membrane proteins play a significant role 
 in myriad biological 
 processes and account for 30% of all proteins in the cell . the transmembrane ( tm ) segments of these proteins are usually composed 
 of hydrophobic helices whose sequence determines their orientation 
 and position of in membranes . despite the hydrophobic nature 
 of the tm segments , occurrences of charged residues are believed to 
 be important for the function of membrane proteins . in integrins , 
 for instance , basic amino acid side chains that are buried in the 
 membrane regulate transmembrane signaling , and the ion selectivity of nicotinic - type receptors is determined 
 by the presence or absence of a pore facing carboxylate ring in the 
 membrane bilayer . recent studies suggest that the 
 microenvironment of these buried residues , for example , lipids and 
 phosphate head groups , has a profound effect on their charged states , 
 which would influence the orientation of the titratable side chains 
 and their helical configurations in the membrane . therefore , detailed 
 information about the pka values of buried 
 residues in hydrophobic environments can shed light on the extent 
 of microenvironment effects on the population of the charged and neutral 
 states and , thus , ph - modulated biological function of membrane proteins . the role of buried ionizable residues in determining helix orientation 
 and the effect of the membrane bilayers in modulating their pka values have been investigated by solid state 
 nmr ( ssnmr ) in simple model peptides such as the walp and gwalp series using quadrupolar 
 splitting of labeled ala residues . these tm peptides have provided 
 the opportunity to capture peptide  membrane interactions in 
 great detail and predict possible scenarios for protein have 
 shown that buried arg residues at different positions in the gwalp23 
 peptides gives rise to different peptide behavior in membrane bilayers . the gwalp23 peptide with an arg in position 14 has an average tilt 
 angle of 16.2 which is almost 10 greater than the gwalp23 . in addition , the gwalp23 peptides with one arg in position 12 tend 
 to exit the lipid bilayer and do not form stable tm orientations in 
 the membrane . using the same peptide 
 models , koeppe et al . revealed that arg maintains its positive charge 
 in the membrane bilayer while lys containing peptides titrate and 
 change their tilt angles . for instance , the pka of a lys residue in the 14th position of lys - containing gwalp23 
 peptides is shifted down by 4 ph units ( 6.2 at 323 k and an 
 estimated value of 6.8 at 298 k ) compared to the standard pka of lys in aqueous solution ( 10.4 ) . these peptides 
 also adopt a tilt angle of 15 , which is 10 larger 
 than the tilt angle of the gwalp23 peptide . similar to arg - containing peptides , the gwalp23 with lys in the 12th position shows a smaller tendency 
 to remain in a single membrane bound configuration , which makes it 
 difficult to determine the pka of this 
 residue . these examples and several 
 more are strong evidence of the effect 
 of the microenvironment on the 
 protonation equilibria of protein side chains . thus , along with experimental 
 techniques such as nmr , several computational methods have been developed 
 to calculate the pka values of titratable 
 residues in different environments . among these techniques , constant 
 ph molecular dynamics ( cphmd ) approaches are particularly devised 
 to study ph dependent behavior of proteins for which little information 
 about the charged states of the key residues are available . unlike 
 poisson boltzmann based approaches , in the cphmd methods , protonation states of a side chain are coupled 
 with the protein dynamics and are allowed to propagate with time following 
 degrees of freedom in the system . there are two distinct cphmd approaches 
 that are in use . in discrete cphmd methods , first developed by van 
 gunsteren et al . , the charge states of titratable residues are determined 
 by performing monte carlo ( mc ) steps at specific intervals of regular 
 molecular dynamics simulations . in this approach , the abrupt change 
 in the protonation states of the residues ( and overall charge of the 
 system ) can lead to discontinuity of the potential energy and possible 
 side effects after mc moves along the titration coordinate . this issue 
 is alleviated in the continuous cphmd methods pioneered by brooks 
 et al . in this category of cphmd techniques , the titration coordinates 
 propagate in time using a  dynamics approach , which provides a continuous switch between different protonation 
 states and prevents sudden jumps in the potential energy and its derivatives . we note that  dynamics is related in its underlying formulation 
 to techniques devised by pettitt and co - workers for the addition and 
 deletion of particles within a grand canonical ensemble to achieve 
 constant chemical potential . first implemented 
 in an implicit solvent framework and 
 later improved to include proton tautomerism , continuous 
 cphmd has been shown to be successful 
 in calculating the pka values of titratable 
 residues for a diverse set of proteins . in spite of numerous successes , this method suffers from the well - known 
 disadvantages of the generalized born implicit solvent models . for 
 instance , the overestimation of the desolvation energy for the buried 
 charges in the protein core , or the compactness 
 of the protein structures , can induce systematic 
 errors in pka calculations . more significant 
