interestingly , the trajectory of a proton in the lumen of 
 the so - called m2 channel of the influenza a virus is an example from 
 biology .
the m2 integral membrane protein is a tetramer assembled 
 from four identical subunits , each with 97 residues . as a prerequisite for release of genetic material to the cytoplasm , 
 the interior of a viral particle must become acidified as a means 
 to detect its own entrance in the endosome .
the m2 protein channel fulfills this acidification function by conducting 
 protons through its membrane pore .
the gating of this essential proton 
 transport step in the infection cycle is controlled by ph . among the pore - lining residues , his37 and trp41
were identified 
 as the most important residues in the proton transfer through the 
 m2 channel .
the proton selective conductance in m2 is achieved by 
 the presence of the his37 cluster : substitution of his37 with residues 
 such as gly or ala induces a nonselective channel , indicating a mechanistic 
 role of his37 in proton relay .
a transfer cycle 
 was proposed where a tautomerization of the his37 side chain occurs 
 between the acceptance of a proton from the viral exterior and the 
 release of a proton to the viral interior , to reestablish in full 
 the original configuration for the next cycle .
on replacing the imidazole 
 ring of the his37 side chain with a 4-thiazolyl group , which has the 
 n1 as the only proton acceptor with pka 2.5 , 
 this mutant shows inward proton flux resembling the wild type , thus 
 demonstrating that tautomerization is not necessarily required for 
 proton transport . however , rotation of 
 the imidazole ring during proton translocation can not be ruled out . 

besides the functional role in proton selectivity , his37 is associated 
 with channel activation : binding of a third proton to the his37 cluster 
 under acidic conditions triggers a detectable proton flux , with a 
 peak conductance rate of 10 protons per second .
substitution of trp41 with smaller residues , like gly , ala and phe , 
 induces higher proton conductivity compared to the wild - type channel . despite the relatively small size of the 
 m2 protein , and several 
 high - resolution structures being available ,
the mechanism of proton 
 conduction through the channel is not completely understood ( figure 1a ) .
previously , we 
 studied the addition of a proton to the his37 cluster from the extraviral 
 side , and compared the energetics and 
 dynamics of two configurations of the doubly protonated state at neutral 
 ph  a 4-fold symmetric  histidine - box  and a 2-fold 
 symmetric  dimer - of - dimersand proposed a multiconfiguration 
 model where these configurations are in moderately fast equilibrium . here , we focus our analysis on the configuration 
 of the his37trp41 cluster in the triply protonated 
 state , and its subsequent deprotonation . m2 channel and its two 
 configurations of the his37trp41 
 quartet at low ph .
( a ) shown is the tm domain of m2 protein imbedded 
 in a fully hydrated lipid bilayer .
his37 and trp41 residues and lipids are colored in green , pink , and 
 ice blue , respectively , as space filling spheres .
waters are shown 
 in gray surface . the d - model ( b ) and the h - model ( c ) of the quartet . 

system with the absence of cl ion are shown in 
 stick mode with the same color code as in ( a ) , and the system with 
 cl ion are shown in white stick .
( d ) the principal 
 components of the quartet ,  , in different systems as a function 
 of time ; data for the 2 + state are shown for comparison . herein , quantum mechanics / molecular mechanics ( qm / mm ) 
 molecular 
 dynamics ( md ) simulations reveal insights into the function and mechanism 
 of this protein . specifically , molecular simulations complemented 
 by crystallographic and nmr ( nuclear magnetic resonance ) determined 
 structural data , as well as physiological measurements provide mechanistic 
 clues in understanding this rate - limiting step of proton conduction 
 in m2 , especially the proton trajectory during the translocation  reaction  . 

