recent advances in computer hardware and software have greatly 
 extended the time scales that can be covered by biomolecular simulations . 
 these longer time scales ( beyond nanoseconds )
one important 
 characteristic of these force fields is the ability to accurately 
 model the formation of salt bridges , or pairs of amino acids whose 
 oppositely charged side - chains are within hydrogen - bonding distance 
 in proteins .
however , it has long been 
 suspected that the forces between oppositely charged amino acids are 
 overly attractive in molecular dynamics ( md ) simulations with current 
 biomolecular force fields , and there have been a number of efforts 
 to reduce this artifact in the improvement of various force fields .
previous theoretical studies have analyzed the contribution of salt 
 bridges to protein or protein  protein complex stability , using 
 both implicit and explicit modeling of solvation .
others have 
 studied salt bridges using amino acid analogues , often employing biasing techniques in the simulations .
more recently , a comprehensive comparison of force field / water model 
 combinations was conducted for salt bridge interactions between the 
 amino and carboxyl groups of zwitterionic amino acids , using extensive 
 simulations in explicit solvent on the microsecond time scale . here , we evaluated six biomolecular force 
 fields for their ability 
 to accurately model the strengths of salt bridges between the side - chains 
 of oppositely charged amino acids by unbiased , microsecond - scale md 
 simulations in explicit solvent .
in particular , we directly compared 
 current amber , charmm , and opls force fields in simulations of association 
 between the side - chain analogues of three different pairs of amino 
 acids , arg / asp , lys / asp , and his(+)/asp .
we further tested one of 
 the pairs , arg / asp , by simulating association of blocked amino acid 
 dipeptides .
in addition , we evaluated the influence of the solvent 
 model on the strengths of the salt bridges by simulating the side - chain 
 analogue pairs using a selection of different force field / water model 
 combinations . to our knowledge , our microsecond - scale simulations 

provide the most extensive sampling of salt bridge formation to date , 
 yielding thousands of association / dissociation events , permitting 
 quantitative comparisons , both between the force fields and with experiment . 

our results reveal considerable variability among the current force 
 fields in terms of the resulting strengths of salt bridge interactions , 
 as well as differences from experimental data .
we modeled the formation 
 of salt bridges between the following pairs of oppositely charged 
 amino acids using side - chain analogues : arg / asp ( guanidinium cation / acetate 
 anion ) , lys / asp ( butylammonium cation / acetate anion ) , and his(+)/asp 
 ( imidazolium cation / acetate anion ) .
our systems were constructed to 
 be consistent with the experimental conditions under which the equilibrium 
 association constants ( ka ) of guanidinium 
 acetate and butylammonium acetate have been measured , i.e. , using the same concentrations ( 0.9 m guanidinium 
 and 0.02 m acetate , which corresponds to 100 molecules of guanidinium 
 and two molecules of acetate in the presence of 18  000 
 explicit water molecules ) . to ensure a net charge of zero
, we included 
 98 chloride ions ( the same counterion that is present in the experiments ) . 

the same concentrations of the cation , anion , and chloride ions were 
 also used for the model systems consisting of butylammonium / acetate 
 and imidazolium / acetate . starting models for these simulations
were 
 constructed using the packmol software package , immersing the appropriate number of side - chain analogues 
 in periodic , cubic boxes of explicit solvent . for the arg / asp salt 
 bridge , we also used blocked amino acid dipeptides ( acetyl  arginine 
only a single copy of each 
 blocked dipeptide was included , corresponding to a concentration of 
 0.012 m for each salt - bridging partner , with a distance of 10  
 between the amino acids .
all force field parameters of the side - chain 
 analogues were based on those of the complete amino acids . for the 
 chloride ions ,
parameters derived specifically for the water model 
 were used when available ; otherwise , parameters derived for a similar 
 water model were used .
nonbonded parameters of the side - chain analogues , 
 along with those used to model chloride ions and blocked amino acid 
 dipeptides , are provided in table s1 of the supporting 
 information . to alleviate any unfavorable interactions , 

