lipid membranes provide 
 a key organizing principle for life : they 
 allow compartmentalization into cells and organelles , and two - dimensional 
 organization of enzymatic and signaling components , and exert marked 
 surface effects on biological fluids in their proximity .
multilayer 
 stacks have been extensively studied as a homogeneous model system 
 for physical investigation of membrane properties . however , a single 
 pair of bilayers coming close to one another , as can occur prior to 
 membrane fusion or in tight junction formation , represents a subtly 
 different physical scenario : the proximal leaflets are separated by 
 a thin layer of water , but the distal leaflets remain well - hydrated .
this inhomogeneous prefusion system is difficult to study directly , 
 but a large body of work , both simulation and experimental , has addressed 
 the more general problem of altered lipid and water dynamics at interacting 
 surfaces . although biological membranes contain a complex mixture 
 of different components , the fluid  fluid interfaces and fundamental 
 confinement behaviors that concern us here can be reproduced by much 
 simpler lipid bilayer systems .
interfacial effects in well - hydrated 
 bilayers have been probed by a number of methods , while the slowing of lipid and water diffusion as 
 multilayer stacks are progressively dehydrated has been characterized 
 extensively by spectroscopic and scattering - based experimental measures as well as molecular dynamics simulations or combined 
 methods .
we have previously performed simulations of 
 liposomal membrane 
 fusion where we predict that the interacting membranes may stably 
 approach each other prior to fusion .
this 
 prediction is consistent with analysis of peg - induced fusion experiments 
 by lentz and co - workers .
furthermore , 
 electron microscopy and fluorescence resonance energy transfer experiments 
 have shown that docked vesicles can form extended and stable areas 
 of tight contact , although the nanoscale architecture of these contact 
 areas has yet to be established .
our simulations 
 suggest that the dynamics of water and lipids at such membrane interfaces 
 can have a marked effect on overall fusion dynamics .
in addition , 
 we have developed measures based on theories of glasses that allow 
 us to quantify anomalous diffusion in simulations of fluids near interfaces 
 in a straightforward manner : these methods helped demonstrate a general 
 effect of dynamic heterogeneity that slows fluid diffusion near surfaces .
an alternate approach was also developed by 
 netz and co - workers . here ,
we apply these 
 methods to the close approach of two lipid bilayers , showing that 
 this confined  double interface  between two bilayers 
 leads to an even more pronounced effect on dynamics .
we primarily 
 concern ourselves with this striking effect on dynamics rather than 
 equilibrium static structures .
most surprisingly , we predict that 
 the diffusion of lipids in the two proximal leaflets becomes coupled 
 across the water gap between them , while the distal leaflets remain 
 largely unperturbed .
this coupled diffusion leads to a dramatic slowing 
 down of dynamics between the inner leaflets as the lipid bilayers 
 approach : water diffusion slows down by more than 1000-fold , while 
 the inner lipid diffusion constant goes down by a factor of 10 .
one subtle yet important detail of the inhomogeneous systems that 
 we examine here is that they represent metastable yet nonequilibrium 
 intermediates in the fusion process .
the marked slowing and even glassy 
 dynamics of water in this system further slows relaxation of the system , 
 meaning that such nonequilibrium intermediates can persist at much 
 longer time scales than would otherwise be anticipated .
recent 
 work has suggested that the transition state for membrane 
 fusion stalk formation involves exposure and even contact of lipid acyl tails . in at least some model systems 
 for fusion
, another step precedes stalk formation : the close apposition 
 of two interacting lipid bilayers and the dehydration of the contact 
 area between them .
the high free energy barrier 
 associated with dehydration has long been recognized and approached 
 theoretically .
together , the coupled 
 and slowed lipid motion may help explain how lipid membranes can form 
 a relatively long - lived metastable apposed intermediate prior to fusion 
 stalk formation : fusion stalk nucleation and expansion each depend 
 on the diffusional motion of lipid tails . with current computational 
 resources , we can make a quantitative assessment of the altered dynamics 
 of apposed bilayers that contribute to fusion .
