the process of hydrated 
 excess proton solvation and transport in 
 aqueous systems displays many unique characteristics due the unique 
 nature of the net positive charge defect that an excess proton creates . by altering the covalent bonds and hydrogen bonds of surrounding 
 solvent molecules , the hydrated excess proton charge defect is strongly 
 delocalized and creates a series of dynamically interchanging structures 
 ( i.e. , the zundel h5o2 and eigen 
 h9o4 cations ) . proton  ( or more accurately stated , 
 the charge defect ) is also able to hop between neighboring water molecules 
 by  structural diffusion  via successive hopping events 
 involving the rearrangement of the local bonding topologies . , is crucial to a number of fundamental processes in chemistry , physics , 
 biology , and materials science . in biology , protons are widely 
 used for the transduction of signals 
 and energy ( e.g , in channels , transporters , and enzymes ) . they are 
 transported through both protonatable residues and buried water molecules 
 via grotthuss shuttling . hence , studies on proton transport ( pt ) in biological systems have 
 almost always started with the assumption that pt follows aqueous 
 ( already hydrated ) pathways , which can be obtained from experimental 
 data or by computational predictions . however , hydrophobic 
 regions are commonly found in proteins , which complicates the interpretation 
 of pt . carbon nanotubes ( cnts ) have provided insight into the 
 solvation 
 and ion transport properties of homogeneous hydrophobic spaces . experiments 
 and computer simulations have shown that water molecules can stably 
 occupy the interior of cnts . theoretical studies and recent experiments have further 
 shown that proton diffusion through nanoconfined spaces , such as hydrophobic 
 channels and nanotubes , can be facile ( and possibly even faster than 
 in bulk water ) . these results provide support for the supposition 
 that the hydrophobic spaces in biomolecules may also transiently contain 
 water molecules capable of proton conduction . however , a common assumption 
 is that hydrophobic spaces must be solvated prior to pt . this logic has led to numerous mechanistic predictions based 
 on the existence of a quasi - stable water wires ( e.g. , see refs ( 3133 ) ) . however , it has also been clearly demonstrated 
 that the presence of an excess proton greatly influences the local 
 water solvation structure ( see ref ( 4 ) for a discussion ) . in the present work , it is 
 in fact found that as soon as a charge defect associated with a hydrated 
 excess proton charge nears a hydrophobic space , the associated solvating 
 water can experience a strong driving force to fill that space . moreover , this finding naturally leads to the possibility that 
 when an excess proton deprotonates from a peripheral amino acid residue 
 or is solvated outside a hydrophilic ( or amphiphilic ) region , it can 
 initiate additional solvation of such a region , which will in turn 
 be coupled to the pt process through it . herein , multiscale 
 reactive molecular dynamics ( ms - rmd ) is used 
 to study pt through a cnt penetrating a graphene sheet . as described 
 in the previous paragraph , a surprising phenomenon is revealed in 
 which an excess proton charge defect creates its own aqueous transport 
 pathway by shuttling water molecules through it into 
 the hydrophobic nanoconfined space . this process can be described 
 as a variant of grotthuss shuttling , wherein water molecules travel through a hydrated excess proton charge defect . the induced 
 wetting is shown to be excess proton specific ; it does not happen 
 when the excess proton ( h ) is replaced by k or even a the two - dimensional free energy surface reveals 
 a three - step mechanism by which the protonic charge defect is transiently 
 stabilized at the nanotube entrance , facilitates nanotube wetting 
 via grotthuss - facilitated water migration through the charge defect , 
 and then traverses a lower free energy barrier for grotthuss shuttling 
 proton permeation via activated ( infrequent event ) dynamics . this 
 finding has widespread implications for pt through hydrophobic ( and 
 likely other ) regions in molecular systems such as proteins , by demonstrating 
 that protons can dynamically create their own solvation pathways that 
 would not be detected by experimental or computational means in absence 
 of an explicit protonic charge defect . the system studied in this work consists of a 29.4  ( z - dimension ) armchair - type ( 6,6 ) single walled carbon nanotube 
 ( cnt ) with a single layer of graphene and bulk water on either side 
 ( figure 1a ) . the space between the graphene 
 layers was left empty ( it is merely intended to provide a low dielectric 
 environment ) . the graphene layers extend 41.82 and 42.5  in 
 the x and y dimensions and are replicated 
 under periodic boundary conditions . the two slabs of water molecules 
