inhomogeneous fluid 
 solvation theory ( ifst ) is a statistical 
 mechanical framework for calculating the 
 effect of a solute on the free energy of the surrounding solvent relative 
 to its bulk state . the solute can be a 
 protein , peptide , or small molecule and the solvent is 
 commonly water . ifst has found particular 
 use in the pharmaceutical industry with the advent of schrdinger s 
 watermap software . it has also been developed 
 in the solvation theory of ordered water ( stow ) package , and recent work using grid inhomogeneous solvation 
 theory ( gist ) has explored the results of performing ifst calculations 
 on a cartesian grid . one of the useful 
 features of ifst is that the free energy changes are calculated for 
 small subvolumes surrounding the solute and this allows the contribution 
 of different regions of space to be calculated and visualized . this 
 has been used to understand the determinants of binding affinity and design new inhibitors in the hit - to - lead 
 and lead optimization stages of drug development . work in this lab has focused on the importance of modeling 
 solvation at protein surfaces and the 
 data requirements for convergence of the thermodynamic quantities 
 computed by ifst . one important issue 
 that has not been addressed in detail is the quantitative accuracy 
 of ifst . initial work suggested a reasonable comparison with the experimental 
 solvation free energy of methane and recent 
 work notes solvation free energies as a key benchmark for the method . while a direct comparison with experiment is 
 interesting , the results rely on the force field and particularly 
 the water model that is used . this decouples testing of the method from testing of the parameters . 
 in this work , we compute solvation free energies for six simple molecules 
 using ifst and compare the results with solvation free energies calculated 
 using free energy perturbation ( fep ) . hydration free energies for six simple 
 molecule were calculated 
 using two statistical mechanical computational methods , fep and ifst . fep calculates the hydration free energies directly , whereas ifst 
 calculates the hydration enthalpies and entropies and these are combined 
 to yield the predicted hydration free energy . all molecular dynamics 
 ( md ) simulations in this work were performed with the tip4p-2005 water 
 model . the six solutes studied were acetamide , 
 benzene , isobutane , methane , methanol , and n - methylacetamide . the parameters for acetamide , benzene , isobutane , methanol , and n - methylacetamide were taken from the charmm36 force field . the parameters for methane were not present 
 in the charmm36 force field and were thus adapted from ethane . the 
 methane carbon atom was assigned an atom type of cg331 and a partial 
 charge of 0.36 . the methane hydrogen atoms were assigned an 
 atom type of hga3 and a partial charge of + 0.09 . the bond lengths , 
 bond angles , and dihedral angles were set to their force field equilibrium 
 values for all molecules . to generate a reasonable 
 initial water 
 density , a water shell of radius 50.0  was generated around 
 each biomolecule with the solvate program version 1.0 from the max 
 planck institute . the resulting water 
 globules were then cut to rhombic dodecahedral unit cells with side 
 lengths of 25.0  . to standardize the geometries of the water 
 molecules , every hydrogen atom was deleted and all the necessary hydrogen 
 atoms and lone pairs were built using the appropriate geometry for 
 tip4p-2005 water . the boxes contained 384 , 371 , 376 , 394 , 376 , and 
 374 water molecules for the molecules acetamide , benzene , isobutane , 
 methane , methanol , and n - methylacetamide , respectively . equilibration was performed for 
 1.0 ns in an npt ensemble at 300 k and 1 atm using langevin temperature 
 control and nos  hoover langevin piston pressure control . all 
 systems were brought to equilibrium before continuing , by verifying 
 that the energy fluctuations were stable . electrostatic interactions were modeled 
 with a uniform dielectric and a dielectric constant of 1.0 throughout 
 the equilibration and production runs . van der waals interactions 
 were truncated at 11.0  with switching from 9.0  . electrostatics 
 were modeled using the particle mesh ewald method , and the systems were treated using rhombic dodecahedral 
 periodic boundary conditions . all solute atoms were fixed for the 
 entirety of the equilibration and production simulations . 100.0 ns of production simulation in 
 an npt ensemble were performed at 300 k and 1 atm for each system . system snapshots were saved every 10.0 fs , yielding 10  000  000 
 snapshots in total for each system . md simulations for ifst were performed 
 using namd version 2.8 compiled for use 
 with cuda - accelerated gpus . an important 
 decision in implementing 
 ifst binding sites , water molecules commonly cluster in distinct 
 locations and the concept of a hydration site is useful to calculate 
 contributions to the free energy from spherical regions . in the context 
 of small molecule solvation , the water molecules do not cluster in 
 distinct locations and the concept of a hydration site is not useful . two approaches have been used to account for this in previous work . 