each model was subjected to energy minimization followed by a two - stage 
 equilibration with harmonic position restraints on all heavy atoms 
 of the side - chain analogues ( force constant of 10 kcal mol  ) using the desmond 3.0.1.0 software package . in the first stage ,
the energy - minimized system 
 was equilibrated for 20 ps at constant temperature ( 25 c ) using 
 a weak langevin thermostat ( frictional constant of 1 ps ) . during the second stage ,
the system was equilibrated for 1 ns 
 at constant temperature ( 25 c ) and pressure ( 1 atm ) using the 
 martyna 
klein thermostat and barostat ( coupling time constants of 1.0 and 2.0 ps , 
 respectively ) . to enable a 2 fs time step , bonds to hydrogen
a short - range nonbonded cutoff of 10.0  
 was used , and long - range electrostatics were calculated using the 
 particle mesh ewald ( pme ) method .
the 
 frame from the second half of the npt equilibration with volume closest 
 to the average was used to start the production simulation . to obtain extensive sampling of 
 salt bridge association ( and dissociation ) events ,
1-s md simulations 
 were performed for each side - chain analogue system ; 10-s simulations 
 were performed for the blocked arginine and aspartate dipeptide systems . 

all simulations were carried out in the nvt ensemble using a 64-node 
 anton special - purpose supercomputer , which is able to run md simulations 
 roughly 2 orders of magnitude faster than conventional hardware ( altogether , the simulations required a total 
 of 40 machine - days ) .
the temperature was maintained at 25 c 
 using the nos  hoover thermostat with a weak coupling 
 constant of 0.5 ps .
van der waals and 
 short - range electrostatic interactions were truncated at 10.0  ; 
 long - range electrostatic interactions were calculated using the gaussian 
 split ewald method . to enable a 2.5 fs 
 time step , bonds to hydrogen
equilibrium 
 association constants ( ka ) were calculated 
 from the populations of the bound and unbound states of the oppositely 
 charged side - chain analogues .
for example , the ka for association between guanidinium and acetate was calculated 
 using the following:1where pbound is 
 the population of the bound state , punbound  guanidinium and punbound  acetate are the populations 
 of unbound guanidinium and acetate , respectively , and c0 is the reference concentration of guanidinium ( i.e. , 
 0.9 m ) .
in addition to species in which a single acetate molecule 
 is bound to a single cation molecule , forming a 1:1 complex ( e.g. , 
 the guanidinium / acetate complex ) , species in which acetate is bound 
 to two cation molecules , forming a 1:2 complex ( e.g. , the diguanidinium / acetate 
 complex ) were observed .
ka values for 
 the latter are included in table s2 of the supporting 
 information ; the results discussed below focus on formation 
 of the major complex , which is the 1:1 complex .
standard errors in 
 the ka values were calculated using a 
 block averaging method . for each 
 side - chain analogue system , the unbound and bound states were defined 
 using the potential of mean force ( pmf ) as a function of the minimum 
 distance between the nitrogen and oxygen atoms of the positively and 
 negatively charged analogues , respectively ( minimum n  o distance ; 
 see figure 1 ) .
in particular , the point of 
 inflection between the bound state free energy minimum ( 2.53 
  ) and the desolvation barrier ( 33.5  ) 
 was used as the bound state cutoff , while 4.5  was used as the 
 unbound state cutoff .
if the minimum n  o distance between an 
 analogue pair dropped below the bound state cutoff they were classified 
 as bound until they crossed the unbound state cutoff , and vice versa . 
 for simulations of the blocked arginine and aspartate dipeptides , 

the same definitions of the unbound and bound states were used as 
 for the guanidinium / acetate system .
potentials of mean force ( pmf ) between 
 three different pairs of 
 oppositely charged side - chain analogues using six biomolecular force 
 fields with the tip4p - ew explicit water model .
the 
 dielectric constant of water in each simulation , water , was calculated using the following equation:2where mwater is 
 the net dipole moment of water , vwater is the volume occupied by water , t is the temperature 
 of the system , kb is the boltzmann constant , 
 and 0 is the permittivity of free space .
the net 
 dipole moment of water was calculated using the following:3where q is the atomic 
 charge 
 of each water site , and r is its position vector .
the dielectric constant of water , rather than that of the complete 
 system , was used since it is impossible to calculate the contributions 
 of molecules with a net charge to the system dipole moment from simulations 
 with periodic boundary conditions .
the 
 appropriate volume was thus the volume of the water molecules present 
 in the system .
for each water model used , a pure water system of the 
 same total volume as that of the side - chain analogue systems was equilibrated 
 using the same protocol , and the molecular volume of water calculated . 
 for each analogue system ,
the number of water molecules present was 
 multiplied by the molecular volume to calculate the approximate volume 
 of water present in the system .
we compared 
 the following six current biomolecular force fields 
 in terms of their ability to model salt bridge interactions : amber 
 ff99sb - ildn , amber ff03 , amber ff13 , charmm27 , charmm22 * , and opls_2005 .
in particular , we simulated association ( and 
 dissociation ) of salt bridges between the following three pairs of 
 oppositely charged amino acids : arg / asp , lys / asp , and his(+)/asp . 

