the 
 amide i vibration arises predominantly from the stretching 
 vibration of the carbonyl group in the peptide bond with small contributions 
 from cn and hn bond vibrations and ccn angle bending .
this vibration 
 is notable due to its substantial oscillator strength and dependence 
 on backbone secondary structure , while being relatively insensitive 
 to the geometries of the amino acid s side chain .
this vibration 
 is often used to probe and examine the secondary structure of proteins , 
 both experimentally and in computational studies .
a number of observations have been made for relating amide 
 i vibrational 
 shifts to the local conformation of the peptide backbone .
approaches are based on relative simple rules for assigning the secondary structure based on an amide i vibration 
 spectrum .
( i ) -helix has a peak typically located near 1655 
 cm , which shifts toward lower frequencies with 
 increasing helix length ; this peak does not appear for peptides shorter 
 than six amino acids .
( ii ) -sheet exhibits a strong peak near 
 1630 cm and a weak peak near 1685 cm .
( iii ) parallel -sheets have a main peak at slightly higher 
 wavenumbers than antiparallel -sheets , but the difference does 
 not typically allow one to distinguish between them in many experimental 
 studies .
detailed discussions of the amide i vibration can be found 
 elsewhere . a number 
 of refined methods for computing amide i vibrational spectra 
 of globular proteins have been developed .
these methods typically 
 make use of structural data for the protein derived from molecular 
 dynamics simulation .
the models are often based on the vibrational 
 exciton approximation , where the local amide i vibrations have frequencies dependent on 
 the environment ( or isotopic labeling ) and are coupled through dipole 
these techniques have 
 proven highly successful in the interpretation of spectra of globular 
 proteins in aqueous environments .
, there has been increasing interest in the 
 interpretation 
 of amide i spectra of peptide systems other than globular proteins , 
 including ( 1 ) smaller peptides and ( 2 ) peptides and proteins in more heterogeneous environments . for peptides in reverse micelle environments ,
direct interaction 
 with the surfactant and nonpolar phase , as well as interaction with 
 aqueous solvent , must be addressed . for 
 peptides in membrane environments , there may be widely varying local 
 environments , including the lipid tail region of a bilayer , for transmembrane 
 peptides , or the headgroup region , which may include direct interactions 
 with mono- and multivalent ions .
methods for the calculation of amide 
 i spectra in these highly heterogeneous environments must account 
 for the substantial changes to the local amide i frequencies and their 
 coupling induced by the more heterogeneous solvation surroundings .
this work presents an extension of the vibrational exciton based 
 models for the calculation of amide i vibrational spectra of peptides 
 and proteins designed to be applicable to peptides and proteins in 
 heterogeneous environments .
the method is parametrized based on simulations 
 of a small molecule , n - methylacetamide , in a variety 
 of solvents , including water , dmso , and chloroform , and applied to 
 the calculation of spectra for a set of proteins using the charmm22 
 force field .
a comparison of the resulting 
 spectra with experimental data suggests that the method is robust 
 in capturing essential features of spectra in a variety of systems .
ab 
 initio calculations 
 of ir spectra including the amide i mode contribution are computationally 
 demanding for large proteins making it necessary to find methodologies 
 that can simplify such calculations from data generated in standard 
 molecular dynamics ( md ) simulations of a protein .
the protein 
 is represented by a set of oscillators , also called chromophores , 
 one for each peptide bond .
it is assumed that the amide i modes do 
 not couple with other types of vibrations in the system , only to the 
 corresponding amide i mode of another peptide bond .
the hamiltonian 
 of the system is expressed in terms of creation and annihilation operators , bi and bi , as1 the 
 diagonal element , i = ( ei,1  ei,0)/ , 
 is a frequency of transition between the vibrational ground and first 
 excited states of the i - th oscillator .
this fundamental 
 frequency corresponds to the frequency of an oscillator unperturbed 
 by interactions with other oscillators .
off - diagonal elements , ij , represent coupling between oscillators i and j , and i is the fluctuating transition dipole moment of oscillator i interacting with applied electric field e(t ) .
the linear spectra were calculated as 
 the fourier transform of 
 the correlation function of the transition dipole moments with the 
 phenomenologically added term e to account for the vibrational lifetime , 
 according to the method presented by jansen and knoester2where t1 is the 
 lifetime of the singly excited states , u(t , 0 ) represents time evolution operator , described in more details 
 in supporting information .
couplings between the i - th and j - th peptide bonds can be calculated in 
 the transition dipole coupling approximation .
the electrostatic interaction between two peptide bonds is modeled 
 by the interaction of the transition dipole moments , i and j , associated with these two peptide 
 bonds , asthis approximation is assumed to be reasonable 
 if the separation between peptide bonds , rij , is greater than their dimension .
it should not 
 be applied to model interaction between the nearest neighboring peptide 
 bonds . in works by jansen et al .
, gorbunov et 
 al . , and torii and tasumi , couplings between the nearest neighboring peptide 
 bonds were calculated ab initio and represented as functions of ramachandran 
 angles ,  and . there are several methods for determining 
 values of the fundamental frequencies and two methods are briefly 
 presented below .
( i ) the fundamental 
 frequency is represented as a sum of a constant , 
 const , and frequency shift ,  , reflecting 
 when the oxygen or nitrogen atoms from the peptide bond form a hydrogen 
 bond .
 depends on the length of the hydrogen 
 bond and is typically taken to be 20 and 10 cm for oxygen or nitrogen atoms , respectively .
an isotopic 
 shift can also be included in the model as a constant value added 
 to const .
the 
 second approach employs the electric field or electrostatic 
 potential at the peptide bond atoms and therefore introduces a dependence 
 on the surrounding environment .
( ii ) the fundamental frequency 
 for each peptide bond is calculated 
 as a function of the electrostatic potential or electric field or all of them experienced by atoms of the peptide bond , which may be 
 approximated in terms of the partial charges of the surrounding solvent 
 molecules and the electrostatic potentialor the electric fieldwhere i runs over atoms of 
 the peptide bond , c , o , n , h ,  = { x , y , z } , and j runs over 
 point charges surrounding the i - th peptide bond . 
 coefficients ci and ci are determined by 
 fitting the frequency to the electrostatic potential or electric field 
 on a test system such as n - methylacetamide ( nma ) 
 to reproduce either ab initio calculations for nma  water clusters , 
 containing up to four water molecules , or the experimentally measured transition frequencies for nma .
the 
 intercept , 0 , is often chosen to be the gas - phase 
 amide i frequency of nma equal to 1717 cm . therefore , 
 the value of the shift in the fundamental frequency ,   