 errors can occur for membrane proteins with buried charge residues 
 as a result of assumptions used in the implicit membrane models , such 
 as the rigid nature of the membrane bilayer , the insertion 
 of a charged residue in the hydrophobic core of the membrane requires 
 complete loss of its solvation shell . however , as evidenced in detailed 
 explicit membrane / solvent simulations , charged residues in the membrane 
 are surrounded by a few water molecules and possibly phosphate head 
 groups . partial solvation of the charged residues 
 helps to compensate for the low dielectric environment of the membrane 
 and significantly reduces the insertion energy , while total loss of 
 the solvation shell in implicit membrane models leads to systematic 
 overestimation of side chain pka s . recently , brooks and co - workers developed a novel explicit solvent 
 cphmd approach based on a new multisite  dynamics framework 
 ( cphmd ) and applied it to study 
 the ph - dependent dynamics of several rna and protein systems . in addition , to 
 address the convergence problems of earlier cphmd variants , ph - based replica exchange may be employed to enhance the sampling 
 of the spatial and titration coordinates . inspired by the recent pka measurements 
 of the buried lys residues in 1,2-di(9z - octadecenoyl)-sn - glycero-3-phosphocholine ( dopc ) bilayers , we were motivated to utilize the cphmd method on several tm - gwalp23 peptides containing titratable residues 
 at position 12 or 14 to examine the influence of the membrane on the 
 structure and pka of the ionizable residues 
 in these peptides . our results indicate that the cphmd method reproduces the pka s of 
 lys residues in the lys - containing gwalp23 peptides inserted in the 
 membrane bilayer , in good accord with the pka measurements from quadrupolar splitting ( qs ) of deuterated 
 ala residues . in addition , we observe 
 that the peptide tilt angle is affected by the protonation state of 
 the titratable residues : for example , the peptides are significantly 
 more tilted in charged states , and this general trend of the tilt 
 angle variation is in agreement with the ssnmr data . in addition , 
 we directly predict the pka variations 
 of his in an ether - linked dopc bilayer and glu and asp in an ether - linked 
 1,2-dilauroyl - sn - glycero-3-phosphocholine ( dlpc ) 
 in the context of tm - gwalp23 peptides . overall , our results indicate 
 that both protonation states and tilt angles in the peptides containing 
 titratable residues are considerably influenced by their surrounding 
 environment . the list of the peptides 
 simulated in this paper along with their 
 sequence and the membrane they are inserted in are provided in table 1 . insertion of the peptides along with the equilibration 
 steps are described in more detail in the supporting 
 information . the ph - replica exchange 
 simulations ( ph - rex ) on the membrane - inserted 
 peptides were performed in the following manner . the structures obtained 
 from the equilibration runs of protonated and unprotonated side chains 
 were used as the initial structures of the ph - rex calculations with 
 each equilibrated structure used as alternative replicas . the number 
 of replicas and the ph range for each system is listed in table 1 . replica exchange in the ph variable has previously 
 been shown to improve the convergence of pka calculations . all simulations were 
 performed using cphmd with the block facility 
 and the  functional form with 
 a coefficient of 5.5 . expressing  
 in this particular form in terms of virtual particles that propagate 
 through the course of the simulation (  ) has 
 been shown to increase energy stability . more detailed discussion 
 on the effect of functional form of  versus  is provided in ref . all nonbonded energy 
 terms were linearly scaled by  while all bond , angle and dihedral 
 terms were unscaled . a nonbonded 
 cutoff of 12  was used with an electrostatic force - shifting 
 function and a van der waals switching function . a fictitious mass 
 of 12 amu was assigned to all . in the ph - rex simulations , exchange attempts were 
 made every 1 ps . each ph - rex simulation was repeated 3 times for 5 
 ns per replica , from which the last 3 ns was used for analysis . all parameters for the ph - rex simulations were 
 kept as default values as listed in ref ( 53 ) . the fraction of unprotonated state at 
 each ph ( sunprot ) was determined from 
 the total population of the 
 unprotonated ( nunprot ) and protonated 
 states ( nprot ) states.1these populations are defined as the total 
 number of times in the trajectory that the condition  > 
 0.8 
 for eitnher the unprotonated or protonated state is satisfied . to obtain the pka of the system of 
 interest , sunprot is fitted versus ph 
 using the henderson hasselbalch equation.2 the configuration of the peptides at different ph values was 
 also 
 examined . the tilt angle of the peptides was measured as the angle 
 between the membrane normal ( z - axis ) and the peptide 
 axis , which was defined as the vector connecting the c atoms . the rotation angle is defined as the angle between the vector that 
 connects the helical axis to the c atom of residue leu 14 and 
 is perpendicular to the helix axis , and the projection vector of the z - axis onto the plane made by the second and third principal 
 axes . for a more detailed definition of the tilt and rotation angles we have simulated eight tm peptides , 
 each having one titratable 
 residue ( i.e. , k , h , e , or d ) at position 12 or 14 in the peptide . 