 on either side of the graphene sheets contain seven pairs of k and cl ions collectively . this type of 
 ( 6,6 ) cnt has been the focus of previous computational work , partially because its 8  diameter accommodates a single - file 
 chain of water molecules , which is similar to the solvation structure 
 found in some biological channels . as previously reported , the use of standard force field parameters enables 
 spontaneous wetting of a cnt of this diameter . thus , to mimic hydrophobic 
 environments , the lj lj parameter for the cnt carbon 
 atoms was reduced to provide a mostly dry ( hydrophobic ) cnt in unbiased 
 molecular dynamics simulations , with only two to four water molecules 
 transiently entering the mouth regions ( figure 1a ) . ( a ) construct of the simulation 
 system . the armchair - type ( 6,6 ) cnt structure is assembled between 
 two graphene single layers that separate the bulk water . ( b ) overview 
 of the proton induced wetting process along with the motion of the 
 excess proton from bulk  tube interface into about 4  
 of the nanotube . ( c ) real - time densities traces of the channel water 
 molecules starting from a partially dry nanotube with the existence 
 of the excess proton . each bright line can represent the trace of 
 the oxygen atom in a water molecule . ( d ) simulation with the k inside the nanotube , which remains mostly dry . the hydrated excess proton was treated explicitly 
 with the multiscale 
 reactive molecular dynamics ( ms - rmd ) method developed by the voth 
 group . the multistate empirical valence bond version 3 ( ms - evb3 ) model and the spc / fw water 
 model were used . all other parameters ( for ions and carbon atoms ) 
 were taken from the standard charmm22 force field . the depth of the lennard - jones potential well for cnt carbon 
 atoms is scaled to 80% of the standard value to make the cnt more 
 hydrophobic as noted above and hence dry in the absence of ions restrained 
 to be in the cnt . the simulations were run with raptor , an in - house extension of the lammps software . the particle  particle , particle  mesh 
 method was used to treat long - range electrostatics . the nos  hoover thermostat at 300 k and a time step 
 of 1.0 fs were used . to construct the free energy surface for 
 the wetting process inside 
 the cnt , we defined a water occupancy collective variable:1where nh2o is total number of the water molecules 
 and ni is the occupancy 
 of the ith water molecule in a defined rectangular 
 box:2the dimensionless coordinate ri, is defined as3where r0 and ri are the positions of the 
 center of the cnt and the oxygen atom of the ith 
 water molecule , respectively . a box similar to the shape of the cnt 
 was defined by bx = by = 4.0  and bx = 14  , while d was chosen to be 5.0  to allow a smooth transition 
 of the water occupancy from zero ( when the molecule is at the graphene  water 
 interface ) to 1 ( when the molecule is inside the cnt ) . the umbrella - sampling 
 technique and the wham method were used 
 with the bias potential defined by4applied 
 to two independent reaction 
 coordinates  : the z - axis position of the positive 
 charge ( h , k , or h3o ) and the water occupancy number in the cnt . the resulting 2d free 
 energy surface was constructed from 325 sampling windows covering 
 the range of charge locations from 9.0 to 21.0  in 1.0  
 intervals and for water occupancies ranging from 2 to 14 with an interval 
 of 0.5 . the bias force constants were chosen to be 10.0 kcal mol  and 5.0 kcal mol , respectively , to ensure sufficient window overlap . as described 
 in the section methods , the cnt studied herein 
 was modified to be more hydrophobic and hence mostly dry . in unbiased 
 md simulations only one to two water molecules transiently enter the 
 mouth regions on either side of the cnt ( figure 1a ) . these waters are partially stabilized by interactions with the 
 graphene atoms , which were simulated with the standard lj parameters . the hydrated excess proton ( or more accurate the net positive charge 
 defect associated with an excess proton ) was described with the ms - rmd 
 method , which as noted earlier has been shown to successfully model 
 pt in numerous aqueous and biomolecular systems . since there is a large free energy penalty for any 
 ion to shed its solvation shell and enter a nanoconfined hydrophobic 
 region , umbrella sampling was used to calculate the free energy profiles 
 for ion transport through the cnt as described in methods . figure 1 shows how the 
 charge defect associated with the hydrated excess proton strongly 
 influences the cnt hydration . we note that hereafter this net positive 
 charge defect will be referred to as just the  hydrated excess 
 proton  or  the proton  even though it is in 
 fact a positively charged defect having more than one proton and water 
 molecule involved in its definition ( see ref ( 5 ) for more information ) . 