0 , can be understood as the first order perturbation 
 correction to the frequency in vacuum due to interactions with solvent 
 molecules .
this model reminds one of the stark effect in which each 
 component of the electric field on each atom may have a different 
 proportionality coefficient .
work presented in this paper 
 is focused on improving the second method presented above through 
 the use of data obtained from molecular dynamics simulations .
( i ) if the amide i frequency of nma in vacuum is chosen as the reference 
 ( i.e. , unperturbed ) frequency , to first order the corrections to the 
 frequency arise from interactions of nma with solvent molecules .
there 
 are two types of such nonbonded interactions , electrostatic and van 
 der waals , and both are included in the frequency shift .
( ii ) 
 in existing methods , the electrostatic potential and electric 
 field employed in the fits are typically derived from partial charges 
 on selected solvent molecules surrounding the nma molecule .
such a 
 field or potential does not fully represent an actual field or potential 
 on the nma molecule during molecular dynamics simulations , where periodic 
 boundary conditions are employed and electrostatic interactions are 
 calculated using the ewald summation . in this work , all fits presented 
 were obtained based on the total electrostatic and van der waals forces 
 exerted on the atoms of peptide bonds during simulations .
( iii ) 
 the proposed method uses data obtained from standard all - atom 
 molecular simulations carried out with the namd package where the shake algorithm 
 was applied to fix the length of bonds to hydrogen atoms .
this stands in 
 contrast to other approaches in which additional restrictions are 
 imposed in the calculation of the spectrum , such as fixing the length 
 of all other bonds using the links algorithm 
 ( which is not implemented at this time in charmm or in namd ) .
( heavy 
 atom bonds vibrate with a period of at least 20 fs that is equal to 
 the shortest period of angle vibrations for c  o  h .
therefore , 
 constraining all bonds can take full advantage of the links algorithm 
 only when those angles are also constrained . )
results 
 based solely on md simulations of nma in water may not be representative 
 of more heterogeneous environments experienced by a peptide bond in 
 a protein .
reliable fits should also incorporate the hydrophobic surroundings 
 of an amino acid buried inside a protein , interactions with lipophilic 
 regions of a membrane , or contact with monovalent ions .
this can be 
 accomplished by fitting data from md simulations of nma in water and 
 in solvents representing a range of dielectric constants including 
 dmso and chloroform .
( v ) finally , 
 the maps developed in this work are designed to highlight 
 the difference between the amide i frequency of an -helix and 
 of a -sheet .
such fits are especially useful in studying aggregation 
 processes where proteins commonly undergo changes in secondary structure . in the next sections , new maps are presented together with 
 the 
 methodology employed in their calculation .
the amide i spectra of 
 a test set of proteins are presented to validate the quality of the 
 proposed maps .
all fits presented below were calculated 
 based on the results of md simulations performed using the charmm22 
 force field and the namd package .
a single molecule of nma was placed 
 in the center of a pre - equilibrated cubic box ( 70  70  
 70  ) of solvent and equilibrated at 300 k. three 
 solvents were considered , water , dmso , and chloroform .
water was represented 
 by the tip3p model , parameters for dmso 
 were taken from the work by strader and feller , and parameters for chloroform were derived from the work 
 of cieplak et al .
periodic boundary conditions 
 and particle mesh ewald summation were employed , nonbonded interactions 
 were switched to zero over the window 10 to 12  , the time step 
 was set to 1 fs , geometries were saved every 100 fs , and all bonds 
 with hydrogen atoms were constrained using the shake algorithm .
all forces on the c , o , n , and h 
 atoms of nma were computed under the same conditions used during the 
 production md runs , including the same cutoffs , pme parameters , and 
 box size .
all force vectors were aligned in such a way that the xy - plane was defined by the c , o , and n atoms of a peptide 
 bond with the co bond oriented along the y - axis . 