 in the lazaridis work on the solvation of methane , the region surrounding the solute was split into subshells 
 at different distances from the origin . for more complex molecules , spherical polar coordinates could usefully be used to further split 
 these subshells . in the recent work on gist , the region surrounding 
 the solute was split into cubic voxels on a cartesian grid . there are a number of other possibilities for partitioning 
 a volume into subvolumes and these different methods of honeycombing 
 space are likely to affect the performance of ifst . in this work , we have used a cartesian grid to honeycomb the volume and we use the 
 term voxel to specify one cubic unit in this space . we consider all 
 voxels within 12.0  of the origin in the calculation , where 
 the centroid of each solute lies at the origin . in this study , we 
 have not taken advantage of the symmetry of the solute molecules , 
 which would provide more data , as we are interested in applying ifst 
 to systems that do not have such symmetry in the future . ifst calculates the difference in 
 interaction energy ( eifst ) and 
 correlation entropy ( sifst ) between 
 each subvolume ( v ) and the equivalent number of bulk 
 water molecules ( n ) . these can be termed the local 
 quantities . water 
 interaction energy ( esw ) , the mean water  water 
 interaction energy ( eww ) , and the mean 
 interaction energy of a bulk water molecule ( ebulk ) as follows:1for the tip4p-2005 water model , ebulk is calculated from a 100 ns npt simulation of bulk 
 water at 300 k and 1 atm as 11.5813 kcal / mol . in this work , ebulk and eww are 
 defined as half the interaction energy of one water molecule with 
 all other water molecules . previous work have defined ebulk and eww as the total 
 interaction energy of one water molecule with all other water molecules 
 and included factors of one - half in eq 1 . water entropy ( ssw ) , the water  water entropy ( sww ) , 
 and the entropy of a bulk water molecule ( sbulk ) as follows:2all entropies calculated in this work exclude 
 vibrational entropy changes . for each subvolume , ssw is calculated from the translational and orientational 
 contributions using the translational and orientational correlation 
 functions , gsw(r ) and gsw(|r).34k is boltzmann s constant , 
  is the number density of bulk water , and  is 
 the integral over the angles . for the tip4p-2005 water model , is calculated from a 100 ns npt simulation of bulk water at 300 k 
 and 1 atm as 0.0331  707 molecules /  . the solute  water 
 orientational correlation functions were calculated using euler angles 
 by computing  , cos  , and  in a fixed reference 
 frame . the limits of integration for the water molecule are between 
 0 and 2 for  , between 1 and 1 for cos  , 
 and between 0 and  for  , due to water s c2v symmetry . the orientational 
 correlation functions were assumed to be independent of the position 
 within the hydration sites . the default grid resolution was 0.5  
 and the default angular bin size was 45. this leads to 8 , 4 , 
 and 4 angular bins for  , cos  and  and thus 128 
 angular bins in total . a rigorous treatment would use the inhomogeneous water  water 
 pair - correlation functions gww(r , r ) and gww(,|r , r ) from the system and the homogeneous water r and  are the distance and relative orientation between two water 
 molecules in bulk water.56however , converging calculations 
 of the inhomogeneous 
 water  water pair - correlation functions requires a very large 
 amount of data and thus the kirkwood superposition approximation ( ksa ) 
 is used . the ksa provides an approximation 
 of a third - order correlation function in terms of lower order correlation 
 functions . in this context , the ksa is applied to the homogeneous 
 triplet solute  water water correlation functions 
 and thus equal to the water  water correlation function in bulk 
 solvent . the ksa is used for both gww(r , r ) and gww(,|r , r):78these correlation 
 functions can be converged 
 in bulk water due the increased data available from it being a homogeneous 
 and isotropic system . previous work on the solvation of methane suggests 
 that these ksas lead to reasonable results due to the cancellation 
 of errors between more and less structured regions . in this work , this is likely a 
 good assumption for the translational contributions , which in bulk 
 water are derived almost exclusively from the excluded volume and 
 the first solvation shell . the orientational 
 contributions to sww ( and sbulk ) are expected to be underestimated , as only approximately 
 75% of the orientational entropy in bulk water is derived from the 
 first solvation shell . calculations for gww(r ) and gww(|r ) were performed on pairs 
 of voxels on the cartesian grid from the 100 ns npt simulation of 
 bulk water at 300 k and 1 atm . the difference in free energy ( gifst ) for each voxel is then calculated from 
 e and s.9 the equilibrated systems 
 generated for 
 the ifst simulations were used as the start points for the fep systems . these systems consist of the solute in water and correspond to the 
  = 0.0 states . fep calculations were performed in both forward 
 and backward directions to yield corresponding predictions for annihilation 
 (  = 0.0 to  = 1.0 ) and creation (  = 1.0 to  
 = 0.0 ) of the solutes . each annihilation and creation was split into 
 24 steps to yield 48  windows per system . two measures were 
 adopted to avoid the numerical instabilities termed  end - point 
 catastrophes  that occur when  approaches 0.0 or 1.0 . first , a soft - core potential was employed with a van der waals radius - shifting 
 coefficient of 5.0 . second , van der waals interactions 
 were scaled down to zero between  = 0.0 and  = 1.0 whereas 
 electrostatic interactions were scaled down to zero between  
 = 0.0 and  = 0.4 . the 24 fep windows used in the 