 when the proton is far from the mouth of the nanotube , no significant 
 change in the hydration can be observed . as the proton approaches 
 the entrance ( within a few  ) , the number of pore water molecules 
 increases from 2 to 4 . as the proton enters the channel , it drags 
 a few waters with it . surprisingly though , once the proton has entered 
 the mouth of the nanotube , the number of water molecules in the cnt continues to increase by having the waters shuttle 
 through the excess proton charge defect . in other words , the proton  shoots  waters into the nanotube , thus creating 
 its own water wire  for subsequent transport . by the 
 time the excess proton is 23  into the cnt , the tube 
 transitions to the fully hydrated or wet  state ( figure 1b ) . to analyze the origin of water molecules 
 that wet the cnt relative 
 to the position of the excess proton , we traced the positions of the 
 water oxygen atoms over the course of a simulation ( figure 1c ) . this demonstrates that water molecules originate 
 on the same side of the graphene sheet as the excess proton defect 
 and hence have to pass through it to enter the cnt . the length of 
 the water wire ahead of the proton fluctuates until it connects with 
 waters from the other side to fully wet the nanotube . therefore , the 
 transport of water molecules into the nanotube is enabled by an unusual 
 manifestation of the grotthuss shuttling mechanism involving the rearrangement 
 of covalent bonds as water molecules pass through the relatively stationary protonic charge defect near the mouth 
 of the channel . to check whether other monatomic ions can also 
 induce a similar 
 wetting process , the same simulations were carried out with k in place of an excess proton . although k pulls 
 four water molecules into the nanotube , two on each flanking side , 
 to form its hydration structure , it does not induce a full wetting 
 transition ( figure 1d ) . the free energy profiles 
 for the ion permeation ( figure 2a ) are also 
 different for h and k. the energy barrier 
 for k to penetrate 5  into the cnt is over 30 kcal / mol , 
 while that for the excess proton is less than 15 kcal / mol ( see figure 2a ) . the large difference in these two free energy 
 profiles is consistent with the principal that the free energy barrier 
 for an ion to enter a nanoconfined region is strongly influenced by 
 the cost of dehydration . since the excess proton can effectively keep 
 part of its solvation shell as dynamical h5o2 and h7o3 structures , it has a lower barrier for cnt penetration . free energy 
 profiles of the ion permeation and the water occupancy 
 in different simulation systems . the free energy of h ( the hydrated excess proton ) has much lower energy barrier than 
 the others , displaying the unique features of the excess h. ( b ) free energy profiles of the water occupancy with the h charge defect ( green ) , k ( red ) , or classical 
 h3o ( yellow ) fixed at z = 
 12.0  ( 23  inside the mouth of the nanotube ) , 
 compared to the result without the ions present ( blue ) . the induced 
 wetting process is only seen in the system with h. the 
 average errors are ( a ) 0.45 kcal / mol and ( b ) 0.30 kcal / mol 
 calculated from 500 ps block averages . moreover , the excess proton charge defect can transiently 
 delocalize 
 the net positive charge over even more water molecules and therefore 
 reduce the dehydration penalty in this fashion . similar to the situation 
 with k , replacing the excess proton with a classical approximation 
 of a hydronium cation ( a simple ion with no possibility of grotthuss 
 shuttling and charge defect delocalization ) also results in a large 
 free energy cost for cnt penetration ( > 25 kcal / mol ; see figure 2a ) . thus , the excess proton s ability to 
 distribute the charge defect to surrounding water molecules within 
 the cnt clearly also contributes to its decreased translocation barrier . to further study the underlying mechanism of this proton induced 
 cnt wetting process , a water occupancy reaction coordinate ( see methods , eqs 13 ) was defined to calculate the free energy profiles 
 for nanotube wetting as well as those for ion transport at different 
 hydration levels . first , we obtained the free energy profile of the 
 wetting process in the absence of an ion ( figure 2b , blue curve ) . similar to previous work , the free energy profile of water occupancy has dry and 
 wet minima ( at nw = 4 and nw = 13 , respectively ) separated by a barrier ( near nw = 12 ) . consistent with a dry cnt , the fully 
 wet ( water occupied ) state is 1 kcal / mol less stable than 