the present study elaborates our previous computational works , and 
 explores the free energy profile with the explicit presence of the 
 complete transmembrane domain of the protein as well as a fully hydrated 
 membrane environment .
moreover , to explore the effect of the proton 
 filter and the channel gate , the entire his37trp41 
 cluster and the nearby water clusters are treated within a quantum 
 mechanical methodology . in this manuscript , we document multiple 
 calculations : first , we 
 studied the structural integrity of the m2 protein with two models 
 at low ph with qm / mm md simulations .
we find that the structures of 
 the his37 cluster starting from both models converge at low ph , and 
 are stable within the simulation time scale : both models appear ready 
 for the subsequent proton release toward the intraviral side .
then , 
 we calculated potentials of mean force ( pmfs ) of the deprotonation 
 by constrained qm / mm md simulations : the pmfs of both models have 
 barriers 6.5 kcal / mol . compared to previous simulation studies , 
 the local electrostatic environment of the hydrated membrane significantly 
 lowers the energy cost .
finally , we explored the possible role of 
 a cl anion in the pore at low ph , which was found 
 to stabilize the highly charged 3 + histidine cluster , but also to 
 impede proton release by stabilizing the hydronium species within 
 the channel pore .
configuration 
 at the 2 + state ( with 2 of 4 his37 side chains charged ) at neutral 
 ph as the  d2-model  , and the subsequent 3 + state obtained 
 by adding a third proton as the  d3-model  ( figure 1b ) .
correspondingly , the  histidine - box  
 at 2 + state and the subsequent 3 + state structures are designated 
 as the  h2-  and  h3-models  ( figure 1c ) , respectively
. the 1.65  resolution 
 x - ray structure ( pdb entry : 3lbw , residues
two and three of the four his37 residues were 
 initialized to be charged in the 2 + and 3 + states , respectively .
the 
 protein was then embedded in a previously equilibrated 80  80 
  lipid bilayer containing 171 1-palmytoyl-2-oleoyl - sn - glycero-3-phosphatidylcholine ( popc ) molecules , hydrated 
 by 10,031 water molecules .
potassium and chloride ions were added 
 to neutralize the system , and to provide a solution buffer with ionic 
 concentration of 150 mm .
periodic boundary conditions were applied , 
 and long - range electrostatic interactions were treated with the particle 
 mesh ewald method .
a time step of 2 fs 
 was used , and all of the bonds involving hydrogen atoms were constrained 
 with the shake method . after an equilibration 
 period with gradually released harmonic restraints , production simulations 
 were performed at 310 k and 1 atm using langevin temperature and langevin 
 piston pressure coupling schemes .
the tip3p 
 force field was used for water molecules , and charmm force field was used for the protein and lipid atoms .
simulations were performed with namd , and continued for 200 ns for the 2 + state , and 
 300 ns for the 3 + state . to prepare the his37trp41 
 quartet structures for the subsequent h3- and d3-models at the acidic 
 condition with qm
/ mm md simulations , we followed the protocol used 
 in our previous work to optimize the his37trp41 
 quartet structure at the 2 + state with the oniom method implemented in gaussian 03 . on the basis of the optimized his37trp41 
 quartet structure in the h2- and d2-models
, a third proton was added 
 to a neutral his37 side chain , and oniom was used to optimize the 
 system after this addition .
then , the h3 and d3-models were constructed 
 with the original quartet in the corresponding h2(d2)-model replaced 
 with the newly optimized quartet at the 3 + state .
therefore , the initial 
 backbone of the h3(d3)-model is similar to the preceding h2(d2)-model . 
 with the quartet structure held fixed , we then relaxed the remaining 
 atoms of the h3(d3)-model with classical md simulations for 20 ns . 