the dynamics 
 of partially hydrated lipid bilayers are particularly 
 interesting from a physical point of view because the system comprises 
 two mobile and interacting components , the lipids and the water between 
 them .
we use both conventional mean squared - displacement measurements 
 and event - based measures from from the physics of glassy systems to 
 help quantitate motion within this heterogeneous coupled environment . 
 using such measures we find , as expected , a slowing of lipid and water 
 diffusion as the two bilayers approach one another .
strikingly and 
 unexpectedly , the motion of lipids in the apposed inner leaflets becomes 
 coupled across the intervening water layer .
this occurs at a level 
 of hydration where the static structure of the bilayer is preserved . in order to examine the 
 dynamics within and between two bilayers
as they approach one another , 
 we performed a series of atomic resolution molecular dynamics simulations 
 of two lipid bilayers with a varying amount of water between them , 
 as shown in figure 1 .
shown in panel a is the 
 simulation geometry : two bilayers ( red 
 and green ) with a varying amount of water between them ( blue ) . in 
 panel
b the pair of opposed inner leaflets are rendered at a ratio 
 of 3 waters per lipid . at this ratio , extensive headgroup 
the simulated system 
 consists of two bilayers with 256 or 128 palmitoyl - oleyl - phosphocholine 
 ( popc ) molecules per bilayer , making the number of lipid molecules 
 in the inner two leaflets nl = 128 or 
 256 .
the amount of water between the two bilayers was varied 
 from nw = 16 to 0 waters per inner leaflet 
 lipid , 
 resulting in the headgroup  headgroup spacing shown in figure 2 .
additionally , 32 waters per outer leaflet lipid 
 were maintained at the  outside  of the two bilayers 
 to maintain a region of bulk water between the periodic images of 
 the system and thus model a pair of bilayers rather than a multilayer . 

compartment and similarly to maintain 
 bulk lipid dynamics in the outer leaflets of the bilayers .
bulk dynamics 
 were assessed by comparison to the dynamics of a single lipid bilayer 
 with 64 waters per lipid and to the results reported in prior simulation and experimental work .
headgroup center of mass distance between the inner leaflets in z - coordinates , as a function of number of waters per lipid 
 between the inner leaflets .
the distance plotted is the z - distance between the centers of mass for all headgroup atoms of 
 each inner leaflet .
this system is not in 
 strict thermodynamic equilibrium with regard 
 to water , as water molecules will be more likely to cross from the 
  outer  to the  inner  compartment than 
 the reverse .
however , such crossings occur on very slow time scales : 
 total water crossings ( in either direction ) were observed at a rate 
 of roughly 0.07  0.02 per water per microsecond .
the distribution 
 of water between compartments is thus metastable on the time scales 
 considered here .
average diffusion 
 constants were calculated in each simulation 
 as a function of the ratio of water molecules in the inner compartment 
 to lipid molecules in the inner bilayers of that simulation and are 
 plotted in figure 3 . as the number of water 
 molecules decreases , the diffusional dynamics of the outer leaflets 
 remain constant .
the inner leaflet diffusion slows substantially , 
 and the diffusion of the water between the bilayers slows to approximately 
 that of the outer leaflet lipids .
similar effects have been reported 
 before , both in simulations and in experiments 
 on lipid multilayers .
diffusion coefficients were calculated from a linear fit to the mean 
 squared displacement as a function of time .
a two - dimensional model 
 was used for fitting displacements ; this is appropriate for lipid 
 diffusion and water diffusion at low hydration . at full hydration
, 
 the water diffusion will be more appropriately fit by a 3d model , 
 but the model error is bounded at 50% ( r = 6dt versus 4dt ) , while the observed diffusional slowing effect is several orders 
 of magnitude .
the slowing of 
 lateral diffusion in both inner leaflets raises the question of whether 
 individual lipid motion might be correlated in the two inner leaflets , 
 as in a coupled system . to measure the extent to which this diffusion 
 is coupled , we utilize event - based measures of diffusion :
an exchange 
 event is the time it takes for a particle to diffuse a characteristic 
 distance d , such as the typical nearest neighbor 
 distance .