 the dry state . however , when an excess proton is located in the region 
 around z = 12  ( just 23  inside 
 the cnt ) , the wetting free energy profile changes dramatically , as 
 seen in figure 2b , green curve . the wet minimum 
 becomes 6 kcal / mol more stable such that wetting becomes spontaneous , 
 and the transition along this wetting coordinate is nearly barrierless . when a k ion is located in the same location ( z = 12  ) , the barrier for wetting is increased to 
 5 kcal mol and the wet minima is destabilized by 2 
 kcal / mol ( figure 2b , red curve ) . the case for 
 the classical h3o ion is even more dramatic , 
 replacing the wet minimum with a 6 kcal / mol barrier ( figure 2b , yellow curve ) . the collected results described 
 above highlight the excess proton s 
 unique ability to self - solvate and project outward a water wire into 
 a hydrophobic space , thus wetting a dry region and thereby decreasing 
 the barrier it has to overcome to transport through it . such a phenomenon 
 may have significant implications for understanding pt through hydrophobic 
 regions of biomolecules and materials . the free 
 energy profiles of figure 2 indicate that the 
 excess proton can induce the wetting of the hydrophobic nanotube and 
 also that the proton has higher conductance ( i.e. , lower transport 
 barrier ) compared to k. are the two processes related ? 
 to answer this , two independent collective variables , the water occupancy 
 number and the position of the excess proton charge defect , were sampled 
 from 325 simulation windows to construct a two - dimensional ( 2d ) free 
 energy surface . from the 2d surface ( figure 3 ) , a fascinating coupled , 
 stepwise mechanism is clearly seen for the wetting and proton permeation . first , the excess proton is trapped close to the mouth of the nanotube 
 in a free energy minimum 1 kcal / mol more stable than bulk . hummer and collaborators have reported similar results with a proton 
 minimum at the entry of the cnt . this 
 result is also consistent with the amphipathic nature of the hydrated 
 proton , as reported in several theoretical studies . the vacuum 
 and nanotube wall are hydrophobic while bulk water and the graphene 
 surface are more hydrophilic creating an amphipathic interface where 
 the excess proton is stabilized . second , after being trapped at the 
 entry of the nanotube , the proton initiates the wetting transition 
 described earlier by greatly lowering the free energy barrier for 
 water penetration and stabilizing waters in the previously dry space 
 ( cf . when the proton is 23 
  into the cnt ( zcec  1213 
  in figure 3 ) , the relative free energy 
 for wetting becomes very favorable with a negligible barrier ( figure 4a , blue , green , and red curves ) , transitioning the 
 hydrophobic nanotube to the fully wet state . as the cnt hydration 
 level increases , the barrier for the proton transport into the nanotube 
 also greatly decreases ( figure 4b ) and the 
 proton can progress further into the cnt and eventually through via 
 activated ( barrier surmounting ) dynamics . indeed , the free energy 
 penalty for the proton moving into the nanotube is greatly reduced 
 from when the nanotube is dry . in fact , the free energy for proton 
 permeation goes from > 36 kcal / mol for the dry cnt , which is close 
 to the energy barrier for k , to 18 kcal / mol for 
 the fully wet cnt ( figure 4b ) . it is interesting 
 to note that the lowest barrier for a constrained solvation state 
 is 18 kcal / mol for nc = 13 ( i.e. , the fully wet state ) , while the 
 free barrier with no solvation constraints is only 15 kcal / mol ( figure 2a ) . thus , the proton induced wetting and proton 
 permeation are dynamic and inherently coupled . the 
 horizontal axis represents the z - position of the 
 hydrated excess proton charge defect , while the vertical axis represents 
 the level of cnt water occupancy . the white dotted line ( z = 14.7  ) indicates the position of the graphene layer and 
 the mouth of the nanotube . a stepwise but coupled mechanism can be 
 observed from the 2d free energy surface , in which three steps , trapping  wetting  permeation , 
 are highlighted by yellow dashed arrows . 1d free energy profiles extracted from the 2d 
 free energy surface 
 in figure 3 . ( a ) free energy profiles of the 
 wetting process when the excess proton charge defect is located at 
 different positions along the nanotube axis . ( b ) free energy profiles 
 of proton permeation while the nanotube is in different hydration 