 annihilation and creation simulations of the six solutes . starting with 
 the equilibrated systems 
 generated for the ifst simulations , further equilibration was performed 
 for 800 ps in an npt ensemble for each lambda window . 7.0 ns of production simulation in an 
 npt ensemble were performed at 300 k and 1 atm for each lambda window . for fep , the free energy of a change 
 ( gfep ) is calculated as the sum 
 of free energy changes for a series of n small steps between intermediate 
 states a and b.10the 
 free energy change for each small step 
 ( gab ) is calculated using the partition functions ( q ) for the two states which are calculated using the hamiltonians 
 ( h ) for the two states.11we employed the bennett 
 acceptance ratio ( bar ) 
 method , a technique that combines forward 
 and backward fep simulations to provide efficient estimates of free 
 energy changes . the parsefep plugin is described in 
  a toolkit for the analysis of free - energy perturbation calculations  
 and the free energy and the statistical error are computed using eqs 
 11 and 14 from that paper . the estimated 
 statistical error in the fep free energy predictions using bar was 
 less than 0.1 kcal / mol in all cases . ifst calculations equate 
 the change in enthalpy ( h ) with the change 
 in potential energy ( e ) . for calculations 
 in an npt ensemble , there is an additional contribution to the free 
 energy of pv , where p is the pressure and v is the change 
 in volume . however , for solvation of small molecules in water under 
 ambient conditions , pvis 
 significantly smaller than e and can be safely 
 neglected . in addition , the fep and ifst 
 calculations in this study both use a nonpolarizable force field . the parameters for the solutes are for prepolarized molecules and 
 thus the free energy change associated with polarization of the solutes 
 is ignored . as noted previously , 
 such calculations also ignore the difference in polarization of the 
 water molecules between bulk water and the solution . an additional consideration when comparing ifst calculations 
 to experiment are terms that arise from the thermal motion of the 
 solute and the change in ideal solvent entropy upon solute insertion . the additional terms are commonly termed the liberation contributions 
 ( elib and slib ) and the volume entropy contribution ( sve ) . collectively , they are 
 termed the nonlocal contributions and are distinct from the correlation 
 terms in eqs 1 and 2 . the local contributions eifst , sifst , and gifst represent ben - naim s standard energy , 
 entropy , and free energy of solvation . the liberation enthalpy elib is 
 calculated from the solvent s thermal expansion coefficient 
  and isothermal compressibility :12for solvation in water under standard ambient 
 conditions , elib is approximately 
 + 0.05 kcal / mol . ifst is formulated in such a way that portions of 
 slib and sve cancel with some of the correlation terms . the entropy from the nonlocal contributions snonlocal is calculated from the remaining terms:13for solvation 
 in water under standard ambient 
 conditions snonlocal makes a contribution 
 of + 0.55 kcal / mol to the free energy . in this work , we compare the 
 predictions of fep and ifst with ben - naim s experimentally 
 determined standard energy , entropy , and free energy of solvation . these do not include the nonlocal contributions , which are thus excluded 
 from our calculations . the standard energies , 
 entropies , and free energies of solvation 
 of solvation for benzene , isobutane , methane , and methanol are taken 
 from the same source . the standard free 
 energies of solvation for acetamide and n - methylacetamide 
 are derived from wolfenden and taken 
 from the same source . the enthalpies 
 of solvation for acetamide and n - methylacetamide 
 are taken from the same source and then 
 modified to yield the standard enthalpies of solvation . the simulation of bulk water is a key part of this work , as eifst depends critically upon the calculated 
 value of ebulk . this is because the volume 
 of solvent we are considering ( voxels within 12.0  of the origin ) 
 contains approximately 240 water molecules . thus , a difference of 
 0.01 kcal / mol in ebulk leads to a difference 
 of 2.4 kcal / mol in eifst and efep . a simple calculation suggests that ebulk must be correctly converged to within 0.0002 
 kcal / mol for eifst and efep to be correctly calculated to within 0.1 
 kcal / mol . this extreme dependence means that it is thus vital that 
 the calculation of ebulk is converged . after approximately 
 75 ns , the running average remains within 0.0002 kcal / mol of the final 
 calculated value , yielding a final ebulk of 11.5813 kcal / mol for the tip4p-2005 water model . convergence 
 of ebulk for a 100 ns simulation 
 of bulk tip4p-2005 water : the running average of ebulk for a 100 ns npt simulation of bulk tip4p-2005 water 
 at 300 k and 1 atm . each block is the average potential energy per water molecule 
 taken from 2500 samples with one every 100 fs . the simulation of bulk water also allows calculation of the 
 excess 
 entropy ( sbulk ) . numerous works have reported 
 the excess translational entropy of bulk water based on ifst calculations 
 using spherical polar coordinates . due to bulk water being isotropic , the excess translational 
 entropy can be calculated from the radial distribution function ( rdf ) . using the rdf with a radial bin size of 0.1  , the excess translational 
 entropy in the first solvation shell ( between 0.0 and 3.6  ) 
 is calculated to be 3.29 cal / mol / k for the tip4p-2005 water 
 model . this makes a contribution of + 0.98 kcal / mol to the excess free 
 energy . it is interesting to compare this with the translational entropy 
 based on ifst calculations using a cartesian coordinate system . using 