 the purpose of this study is to investigate the effect of the membrane 
 bilayers on the pka values of these residues , 
 as well as to examine the ph - dependent variation of the peptide configurations 
 in the membranes . in addition , we compare the pka values obtained from the cphmd simulations 
 with those of lys containing residues from the ssnmr measurements and make direct predictions for the other titratable 
 side chains . the pka values for 
 different side chains , 
 averaged over three runs , are listed in table 1 . our results show that the lys residue in the k14 
 peptide has a pka of 5.6  0.2 , in 
 good agreement with the estimated experimental value of 6.8 at 300 
 k and within the error bars observed 
 for insertion free energies of different side chains in membrane bilayers . the difference we see here may be due to the 
 steep gradient of the membrane dielectric across its normal . small 
 changes in the position of the side chain across the membrane normal 
 is accompanied by large variation in the apparent dielectric constant 
 of the membrane , which can cause significant changes in the side chains 
 pka . the qs measurements 
 of ala residues for the k12 peptide only determined an upper bound 
 of 7 for the pka value of the lys side 
 chain . thus , 
 we find that , consistent with the ssnmr experiment , the pka of lys residues at the 12th or 14th position of gwalp 
 peptides are shifted by 4.4 ph units . interestingly , similar 
 pka shifts were previously observed for 
 lys residues in engineered mutants of staphylococcal nuclease . among 25 single mutations , 4 mutants with lys 
 residues located in the inner core of the protein showed depressed 
 pka values between 5.3 and 6.5 , which were accompanied by partial or global 
 unfolding of the protein at low ph values . titration curves for 
 three trials of ph - rex for different peptides 
 listed in table 1 . the unprotonated fractions 
 obtained from ph - rex are shown with circles , and the lines represent 
 the henderson  hasselbach fit . in some panels , due to overlap 
 of the curves and data points , since no measurements yet exist 
 for substitutions of his , asp , 
 or glu at these same positions in the gwalp peptides , we decided to 
 make direct predictions of the pka values 
 and the corresponding peptide configurations . for all substituted 
 residues , significant pka shifts with 
 respect to the standard reference pka values 
 are observed . in the case of the his - containing peptides , h12 and 
 h14 in table 1 , pka shifts of 2 and 1.5 units toward the neutral form 
 are observed , respectively . glu residues at these positions ( e12 and 
 e14 ) yield calculated pka values of 9.8 
  0.1 and 9.7  0.1 . for the asp residue at position 12 
 ( d12 ) and 14 ( d14 ) , pka values of 9.4 
  0.2 are obtained . we note that in a different study using fluorescence 
 emission of a trp residue , a pka of 8.7 
 was reported for an asp residue in the transmembrane helix formed 
 by the peptide k2gl7dlwl9k2a ( termed pl(d11 ) ) indicating a 4.7 ph unit shift in favor 
 of the neutral state in a dopc bilayer . while , due to different peptide sequences and membrane compositions , 
 direct comparison between this value and the pka observed in our simulations is difficult , the difference 
 can be attributed to the interfacial orientation of the peptide that 
 is suggested to be adopted in the latter study . the significant shift of the pka values of e and d at positions 12 and 14 suggest that the ratio 
 of protonated versus unprotonated side chains in membranes is severely 
 shifted toward the latter and , perhaps , in the absence of any other 
 stabilizing interactions ( e.g. , salt bridges with neighboring residues ) , 
 these side chains tend to stay protonated in the membrane within the 
 biologically relevant ph ranges . in order to investigate the 
 effect of ph on the charge state and 
 eventually the configurations of these peptides in membrane bilayers , 
 we examined the tilt and rotation angles of the peptides at different 
 ph values . the potential of mean forces ( pmf ) for basic ( k and h ) 
 and acidic ( e and d ) side chains along their tilt and rotation angles 
 were calculated and are shown in figures 2 and 3 , and the dominant structures extracted from the 
 replicas with specified ph values are depicted in figures 4 and 5 , respectively . for 
 positively charged side chains , depicted in the left column of figure 2 , the peptides adopt tilt angles between 30 
 and 50 , and rotation angles between 20 and 100. 