we took the last snapshot from the md simulations , and minimized the 
 system with the his37trp41 quartet fixed .
the minimized 
 structures were used for the following qm / mm md simulations . in the qm / mm scheme , as in our 
 previous study
, we included in the qm 
 region the his37trp41 quartet and thirteen water 
 molecules nearby ( corresponding to the three water clusters identified 
 in the 3lbw.pdb 
 structure : six waters just above the 
 his37 tetrad , two in the his37trp41 cavity , and 
 five below the trp41 gate ) .
these atoms were treated at the density 
 functional theory ( dft ) level using a mixed gaussian and plane - waves 
 treatment , while the rest of the system , 
 including the protein , the lipids , and waters , was treated with the 
 mm method ( charmm force field and tip3p ) .
the generalized gradient approximation ( gga ) 
 functional blyp with the d2 level dispersion - correction 
 ( blyp - d2 ) , the triple- basis set 
 with two polarization functions , and 
 the goedecker , teter , and hutter type pseudopotentials were used .
a wavelet - based poisson solver was used to remove 
 the spurious interactions of the qm region atoms with the periodic 
 images . a box size of 32  32  
 32  was used for the qm region so that the buffer 
 between qm atoms and the box edge is 8  .
we saturated 
 the broken bonds with hydrogen atoms , and combined the qm and mm subsystems 
 with the imomm methodology , where the 
 scaling factors of 1.355 , 1.384 , and 1.416 were used to relate the 
 qm c  h bond distance to the mm cc , cn , 
 and cc distances , respectively .
for the 
 qm / mm md simulations , after 2 ps equilibration for each model , we 
 accumulated 9 ps trajectories for the d3-model with and without cl , and 4 and 7 ps for h3-model with or without cl , respectively . to characterize the free energy 
 profile for proton release from 
 the his37 cluster in m2 protein
, we followed the well - tested protocol 
 used in the previous work from our group to run constrained 
 qm / mm md simulations .
the starting configuration was adopted from 
 the preceding 3 + state qm / mm md simulations .
the reaction coordinate 
  was defined as the distance between the n2 on one his37 
 side chain and its neighboring h2 , in the range of 1.0  
 to 1.6  . with the reaction coordinate  fixed in each 
 window , constrained qm /
mm md simulations were carried out for times 
 varying between 5 and 8 ps to obtain a converged pmf .
forces after 
 the initial 1 ps of each constrained simulation were collected to 
 calculate the mean constraint force .
free energy profiles for the 
 proton release were estimated by thermodynamic integration of the 
 mean force along the reaction coordinate .
all of the qm / mm md 
 simulations were carried out with the cp2k 
 program with a time step of 0.4 fs .
nbo was used to 
 calculate the partial charge at the mp2/6 - 311++g(d , p ) level , performed 
 with gaussian 03 . in those calculations , 
 only the side chains of the his37 and trp41 residues
the conformation 
 of the his37 
 cluster in both the d3-model and the h3-model was quantified by a 
 single parameter ,  , defined as the projection of the atomic 
 coordinates of his37 along the displacement vector connecting the 
 two models , where  = 0 represents the  dimer - of - dimers  
 ( d2-model ) and  = 1 the  histidine - box  ( h2-model ) . upon binding the third proton , as shown 
 in figure 1d ,
the -value in the h3-model 
 remains at 1 , indicating that the protonation does not change 
 the conformation of the his37 cluster significantly . in the d3-model , 

his37 shifts from  = 0 to  = 0.4 , showing that the d2-model 
 and the corresponding d3-model are connected by a ph - dependent transformation . 

furthermore , this transformation appears to form an intermediate state 
 of the one leading from the  dimer - of - dimers  (  
 = 0 ) to the  histidine - box 
this conformational 
 change has been previously proposed for the  dimer - of - dimers  
 at acidic conditions , where one dimer is broken upon taking a third 
 proton , to avoid electrostatic repulsion .
the structure of the his37 cluster after this conformational change 
 is closer to the  histidine - box  conformation . in both models ,
the presence of a cl ion in 
 the his37trp41 cavity does not have a major impact 
 on the protein s conformation ( figure 1b  d ) , but has more profound effects on proton conduction , 
 which is further described below .
we monitored the specific structural motifs of 
 either model by exploring the rotamer structures of his37 and trp41 . 

as disclosed by experimental determined structures at different conditions , 
 these two key residues at both high and low phs adopt rotameric angle 
 1 = 180 , whereas the angle 2 is relatively flexible .
in particular , the side chain dynamics of the two residues are distinct 
 between the d- and the h - models . in the qm / mm md simulations 
 at the 2 + state ( figure 2a )
, the his37 cluster 
 in the d2-model adopts a 2-fold symmetry , where the two dihedral angles 
 [ 1 , 2 ] of the charged his37 side 
 chains are [ 180 , 360 ] and those of the neutral ones are 
 [ 180 , 260 ] . the [ 180 , 360 ] configuration of 
 his37 was rarely sampled in the classical md simulations ( figure 2b and 2b ) , largely 
 because of the inability of the classical force field to reproduce 
 the strongly hydrogen bonded
 dimer - of - dimers  of the 
 d2-model . in the d3-model ( figure 2a ) ,
one of the charged his37 side chain in the broken 
 dimer remains at the [ 180 , 60 ] configuration with the 
 other one swings at [ 180 , 150  220 ] , and 
 the intact histidine - pair resembles those in the d2-model .
interestingly , 
 this [ 180 , 60 ] configuration is the characteristic of 
 the low ph structure , which was occasionally 
 sampled in the classical md simulations at the 2 + state , but never 
 reached in the corresponding qm / mm md simulations . in both the h2- 
 and h3-models , all of the four his37 side chains have [ 1 , 2 ] values of [ 180 , 180 ] .
dihedral 
 angle distributions of the his37 and trp41 side chains 
 from the d- and h - models are plotted at neutral and acidic ph conditions . 

