investigating 
 factors that influence the stability of the secondary 
 structure of peptides and proteins , such as confinement , competitive 
 solvation in a heterogeneous environment , and peptide functional group 
 modifications , is important to our understanding of why proteins misfold 
 and aggregate . reverse micelles ( rms ) are a convenient environment 
 in which to encapsulate and probe biological molecules . the water cores of rms are similar to cavities found in biological 
 systems , such as water molecules near 
 the water  membrane interface of a cell . because the size of 
 rms is determined by the water to surfactant ratio ( water loading , w0 = [ h2o]/[surfactant ] ) , rms represent 
 a environment for the study of the effects 
 of limited hydration and confinement on protein folding , aggregation , 
 and function . a significant effort has 
 been made to explore the properties of rms using computer simulation , 
 beginning with the influential work of ladanyi and coworkers . that work provided the foundation for subsequent studies of rms 
 employing all - atom and coarse - grained models . subsequent studies explored the nature of water dynamics in rm environments , where it has been shown that water rotational relaxation is dramatically 
 slowed relative to water in the bulk . the seminal experimental 
 work of mukherjee et al . explored the 
 structure of capped alanine - rich peptides 
 akan ( ace - ygakaaaa-(kaaaa)ng - nh2 ) in aot rms ( using nonpolar 
 solvent isooctane = 2,2,4-methylpentane ) and in bulk water . sodium 
 bis(2-ethylhexyl ) sulfosuccinate ( aot ) is a widely used anionic surfactant 
 that forms monodisperse rms in nonpolar solvents . using cd and ir spectroscopy , they observed that upon encapsulating 
 the peptides in rms of low w0 the helical 
 content increased significantly as compared with that measured in 
 bulk water or a buffer . tian and garcia performed molecular 
 dynamics simulations of self - assembling rms and encapsulated zwitterionic 
 aka4 peptides . they observed nonspherical shape fluctuations 
 of the rms and also found that the peptides preferred to reside at 
 the water abel and coworkers obtained similar results for previous simulations of zwitterionic 
 octa - alanine peptides in rms . martinez and coworkers performed simulations 
 on capped aka2 peptide in bulk water and in rms of w0 = 6 that were both spherically restrained 
 and unrestrained . for reference rms of w0 = 6 , the results indicated that the peptides were more helical 
 in rms than in bulk water . additionally , the shape of unrestrained 
 rms fluctuated significantly from an initial spherical geometry , facilitating 
 interaction between the dehydrated peptide and the aot aliphatic tails 
 that appears to be important in stabilizing the peptide s partial 
 helical character . these results are 
 in agreement with experiments as well 
 as previous computational studies . it is known that the treatment of n- and c - termini with neutral caps 
 can influence the peptide structure . however , while experimental studies 
 of alanine - rich peptides in rms were performed with capped peptides , simulations studies by abel and coworkers and tian and garcia have employed zwitterionic termini , and those by martinez and coworkers have employed capped termini . the experimental 
 observables in the original studies of mukherjee et al . were cd and ir spectra . however , no simulation 
 studies have computed spectra to be directly compared with experiment . this study explores the effects of capped versus zwitterionic 
 n- 
 and c - termini on the helix stability of these same peptides in rms 
 using two force fields . we performed simulations of the aka2 peptide in two forms , capped ( ace - ygakaaaa-(kaaaa)2g - nh2 ) and zwitterionic ( nh3 + -ygakaaaa-(kaaaa)2g - coo ) , in spherically restrained and unrestrained 
 rms of w0 = 6 . the results demonstrate 
 that capped aka2 peptides form more stable helices than 
 zwitterionic aka2 peptides . the ir spectra of the amide 
 i bond of the peptides were computed and directly compared with experiment . the computed peptide amide i ir spectra and water 
 rotational anisotropy decay were found to be largely insensitive to 
 the treatment of the peptide termini , while showing a distinct dependence 
 on shape fluctuations in the rm environment . overall , our results 
 provide insight into the nature of peptide confinement and hydration 
 in a rm environment and the importance of considering shape fluctuations 
 in characterizing the rm ensemble . the rms each contained a peptide monomer , and the starting structure 
 for the peptides was an -helix . table 1 contains a summary of the simulation details for all systems , including 
 the number of all molecules ( surfactant , ions , water , and solvent ) 
 used and simulation times . the composition of the rms was determined 
 from the saxs experiments of amararene et al . this composition differs from that suggested by the experiments 
 of eicke and rehak . in a separate study , we have explored the structure and dynamics of alternative interpretations 