 states where nc is defined as the number of confined waters in the 
 nanotube . the 2d free energy surface in figure 3 reveals the sensitivity of the cnt s solvation 
 structure 
 and stability to the position of the excess proton charge defect . the excess proton changes the water occupancy in the cnt even before 
 it enters . although the excess proton is weakly attracted to the entrance 
 to the nanotube , it does not block water penetration as other ions 
 will do . instead the excess proton defect shuttles waters 
 through it into the nanoconfined space via an unique manifestation 
 of the grotthuss shuttling mechanism , thereby lowering its own barrier 
 for subsequent permeation . the 2d free energy surface for k permeation versus 
 nanotube hydration ( figure 5a ) highlights two 
 important differences between h and k. first , 
 there is no energy minimum that indicates trapping at the mouth of 
 the cnt . this is consistent with the common finding that k prefers to be fully solvated in the bulk rather than at an interface . in fact , the wetting free energy 
 shift ( and barrier ) remains positive no matter where the k ion resides and is highest ( least favorable ) when k is 
 at the mouth of the cnt . consistent with previous studies , 
 the water molecules in the cnt are highly mobile in the absence of 
 ions , entering and leaving the tips of the nanotube frequently . however , 
 when k is near the entry of the nanotube , it blocks the 
 water flux , which is entropically unfavorable . in contrast , water 
 molecules in the presence of the excess proton charge defect at the 
 entrance of the nanotube retain their ability to move in and out of 
 the channel through the grotthuss mechanism . thus , delocalization 
 of the excess proton charge defect is essential to decreasing the 
 cost of wetting and ion permeation . 2d free energy surfaces for ( a ) a k cation and ( b ) 
 a  classical  h3o ( non - grotthuss 
 shuttling ) cation showing the free energy for ion permeation relative 
 to nanotube water occupancy and prepared in the same way as for figure 3 . to confirm this hypothesis , we 
 conducted another set of free energy 
 surface calculations with a classical hydronium model ( simple h3o cation ) , in which the charge defect delocalization 
 and grotthuss shuttling are disabled . as discussed above , the free 
 energy profiles for h3o permeation and wetting 
 ( shown in figure 2 ) are more similar to the 
 results for k than to those for h. the 2d 
 free energy surface ( figure 5b ) reveals that 
 h3o also has a sort of trapping state near 
 the mouth of the cnt as seen for h. however , the classical 
 hydronium does not exhibit the favorable wetting transition ( compare 
 figure 3 to figure 5b ) . in fact , just as with k , water molecules are blocked 
 from entering and leaving the cnt . in order to quantify the 
 degree of charge defect delocalization 
 of the excess proton in the cnt , we analyzed the magnitude of excess 
 positive charge owned by each water molecule in the simulations with 
 h restricted at z = 12.5  . this 
 is the case when the proton defect center of excess charge coincides with the second cnt water molecule . when the nanotube 
 is dry ( nw = 4 ) , about 99% of the positive 
 charge is distributed on three water molecules with the percentages 
 67% , 20% , and 12% , respectively . when the nanotube is fully wet ( nw = 14 ) , the distribution shifts to 55% , 33% , 
 and 10% . in the bulk , eigen cation , h9o4 , with 62% of 
 the charge on the central water molecule and the three surrounding 
 waters that possess 19% , 10% , and 5% of the excess charge . thus , although 
 the charge defect delocalization in the cnt is weaker than it is in 
 the bulk system , because of the strong spatial confinement , it is 
 still significant . moreover , it shifts to a more zundel - like delocalized 
 species in the fully wet nanotube , which 
 will contribute to the stabilization of the fully wet state . thus , 
 charge defect delocalization is again confirmed to be essential to 
 the wetting mechanism and decreases the free energy barrier for ion 
 permeation . for many years , 
 studies of pt in biological systems have largely 
 focused on the identification and the analysis of aqueous pathways 
 interlaced with protonatable residues through which excess protons 
 might migrate ( especially via grotthuss shuttling ) . great effort has 
 been devoted to characterizing internal hydration structures that 
 connect protonatable residues to form such pathways . when hydrophobic 
 cavities are encountered , i.e. , those lacking crystallographically 