the top panel shows the plots at neutral conditions ( 2 + state ) , which 
 are labeled as a 
f ; the corresponding plots at acidic conditions 
 ( 3 + state ) are labeled as af , shown in the 
 bottom panel .
panels a and b show the correlation between 1 
 and 2 on his37 side chain from the qm / mm and classical md simulations , 
 respectively .
panels c and d show the correlation between 1 
 and 2 on trp41 side chains .
panels e and f show the correlation 
 between 2 on his37 and 2 on trp41 .
the trp41 side chains feature a  flip  
 variant in the h - models ( the n1-h1 bond of the indole 
 group points toward the central pore ) and a  flop  variant 
 in the d - models ( the same bond points away from the central pore ) . 

these variants correspond to 2 angles located at 
 80 ( tp rotamer , the  flip  
 variant ) and at 280 ( tm rotamer , the 
  flop  variant ) , which are retained at both high and 
 low ph conditions in each model ( figure 2c 
 and 2c ) . however , the 2 angle of trp41 at the low ph conditions in the d3-model is more 
 diffuse than the congener in the d2-model , indicating a more dynamic 
 trp41 gate in the d - model under acidic conditions .
in contrast , this 
 gate seems to be more rigid in the h - models , as evidenced by the similar 
 distributions of 2 angle at neutral or acidic ph 
 conditions . due to the inward orientation of trp41 in the h3-model , 
 the excess
proton is less easy to be released toward the intraviral 
 end of the channel , as further described below .
however , this orientation 
 enables the trp41 side chains to form water - mediated hydrogen bonding 
 interactions with asp44 ( figure 3 ) , which was 
 proposed to stabilize the trp41 gate , a critical factor for the asymmetric 
 proton flux .
the outward orientation of the 
 trp41 in the d3-model , on the other hand , points the amide group toward 
 the hydrophobic wall , which seems to be a less favorable factor for 
 its gating .
shown is 
 the top view of the channel , in which trp41 , asp44 and water molecules 
 are the sticks , and the backbone of the protein is the spiral .
it should be noted that , in the classical and qm / mm md simulations 
 of both d - models , only the tp rotamer of trp41 was 
 observed ( figure 2d and 2d ) , as the  histidine - box  x - ray structure was used as the initial structure and no indole 
 ring flipping happened in the submicrosecond time scale simulations .
the average h2h2 distance of neighboring 
 trp41 residues in the d2- and d3-models are 4.7 and 7.2  , respectively , 
 which are consistent with the data derived from f nmr 
 measurement on f(hnm ) m2tm sample ( 3.2  
 at ph 8.0 and 8.0  at ph 5.3 ) .
in contrast , the average h3h3 distance 
 is 11  in both the h2- and h3-models .
this is in line 
 with a nmr experiment under different conditions , in which the f(h3 ) m2tm sample was found to have the closest distance 
 of 11  at both high and low ph conditions . as the m2 protein
s 
 structure is sensitive to the change in the solubilizing environment , the diversity of the his37trp41 
 contact depends on the balance between different rotamers .
the nature 
 of the interaction between his37 and trp41 differs between the d- 
 and h - models , as the former is more sensitive to the protonation state 
 ( figure 2e , e,f , f ) .
this difference 
 in the his37trp41 packing and its response to the 
 environment can be mainly attributed to the higher flexibility of 
 the his37 side chain compared to trp41 . in the h - model ,
the orientations 
 of the two residues and their coupling are less dependent on ph condition , 
 showing only small thermal motions for both the imidazole ring of 
 his37 and indole ring of trp41 . due to the different rotameric 
 conformations , distances between his37 and trp41 are also distinct 
 in the d- and h - models , which can be determined by different techniques . 