 of the water loading for comparison . rm systems were generated using the charmm32 package with the charmm27 all - atom force field for proteins 
 and lipids and the tip3p water model for charmm . charmm parameters 
 for aot and isooctane were taken from the work of abel et al . to construct the rms the helical structure 
 generated for the peptide was solvated with a sphere of water , and 
 random water molecules were replaced with 76 sodium cations ( one for 
 each aot molecule to be added ) and three chlorine anions ( one for 
 each lys ) to create a neutral system . a spherical aot shell was added 
 to the rm and was centered in a truncated octahedron of isooctane . for the spherically restrained rms , a massless dummy atom was fixed 
 in the center of the rm , and a harmonic restraint was placed on the 
 sulfur atom of each aot molecule to keep it within 11.25 and 15.25 
  of the dummy atom . the distance restraints were chosen to agree 
 with experimental measurements of the solution density . the cutoff for the short - range electrostatics calculations was set 
 to be 12  , and particle - mesh ewald was used to treat the long - range 
 electrostatics . the temperature was held constant at 300 k , and the 
 pressure was held constant at 1 atm using the langevin piston . each 
 trajectory was run for 50 ns using a 1 fs time step and saving data 
 every 0.1 ps . the same systems were also run using gromacs and 
 the gromos96 53a6 
 united atom force field . the electrostatics 
 were treated as in the charmm simulations . the temperature was held 
 constant at 300 k , and the pressure was held constant at 1 atm using 
 the berendsen piston . each trajectory 
 was run for 50 ns using a 2 fs time step and saving data every 0.1 
 ps . analysis of all systems was performed using charmm , gromacs , mdanalysis , and vmd . consistent with 
 experimental observations by halle and 
 theoretical considerations by chandler , recent results from simulation and experiment suggest that 
 unrestrained rms showed significant shape fluctuation . figure 1 shows representative structures taken from unrestrained 
 charmm simulations after 50 ns of simulation time . the water and aot 
 molecules are found to pucker around the peptide , allowing for significant 
 interaction of the aot tail groups and at times the isooctane with 
 the nonpolar surface of the peptide . these observations of nonspherical 
 rm shape fluctuations and contacts between the peptide and the environment 
 were also observed by tian and garcia in their simulations of similar 
 systems . to characterize these structural 
 fluctuations , we calculated the average elliptical radii and the radius 
 of gyration for each rm system . the results ( not shown ) indicate an 
 elliptical geometry for the unrestrained rms that are consistent with 
 the results of previous experimental and simulations studies . helical peptides form dipoles with 
 a partial positive charge at 
 the n - terminus and a partial negative charge at the c - terminus . capping 
 the termini eliminates the charge repulsion present when the terminal 
 residues are charged and tends to stabilize the helix . figure 2 shows the secondary 
 structure progression with respect to time for the residues of each 
 of the aka2 peptides in rms for the charmm trajectories . the structure of the capped aka2 peptides changes very 
 little during the simulation with the peptides remaining almost entirely 
 -helical . the structure of the terminal residues of the zwitterionic 
 aka2 peptides shows significant fluctuations , especially 
 in the case of the unrestrained rms , suggesting that the zwitterionic 
 termini contribute to the destabilization of the helical secondary 
 structure . similar results were found for the gromacs trajectories 
 ( data shown in supporting information ) . the secondary structure definitions used are those of kabsch and sander s 
 dssp method . charmm unrestrained reverse 
 micelles with capped ( left ) aka2 and zwitterionic ( right ) 
 aka2 peptides . the components 
 of the rm are colored as follows : aot tail groups , white surface ; 
 sulfonate head groups , yellow and red ; sodium ions , dark green ; water 
 molecules , blue ; peptide , bright green . secondary structure progression with respect to time of aka2 peptides in unrestrained ( top ) and spherically restrained 
 ( bottom ) reverse micelles for the charmm systems : capped aka2 ( left ) and zwitterionic aka2 ( right ) . the secondary structure 
 is indicated as helix ( blue ) , turn ( yellow ) , and coil ( white ) . another way to evaluate secondary 
 structure stability is the root - mean - square 
 deviation ( rmsd ) with respect to time . figure 3 presents a histogram of the observed peptide rmsd , demonstrating 
 that the two capped aka2 peptides have a more stable backbone 
 structure and undergo smaller fluctuations compared with the zwitterionic 
 peptides . comparison of the dssp and rmsd plots suggests that fluctuations 
 in rmsd for the capped aka2 peptide , in the unrestrained 