 resolved water molecules , simulations have often been used to try 
 to identify states of the system ( e.g. , via oxidation state or conformational 
 changes ) that induce wetting . in this manner , mechanisms of pt have 
 been proposed based on the existence and stability of hydrogen - bonded 
 water wires . however , the simulations presented herein suggest that 
 the excess proton itself is strongly coupled to the solvation structure 
 and stability in nanoconfined spaces and hence must be explicitly 
 included in the analysis of internal solvation . by 
 simulating pt through a nanotube penetrating a graphene sheet 
 with ms - rmd , we have discovered that a hydrated excess proton charge 
 defect can induce wetting into a previously dry hydrophobic space . this is a novel wetting process in that water molecules actually pass through the protonic charge defect via grotthuss - like shuttling . other ions have the opposite effect , blocking the diffusion of 
 water into the nanotube when they are close to the nanotube s 
 entrance . thus , this wetting process , which relies on charge defect 
 delocalization and grotthuss shuttling , is unique to a hydrated excess 
  proton  ( though something similar may be possible for 
 the hydroxide anion ) . although the present simulations have 
 focused on pt through a cnt , 
 our findings have broad implications for pt in biomolecular and materials 
 systems . just as our simulations have demonstrated in a cnt , an excess 
 proton may actually transiently induce wetting in biomolecular hydrophobic 
 cavities when it is located near a peripheral residue or water cluster . 
 in this manner , the excess proton can create its own aqueous pathway 
 for subsequent charge transport . as shown in this work , water rearrangement 
 around a confined excess proton can be fast ( from hundreds of picoseconds 
 to several nanoseconds ) relative to the rare events of biomolecular 
 pt ( typically microseconds or longer ) . thus , with the strong correlation 
 between solvation rearrangement and the position of a hydrated excess 
 proton , the two processes of pt and wetting are likely to be strongly 
 coupled ( as demonstrated in the cnt ) . indeed , the concept that pt 
 requires an existing  water wire  , e.g. , one seen in 
 an x - ray crystal structure or md simulations without an explicit excess 
 proton , should be questioned . what is more , computer simulations probing 
 pt mechanisms should include an explicit treatment 
 of the hydrated excess proton ( along with its full physics of grotthuss 
 shuttling and charge defect delocalization ) to properly capture the 
 coupling between water dynamics , hydration , and pt . using solvation 
 structures to interpret pt mechanisms in the absence of an explicit 
 excess proton can quite possibly lead to incorrect conclusions .
grotthuss 
 shuttling of an excess proton charge defect through hydrogen 
 bonded water networks has long been the focus of theoretical and experimental 
 studies . in this work 
 we show that there is a related process in which 
 water molecules move (  shuttle  ) through a hydrated 
 excess proton charge defect in order to wet the path ahead for subsequent 
 proton charge migration . 
 this process is illustrated through reactive 
 molecular dynamics simulations of proton transport through a hydrophobic 
 nanotube , which penetrates through a hydrophobic region . 
 surprisingly , 
 before the proton enters the nanotube , it starts  shooting 
 water molecules into the otherwise dry space via grotthuss shuttling , 
 effectively creating its own water wire where none existed before . 
 as the proton enters the nanotube ( by 23  ) , it completes 
 the solvation process , transitioning the nanotube to the fully wet 
 state . 
 by contrast , other monatomic cations ( e.g. , k+ ) 
 have just the opposite effect , by blocking the wetting process and 
 making the nanotube even drier . as the dry nanotube gradually becomes 
 wet when the proton charge defect enters it , the free energy barrier 
 of proton permeation through the tube via grotthuss shuttling drops 
 significantly . 
 this finding suggests that an important wetting mechanism 
 may influence proton translocation in biological systems , i.e. , one 
 in which protons  create  their own water structures 
 ( water  wires  ) in hydrophobic spaces ( e.g. , protein 
 pores ) before migrating through them . 
 an existing water wire , e.g. , 
 one seen in an x - ray crystal structure or md simulations without an 
 explicit excess proton , is therefore not a requirement for protons 
 to transport through hydrophobic spaces .