( black ) is set at sz for 
 pure popg .
( b ) time course of the mean sz for the protein ( black ) and opposite ( red ) monolayers 
 as the tubule develops .
( c ) time course of the average difference 
 sz across the 
 membrane ( sz = sz , opposite  sz , protein ) . at the core of the protein assembly ,
the increased 
 splay is significant 
 enough to drive antialignment of the acyl chains ( chain orientation 
 orthogonal to the local bilayer normal ) .
we 
 quantified this monolayer coupling by determining the total number 
 of interleaflet acyl - chain contacts in regions near the protein and 
 regions in the bulk membrane .
the number of first - shell acyl - chain - to - acyl - chain interactions ( inset ) 
 exhibits an 2-fold increase in the number of contacts near 
 the protein relative to the bulk .
this is a consistent trend for all 
 three protein conformations ( see supplemental 
 figure 11 ) .
total number of interleaflet contacts ( acyl - chain - to - acyl - chain ) 
 for lipids near the protein ( black ) vs lipids in the bulk ( red ) in 
 the spoke conformation .
numerous 
 computational studies have explored protein - driven membrane 
 remodeling . a major focus of many of these studies
bar - domain proteins are a curvature - inducing 
 class of proteins that can contain both a rigid scaffolding and an 
 ah domain , and similar to -syn , these proteins 
 have been shown to both sense and generate curvature . in n - bar proteins , 
 the ah plays an essential role in curvature generation and the stability 
 of the membrane tube by stabilizing dimer 
furthermore , evidence exists that the ah , and not the scaffolding 
 domain , is responsible for the protein s curvature - sensing 
 abilities .
ah curvature induction can be so extreme as to promote membrane 
 scission , as is the case for the enth domain of epsin and the monomeric family of synucleins ( -syn , -syn , 
 and -syn ) . 

there is a balance between the remodeling effects induced by the rigid 
 scaffold and those driven by the ah , and elucidating the role of each 
 mechanism remains an active area of investigation .
there are several potential complementary mechanisms 
 for -syn - induced 
 membrane curvature and tubulation .
we have shown that at equal bound 
 density the protein has a dramatically reduced effect on tubulation 
 of pg : pc mixtures compared with popg bilayers .
we correlated this 
 effect with an experimentally measured decrease in binding affinity 
 ( 60-fold ) and a simulated increase in hydrophobic thickness , 
 partition depth , and order parameter asymmetry .
this finding raised 
 the question of whether depth and order asymmetry alone can explain 
 tubulation differences .
to at least in part address this , we designed 
 an -syn variant lacking the nac domain ( nac - null ) , which we 
 predicted would have reduced affinity but partition to approximately 
 the same depth as wild - type -syn in popg vesicles having consistent 
 hydrophobic thickness .
removal of the nac did in fact reduce binding 
 to popg vesicles ( by 1 order of magnitude ) .
this more mild 
 reduction in affinity correlates with a more mild reduction in tubulation , 
 despite the fact that the nac - null mutant partitions to a slightly 
 less shallow depth than the wild - type protein ( and actually slightly 
 increases the induced curvature field ) and has the same impact on 
 the order parameter asymmetry .
this finding suggests that depth and 
 order asymmetry alone do not explain the reduction in tubulation , 
 though it certainly does not rule out their potential contribution 
 in the case of the pg : pc mixture ( supplemental 
 figure 5d ) .
rather , our simulations suggest that the nac domain 
 may be essential in stabilizing protein  lipid complexes and , 
 in so doing , promoting organization on the bilayer surface .
indeed , 
 a very recent study supports our findings on the importance of the 
 hydrophobic core of the nac domain in -syn - induced membrane 
 remodeling . using supported lipid bilayers
, that study shows a loss 
 of induced membrane defects and reduced membrane - bound protein cluster 
 size with an -syn variant lacking the hydrophobic sixth heptad . in a recent study ,
lipowsky discussed 
 how the adhesion energy of 
 an adsorbing particle can induce spontaneous membrane curvature .
using n - bar as an example , the theory predicted 
 that the remodeling capacity of the n - bar scaffolding domain is directly 
 coupled to the adhesion energy it gains upon interacting with the 
 membrane .
if the adsorbing n - bar protein imparts sufficient adhesion 
 energy with the membrane ( i.e. , greater that the bending energy required 
 to deform the bilayer ) , the membrane will buckle and adopt the intrinsic 
 curvature of the protein .
recent work from the voth group has characterized 
 the role of binding energy for exactly this n - bar / membrane system . using their recently developed hybrid cg model
, 
 the authors varied the cg n - bar binding affinity for the lipid headgroup . 
 in doing so
, they were able both to inhibit protein aggregation and 
 macroscopic membrane remodeling ( low adhesion energy ) and to induce 
 disruptions and tears within the membrane ( high adhesion energy ) . 
 because -syn lacks a scaffolding domain , the notion of adhesion 
 energy must be taken in a slightly different context .
instead of the 
 adhesion energy coupling the membrane to a rigid scaffold domain , 
 weaker binding would increase lipid exchange within the lipid solvent 
 shell around the protein .
lipid complex , potentially accelerating 
 the protein dynamics on the surface and reducing the likelihood of 
 nucleating stable protein assemblies .
this is not to say that 
 partition depth and hydrophobic thickness 
 are not significant .
it was surprising to us that given similar relative 
 partition depths , such a small change in the hydrophobic thickness 
 in the pg : pc mixture ( 0.16 nm thinner than pg ) might correspond 
 to a such a large experimental observable .
however , the recent theory 
 of ah curvature induction developed by may s group predicts 
 a partition depth and hydrophobic thickness dependence on the spontaneous 
 curvature and bending rigidity of a membrane . as the hydrophobic thickness increases , the range and magnitude 
 of the predicted spontaneous curvature is expanded ( e.g. , an increase 
 of 0.2 nm in 2dc  on the order of 
 the difference we observed between pure pg and the 1:1 mixture  corresponds 
 to a doubling of the curvature intensity for the same partition depth ) .
all of this leads to the following question : 
 are individual curvature fields the necessary piece , or is it organization 
 of the fields that dominates ? perhaps it is a combination of the two . 