 the default grid resolution of 0.5  , the excess translational 
 entropy for voxels within the first solvation shell ( between 0.0 and 
 3.6  ) this makes 
 a contribution of + 0.63 kcal / mol to the excess free energy . the true 
 rdf and an  effective rdf  using the cartesian coordinate 
 system can be seen in figure 2 . the rdf between 0.0 and 3.6  from the bulk water 
 simulation of tip4p-2005 ( blue line ) and an  effective rdf  
 computed for voxels at the given distance from the origin ( red line ) . the effective rdf is calculated by first computing the distance between 
 the origin and the center of each voxel . the value of g(r ) at each distance is calculated from the average 
 number of water molecules in the group of voxels at that distance 
 and their summed volume . the curve is much flatter for the cartesian coordinate system , 
 with a significantly reduced contribution from the excluded volume . this suggests that a cartesian grid of 0.5  may be too coarse 
 to fully capture the translation probability density function . however , 
 similar results are observed for the solute water rdfs ( data not shown ) 
 and the errors in the translational entropy for the bulk system and 
 the solute a similar approach 
 can also be taken for the orientational entropy . using spherical polar 
 coordinates with a radial bin size of 0.1  and an angular bin 
 size of 10 , the excess orientational entropy in the first solvation 
 shell ( between 0.0 and 3.6  ) is calculated to be 7.28 
 cal / mol / k for the tip4p-2005 water model . this makes a contribution 
 of + 2.17 kcal / mol to the excess free energy . for the cartesian coordinate 
 system using a grid resolution of 0.5  and an angular bin size 
 of 10 , the excess orientational entropy in the first solvation 
 shell ( between 0.0 and 3.6  ) is calculated to be 4.70 
 cal / mol / k . this makes a contribution of + 1.40 kcal / mol to the excess 
 free energy . figure 3 shows the cumulative 
 orientational contributions to sbulk between 
 0.0 and 3.6  for the radial and cartesian coordinate calculations . these findings show that sbulk is underestimated 
 using a grid resolution of 0.5 and this suggests that sww is likely to be misestimated . cumulative orientational 
 contribution to tsbulk for bulk tip4p-2005 
 water : the cumulative contribution 
 to tsbulk between 0.0 and 3.6  from 
 the bulk water simulation of tip4p-2005 using the radial coordinate 
 system ( blue line ) and the cartesian coordinate system ( red line ) . after calculating the necessary 
 values for the bulk water simulation , 
 we tested the method by using the bulk simulation as a basis for ifst 
 calculations . the ifst quantities were calculated for all voxels within 
 12.0  of the origin . in all the following work , we report the 
 entropic contributions to the free energy ( tsifst ) in kcal / mol rather than 
 the entropies ( sifst ) in cal / mol / k , 
 as this allows a direct comparison with the enthalpic contributions 
 to the free energy . the second column of table 2 shows the contributions from the different ifst quantities for the 
 bulk water simulation , which should all be zero when there is no perturbation 
 from a solute . it is clear that the orientational contributions to tssw are overestimated by this method 
 and this is due to the inherent bias in the histogram method . the 
 overestimate is very small for each voxel ( approximately 0.000  015 
 kcal / mol ) but there are approximately 60  000 voxels and this 
 leads to a significant overestimate in total . for this reason , we 
 expect that the orientational contributions to ssw will be overestimated for the solute systems . the other 
 contributions to the free energy are close enough to zero to be acceptable . the calculated ifst quantities 
 for bulk water and the six solutes from the 100 ns simulations . the 
 total translational and orientational contributions are the sums of 
 the solute  water and water  water terms . we then moved on to consider the 
 solute  water systems . a 
 key question that we have previously attempted to address is the size 
 of the solvation shell around a solute that is affected by its presence . however , previous studies were incomplete because they considered 
 the per voxel values of eifst , 
 sifst , and gifst with increasing distance from the origin rather than 
 the total eifst , sifst , and gifst . these total values are affected by the volume increasing with the 
 cube of the distance from the origin and are more revealing . we have 
 calculated these values for the six solutes to more thoroughly address 
 this issue . cumulative contributions to eifst , sifst , and gifst for acetamide at increasing distances from 
 the origin : 
 the cumulative contributions to eifst ( blue diamonds ) , tsifst ( red squares ) , and gifst ( green triangles ) for acetamide between 0.0 and 12.0  from 
 the origin . the total sifst approaches its 
 final value at around 5.0  from the origin whereas the total 
 eifst and thus the total gifst approach their final value at around 9.0 
  from the origin . the slight peaks in sifst at 5.0 and 9.0  are due to the first and second 
 solvation shells , as the plot is of the distance from the origin and 
 acetamide has an approximate  radius  of 3.0  . when the size of the solutes is considered , the results indicate that 
 the solvent is perturbed to a distance of approximately 7.0  
 from the surface of a solute . this corresponds to the first two solvation 
 shells , with the first solvation shell contributing around 80% to 
 gifst . as discussed previously , 
 these distances may be much larger for charged systems and they may 
 also be different for larger solutes . indeed , studies on a 16-residue 
 peptide suggest that significant perturbations may extend to the third 
 solvation shell at around 10  from the surface . as previously , we distinguish between the convergence with increased 