finally , forces were converted from kcal / mol /  to atomic units 
 by a factor 0.0008432983 .
new maps for the fundamental 
 frequency 
 proposed in this work include not only the electric field vectors 
 on the atoms of the peptide bonds , but also van der waals forces . 

initially , the fitting function contained 25 parameters , 12 for components 
 of electric fields , ei , on c , o , n , and h atoms of nma , 12 parameters corresponding 
 to vectors from van der waals forces , fi , and one parameter for the intercept3where frequency 
 is in units of wave numbers .
frequency functions 
 were fitted to 
 six experimental values including positions of the peak maximum , exp , and full width at half - maximum , exp , 
 of the amide i frequency of nma in water , dmso , and chloroform .
several 
 forms of the penalty function were employed in the fitting process 
 ( for details see supporting information ) .
some field or force 
 components make greater contributions to the 
 fundamental frequency than others , and their analysis can help in 
 identifying the most important parameters .
figure 1 shows histograms of the field and force components on the 
 nma peptide bond atoms derived from md simulations in three solvents . 

we observed that on average only 9 out of 24 components made a greater 
 than 0.001 au contribution .
as the amide i frequency consists mostly of vibrations 
 of the carbonyl group in peptide bonds , it is not surprising that 
 force components in the direction of the co bond ( which defines the y - axis ) are the most dominant contributions .
there is only 
 one other component , ehx , with a peak further from zero than 0.002 au . out of 12 parameters 
 for van der waals forces ,
only the y - components on 
 oxygen and nitrogen atoms appear to be significant . apart from 
 analyzing the field and force components on nma peptide 
 bond atoms ,
one can test the components together with corresponding 
 fit coefficients to determine which coefficient provides the largest 
 contribution to the fundamental frequency shift .
( a sample of results 
 for some 25 parameter fits is shown in figure 7 in supporting information . ) in each case , a different set of 
 fit parameters was found to be important in determining the frequency 
 shift including components that were neglected based solely on the 
 field and force histograms .
this indicates that an analysis of fit 
 parameters alone or forces alone might be misleading .
each set was 
 chosen as input for another fitting procedure and this process was 
 repeated until the most significant fit parameters were determined .
histograms 
 of field and force components on nma peptide bond atoms 
 in water ( left ) , dmso ( center ) , and chloroform ( right ) .
top panel 
 refers to electric field components , while bottom shows van der waals 
 forces .
dotted lines show positions of 0 ,  0.002 au . only components 
 with absolute mean value greater than 0.001 au are shown .
if the absolute 
 mean value is in the range 0.001 and 0.002 au , its histogram is shown 
 as a dashed line .
the number of variables in the fit formula led to the 
 generation 
 of many maps by a multivariable fitting procedure .
the choice of the 
 best maps was based on reproducing amide i spectra of two proteins , 
 an alanine - based peptide with sequence ( aaaak)4aaaay ( referred 
 to as aka5 ) and trpzip2 ( 1le1 ) .
aka5 consists 
 of only 25 residues and forms one well - defined -helix , while 
 even smaller trpzip2 is an example of -hairpin protein .
aka5 and trpzip2 make a complementary set to study the assignment 
 of secondary structure based on amide i vibrational spectra .
both fits consist of nine components . from the analysis of fields and forces on the atoms of nma presented 
 above
, only two components of van der waals forces were found to be 
 significant , the y - component on the oxygen and nitrogen 
 atoms , oyvdw and nyvdw , respectively . only these two 
 components were expected to make a significant contribution to the 
 frequency shift .
surprisingly , for both fits the coefficient corresponding 
 to the x - component of the van der waals force on 
 the nitrogen atom , nxvdw , is the largest of all .
however , analysis 
 of the frequency shift caused by this component in the case of the 
 nma spectrum ( presented in figure 2 ) shows 
 that despite the value of this coefficient , its contribution is less 
 than 5 cm for the spectrum of nma in dmso .
histograms 
 of the main contributions to the nma amide i frequency 
 shift in water , dmso , and chloroform for the two best fits
the main contributions to the 
 frequency for all fits come from 
 three components of the electric field , oy , ny and hy . the contribution from the carbon atom is found to be negligible 
 even though the amide i vibration consists primarily of the co vibration . 