as shown in table 1 , the distances measured 
 in our md simulations are quantitatively consistent with experimental 
 structures or nmr measurements . taking the c(his37)h3(trp41 ) 

distance as an example , at neutral ph condition , the average distances 
 ( figure 4a ) in the d2- and h2-models are 6.8 
 and 4.7  , respectively , corresponding to 6.5  in the 2l0j.pdb and 5.0  in the 3lbw.pdb .
the dashed line connecting h1 on his37 and c on trp41 
 indicates the reaction coordinate used to scan the change of partial 
 charge , as shown in panel b. nbo analysis was used to calculate the 
 partial charge at the mp2/6 - 311++g(d , p ) level .
ensemble average of the eight snapshots 
 of the nmr structure . among 
 the eight snapshots of the 
 nmr structures ,
data at ph = 8.5 and ph = 4.5 ( in 
 parentheses ) are shown .
ssnmr : solid - state nmr . to explore the free 
 energy cost for the his37 cluster to release a proton at low ph conditions
, 
 we carried out constrained qm / mm md simulations on the d3- and h3-models 
 imbedded in the fully hydrated lipid bilayers , in which the geometrical 
 parameter of the distance between n2 on one his37 side chain 
 and its neighboring h2 was selected as the reaction coordinate 
 . among the three charged his37 residues , the one with the 
 [ 1 , 2 ] of [ 180 , 60 ] was selected to release 
 a proton , as this his37 has an orientation similar to those found 
 in the low ph condition x - ray structure .
the free energy profiles for deprotonation and the representative 
 snapshots along the reaction pathways are shown in figure 5 .
the calculated pmfs was obtained by thermodynamic 
 integration of the average force along the deprotonation pathway , 
 where all free energy values are shown relative to the value of the 
 lowest pmf calculated in each system ( figure 5a ) .
the deprotonation curves are quite similar between the d3- and 
 h3-models , but the presence of cl imposes significant 
 perturbation on his37 deprotonation ( describe later ) . in the d3-model
, 
 the minimum of the free energy profile is located at  = 1.024 
  , corresponding to the triply charged his37 cluster state ( figure 5a , b ) . along with the increase of the n2h2 
 bond until  = 1.30  , the pmf increases , showing that 
 the proton moving from his37 to the neighboring water is energetically 
 unfavorable ( figure 5a , b ) . at  

= 1.30  , the proton is shared by his37 and the neighboring water , 
 with the average n2(his37)o(water ) distance 
 of 2.52  , where the proton is closer to the water ( the averaged 
 h2o(water ) distance is 1.24  ) .
the 
 newly formed hydronium is stabilized by the surrounding hydrogen - bond 
 network , which extends to the waters at the c - terminal side ( figure 5b ) . at high ph conditions ,
these interactions 
 are interrupted as the trp41 gate is closed . meanwhile , one proton 
 of the hydronium points to the neighboring water , and is ready to 
 be released .
the additional proton on the 
 hydronium is expected to release to the c - terminal side of the pore . 
 at 
= 1.5  , the proton transfer is complete ( the averaged 
 h2o(water ) distance is 1.06  ) , and 
 the hydronium group is separated from his37 by three water molecules . 

c ) is very similar to that in the d3-model , 
 with the free energy barrier height of 6.63 kcal / mol , located at  
 = 1.36  : at this point , a hydronium is formed next to the deprotonated 
 his37 ( with the n2(his37)o(water ) and h2o(water ) 
 distances of 2.53 and 1.22  , respectively ) .
( a ) shown are the free 
 energy profiles for proton release under 
 different starting configurations .
both the d3- and h3-models have 
 similar deprotonation pathways , while the presence of cl in the h3-model inhibits proton release .
panels b  d show 
 the representative snapshots during the proton release in the d3-model 
 ( b  b ) , the h3-model ( c  c ) , and the h3-model 
 with cl ( d ) .
their locations are labeled in panel 
 a. taking the d3-model as an example , along its deprotonation pathway , 
 one proton originally attached to the n on a charged his37 
 residue gradually moved to the neighboring water cluster at the c - terminal 
 side , with the nh distance increased from 1.024  
 ( b ) to 1.20  ( b ) and to 1.30  ( b ) . at 
 1.30  ,
further increase of the nh distance enables the fully 
 release of the proton from his37 , as shown on the red dashed line 
 in ( a ) .
previously , we demonstrated that 
 two alternative configurations 
 ( the d2- and h2-models ) are capable of stabilizing the charges in 
 the pore at neutral ph condition . here 