the exchange time tx is the time between consecutive exchange events : its average 
 is analogous to the time interval between steps in a random walk taken 
 and is therefore inversely related to the diffusion constant d = c/tx , where d is the bulk diffusion 
 constant , and c is a constant factor that depends 
 on the exchange event distance d and the physical 
 details of the system being studied . to assess diffusional coupling ,
we calculate 
 the ratio dref / d , where d is an standard diffusion constant and dref is a diffusion constant calculated using a reference 
 frame derived 
 from lipids in the opposite leaflet .
this reference frame is defined 
 by the center of mass of the closest four lipids in the opposite leaflet , 
 so the coupled diffusion constant reflects average motion lipid relative 
 to nearby lipids in the opposite leaflet . as above
, we calculate the 
 exchange time txref and use it to define the coupled 
 diffusion constant dref = c/txref. here , we have set the 
 exchange event distance d = 0.28 nm , the first peak 
 in the water  water radial distribution function . for 
 an uncoupled system , both the diffusing particle and the reference 
 point for coupling diffuse independently , and therefore
, the ratio dref / d = 2 , twice as fast as 
 the single particle diffusion of d ( as in a random 
 walk with two steps per time step ) .
if diffusion is strongly coupled , 
 the ratio will be smaller : diffusion away from particles in the opposite 
 leaflets is slower than overall diffusion , making the value of the 
 ratio dref / d < 1 .
the inner leaflets of the double - bilayer system display this coupled 
 behavior as they approach one another .
as shown in figure 4 , both leaflets display uncoupled diffusion at 16 
 water molecules per lipid .
( dref / d  2 ) . at closer approach , the coupling ratio progressively 
 decreases ,
coupling 
 is estimated as the ratio between an uncoupled estimate for the diffusion d and diffusion relative to the opposing leaflet dref : diffusion relative to a reference frame 
 defined by the center of mass of the closest 4 lipids on the opposing 
 leaflet .
the normal diffusion d for the top lipid is calculated purely on the basis of its motion 
 relative to the leaflet center - of - mass , while the dref is measured relative to the center of mass of the 
 bottom lipid ( and three other neighbors ) . when these motions are strongly 
 correlated , the estimated coupled diffusion constant will be slower 
 than the uncoupled diffusion constant .
this diffusional coupling between 
 lipid molecules on opposite sides of the water gap suggests a physical 
 interaction between phospholipid headgroups , either direct or mediated 
 by water .
water interfaces feature strong 
 hydrogen bond interactions between water and the lipid headgroups , in addition to extremely favorable water 
water hydrogen 
 bonds in the inner water region versus water  headgroup hydrogen 
 bonds .
these data 
 are plotted in figure 5 and show a crossover 
 at approximately 6 waters / lipid : below this level of hydration , water 
 molecules are on average more likely to be hydrogen - bound to lipids 
 than to other waters . this crossover coincides with the onset of coupling 
 between opposite inner - leaflet lipids , suggesting that the lipid  water 
lipid 
 hydrogen bonding network may in part be responsible for the observed 
 diffusional coupling .
hydrogen bonding partners for confined water . the average 
 number 
 of water  lipid and water 
water hydrogen bonds is plotted 
 per water molecule in the inner compartment between bilayers as a 
 function of water - to - lipid ratio .
the inset shows the number of water - to - lipid 
 hydrogen - bonds per inner - leaflet lipid . to examine how this behavior may affect membrane fusion dynamics , 
 we calculated diffusional coupling between lipids in the apposed surface 
 patch between two vesicles prior to fusion .
calculations were performed 
 on the vesicle fusion system we have previously reported , using lipids starting in a 3.14 nm central contact region . over a 10 ns interval
prior to stalk formation , 
 the ratio dcoupled / duncoupled was 0.83 , indicative of substantial diffusional coupling 
 across the water layer between vesicles .
these marked 
 changes in lipid and water diffusion between apposed bilayers appear 
 to be primarily a dynamic effect , driven in part by the change in 
 hydrogen bonding patterns , which we would classify as subtle rather 
 than gross structural changes .
to rule out gross structural changes , 
 we calculated water radial distribution functions ( figure 6a ) and lipid tail order parameters ( figure 6b ) .
these indicate that fluid water structure and 
 lamellar bilayer structure are both mostly preserved at 4 waters / lipid , 
 a level of hydration at which coupled diffusion has clearly emerged . 