 rm , in particular , result from the changes in the secondary structure 
 in the terminal residues . significant interaction of the aka2 peptides 
 with the surrounding environment of the rm is observed in all systems 
 studied . in the unrestrained rms , however , in addition to the interaction 
 between the peptides and water molecules , there is significant contact 
 between the peptides and the surfactant molecules , especially the 
 aliphatic aot tail groups . distribution of the peptide backbone rmsd for 
 the last 30 ns of 
 simulation for the aka2 peptides in rms for the charmm 
 systems . data are shown for capped / zwitterionic peptides in restrained 
 ( blue / yellow ) and unrestrained ( pink / green ) rms . fluctuations of the 
 capped peptides are substantially smaller than for the zwitterionic 
 peptides . figure 4 shows the average number of aot 
 tail groups and water molecules within 4  of each residue of 
 the aka2 peptides in rms for the charmm systems . the core 
 residues of the peptides in the restrained rms are significantly more 
 hydrated than the residues of the peptides in the unrestrained rms , 
 which are in contact with more aot tail groups . average number of aot 
 tail groups ( top ) and water molecules ( bottom ) 
 within 4  of each aka2 residue in the charmm rms . data are shown for capped / zwitterionic peptides in restrained ( blue / yellow ) 
 and unrestrained ( pink / green ) rms . figures 5 and 6 show 
 the number of aot tail groups and water molecules within 4  
 of each of the aka2 peptides . the distributions show good 
 agreement between peptides in the same environment ( restrained or 
 unrestrained rm ) regardless of nature of the n and c  termini . the distribution of the hydration values of the two peptides in the 
 restrained rms is almost identical . peptides in the unrestrained rms have more contact with the tail groups 
 than peptides in the restrained rms . data are shown for capped / zwitterionic 
 peptides in restrained ( blue / yellow ) and unrestrained ( pink / green ) 
 rms . data are shown for capped / zwitterionic peptides in restrained ( blue / yellow ) 
 and unrestrained ( pink / green ) rms . the level of hydration of the peptides 
 is similar in each environment with peptides in the restrained rms 
 being more hydrated than peptides in the unrestrained rms . figure 7 shows snapshots 
 of charmm aka2 in restrained and unrestrained rms with 
 the surrounding water 
 and aot tails after 50 ns of simulation . the peptide in the restrained 
 rm is almost completely hydrated , while the peptide in the unrestrained 
 rm is in contact with aot aliphatic tails . tian and garcia noted similar 
 behavior in their simulations of aka4 peptides in rms . they observed significant contact between the 
 nonpolar peptide core and the aot / water interface as well as some 
 contact with isooctane molecules . water molecules bound to the interface and may increase the entropy 
 of the system . the lysine residues , in particular , were either well - hydrated 
 or in contact with the aot head groups . similar results were obtained 
 for systems modeled using the gromos force field with the exception 
 that , in general , the aka2 peptides in the rms are less 
 hydrated than those for the charmm systems . capped aka2 in a restrained ( left ) and unrestrained 
 ( right ) rm . the snapshot on the left shows the peptide in pink , and 
 the snapshot on the right shows the peptide in green . each peptide 
 is shown with the surrounding water molecules in blue and aot tails 
 groups in gray . infrared spectra for the amide i modes of capped 
 and zwitterionic aka2 peptides encapsulated in rm were 
 calculated and compared with experimental data measured for capped 
 aka2 peptides in rms of w0 = 
 6 at room temperature . simulated spectra 
 were computed using a vibrational exciton model , in which the fundamental 
 frequencies ( ffs ) and couplings are expressed as a function of electric 
 field and van der waals forces on the atoms of the peptide bonds . in that recently developed approach , the ff 
 for a particular amide i mode is derived from a  map parametrized as1 in terms 
 of the components of the electric 
 field , ei , and 
 van der waals force , fi , at atom i ( which includes the o , c , n , and h atoms 
 of the peptide bond ) , where 0 is a static frequency 
 ( which may be taken to be the gas phase value ) and ci and di are fitting coefficients as a function of 
 the sum over parameters . all forces were computed using 
 the full interaction between peptide bonds and the surrounding environment , 
 the same forces that inform the molecular dynamics . the proposed maps 
 successfully reproduced experimental data for a set of proteins with 
 a wide range of sizes and secondary structures as well as model peptides 
 in polar and nonpolar solvents . this broad range of applicability 
 is essential for any method that aspires to compute accurate amide 
 i vibrational spectra for peptides in the heterogeneous rm environment 
 such as a rm , that includes polar , nonpolar , and charged domains . the carbonyl stretch makes the primary 