interestingly , for map # 1 the van der waals forces contribute more 
 than 1 cm only in the case of spectra in dmso . 
 for map # 2 the van der waals
for nma in chloroform , 
 van der waals forces make negligible contributions for both maps .
figure 3 presents the comparison of experimental 
 and computational amide i spectra for nma in three considered solvents . 

black lines 
 represent experimental data , while cyan lines and magenta circles 
 show spectra calculated using the # 1 and # 2 proposed maps , respectively . 

experimental data ( digitized and interpolated ) were derived for nma 
 in water and dmso from hamm et al . and 
 for nma in chloroform from wang et al .
to validate the new maps , amide 
 i frequency spectra of four additional 
 proteins were calculated and compared with experimental results . for 
 benchmark calculations , a series of proteins
were chosen including 
 ubiquitin ( 1ubq ) , ribonuclease ( 7rsa ) , myoglobin ( 1wla ) , and concavalin 
 ( 1jbc ) .
the set of six proteins include a wide range of structures 
 and sizes as shown in figure 4 from the 12-residue 
 -hairpin trpzip2 , through the 153-residue myoglobin ( formed 
 almost exclusively of -helices ) , to the 237-residue concavalin 
 ( including two large -sheet surfaces ) .
each peptide was placed in a pre - equilibrated 
 water box , neutralized , energy minimized , heated , and equilibrated 
 at 300 k. for aka5 , trpzip2 , ubiquitin , ribonuclease , and 
 myoglobin , a cubic box of 70  70  70  was used , while for concavalin an orthorhombic box of size 70  
 70  85  was employed . the simulations were 
 run under the same conditions as described for nma .
ribbon structures of 
 the six proteins in the test set showing -strands 
 ( yellow ) , -helices ( cyan ) , and 310-helices ( pink ) . 