lamellar structure and fluid water structure break down at approximately 
 1 water / lipid , a much lower level of hydration .
our simulations show 
 a trend toward lower lipid tail order in the inner leaflets at lower 
 levels of hydration ; prior studies on equilibrated multilayer stacks 
 have shown an increase in tail order .
this difference is likely due to differences in area per lipid headgroup , 
 since acyl tail order parameters shift in rougly proportional response 
 to lipid lateral area .
( a ) the 3d radial 
 distribution 
 function ( rdf ) of water confined between two bilayers shows the appearance 
 of structure dictated by the presence of the lipid bilayer headgroups , 
 at very close approach ( approximately nw / nl < 4 ) .
( b ) lipid tail sz order parameter calculated for the popc sn1 chain 
 at varying hydration levels shows decreased ordering for closer approach . as average water diffusion 
 slows from bulk values , it also becomes 
 markedly heterogeneous in space and time ; the spatial heterogeneity of the system leads to temporal heterogeneity 
 in diffusion , leading to observations of dynamics analogous to those 
 in glassy systems : the decoupling of diffusion from viscosity and 
 anomalous diffusion . to test for these changes in a quantitative manner
, 
 we use the exchange time tx , the time between consecutive exchange events , and compare 
 this to the persistence time tp , the time it takes to undergo an exchange event starting from 
 any configuration at any time ( i.e. , not starting at a previous exchange 
 event ) . observing a single water molecule over time starting 
 from some initial configuration , the time until the first exchange 
 event is a persistence time ( because the starting time is essentially 
 a random point between exchanges ) , and then the subsequent intervals 
 between events are exchange times . under normal fluid conditions , 
 the average persistence and exchange 
 times should be the same : exchange events should be uniformly and 
 randomly distributed over time . in dynamically heterogeneous 
 systems , however , there will be times when there are rapid successions 
 of exchange events followed by long waits ; this will lead to the ratio 
 tp/tx to be significantly 
 different from 1 .
figure 7 shows the 
 ratio tp/tx for water between 
 the bilayers 
 as a function of bilayer separation .
this difference becomes 
 even more pronounced when the exchange event displacements are calculated 
 relative to the closest set of lipid headgroups , in effect correcting 
 for the lipid diffusion .
ratio of average persistence time tp and exchange time 
 tx as 
 a function of 
 bilayer separation .
dynamic heterogeneity is readily evident in this 
 system . in the regime where slowed diffusion is observed ,
this heterogeneity 
 and the associated nonuniformity of diffusion is of even greater magnitude 
 when water diffusion is measured relative to the nearest lipids , suggesting 
 a coupling between the water and lipid diffusion .
for reference , the 
 ratio tp/tx is also plotted for 
 water close to a single lipid bilayer .
while some dynamic heterogeneity 
 is present in this single - interface regime , it is markedly lower .
this altered ratio tp/tx reflects an altered ratio between 
 diffusion and viscosity , 
 leading to a breakdown of the stokes 
part of this process can be ascribed to the self - lubrication of 
 water motion : the presence of water facilitates the breakup and reconfiguration 
 of hydrogen bonds of other water molecules .
viscosity 
 decoupling at bilayer separations larger than the close approach where 
 water  water contacts become rare .
we have previously shown 
 how this is a general feature of fluids at interfaces that is strengthened 
 by favorable molecular interactions such as those between water molecules 
 and lipid headgroups . here ,
partially hydrated multilamellar stacks have 
 been observed to undergo 
 area condensation in a manner that depends on both acyl chain length 
 and unsaturation . the inhomogeneous system considered 
 here , two bilayers approaching each other , is thus composed of inner 
 and outer leaflets at levels of hydration where the corresponding 
 homogeneous multilayer stacks would have different lateral lipid densities . 