our simulation and experimental results suggest that lipid order asymmetry 
 ( either through protein partition depth or membrane hydrophobicity ) 
 and binding affinity are both necessary but not sufficient components 
 of the ah tubulation mechanism .
more generally speaking , increased 
 spontaneous curvature is the 
 result of an area mismatch between monolayers , and it has been shown 
 experimentally through the use of transiently asymmetric lipid vesicles 
 ( protein - free ) that an increase in area mismatch by as little as 1% 
 is enough to initiate the macroscopic remodeling of lipid vesicles . in those experiments , the transient asymmetry relaxed with time 
 as a result of lipid flip - flop .
the rate of lipid flip - flop is typically 
 very low ( corresponding to a time scale of minutes to hours ) in pure 
 lipid vesicles .
however , ahs have been shown to greatly enhance lipid 
 flip - flop rates . in the case of -syn tubulation 
 experiments , where a high concentration of -syn is added to 
 solution , the relationship among binding kinetics , protein reorganization 
 ( e.g. , into organized pretubule structures )
, the development of local 
 curvature stresses and the resulting curvature fields , lipid flip - flop , 
 and tubulation remains unknown . in one scenario , where binding is 
 presumed to be much faster than tubulation , every lipid in the outer 
 leaflet of the vesicle would be occupied in forming the solvation 
 shell of a neighboring protein . in that case
our simulations were designed 
 to test a second scenario in which 
 the nucleation of tubules occurs rapidly and locally .
indeed , high 
 local densities can induce curvature and recruit more proteins . in this case , accelerated local lipid flip - flop 
 seems likely in order to relieve the local curvature strain . in order 
 to test this
, we eliminated the area mismatch between the leaflets : 
 the small systems had protein on both leaflets , while in the large 
 systems ( protein in only one leaflet ) we eliminated the excess area 
 by removing lipids .
this choice was made in order to probe whether 
 the proteins themselves can still cause remodeling and tubulation 
 in the case where there is time for lipid flip - flop .
previous work by our group has focused 
 on the coupling of lipid 
 order across the bilayer leaflets , where we identified acyl - chain 
 interdigitation as central to the propagation of order across monolayers 
 in phase - separated bilayers . in the case 
 of the -syn
tubulation simulations presented here , we have 
 also observed interleaflet coupling , though the character of the interdigitation 
 is quite different .
as a tubule develops , lipids in both monolayers 
 adopt an antialigned conformation , increasing favorable chain 
chain 
 interactions between the monolayers ( see figure 6 and supplemental figure 11 ) . the drive 
 toward order parameter symmetry observed in the tubulation simulations , 
 which is coupled to these additional contacts , may provide an important 
 additional piece of the biophysical driving force for tubulation . in this study we have discussed -syn100-induced 
 membrane remodeling / tubulation in the context of in vitro studies 
 showing that -syn tubulates synthetic vesicles . in vivo , -syn has been shown to interact with both the inner 
 and outer membranes of the mitochondria .
overexpressed 
 -syn , which is associated with parkinson s disease , induces fragmentation of mitochondria and impairs mitochondria complex 
 1 activity .
mitochondria have 15% 
 anionic lipids , the majority of which is cardiolipin ( an anionic lipid 
 with four acyl chains and a headgroup charge of 2 ) .
this association of 
 -syn with mitochondria coupled with its affinity for cardiolipin 
 lead us to predict that many of the mechanisms discussed here are 
 at play in this pathological condition .
the different structural characteristics 
 of cardiolipin may result in a unique remodeling capacity relative 
 to more typical anionic phospholipid mixtures ( e.g. , popg : popc ) .
 we have investigated 
 the membrane remodeling capacity of the n - terminal 
 membrane - binding domain of -synuclein ( -syn100 ) . using fluorescence correlation spectroscopy and vesicle clearance 
 assays , 
 we show that -syn100 fully tubulates popg 
 vesicles , the first demonstration that the amphipathic helix on its 
 own is capable of this effect . 
 we also show that at equal density 
 of membrane - bound protein , -syn has dramatically reduced affinity 
 for , and does not tubulate , vesicles composed of a 1:1 popg : popc mixture . 
 
 coarse - grained molecular dynamics simulations suggested that the difference 
 between the pure popg and mixture results may be attributed to differences 
 in the protein s partition depth , the membrane s hydrophobic 
 thickness , and disruption of acyl chain order . to explore the importance 
 of these attributes compared with the role of the reduced binding 
 energy , we created an -syn100 variant in which we 
 removed the hydrophobic core of the non - amyloid component ( nac ) domain 
 and tested its impact on pure popg vesicles . 
 we observed a substantial 
 reduction in binding affinity and tubulation , and simulations of the 
 nac - null protein suggested that the reduced binding energy increases 
 the protein mobility on the bilayer surface , likely impacting the 
 protein s ability to assemble into organized pretubule structures . 
 
 we also used simulations to explore a potential role for interleaflet 
 coupling as an additional driving force for tubulation . 
 we conclude 
 that symmetry across the leaflets in the tubulated state maximizes 
 the interaction energy of the two leaflets and relieves the strain 
 induced by the hydrophobic void beneath the amphipathic helix . 
Results
Discussion