off - diagonal 
 couplings between the nearest neighbor peptide bonds are taken from 
 jansen s maps .
as such , partial charges of all 
 backbone atoms of the neighboring residues should not contribute to 
 the fundamental frequencies .
partial charges on all remaining 
 atoms of the protein were included in the calculations .
each vector s 
 length was set to 2.73 d with the vector displaced 10 from the 
 co bond in the con plane .
its origin was located at rc + 0.665 nco + 0.258 ncn , where rc is the position of the carbon atom of the peptide bond , while nco and ncn are normalized vectors in the directions of the co and cn 
 bonds , respectively .
the fundamental frequency for each peptide bond ( the diagonal values 
 of the hamiltonian matrix ) was calculated as a sum of three terms : 
 ( 1 ) the unperturbed oscillator frequency calculated from the frequency 
 fit , ( 2 ) the shift caused by the closest neighboring peptide bond 
 on the n - site ( for the i - th oscillator that shift 
 is a function of two ramachandran angles i , i1 and i , i1 ) , and ( 3 ) the corresponding shift caused on the c - side of the peptide 
 bond ( function of angles i , i+1 and 
 i , i+1 ) . both types of shifts were 
 taken from tables calculated by jansen and co - workers .
the only exceptions were made for the fundamental frequencies of 
 the amide groups in the side chains and for the peptide bond associated 
 with proline , where , due to the lack of the hydrogen atom in the peptide 
 bond , the frequency fit can not be used .
both cases have been treated 
 explicitly in the recent papers using approaches that 
 impose constraints on all bonds , and as such could not be applied 
 in the present work .
hence , the amide groups located on the side chains 
 were not taken into account , and values of 1620 or 1670 cm were used for proline .
the off - diagonal couplings for the 
 nearest neighbors as functions 
 of the ramachandran angles between adjacent peptide bonds were taken 
 from maps provided by jansen .
the remaining off - diagonal 
 couplings were calculated in the transition dipole coupling approximation .
spectra were 
 calculated according 
 to eq 2 with the moving window approach skipping 
 10 frames between windows .
md simulation data were collected every 
 100 fs and this time step was chosen to be the integration step in 
 the eq 2 . to validate the 100 fs time step employed
, 
 line shapes were also computed using a time step of 10 fs for nma 
 in three solvents and the two smallest and most mobile proteins , see supporting information in figure 8 .
the homogeneous dephasing time t1 was set to 1.0 ps for proteins , and to 0.45 
 ps for nma .
frequencies and couplings were converted from cm to ps using the factor 2c before integration , where c is the speed of light . 

calculations were performed using in - house python scripts , written 
 using the mdanalysis package , and can 
 be shared upon request .
amide i spectra calculated 
 using maps # 1 and 
 # 2 for proteins in the test set are presented in figure 5 together with experimental data .
comparison of the experimental and calculated 
 spectra for the amide 
 i vibration for the six test proteins .
black lines indicate experimental 
 data , while blue and red lines show spectra calculated using the # 1 
 and # 2 proposed maps , respectively .
experimental data ( digitized and 
 interpolated ) were derived for trpzip2 from the work of smith and 
 tokmakoff , for aka5 from barber - armstrong 
 et al .
, for ubiquitin , ribonuclease , 
 and myoglobin from ganim et al . , and 
 for concavalin from karjalainen et al .
the two smallest proteins in the 
 benchmark set , trpzip2 and aka5 , are of special interest . 
 as shown in figure 4 , trpzip2 consists of only 
 one -hairpin , while aka5 forms one -helix . 
 because of that substantial difference 
 in the secondary structures ,
these two peptides serve as excellent 
 benchmarks for methods proposed for the determination of amide i spectra . 

successful capture of the discrepancies between the amide i spectra 
 of -helical and -type proteins is a validation of the 
 usefulness of the fits in distinguishing between these two types of 
 secondary structure .
positions of the experimental main peaks 
 for both proteins are 
 separated by only 5 cm with 1636 cm for trpzip2 and 1631 cm for aka5 .
this separation 
 is too small for reliable assignment of the secondary structure based 
 on positions of the main peaks .
however , the experimental spectrum 
 of trpzip2 also exhibits a weak second peak near 1673 cm .
consequently , the secondary structure 
 can be determined by the presence of the weak second peak in the spectrum . 

for this reason , all presented fits somewhat overestimate the weak 
 peak in the spectrum of trpzip2 . in the case of larger proteins 
 from the test set with more complex 
 tertiary structure ( ubiquitin , ribonuclease , myoglobin , and concavalin ) 
 good agreement between the experimental and the computed spectra
the positions of the main peaks are reproduced as well as 
 the line widths .
the two proposed maps presented here do not 
 utilize the same set 
 of parameters for the contribution of van der waals forces , but the 
 most important aspects of the spectra are captured in both fits .
two come from 
 the y - component of the electric field on the oxygen 
 and nitrogen atoms and with opposing sign from the y - component of the electric field on the hydrogen atom ( shown in figure 6 with black , blue , and cyan for both maps , respectively ) . 

similar behavior was observed for the case of the nma molecule , especially 
 in water and dmso .
van der waals forces on the oxygen atom appear 
 only in map # 2 , 
 while map # 1 utilizes the x - component on the nitrogen 
 atom .
however , the y - component of the van der waals 
 forces on the nitrogen atom makes the dominant contribution of all 
 van der waals force components . for both maps ,
this component plays 
 a significant role in spectra calculations for each protein in the 
 benchmark set ( except the smallest protein trpzip2 , where only electric 
 field components contribute to the fundamental frequency ) .
histograms 
 of the contributions to the frequency shift for six 
 proteins in the test set for the maps # 1 and # 2 .
panels show contributions 
 from the electric field and van der waals force components , respectively . 