to control for bilayer stresses that might be introduced as a result 
 of such asymmetry , we performed an additional set of simulations where 
 the inner leaflets were initialized to a lipid lateral density 10 
 anticipated lipid density differences in fully hydrated bilayers versus 
 partially hydrated multilayer stacks , using data for dopc multilayers 
 as a reference .
these bilayers of asymmetric 
 lipid density displayed a similar slowing of inner - leaflet lipid and 
 water diffusion to symmetric lipid bilayers ( supporting 
 information figure s1 ) .
they also displayed diffusion - velocity 
 decoupling and coupled diffusion ( supporting information figure s2 ) .
structural parameters for the asymmetric bilayers are 
 plotted in supporting information figure 
 s3 .
a comparison of lateral tension profiles between symmetric and 
 asymmetric bilayers is given in supporting information figure s4 , and the chemical potential difference of removing randomly 
 selected water molecules from either the fully hydrated region or 
 the partially dehydrated region , as calculated via free - energy perturbation 
 simulations for both symmetric and asymmetric bilayers , is plotted 
 in supporting information figure s5 .
our study of water dynamics at bilayer interfaces 
 has been motivated 
 by the close approach prior to membrane fusion of two phospholipid 
 bilayers with a thin water layer between . in initial simulations of 
 membrane fusion
, we noted that this water layer had unusual dynamics 
 and that perturbing the fine structure of that water layer altered 
 fusion dynamics in our simulations .
we have developed concepts from 
 the theory of glasses to measure these dynamics in greater detail ; 
 we found that altered fluid dynamics are a fundamental property of 
 surface interfaces and that interactions between the surface and fluid 
 ( such as lipid 
water hydrogen bonds ) serve to strengthen this 
 effect . here , we bring these tools back to the study of water 
 layers between 
 two phospholipid membranes . we find that the double interface thus 
 produced further accentuates nonuniform diffusion in these thin water 
 layers , resulting in glassy water dynamics in our simulations . both 
 water and lipid dynamics slow as the bilayers approach each other , 
 but the slow - down is only glassy for the water , not for the lipids . 

this is likely due to the self - lubricating properties of water : a 
 water molecule is more likely to undergo diffusional motion when the 
 molecule has other water molecules as immediate neighbors : this creates 
 a self - reinforcing effect on water dynamics .
we also find that 
 water acts to couple the dynamics of lipids in 
 opposing bilayers , such that lipids in the inner leaflets of these 
 membranes on average codiffuse with their partners across the water 
 gap .
these properties begin at a ratio of approximately 5 water molecules 
 per inner - leaflet lipid in popc bilayers .
strikingly , we observe similar 
 coupled diffusion in simulations of vesicle pairs prior to fusion .
we therefore believe that water - mediated coupling acts to slow 
 lipid dynamics in lipid vesicles prior to membrane fusion ( such as 
 the peg - mediated liposomal fusion measured by lentz and co - workers 
 where liposomes partially dehydrate prior to fusion ) and that this prolongs the aggregated and partially dehydrated 
 but prefusion step . such diffusional slowing mediated by coupling 
 between inner - leaflet membranes may also be important in maintaining 
 restricted diffusion in epithelial tight junctions , where free diffusion 
 of membrane probes is correlated to the ability to exchange between 
 proximal ( coupled ) and distal ( uncoupled ) leaflets .
the extent to which diffusional slowing affects the rates 
 of different physiological fusion reactions such as viral membrane 
 fusion and synaptic membrane fusion remains to be determined .
we speculate 
 that some of the regulatory machinery for fast membrane fusion such 
 as occurs at presynaptic termini may act to help avoid kinetic
 traps  
 such as the slowed and coupled movement of lipids we observe here .
simulations were performed 
 with two popc lipid bilayers of 128 
 or 256 molecules each separated by a variable number of waters : 0 
 to 16 waters / inner leaflet lipid in the inner water layer and 32 water / outer 
 leaflet lipid in the outer water layer .
the berger force field parameters 
 were used for the popc molecules , and the tip3p model was used for 
 water .
simulation details are similar to those of ref ( 25 ) and are summarized briefly 
 as follows .