 simulation time for a given sampling frequency and the convergence 
 with increased sampling frequency for a given simulation time . the convergence with increased simulation time can be seen for acetamide 
 in table 3 for a sampling frequency of 10 fs . the result for eifst after 20.0 
 ns differs from the result after 100 ns by only 0.1 kcal / mol but the 
 result for tsifst differs by more than 0.1 kcal / mol , even after 50.0 ns . it is the 
 difference in the orientational component of ssw that is notably different as the simulation time is decreased . this is not unexpected , as there are 128 times as many histogram bins 
 for the orientational component of ssw as for the translational component . these calculations suggest that 
 converged predictions for ifst require at least 100 ns of simulation 
 with a grid resolution of 0.5  and an angular bin size of 45 
 but that simulations of 20 ns may be sufficient to predict eifst . the convergence with increased sampling 
 frequency for acetamide can be seen in table 4 for a simulation time of 100 ns . the result for eifst using a sampling frequency of 1000 fs is the same 
 as the result using a sampling frequency of 10 fs to one decimal place , 
 and the result for tsifst using a sampling frequency of 20 fs is the same as the 
 result using a sampling frequency of 10 fs to one decimal place . again , 
 it is the orientational component of tssw that is notably different as the sampling frequency is decreased . these calculations suggest that converged predictions for ifst using 
 a histogram method require at least 5  000  000 samples 
 from a 100 ns simulation with a grid resolution of 0.5  and 
 an angular bin size of 45. other methods , such as the k - nearest neighbors ( k - nn ) algorithm , may require shorter simulations and less sampling . the calculated enthalpic and 
 entropic contributions to the free energy of acetamide calculated 
 using all snapshots within 10 , 20 , 50 , and 100 ns . the calculated 
 enthalpic and 
 entropic contributions to the free energy of acetamide calculated 
 using 100 ns of data with sampling frequencies of 1000 , 500 , 200 , 
 100 , 50 , 20 , and 10 fs . we also wished to consider the effect of the grid resolution and 
 angular bin size on the orientational and translational components 
 of ssw . the results in tables 3 and 4 indicate that the 
 translational component of ssw is well 
 converged for a grid resolution of 0.5  . we also studied the 
 results for grid resolutions of 0.25 and 0.75  to assess whether 
 the translational component of ssw is 
 fully quantified with the default grid resolution of 0.5  . the 
 results for acetamide are reported in table 5 and indicate that the answer is no . a grid resolution of 0.25  
 yields a converged value of 4.3 kcal / mol for the translational component 
 of tssw in comparison with a value 
 of 3.7 kcal / mol for a grid resolution of 0.5 . smaller grid 
 resolutions , which may yield a higher prediction , were not tested . testing the orientational component of tssw in this fashion is more complicated because it requires 
 a grid resolution in addition to an angular bin size . in this work , 
 we have only explored the variation in entropy with respect to the 
 angular bin size at the default grid resolution of 0.5  . we 
 studied the results for angular bin sizes of 36 and 60 
 to assess whether the translational component of tssw is fully quantified with the default angular bin size 
 of 45. the results for acetamide are reported in table 6 . an angular bin size of 36 yields a value 
 of 3.6 kcal / mol for the orientational component of tssw in comparison with a value of 2.9 kcal / mol 
 for an angular bin size of 45. however , it is not clear that 
 the results for an angular bin size of 36 are fully converged 
 from 10  000  000 samples over 100 ns and thus the question 
 can not be answered . indeed , the results from the simulation of bulk 
 water presented in the first column of table 2 suggest that the orientational component of tssw is not fully converged from 10  000  000 
 samples over 100 ns for an angular bin size of 45. due to computational 
 restrictions , we have not tested effect of the grid resolution and 
 angular bin size on the orientational and translational components 
 of sww . however , the results from 
 the simulation of bulk water suggest that the effects on ssw and sww may counterbalance 
 one another . the translational component of 
 tssw for acetamide , calculated 
 from 1  000  000 , 2  000  000 , 5  000  000 , 
 and 10  000  000 samples with grid resolutions of 0.25 , 
 0.5 , and 0.75  .. the orientational component of 
 tssw for acetamide , calculated 
 from 1  000  000 , 2  000  000 , 5  000  000 , 
 and 10  000  000 samples with angular bin sizes of 30 , 
 45 , and 60. the ifst predictions can be seen in table 2 . calculations suggest that the translational and orientational contributions 
 to the solvation entropy are of a similar magnitude in all cases , 
 though the orientational contributions are always slightly larger . water terms are predicted to be 58-fold 
 larger than the water  water terms . water term is negative 
 due to the solute excluded volume , but the orientational water  water 
 term is also small . the first is that the water  water terms depend on the validity 
 of the ksas , which have not been thoroughly explored . the second is 
 that our calculations suggest that the water  water terms are 
 misestimated using a cartesian grid with a resolution of 0.5  . it is interesting to note that the solute  water interactions 
 ( esw ) are highly favorable in all cases , 
 at the expense of an unfavorable change in water this leads to a favorable 
 change in overall energy ( eifst ) that is approximately half the magnitude of esw for the majority of solutes . assessing the data generated 
 using ifst , it is clear that there 