 the neutral peptides , which are populated at high ph values , on the 
 other hand adopt smaller tilt angles roughly form 5 to 25 
 with rotation angles that are not significantly affected ( figure 2 right column ) . the experimental values for the 
 k14 peptide at high and low ph values and for k12 at high ph obtained 
 from the qs of deuterated ala residues are marked in the figure with red circles . due to complexity of 
 the qs data for k12 at low ph , no tilt and rotation angles were reported . it can be seen that the tilt and rotation angles obtained experimentally 
 for k12 and k14 at high ph values are part of diverse ensembles that 
 are sampled by these peptides in our simulations . for positively charged 
 k14 , on the other hand , the tilt and rotation angles that are adopted 
 by the peptide in our simulations are significantly larger . 2d pmfs of 
 rotation angle vs tilt angle for tm helices containing 
 k and h side chains for low and high ph values where the titratable 
 side chains are predominantly protonated ( positively charged ) and 
 unprotonated ( neutral ) , respectively . 2d pmfs of rotation angle 
 vs tilt angle for tm helices containing 
 e and d side chains for low and high ph values where the titratable 
 side chains are predominantly protonated ( neutral ) and unprotonated 
 ( negatively charged ) respectively . representative structures of tm peptides containing 
 one basic side 
 chain obtained from the replica with specified ph value . the peptide 
 backbone is depicted with green cartoon representation , while the 
 titratable side chains are shown with blue van der waals representations . water molecules whose 
 center of masses are within 5  of the side chains are illustrated 
 with van der waals spheres and red color . we also examined the distribution of tilt and rotation 
 angles for 
 the acidic side chains at both high and low ph ( see figure 3 ) . at low ph , where the side chains are protonated 
 and neutral ( figure 3 left column ) , the peptides 
 tend to have smaller tilt and rotation angles compared to high ph 
 ( figure 3 right column ) , where the side chains 
 are negatively charged . while the ph dependent variations of 
 the tilt and rotation angles 
 of k12 and k14 agree well with the experimental values , the values 
 we observe are larger than those reported from the experimental measurements . similar apparent disagreements between tilt and rotation angles obtained 
 from molecular dynamics simulations and the values calculated from 
 ssnmr observables have been noticed before for several tm peptides 
 including the walp series . these discrepancies are believed 
 to stem from orientational fluctuations of the peptides in membrane 
 bilayers . recently , extensive attempts have been made to capture the 
 complex motions of tm helices in different models in order to extract 
 more representative tilt and rotation angles from ssnmr qs measurements . however , ssnmr observables are time and ensemble averaged data , which 
 may not fully represent a single helix orientation . therefore , more 
 complicated methods are needed to obtain the tilt and rotation angles 
 from these measurements . finally , 
 the effect of ph on the orientation of the peptides and 
 the structure of the membrane aqueous interface can be highlighted 
 with further details by looking at representative structures from 
 our simulations . the dominant structures of each peptide at high and 
 low ph values were selected as noted in the computational methodology 
 and the results for positive and negative side chains are depicted 
 in figures 4 and 5 , 
 respectively . for the basic side chains , as illustrated in figure 4 , at low ph ( left column ) , the peptides tend to 
 have highly tilted structures with more interfacial exposure of the 
 side chain . the tilting of the peptides accompanied by the deformation 
 of the bilayer , which allows solvation of the charged state with water 
 molecules and head - groups , leads to considerable stabilization of 
 the charged states . however , increasing the ph ( figure 4 right column ) causes the solvation shell to be 
 lost and the tilt angle to decrease . the same effect can be observed 
 in figure 5 for acidic side chains . at low 
 ph values , the peptides tend to have smaller tilt angles while at 
 high ph the tilt angles are increased and the solvation shell around 
 the side chains is formed ( compare left and right columns of figure 5 ) . in addition to the improved charge solvation 