 contribution to the amide 
 i vibration , with minor contributions from the c -helices typically display a peak at 1655 cm , which shifts to lower frequency with increasing helix length . several 
 other factors , including hydrogen bonding and solvation , contribute 
 to the peak location . typically , hydrogen bonding lowers the frequency 
 of bond stretching , and solvated helices may have peaks up to 20 
 cm lower than nonsolvated helices . calculated ir spectra for capped and zwitterionic aka2 peptides in restrained and unrestrained reverse micelles , 
 with w0 = 6 at room temperature , compared 
 with experiment . in our simulations , we 
 observed that systems with more helical 
 structures were associated with red - shifted spectra . we further observed 
 that capped systems exhibited red - shifted spectra when compared with 
 zwitterionic systems . the most helical peptide , capped aka2 in a restrained rm , was associated with a main peak at 1637 cm , while the peptide with the least helical content , 
 zwitterionic aka2 in an unrestrained rm , produced a major 
 peak with the highest frequency at 1646 cm . in 
 fact , in our simulated spectra the positions of the main peak for 
 all systems , with the exception of capped aka2 in a restrained 
 rm , were nearly identical . additionally , the two peptides in 
 the restrained rms were observed 
 to be more hydrated than those in the unrestrained rms . as a result , 
 the amide i spectra were found to be broader and peaked at lower frequencies , 
 1637 cm for the capped aka2 and 1645 
 cm for the zwitterionic aka2 . other features present in our calculations include additional small 
 peaks , both red- and blue - shifted with respect to the main peaks . 
 to explain the origin of these peaks , we examined the ffs of each 
 peptide bond and included contributions from peptide , water , counterions , 
 and aot surfactant molecules . figure 9 shows 
 histograms of ff for each peptide bond , sums of the ffs , and the calculated 
 spectra . our analysis demonstrates that the small peak at 
 1610 cm for the capped aka2 in a restrained 
 rm can be associated with the 18th peptide bond , resulting from strong 
 interactions with counterions . similarly , the appearance of a small 
 peak at 1613 cm for zwitterionic aka2 in an unrestrained rm resulted from strong interactions of the fourth 
 peptide bond with counterions . for the same system , the peak at 1663 
 cm is associated with large couplings of the 13th 
 peptide bond with the nearest peptide bonds . histograms of the environmentally 
 induced ff shift contributions provide additional insight into the 
 role of the environment in inducing spectral heterogeneity . comparison 
 of histograms of ffs of each peptide bond ( low lying 
 histograms ) , sum of ffs ( green lines ) , and the calculated spectrum 
 ( orange lines ) for each studied system . red - shifted ffs are shown 
 as thin lines , and blue - shifted ffs are shown as dotted lines . the orientational dynamics of water confined 
 in rms has been shown to be qualitatively different than the dynamics 
 of bulk water . however , in an rm environment there are clear 
 signs of stretched exponential and power - law decay resulting from 
 the heterogeneous environment of water molecules under nanoscale confinement , as observed in other nanoconfined water systems . less is known about the how the presence of peptide in a rm influences 
 the water dynamics , through direct interactions with the peptide , 
 disruption of the water nanopool , and impact on the water h 
 bond can be described through the autocorrelation function2where p2 is the 
 second legendre polynomial and u(t ) 
 is the unit vector along the o h bond at time , t. figure 10 shows c2(t ) reorientational correlation functions for water 
 in six distinct rm environments , including restrained and unrestrained 
 rms with capped aka2 peptide , aka2 peptide in 
 a zwitterionic form , and rms without peptide . data for rms in the absence of peptide show faster relaxation than 
 either peptide system . it is likely that this is due to the fact that 
 the water rotational anisotropy decays faster for bulk water , and 
 there is the largest percentage of bulk - like water in the rm with 
 no peptide . table 2 contains parameters for 
 fits of the rotational anisotropy decay to a piecewise continuous 
 function formed from a short - time stretched exponential decay and 
 long - time power - law decay . these parameters provide further evidence 
 that the rotational anisotropy decay of water is slowed by the presence 
 of peptide . rotational anisotropy decay autocorrelation functions for restrained 
 and unrestrained rms with capped aka2 peptide , aka2 peptide in a zwitterionic form , and rms without peptide . for rms encapsulating aka2 peptide , water in the restrained 
 rm systems shows slightly faster relaxation than water in the unrestrained 
 rm up to 30 ps . this may be due to the fact that the aka2 peptides are more hydrated in the restrained rm system than in the 