 are a number of issues with the method . the selection of grid resolution 
 and angular bin size affects all the calculated entropies and in addition 
 the use of the ksas has not been comprehensively validated . however , 
 these issues affect all solutes and thus we might expect a systematic 
 misestimation of the entropies in comparison with fep . the results from experiment along with the predictions 
 from fep and ifst can be seen in table 7 . the 
 correlation plots between experiment , ifst , and fep can be seen in 
 figure 5 . the experimental 
 hydration enthalpy , 
 entropy , and free energy for the six solutes , along with the predictions 
 of fep and ifst . correlation plots between g , h , and ts for experiment 
 and the predictions of fep and ifst . plots of the correlation between 
 ( a ) gifst and gfep with blue diamonds , ( b ) gifst and gexperimental with 
 blue triangles , ( c ) hifst and hexperimental with red triangles , and ( d ) tsifst and tsexperimental with green triangles . the 
 mean unsigned difference in the solvation free energies is 0.7 kcal / mol , 
 with the ifst predictions tending to be less favorable than the fep 
 predictions . fep and ifst both yield reasonable predictions of the 
 experimental quantities with mean unsigned errors for the solvation 
 free energies of 1.3 and 1.8 kcal / mol , respectively . agreement of ifst with the experimental enthalpic and entropic contributions 
 is reasonable , with mean unsigned errors of 0.9 and 1.2 kcal / mol , 
 respectively . however , the results suggest that the entropic component 
 ts tends to be overestimated 
 by ifst , with a mean signed error of + 1.2 kcal / mol . these results 
 may explain why the ifst predictions of the hydration free energies 
 tend to be less favorable than the fep predictions . they are also 
 commensurate with the overestimation of ts by 1.0 kcal / mol for the simulation of bulk water . one of the main advantages of ifst calculations is the ability 
 to break the solvation free energies into contributions from different 
 regions and visualize these contributions . this promotes understanding 
 of the system being studied and an insight into the thermodynamics 
 of solvation . figure 6 shows the contributions 
 from different regions to the hydration free energy of acetamide at 
 different contour levels , visualized using vmd . visualizations of the relative free energy density relative to 
 bulk water for regions surrounding acetamide . six views of acetamide , 
 with the relative free energy density contoured at different levels . favorable relative free energy density is contoured in red and unfavorable 
 relative free energy density is contoured in yellow . the contouring 
 for the favorable relative free energy increases from ( a ) to ( b ) to 
 ( c ) . the contouring for the unfavorable relative free energy decreases 
 from ( d ) to ( e ) to ( f ) . the region with the highest relative free energy density 
 is a ring 
 surrounding the carbonyl oxygen ( figure 6a ) . the carbonyl group is actually predicted to contribute approximately 
 6.0 kcal / mol to the hydration free energy of acetamide ( figure 6b ) . at lower contour levels , the contributions from 
 the amide hydrogens are visible , with each contributing approximately 
 1.5 kcal / mol to the hydration free energy ( figure 6c ) . it is worth noting that the favorable regions 
 surrounding the amide hydrogens would be well described by spherical 
 hydration sites but the favorable regions surrounding the carbonyl 
 oxygen would not . contouring from positive values , the regions contributing 
 most unfavorably to the hydration free energy are above and below 
 the plain of the amide bond ( figure 6d ) . this 
 effect has been noted in previous studies using watermap and agrees with observations from the cambridge 
 crystallographic data centre on the hydrophobic character above and 
 below the plane of amide bonds ( personal communication with oliver 
 korb ) . it may also explain why defectively packed backbone hydrogen 
 bonds , which have been termed dehydrons , lead to hotspots at protein 
 surfaces . at lower contour levels , the 
 contributions from the methyl group are visible , again contributing 
 unfavorably to the solvation free energy ( figure 6e ) . at very low contour levels , one can observe the small 
 and unfavorable contributions from water molecules in the second solvation 
 shell ( figure 6f ) . the presence of regions 
 with high number density that contribute 
 unfavorably to a favorable hydration free energy may seem counterintuitive . the reason why a vacuum is not present within such regions can be 
 understood using a simple example . water interactions ( esw = 1.0 kcal / mol ) and water  water interactions 
 that are more favorable than in bulk ( eww = 2.0 kcal / mol ) that is strongly ordered ( tssw = + 3.0 kcal / mol and tsww = + 0.5 kcal / mol ) . for this voxel , gifst = + 0.5 kcal / mol and 
 the region contributes unfavorably to the solvation free energy . one 
 could view these water molecules as  icelike  given 
 their unfavorable entropy and favorable enthalpy compared with bulk 
 water . however , if such a region is vacated ( without allowing solvent 
 rearrangement ) then all surrounding voxels also lose their pair interactions 
 and correlations with water molecules inside the voxel . the total 
 change in free energy ( going to this unphysical state ) can thus be 
 unfavorable . if subsequent solvent rearrangement around the vacuum 
 region can not overcome this loss , then the voxel will be occupied 
 despite contributing unfavorably to the solvation free energy . clearly , 
 there are cases where water can rearrange around a vacuum , but water 
 molecules at the vacuum interface are likely to show reduced water  water 
 interactions . it is worth noting that the unfavorable contributions 
 are smaller in magnitude than the favorable contributions . considering 