we focused primarily on simulating side - chain analogues ( i.e. , guanidinium , 
 butylammonium , and imidazolium cations for arginine , lysine , and histidine , 
 respectively , and acetate anion for aspartate ) since these analogues 
 are the minimal systems for studying the formation of salt bridges ; 
 in addition , equilibrium association constant ( ka ) values for such systems have been experimentally measured , 
 providing an excellent opportunity to validate the simulations . while 
 blocked amino acid dipeptides ( i.e. , acetyl  amino acid 
n - methyl ) might be regarded as being more representative 
 of the protein environment , no experimental ka values for the association of oppositely charged amino acid 
 dipeptides are available .
nonetheless , we evaluated the force fields 
 in simulating such systems , focusing on just one of the three salt 
 bridges , arg / asp .
finally , in addition to the above simulations , in 
 which each biomolecular force field was paired with the tip4p - ew explicit 
 water model , which reproduces the liquid properties of water at the 
 temperatures and pressures relevant to biology , we also evaluated the influence of the water model on the 
 strength of the salt bridges by testing a selection of force field / water 
 model combinations for all three pairs of side - chain analogues . for 
 each force field a selection of water models drawn from tip3p , mtip3p , tip4p , tip4p/2005 , and 
 spc / e were tested , including the water 
 model with which each force field was originally derived . to validate 
 our simulations of association between oppositely charged side - chain 
 analogues , we computed ka values and compared 
 these to those measured by experiments .
experimental ka values have been measured for guanidinium / acetate and 
 butylammonium / acetate association by monitoring changes in the pka of acetate in the presence or absence of either 
 the guanidinium or butylammonium cation .
our microsecond - long simulations yielded thousands of independent 
 binding events , permitting the extraction of extremely precise ka values , with the mean lifetimes of the bound 
 state ranging from 10300 ps and the mean lifetimes 
 of the unbound state ranging from 20120 ps ( table 
 s2 , supporting information ) .
in general , 
 the ka values computed from our side - chain 
 analogue simulations are overestimated in comparison to experimentally 
 measured values , with the amber ff03 force field overestimating the 
 strengths of the salt bridges to the least extent and the opls_2005 
 force field to the greatest extent , when using the same water model 
 ( table 1 ) .
for example , 
 when using the tip4p - ew water model , the computed ka values for the three types of salt bridges vary by as 
 much as 4-fold , 3-fold , and 4-fold for the 
 associations of guanidinium , butylammonium , and imidazolium with acetate , 
 respectively , which amounts to 1.4-fold , 1.8-fold , 
 and 1.9-fold differences in the probabilities of binding ( pbound ) ( see figure 2 ) . 

we note that our definition of the bound state is very conservative 
 and that the use of less conservative definitions ( e.g. , use of the 
 desolvation barrier as a cutoff ) yields even stronger association 
 constants , without affecting our overall conclusions .
one potential 
 factor that could influence the degree of salt bridge 
 formation in our simulations is the choice of force field parameters 
 for the chloride ions . to verify that these parameters are not the 
 cause for overestimating salt bridge strength
, we carried out simulations 
 of a single guanidinium / acetate pair ( corresponding to concentrations 
 of 0.1 m ) with no chloride ions present .
the resulting ka values are even higher than those measured in the presence 
 of chloride ions , indicating that the chloride ion parameters do not 
 cause disproportionate salt bridge stability ( table s3 , supporting information ) .
results are from 1-s simulations 
 and standard errors were calculated using a block averaging method .
experimental ka values of guanidinium and butylammonium acetate permit only 
 a qualitative estimate of the associated error .
taking two experimentally 
 measured ka values of guanidinium acetate 
 using different protocols into account , we estimate 
 an error of 0.05 , although the true uncertainty is not known . 
 using this estimate
, we have back - calculated the range of simulated pbound values that would be expected in our simulation , 
 based on the experimental ka .
probabilities of binding ( pbound ) between 
 three different pairs of oppositely charged side - chain analogues using 
 six biomolecular force fields with the tip4p - ew explicit water model . 