 unrestrained rm . peptides in the unrestrained rm are found to be in 
 contact with only half the number of water molecules compared with 
 water in the restrained rm simulations . in the unrestrained rm , there 
 is a corresponding increase in the contact between the peptide and 
 aot tail groups . however , this observed difference in the rotational 
 anisotropy decay may not be statistically significant . at longer times , 
 the difference in dynamics for these systems is on the order of the 
 noise . for the aka2 peptide solvated in aot rms , 
 no significant 
 difference is observed in the rotational anisotropy decay of water 
 interacting with the capped or zwitterionic peptides . this is consistent 
 with the observation that the treatment of the n- and c - termini of 
 the aka2 peptide does not dramatically impact interactions 
 of the peptides with the water or surfactant environment . we have studied the effects of capped versus 
 zwitterionic termini 
 on the secondary structure of aka2 peptides encapsulated 
 in spherically restrained and unrestrained rms . our results using 
 two force fields demonstrate that capped aka2 peptides 
 form more stable helices than zwitterionic aka2 peptides . we found that the cap employed on the peptide termini did not significantly 
 alter the interactions between the peptides and their environment . calculation of the ir spectra of aka2 peptides in the charmm 
 systems also suggests that our results are in agreement with the work 
 of mukherjee et al . , with all four systems 
 exhibiting a major peak in the amide i vibrational spectra within 
 a few wavenumbers of the experimental peak . the observed rotational 
 anisotropy decay shows distinct differences in water dynamics induced 
 by the presence of the aka2 . this difference may be detectable 
 in experiment , providing a means of assessing the differing dynamics 
 of water directly involved in peptide solvation . overall , our results 
 provide support for the presence of significant 
 fluctuations in the rm structure away from an ideal spherical geometry 
 as well as the importance of surfactant surface fluctuations in facilitating 
 hydrophobic and hydrophilic interactions . the existence and potential 
 significance of such shape fluctuations away from an idealized spherical 
 geometry continue to be debated , with computational predictions forming 
 a consensus view that is only dependent on force field and interpretations 
 of water loading in terms of absolute numbers of water and surfactant 
 molecules in a characteristic rm . ultimately , these questions 
 must be resolved by experimental studies 
 that directly assess rm structure and allow for direct , critical comparison 
 of observables with the predictions of simulation studies . our simulation 
 results demonstrate the amide i vibrational spectral lineshapes as 
 well as the rotational anisotropy decay of water are sensitive to 
 differences in restrained spherical rms and rms undergoing significant 
 nonspherical fluctuations . as such , measurement of these experimental 
 observables provides one way to critically assess the structure of 
 rms , in both the absence and presence of solvated peptide .
the propensity of peptides to form 
 -helices has been intensely 
 studied using theory , computation , and experiment . 
 important model 
 peptides for the study of the coil - to - helix transition have been alanine 
 lysine 
 ( aka ) peptides in which the lysine residues are placed on opposite 
 sides of the helix avoiding charge repulsion while enhancing solubility . 
 in this study , 
 the effects of capped versus zwitterionic peptide termini 
 on the secondary structure of alanine - rich peptides in reverse micelles 
 are explored . 
 the reverse micelles are found to undergo substantial 
 shape fluctuations , a property observed in previous studies of aot 
 reverse micelles in the absence of solvated peptide . 
 the peptides 
 are observed to interact with water , as well as the aot surfactant , 
 including interactions between the nonpolar residues and the aliphatic 
 surfactant tails . 
 computation of ir spectra for the amide i band of 
 the peptide allows for direct comparison with experimental spectra . 
 the results demonstrate that capped aka2 peptides form 
 more stable  helices than zwitterionic aka2 peptides 
 in reverse micelles . 
 the rotational anisotropy decay of water is found 
 to be distinctly different in the presence or absence of peptide within 
 the reverse micelle , suggesting that the introduction of peptide significantly 
 alters the number of free waters within the reverse micelle nanopool . 
 however , neither the nature of the peptide termini ( capped or charged ) 
 nor the degree of peptide helicity is found to significantly alter 
 the balance of interactions between the peptides and the environment 
 . 
 observed changes in the degree of helicity in aka2 peptides 
 in bulk solution and in reverse micelle environments result from changes 
 in peptide confinement and hydration as well as direct nonpolar and 
 polar interactions with the water 
 surfactant interface .