we find that , under acidic conditions , the mechanism of proton release 
 from the his37 cluster is much less dependent on its configuration 
 ( the d3- or h3-models ) .
in other words , for a charged his37 side chain , 
 which is ready to lose a proton , it is largely unaffected by the configuration 
 of the remaining three his37 residues . therefore , the interplay between 
 his37 residues , the ph sensor of the channel , is ph dependent during 
 the proton relay .
the trp41 gate and the membrane environment , on 
 the other hand , are likely to play a role in modulating the rate of 
 deprotonation and thus the conductance .
different computational 
 approaches have previously been used to 
 explore the deprotonation from the charged his37 cluster in the m2 
 protein .
in one recent paper 
 from our group , the deprotonation from a single histidine and from 
 the histrp motif in water was investigated with 
 dft - based md simulations .
for a single 
 histidine , the free energy barriers were calculated to be 10.010.1 
 kcal / mol at the n position , and 10.510.6 kcal / mol at 
 the n position .
a recent study from voth and co - workers combined 
 an empirical valence bond and a dft - based qm / mm approach to study 
 the proton release at different protonation states , reporting barrier 
 heights of 13 and 10 kcal / mol for proton release from 
 the triply and quadruply charged his37 cluster , respectively . when a single trp residue is included 
 in the calculation with a 
 position resembling that in the protein , the barrier for the n 
 was found to be 9.1 kcal / mol , 1 kcal / mol lower than that in 
 the isolated histidine in water box , suggesting 
 a role of the trp41 gate in regulating the proton relay through his37 , 
 in addition to its known ability to generate an asymmetric flow . specifically , charge transfer from his37 to 
 the bound trp41 through the cation interactions was 
 witnessed , as assessed by the partial charge on each group ( figure 4b ) , consistently with the calculated electrostatic 
 potential .
presumably , this charge delocalization 
 decreases the energy cost to lose a proton . in the present work , 