the pbound values that correspond to the 
 experimentally determined ka values of 
 guanidinium acetate and butylammonium acetate are depicted as horizontal 
 gray bars ; no experimentally measured ka is available for the imidazolium acetate system . 

two obvious features of a force field that influence the 
 strength 
 of the salt bridges are the atomic charges and radii . as expected , 
 the charmm22 * force field yields ka values 
 that are closer to experiment than those from the parent charmm27 
 force field since the atomic charges for the arginine , aspartate , 
 and glutamate residues were parametrized specifically to reproduce 
 the experimental association of guanidinium acetate
. however , the charmm22 * force field does not produce as 
 close agreement with experiment as the amber ff03 force field , which 
 shows good agreement for butylammonium acetate . given these results
, 
 it appears that the general strategy used to derive atomic charges 
 for the amber ff03 force field is reasonably effective for modeling 
 electrostatic interactions .
this strategy involved the derivation 
 of atomic charges in the presence of a continuum solvent model with 
 a dielectric constant of 4 to mimic an organic solvent ( protein - like ) 
 environment .
the resulting atomic charges in the amber ff03 force 
 field are notably less polarized than those in the amber ff9x family 
 ( including the amber ff99sb - ildn force field tested here ) , which were 
 derived in vacuum and share the same set of atomic radii .
the amber 
 ff03 atomic charges are also less polarized than those in the amber 
 ff13 force field , with atomic charges possessing increased 
 polarity relative to previous amber charge models . in the amber ff13 charge model ,
nonpolarizable point 
 charges have been fit to implicitly account for solvent polarization , 
 using iterative cycles of classical md simulations with explicit water 
 ( i.e. , tip4p - ew ) to estimate the water charge density around the solute , 
 followed by quantum mechanical calculations to determine updated solute 
 charges .
interestingly , although certain critical atomic radii 
 ( e.g. , the 
 nitrogen in butylammonium and the oxygen in acetate ) in the amber 
 ff13 force field were adjusted from their original values in 
 the amber ff99 force field to reproduce experimental hydration free 
 energies of the relevant amino acid analogues , the resulting strengths of the salt bridges are more overestimated , 
 relative to the other tested amber force fields .
notably , the amber 
 ff13 force field results in a free energy landscape for salt 
 bridge formation that is significantly different from those of the 
 other force fields . in particular , as shown by the pmfs as a function 
 of the minimum n 
o distance between the oppositely charged 
 analogues for the three types of salt bridges ( figure 1 ) , the free energy minima for the bound states are consistently 
 shifted to the right in the amber ff13 force field relative 
 to the other force fields .
when we substituted the atomic radii in 
 the amber ff13 force field with the original radii from the 
 amber ff99 force field , the free energy minima for the bound states 
 shifted back toward those of the other force fields and yielded significantly 
 deeper minima as well as more pronounced desolvation barriers , particularly 
 for the guanidinium / acetate and imidazolium / acetate systems ( figure 
 s2 , supporting information ) .
since 
 the atomic charges of the opls_2005 force field are not significantly 
 different from those of the other force fields , the most likely reason 
 for the fact that this force field overestimates the ka values to the greatest extent is that the atomic radii 
 of the nitrogen - attached hydrogen atoms are smaller than those used 
 by the other force fields , potentially allowing the pairs to associate 
 more closely and increasing their electrostatic attraction ( table 
 s1 , supporting information ) .
consistent 
 with this notion , simulations using the opls - aa force field , which 
 differs from the opls_2005 force field only in that it omits atomic 
 radii for these hydrogen atoms , resulted in slightly more strongly 
 associated salt bridges ( table s2 , supporting 
 information ) .
we note that the ranking of the strengths of 
 the three types of side - chain salt bridges in our study by the amber 
 ff99sb - ildn , charmm27 , and opls - aa force fields is consistent with 
 that observed for their oppositely charged termini in a recent study 
 by others . as mentioned 
 above , we additionally tested salt bridge formation of the arg / asp 
 pair by simulating association / dissociation of blocked amino acid 
 dipeptides , testing six different force fields in conjunction with 
 the tip4p - ew explicit water model .
as shown in table 2 , the relative ranking of the force fields in terms of the ka is generally consistent with our results from 
 the corresponding side - chain analogue system ( guanidinium / acetate ) . 

