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 ) .