the energy cost for deprotonation in the membrane 
 environment is 6.5 kcal / mol , significantly lower than the 
 one in the histrp motif or the isolated his .
apparently , the present work provides a more 
 realistic model in studying proton transfer , where the backbone of 
 the transmembrane domain of the protein , the trp41 gate , and the explicit 
 membrane environment have significant effects on modulating the dissociation 
 of protons from his37 . for the latter one , to be specific , the confined 
 environment of the pore and the low dielectric constant of the membrane 
 destabilize the charged cluster , and thus facilitate the deprotonation 
 of the charged his37 . by using the following equations and assuming g = 0 for simplicity between his37 and bulk water ,
the upper limit of the pka 
 of his37 in the membrane environment is estimated to be 4.7 in the 
 d3-model and 5.0 in the h3-model , respectively , based on the major 
 barrier heights for deprotonation in both models .
experimentally , 
 the third pka of the his37 cluster  when three 
 of four residues are protonated  was determined as 6.3 and 4.9  0.3 , respectively , by using different protein constructs and lipid membrane 
 compositions .
the backbone conformations 
 in both d3- and h3-models are very similar 
 to those of the relatively compact protein structure at neutral ph . without significant expansion of the backbone
, 
 we demonstrate that both models are able to release a proton with 
 a moderate energy cost .
the presence of the c - terminal amphipathic 
 helix anchoring at the lipid interfacial region is likely to limit 
 the dynamic of the c - terminal segment , compared to what seen for the isolated the transmembrane helices 
 from electron paramagnetic resonance ( epr ) experiments and the x - ray structure determined at low ph conditions . finally , 
 we investigated 
 the possibility of a role for cl or other halide 
 anions in the proton relay mechanism through the pore . in electrophysiology 
 studies ,
the proton conduction rate was found to be unaffected by 
 the concentration of cl in both oocytes and liposomes .
this finding is in apparent 
 contrast with the attractive force that a triply charged his37 tetrad 
 can exert on a cl ion : assuming for simplicity that the rate of proton transfer is only 
 controlled by electrostatics , cl ions should increase 
 the proton conduction rate . in a recent study of the calcium - release 
 activated calcium channel ( crac ) , a cation - conducing channel with 
 a 6  - wide pore and a high density of basic side chains , we observed 
 that cl anions in the pore significantly increase 
 the rate of permeation of na cations .
therefore , we extended the proton transfer calculations 
 to a model including a cl ion bound to the his37 
 tetrad , to explore its impact on the proton conduction rate .
as shown in the pmf calculations , the presence of cl makes the free energy cost of deprotonation much higher . following 
 the increasing n 
h distance , the pmf keeps rising : at  
 = 1.36  , where the major barrier is located in the previous pmfs , 
 the free energy value is 10.5 kcal / mol , 3.9 kcal / mol higher than that 
 in the h3-model ( figure 5a ) .
this demonstrates 
 that the presence of cl creates an unfavorable 
 pathway for a proton to be released . during the simulations ,
the cl ion is located in the highly charged his37 cluster , 
 and has stable interactions with the water in the cavity below , which 
 is formed by the his37 and trp41 clusters ( figure 5d ) .
the arrangement of the hydrogen bonding network of water 
 molecules in the cavity could compensate in principle the energy cost 
 for bond breaking of the proton release . nevertheless , the electrostatic 
 attraction between the anion and the proton attenuates the proton 
 diffusion out of the cavity to the c - terminal even though the trp41 
 gate is occasionally open .
therefore , the presence of anions in the 
 his37trp41 cavity is an unfavorable factor for proton 
 release , which the m2 channel can circumvent by maintaining its pore 
 free of cl ions through its asp44 residues , two 
 helical turns away from his37 .
this is confirmed by mutations of asp44 , 
 which significantly impact the proton conduction profile in a salt 
 solution with a [ cl]/[so4 ] ratio approximately 2:1 .
in this study , we explored the different configurations of the 
 his37trp41 cluster in the m2 protein at low ph conditions , 
 and the subsequent deprotonation via qm / mm md simulations . with regard 
 to the conformation of the key residues , two alternative models ( d3 
 and h3 )
converge to a single deprotonation mechanism , and feature 
 similar free energy profiles to release a proton , with a barrier height 
 of 6.5 kcal / mol .
therefore , the multiconfiguration model proposed 
 in our previous work , includes deprotonation 
 as a mechanism not only for proton conduction , but also for conformational 
 exchange connecting the multiple configurations of this protein .
the 
 confined region between his37 and trp41 also appears to significantly 
 increase the proton affinity of a water molecule compared to the bulk 
 solution .
calculations with a bound cl ion in the 
 pore show that halide anions may contribute to stabilizing the triply 
 charged histidine cluster , but at the same time impede the release 
 of protons .
we suggest that only those viral strains capable of maintaining 
 halide anions outside the pore can maintain a stable proton conduction 
 rate irrespective of the anions bulk concentration .
 the activity of the m2 proton channel 
 of the influenza a virus 
 is controlled by ph . 
 the tautomeric state and conformation of his37 , 
 a key residue in the m2 transmembrane four - helix bundle , controls 
 the gating of the channel . 
 previously , we compared the energetics 
 and dynamics of two alternative conformations of the doubly protonated 
 state at neutral ph , namely , a 4-fold symmetric  histidine - box  
 and a 2-fold symmetric  dimer - of - dimers  , and proposed 
 a multiconfiguration model for this charge state . here , we elaborate 
 this model by further studying configurations of the his37 tetrad 
 in the triply protonated state and its subsequent deprotonation via 
 quantum mechanics / molecular mechanics ( qm / mm ) molecular dynamics ( md ) 
 simulations , starting with the aforementioned configurations , to gain 
 information about proton release in a viral membrane environment . 
 
 interestingly , the two configurations converge under acidic ph conditions . 
 
 protons can be transferred from one charged his37 to a neighboring 
 water cluster at the c - terminal side of the channel when the trp41 
 gate is open transiently . with limited backbone expansion , 
 the free 
 energy barrier for proton release to the viral interior at low ph 
 is 6.5 kcal / mol in both models , which is much lower than at 
 either neutral ph or for an isolated his37 cluster without a membrane 
 environment . 
 our calculations also suggest that the m2 protein would 
 seem to exclude the entrance of anions into the central channel through 
 a special mechanism , due to the latter s potential inhibitory 
 effect on proton conduction . 
Introduction
Computational Details
Results and Discussion
Conclusions