the only exception is the amber ff13 force field , which yields 
 the weakest ka for the association of 
 the amino acid dipeptides , as opposed to an intermediate ka value for the association of guanidinium / acetate . as 
 indicated by the pmf between the arginine and aspartate dipeptides 
 ( figure 3 ) ,
the bound state free energy minimum 
 of the amber ff13 force field is the most shallow among the 
 tested force fields , corresponding to the lowest frequency of salt 
 bridge formation .
the inclusion of the backbone groups , therefore , 
 appears to alter its propensity for salt bridge formation , likely 
 through the competition of side - chain / backbone interactions with the 
 side - chain / side - chain interactions between the two amino acids .
this 
 result emphasizes the benefit of using unbiased simulations ; had the 
 relative orientations of the amino acids been fixed as in previous 
 studies , any effects of significant side - chain / backbone 
 interactions on the frequency of salt bridge formation would not have 
 been apparent .
results are from 10-s 
 simulations and standard errors were calculated using a block averaging 
 method .
potentials of mean force 
 ( pmf ) between blocked arginine and aspartate 
 dipeptides using six biomolecular force fields with the tip4p - ew water 
 model .
the larger noise level compared to the data presented in figure 1 is caused by simulating a single pair of binding 
 partners , rather than a concentrated solution .
to monitor side - chain / backbone association , we used the same 
 minimum 
 n  o distance coordinate and bound and unbound state definitions 
 as used for the side - chain / side - chain interactions .
a comparison of 
 the relative probabilities of side - chain / side - chain versus side - chain / backbone 
 association ( figure 4 ) reveals that the force 
 fields generally prefer side - chain / side - chain association by a factor 
 of 2 or more over side - chain / backbone association .
the exception 
 is amber ff13 , which shows a lower preference for side - chain / side - chain 
 association of 1.3 .
this slight preference over side - chain / backbone 
 association is likely due to the substantially more polarized backbone 
 amide and carbonyl groups of the amber ff13 force field relative 
 to previous amber force fields ( including the amber ff99sb - ildn and 
 amber ff03 force fields ) .
thus , as a result 
 of the delicate balance of side - chain / side - chain and side - chain / backbone 
 interactions , the strength of the arg / asp salt bridge appears to be 
 most accurately modeled ( least overstabilized ) by the amber ff13 
 force field in a model system that is representative of a protein 
 environment .
the probability of side - chain / side - chain association ( pboundsc / sc ) 
 over the probability of side - chain / backbone association ( pboundsc / bb ) 
 for blocked arginine and aspartate dipeptides using six biomolecular 
 force fields with the tip4p - ew water model .
in addition to the force 
 field , the choice of water model can affect the strength of salt bridges . 
 to evaluate the influence of the water model
, we tested the above 
 three side - chain analogue systems with a selection of force field / water 
 model combinations in addition to the force field / tip4p - ew combinations . 

regardless of the water model , the relative ranking of the force fields 
 is unchanged in terms of the ka values , 
 with pbound varying by 510% between 
 the water models ( table 1 ) .
we also evaluated 
 the dependence of salt bridge interactions on the dielectric constant 
 of the employed water model ( water ) .
interestingly , 
 despite the fact that the spc / e water model yields a computed dielectric 
 constant ( water = 70 ; table s4 , supporting information ) that is closest to the experimental 
 value ( water = 78.4 ) among all of the tested water models , the use of the spc / e water 
 model results in stronger salt bridge interactions than seen with 
 the tip4p - ew water model , in which the water value 
 is underestimated ( water = 56 ; table s4 , supporting information ) .
in fact , as shown in 
 figure 5 , there appears to be no clear correlation 
 between water of the water model and the strength 
 of the salt bridges . as an aside
, the charmm27 and charmm22 * force 
 fields were tested with both the standard tip3p and the charmm - modified 
 tip3p ( mtip3p ) water models with which they were developed .
the mtip3p 
 water model includes atomic radii on hydrogen as well as oxygen atoms , whereas standard tip3p includes only the oxygen 
 atom . using the mtip3p water model consistently results in a lower ka values , in better agreement with experiment . 

this suggests that it may be advisible to use of the charmm - modified 
 tip3p , rather than the standard tip3p water model with any charmm 
 force field .
relationship between the probabilities of binding ( pbound ) and the dielectric constant of the water 
 model 
 ( water ) for three different pairs of oppositely 
 charged side - chain analogues .
the displayed data are simulation results 
 using six biomolecular force fields and six explicit water models . 