histograms were smoothed using running averaging over 10 frames . only 
 contributions greater than 1 cm
figures 9 and 10 in the supporting information present comparison of 
 correlations between electric and van der 
 waals contributions to the fundamental frequency for both maps . for 
 small proteins , trpzip2 and aka5
, we observe minor correlation 
 between components , such as between the y - component 
 of the electric field on the hydrogen atom , and between the y - component of the van der waals field on the nitrogen atom 
 for trpzip2 , or between x - component of the electric 
 field on the hydrogen atom and x - component of the 
 van der waals field on the nitrogen atom .
however , for larger proteins 
 correlations become negligible and there is no example of correlation 
 that is present in any of the studied proteins .
van der waals 
 forces make smaller contributions to the fundamental 
 frequency shift than the electric field forces . however , this contribution 
 is not negligible except in the case of trpzip2 .
therefore , while 
 van der waals forces are relatively less important in the calculation 
 of spectra , maps without those components are less accurate .
this paper presents a new approach to the 
 evaluation of fundamental 
 vibrational frequencies and spectra using input from standard classical 
 molecular dynamics simulations .
we have presented a revised methodology 
 for the calculation of infrared spectra of amide i vibrations for 
 proteins in solution .
the couplings between oscillators corresponding to 
 peptide bonds are calculated in the transition dipole coupling approximation . 

the fundamental frequencies are obtained using the total electric 
 field and van der waals forces on atoms of all peptide bonds .
addition 
 of the van der waals forces is a novel approach , as in earlier works 
 only the electric field was utilized .
use of van der waals interactions 
 together with the electrostatic contributions improves the accuracy 
 and robustness of the method . to validate the new methodology 
 over a wide range of secondary 
 and tertiary structures of proteins , a set of six test proteins with 
 varying content of secondary and tertiary structure
was tested . in 
 each case , the calculated spectra satisfactorily reproduced the experimental 
 results , which validates the quality of the proposed maps for amide 
 i frequency calculations and the methodology for the calculation of 
 spectra .
reproduction of the weak second peak in the spectra for -sheet 
 rich proteins is a sensitive measure of the accuracy of any proposed 
 approach for the calculations of amide i spectra of proteins , and 
 the proposed methodology successfully addresses that challenge and 
 sets a standard for other proposed methods .
even linear spectra may be used to gain insight into the predominance 
 of -helices and -strands .
the development of new approaches 
 to the computation of amide i spectra continues to be a highly active 
 field of research [ see refs ( 5 ) , ( 6 ) , ( 8) , ( 11 ) , ( 13 ) , ( 1520 ) , ( 25 ) , ( 3036 ) , ( 51) ] .
the goal of this work was to develop a robust 
 method for computing amide i spectra for proteins in heterogeneous 
 environments .
the method presented may be combined with the widely 
 used charmm22 force field to allow computation of ir spectra as a 
 function of protein conformation and solvent environment .
the methodology 
 has an advantage over existing methods in that it does not require 
 additional constraints of bonds in the system under study or special 
  filtering  of forces .
standard results of molecular 
 dynamics simulations can be used to compute the spectra in a straightforward 
 manner .
the application of this methodology to the calculation of 
 spectra using molecular dynamics other than charmm22 should be straightforward .
 new sets of parameters ( maps ) for 
 calculating amide i vibrational 
 spectra for proteins through a vibrational exciton model are proposed . 
 
 the maps are calculated as a function of electric field and van der 
 waals forces on the atoms of peptide bonds , taking into account the 
 full interaction between peptide bonds and the surrounding environment . 
 
 the maps are designed to be employed using data obtained from standard 
 all - atom molecular simulations without any additional constraints 
 on the system . 
 six proteins representing a wide range of sizes and 
 secondary structure complexity were chosen as a test set . 
 spectra 
 calculated for these proteins reproduce experimental data both qualitatively 
 and quantitatively . 
 the proposed maps lead to spectra that capture 
 the weak second peak observed in proteins containing -sheets , 
 allowing for clear distinction between -helical and -sheet 
 proteins . while the parametrization is specific to the charmm force 
 field , 
 the methodology presented can be readily applied to any empirical 
 force field . 
Introduction
Methods
Model Parametrization for
NMA
The Best
Maps
Validation of the New Maps
and Spectra for Proteins
Conclusions