lipids were modeled using the berger force field , and the water model is tip3p .
a temperature 
 of 303 k was maintained using the velocity - rescaling thermostat , and the pressure 1 bar , well clear of any 2d 
 phase transition .
the pressure was coupled 
 semi - isotropically , allowing the box size to fluctuate by the same amount along the x and y axes or independently along the z axis .
each system was equilibrated for 10 ns , after which 
 point the equilibrium 
 values of box size and pressure were well converged .
production runs 
 were then performed for 400 ns each using a 4 fs time step .
short - range cutoffs of 1.2 nm 
 were used , with long - range electrostatics treated via particle mesh 
 ewald . a 5 ps pressure - coupling constant 
 was employed in conjunction with a 0.1 ps temperature - coupling constant .
bilayers of asymmetric density were prepared by randomly deleting 
 10 outer leaflets of each bilayer at each hydration level .
each system 
 was equilibrated as above and then subjected to a further 100 ns of 
 equilibration prior to production runs of 350 ns each .
differential 
 pressure and surface tension were assessed in these simulations using 
 the gromacs 4.5 local pressure code in 
 a manner similar to that described in the reference publication .
local 
 pressures were calculated on frames at 4 ns intervals and saved onto 
 a grid at 0.15 nm resolution .
the free energy of removal of 
 an internal or external water molecule 
 from the system was calculated by running several systems where gradually 
 an 8.85 kj mol nm umbrella 
 potential was applied to the water molecule relative to a set of water 
 molecules in a cylinder of radius 2.8 nm centered around the water 
 molecule to be removed .
charge interactions between 
 the water and the rest of the system were gradually removed , after 
 which the van der waals interactions were removed while applying a 
 soft - core potential .
all of the intermediate 
 states were kept constant and simulated as equilibrium states with 
 3 ns equilibration time and 1 ns sampling time using stochastic dynamics 
 with a 4 ps time step .
simulations 
 of vesicle  vesicle fusion used identical conditions 
 ( and indeed identical trajectories ) to those previously reported , with the exception that coordinates were analyzed 
 at a 40 ps interval to measure lipid diffusional coupling .
briefly , 
 a pair of 15 nm vesicles was simulated connected by an amide cross - linker .
each vesicle was composed of 877 popc or pope 
 phospholipids using the berger simulation parameters and solvated 
 in explicit tip3p water .
measurements reported in this article 
 were performed on the vesicles after stable contact structures had 
 formed but before fusion stalk formation .
simulations were performed 
 using gromacs 4.5 on one to four cluster 
 nodes with 24 amd opteron 8425he 
 cores per node and a qdr infiniband interconnect , with speeds of approximately 
 77 ns / day for the 512-popc systems on 4 nodes .
additional simulations 
 were performed on 32 cluster nodes with 16 intel e5 - 2670 codes per 
 node and a cray aires interconnect .
 biomembrane interfaces create regions 
 of slowed water dynamics 
 in their vicinity . 
 when two lipid bilayers come together , this effect 
 is further accentuated , and the associated slowdown can affect the 
 dynamics of larger - scale processes such as membrane fusion . 
 we have 
 used molecular dynamics simulations to examine how lipid and water 
 dynamics are affected as two lipid bilayers approach each other . 
 these 
 two interacting fluid systems , lipid and water , both slow and become 
 coupled when the lipid membranes are separated by a thin water layer . 
 
 we show in particular that the water dynamics become glassy , and diffusion 
 of lipids in the apposed leaflets becomes coupled across the water 
 layer , while the  outer  leaflets remain unaffected . 
 
 this dynamic coupling between bilayers appears mediated by lipid  water  lipid 
 hydrogen bonding , as it occurs at bilayer separations where water  
 lipid 
 hydrogen bonds become more common than water  
 water hydrogen 
 bonds . 
 we further show that such coupling occurs in simulations of 
 vesicle  vesicle fusion prior to the fusion event itself . 
 such 
 altered dynamics at membrane  membrane interfaces may both stabilize 
 the interfacial contact and slow fusion stalk formation within the 
 interface region . 
Introduction
Results
Conclusions
Methods