the pbound values that correspond to the 
 experimental association constants ( ka ) for the guanidinium acetate and butylammonium acetate systems are 
 depicted as horizontal gray bars ; no 
 experimentally measured ka is available 
 for the imidazolium acetate system .
the water values 
 were calculated from the first 100 ns of each simulation . for each 
 model ,
the presence of the solutes lowers the water for each system by 1015 relative to that of pure water ( table 
 s4 , supporting information ) .
note that 
 the error bars are not visible since 95% confidence intervals for 
 both pbound and water lie within in the symbols area in the graph .
we compared the modeling 
 of salt bridge interactions using six 
 current biomolecular force fields .
three different salt bridges ( arg / asp , 
 lys / asp , and his(+)/asp ) were simulated and considerable differences 
 in their strengths were noted , both between the force fields and with 
 experiment . given the availability of experimentally measured ka values for the association of oppositely charged 
 side - chain analogues , we have focused primarily on modeling salt bridge 
 formation using these systems .
we also tested the applicability of 
 our results to amino acids by simulating blocked amino acid dipeptides 
 for one of the salt bridges , arg / asp .
our side - chain analogue 
 simulations reveal that the computed ka values are generally overestimated , relative 
 to experimental values , with the amber ff03 force field overestimating 
 the strengths of the salt bridges to the least extent and the opls_2005 
 force field to the greatest extent when using the same water model 
 ( tip4p - ew ) . for the blocked arginine and aspartate dipeptides , we 
 observed general agreement in the relative ranking of the force fields 
 with that obtained from simulations with the corresponding side - chain 
 analogues .
the only exception is the amber ff13 force field , 
 which resulted in the lowest probability of salt bridge formation , 
 likely due to the presence of competing side - chain / backbone interactions . 

thus , while the amber ff03 force field overestimates the strength 
 of salt bridges to the least extent for the side - chain analogue systems , 
 the amber ff13 force field results in an even lower frequency 
 of salt bridge formation than the amber ff03 force field for the complete 
 amino acids . finally , we examined the influence of the water model 
 on the strengths of the salt bridges .
irrespective of the water model , 
 the relative ranking of the force fields remained unchanged , with 
 no clear correlation between the probability of binding ( salt bridge 
 formation ) and the dielectric constant of the solvent ( water ) . in conclusion ,
when running md simulations in 
 which salt bridge 
 formation may be of interest , careful attention should be paid to 
 the specific force field and water model in simulations of protein 
 systems .
several current force fields yield considerably higher ka values than those experimentally determined , 
 a discrepancy that may lead to erroneous conclusions .
our encouraging 
 results with the amber ff13 force field suggest that charge 
 derivation strategies that implicitly incorporate solvent polarization 
 from explicit water may significantly extend the lifetime of fixed - charge 
 force fields , which include all of the force fields tested in this 
 study .
for example , using polarizable force fields 
 that permit varying the charge distribution within a molecule based 
 on both its conformation and environment may alleviate such shortcomings . 
 in the past ,
the solvation of ions and charged 
 small molecules , have been modeled using 
 polarizable force fields , resulting in improved agreement with experiment , 
 compared to charmm27 and amber ff99 force fields ( equivalent to the 
 amber ff99sb - ildn force field used here ) .
future work will determine 
 whether or not this also holds for protein salt bridges .
 recent advances in computer hardware 
 and software have made rigorous 
 evaluation of current biomolecular force fields using microsecond - scale 
 simulations possible . 
 force fields differ in their treatment of electrostatic 
 interactions , including the formation of salt bridges in proteins . 
 here 
 we conducted an extensive evaluation of salt bridge interactions 
 in the latest amber , charmm , and opls force fields , using microsecond - scale 
 molecular dynamics simulations of amino acid analogues in explicit 
 solvent . 
 we focused on salt bridges between three different pairs 
 of oppositely charged amino acids : arg / asp , lys / asp , and his(+)/asp . 
 
 our results reveal considerable variability in the predicted ka values of the salt bridges for these force 
 fields , as well as differences from experimental data : almost all 
 of the force fields overestimate the strengths of the salt bridges . 
 
 when amino acids are represented by side - chain analogues , the amber 
 ff03 force field overestimates the ka values 
 the least , while for complete amino acids , the amber ff13 force 
 field yields the lowest ka value , most 
 likely caused by an altered balance of side - chain / side - chain and side - chain / backbone 
 contacts . 
 these findings confirm the notion that the implicit incorporation 
 of solvent polarization improves the accuracy of modeling salt bridge 
 interactions . 
Introduction
Methods
Results and Discussion
Conclusions