 all voxels in the case of acetamide , the most favorable relative free 
 energy density is 0.28 kcal / mol /  whereas 
 the least favorable relative free energy density is + 0.04 kcal / mol /  . because the exact free energy densities calculated will 
 depend on the grid resolution and angular bin size used , it will be 
 important to test this principle in future work . if these results 
 accurately reflect the thermodynamics , an interesting consequence 
 is the potential for hydration sites in protein binding sites that 
 contribute unfavorably to the hydration free energy . eifst , 
 tsifst , and gifst are calculated as 
 the sum of contributions from each voxel inside 
 a given volume v. the contributions from each voxel 
 include pairwise contributions due to correlations with every other 
 voxel . in the ifst framework , importantly , there are 
 pairs where one of the voxels is not inside the volume v and thus there are regions outside the volume v which contribute to eifst , tsifst , and gifst . , the contribution 
 of voxels outside the volume v is expected to be 
 very small if the volume v is significantly larger 
 than the perturbing solute . in this case , a voxel outside v will only have significant correlations with voxels inside v that are close to the periodic boundary . these will have 
 bulklike properties , leading to esw  
 0 , eww  0 , ssw  0 , sww  
 0 , and gifst  0 . ifst is a useful method to model solvation and has found particular 
 application in understanding hydration phenomena in biological systems . however , there has been little analysis to assess the quantitative 
 predictions of ifst . this study addresses 
 this issue by comparing hydration free energies from ifst with hydration 
 free energies from fep . the findings of this study are that ifst calculations 
 show a good agreement with fep calculations , with a mean unsigned 
 difference of 0.7 kcal / mol in the predicted hydration free energies . comparison of ifst predictions with the experimental hydration enthalpies 
 and entropies suggests that there is a systematic overestimation of 
 the entropies , which leads to a systematic underestimation of the 
 free energies . for the charmm36 force field and the tip4p-2005 water 
 model , the agreement with the experimental hydration free energies 
 is reasonable for fep and ifst , with mean unsigned errors of 1.3 and 
 1.8 kcal / mol , respectively . both ifst and fep rely on the force field 
 and are thus subject to the same problems in this respect . for ifst , 
 the fine dependence of eifst on ebulk means that it is thus vital that the calculation 
 of ebulk is converged correctly . ebulk will depend on the force field , water model , 
 simulation package , and simulation parameters employed . due to cancellation , 
 this fine dependence will be of less importance in calculations of 
 hydration free energy differences or binding energies , but only if 
 the number of water molecules considered is similar . in addition , 
 the systematic overestimations of tsifst are expected to be similar if the grid 
 resolution and bin sizes are the same . thus , predictions for different 
 molecules and different regions are directly comparable for a given 
 ifst implementation , but not necessarily between different ifst implementations . in addition to these results , there are a number of important points 
 raised by the study . ifst has a number of limitations that should 
 be addressed before widespread quantitative application . current implementations 
 are only rigorously valid for a fixed solute and this limits the utility . flexible solutes can be considered in the ifst framework by performing 
 an analysis on a number of solute conformations , but this will require yet more data . one of the major approximations 
 in ifst is the use of the ksas for the water previous work on the solvation of methane suggests that 
 these ksas lead to reasonable results due to the cancellation of errors 
 between more and less structured regions . however , this may not be 
 the case for polar solutes and further testing of the ksas should 
 be a focus of future work . previous 
 work has explored the data requirements for convergence of the solvation 
 energy and entropy . however , the comparison with 
 fep in this work allows a more thorough analysis . the results suggest 
 that converged energies can be effectively sampled from 10  000 
 snapshots over a 20 ns simulation whereas the orientational component 
 of the solute water entropy term requires at least 5  000  000 
 snapshots over a 100 ns simulation to reach a converged prediction 
 even with a modest angular bin size of 45. however , the histogram 
 method introduces a systematic overestimating bias to the entropies 
 and this will scale with the volume of the system . other work has 
 shown that it is also difficult to estimate entropies using perturbation 
 methods such as fep and thermodynamic integration ( ti ) . in the context of ifst , assessment of the entropies may be more feasible using the k - nn algorithm , particularly 
 for the increased sampling requirements of considering a highly flexible 
 solute . it is difficult to fairly assess the computation times required , 
 because the fep calculations are integrated into namd whereas the 
 ifst calculations are not . this requires postprocessing of large - trajectory 
 files at considerable computational cost . comparing just the simulation 
 times , each solute was simulated for a total of 336 ns for fep and 
 100 ns for ifst . while fep is inherently more parallelizable than 
 ifst in its current format , it should be possible to apply ifst to 
 multiple independent md simulations , which would parallelize it effectively . while suffering a number of drawbacks noted above , ifst does have 
 a number of advantages over perturbation methods such as fep and ti . 