 provided by helix tilting , the enhanced tilting of the peptide in 
 the presence of the charged side chain can also be explained by the 
 effect of partial solvation on the membrane thickness . the water molecules 
 and head groups in the solvation shell that surround the charged side 
 chain and penetrate into the hydrophobic core of the membrane , cause 
 the local membrane thickness around the side chain to decrease . the 
 thinning of the membrane causes the helix to tilt to maximize the 
 interactions between membrane core and the hydrophobic peptide . in 
 addition , tilting of the helix when the side chain is charged provides 
 more exposure of the side chain to the membrane exterior where it 
 incurs a lesser desolvation penalty . the effect of peptide sequence 
 and membrane thickness fluctuation on the peptide tilt angle have 
 been discussed in more detail in the following references : ( 45 , 47 , 48 , and 61 ) and the references therein . our simulations 
 suggest that the observed pka values are tightly coupled to the conformation 
 of the peptide and membrane / water interface . detailed explicit solvent 
 simulations of insertion of proteins and small molecules into lipid 
 bilayer have revealed that these fluctuations are 
 typically kinetically hindered and long time scale simulations ( possibly 
 ms ) may be required to ensure convergence of the thermodynamics properties . this may be reflected in the pka values 
 reported here . in principle , cphmd simulations 
 can be combined with umbrella sampling along rotation and tilt angles 
 of the peptide or advanced enhanced sampling techniques such as the 
 ensemble dynamics approach to strengthen the sampling 
 along these two reaction coordinates . however , our generally good 
 agreement with experiment in the case of the lysine based peptides 
 and the similar charge - state dependence of the peptide orientation 
 and membrane interface structure for both basic and acidic peptides 
 suggest that our findings are at least semiquantitatively reasonable . in this study , we have applied for the first time constant ph molecular 
 dynamics techniques to calculate the pka values of titratable side chains in the context of tm helices and 
 investigated the effect of ph on the configuration of the studied 
 peptides . our calculated pka values for 
 the lys - containing peptides and the values previously obtained using 
 ssnmr qs of deutrated ala residues are 
 in good agreement . we also observed that the configuration of the 
 various peptides and the arrangement of the lipid molecules in the 
 vicinity of the side chains are coupled to the external ph . at ph 
 values where the population of the charged states dominates , the peptides 
 tend to have more tilted structures with notable membrane deformation . 
 on the other hand , when the ph is such that the population of the 
 neutral side chains is pronounced , the tilt angles are decreased and 
 the membrane deformation is less significant . the overall good 
 agreement between the calculated pka values 
 and the experimental values especially for the 
 case of lys containing peptides and the 
 variation of the peptide conformation with ph suggest that the cphmd captures the essence of ph dependency of peptide 
 membrane interactions .
in 
 this work , we apply the recently developed constant ph molecular 
 dynamics technique to study protonation equilibria of titratable side 
 chains in the context of simple transmembrane ( tm ) helices and explore 
 the effect of ph on their configurations in membrane bilayers . 
 we 
 observe that , despite a significant shift toward neutral states , considerable 
 population of different side chains stay in the charged state that 
 give rise to pka values around 9.6 for 
 asp and glu and 4.5 to 6 for his and lys side chains , respectively . 
 these charged states are highly stabilized by favorable interactions 
 between head groups , water molecules , and the charged side chains 
 that are facilitated by substantial changes in the configuration of 
 the peptides . 
 the ph dependent configurations and the measured pka values are in good agreement with relatively 
 recent solid state nmr measurements . 
 our results presented here demonstrate 
 that all - atom constant ph molecular dynamics can be applied to membrane 
 proteins and peptides to obtain reliable pka values and ph dependent behavior for these systems .