 because ifst calculations are performed on a single simulation , there 
 is no need for a lambda window schedule and no need to monitor overlap 
 between lambda windows . in addition , there are no end points and thus 
 there are no end - point catastrophes and no need for soft - core potentials . importantly , there is no pathway and thus small and large perturbations 
 can be considered with the same degree of sampling . however , perhaps 
 the most useful feature of ifst is the spatial decomposition of the 
 solvation free energies . indeed , it 
 would be interesting to compare ifst results with the results of 3d - rism and cell theory , which can 
 provide spatially decomposed predictions of solvation free energies 
 using different methods . this work represents a preliminary 
 study on the quantitative application 
 of ifst using a very small set of solutes . the inclusion of charged solutes may necessitate 
 the use of a polarizable force field . prior to this , it would be very 
 useful to test the validity of the ksas for a number of solutes , using 
 the true inhomogeneous water  water correlation functions or 
 via comparison with lower order entropy approximations . this should 
 be done in concert with a thorough determination of the time scales 
 and sampling requirements that are necessary for effective convergence 
 of the thermodynamic predictions at the desired level of accuracy . in addition , care must be taken to employ methods that effectively 
 capture the underlying probability distributions . the combination 
 of gifst with an assessment of 
 protein  ligand interactions will facilitate the calculation 
 of binding free energies . this will augment binding affinity predictions 
 based on a single unbound state simulation , albeit at increased computational cost . to achieve this , the agreement between hydration 
 free energy predictions 
 for ifst and fep is very encouraging . it is clear that the entropic 
 contributions are overestimated by ifst and further work is needed . however , the insight gained by visualizing the relative free energy 
 densities provides a major advantage of ifst that make this a worthwhile 
 objective .
accurate 
 prediction of hydration free energies is a key objective 
 of any free energy method that is applied to modeling and understanding 
 interactions in the aqueous phase . 
 inhomogeneous fluid solvation theory 
 ( ifst ) is a statistical mechanical method for calculating solvation 
 free energies by quantifying the effect of a solute acting as a perturbation 
 to bulk water . 
 ifst has found wide application in understanding hydration 
 phenomena in biological systems , but quantitative applications have 
 not been comprehensively assessed . in this study , we report the hydration 
 free energies of six simple solutes calculated using ifst and independently 
 using free energy perturbation ( fep ) . 
 this facilitates a validation 
 of ifst that is independent of the accuracy of the force field . 
 the 
 results demonstrate that ifst shows good agreement with fep , with 
 an r2 coefficient of determination of 
 0.99 and a mean unsigned difference of 0.7 kcal / mol . 
 however , sampling 
 is a major issue that plagues ifst calculations and the results suggest 
 that a histogram method may require prohibitively long simulations 
 to achieve convergence of the entropies , for bin sizes which effectively 
 capture the underlying probability distributions . 
 results also highlight 
 the sensitivity of ifst to the reference interaction energy of a water 
 molecule in bulk , with a difference of 0.01 kcal / mol changing the 
 predicted hydration free energies by approximately 2.4 kcal / mol for 
 the systems studied here . 
 one of the major advantages of ifst over 
 perturbation methods such as fep is that the systems are spatially 
 decomposed to consider the contribution of specific regions to the 
 total solvation free energies . 
 visualizing these contributions can 
 yield detailed insights into solvation thermodynamics . 
 an insight 
 from this work is the identification and explanation of regions with 
 unfavorable free energy density relative to bulk water . 
 these regions 
 contribute unfavorably to the hydration free energy . 
 further work 
 is necessary before ifst can be extended to yield accurate predictions 
 of binding free energies , but the work presented here demonstrates 
 its potential .