the 
 pursuit for a global and self - consistent conceptual , mechanistic , 
 and theoretical framework within which to discuss the denaturing properties 
 and behaviors of cosolvents such as urea and guanidinium chloride 
 ( gdmcl ) continues to garner a significant amount of scientific curiosity 
 and effort . the quest for a fundamental understanding of protein denaturation 
 has a long and rich history , to which the reader is referred . based on recent experimental and molecular simulation studies , the 
 notion of direct interactions of denaturants with proteins in solution 
 has come to be accepted in consensus . since common denaturants used 
 in practical situations are needed in significantly high concentrations , 
 i.e. , 5 m urea for instance , the notion that there are no direct interactions 
 between denaturant and protein becomes less justifiable . within the context of direct interactions , one 
 of two major mechanisms for denaturation involves the lessening of 
 the hydrophobic effect as it relates to the formation of a compact 
  prefolded  ensemble of states where protein hydrophobic 
 surface exposure to solvent the idea is that by associating with hydrophobic 
 regions of the protein ( specific residues , clusters of residues forming 
 extended topographical  surfaces  , hydrophobic side 
 chains , etc . ) , denaturant molecules can shield the hydrophobic surface 
 area even in unfolded or extended configurations of the peptide / polymer . this chemical denaturation mechanism naturally involves direct interaction 
 of the cosolvent molecule with regions of the protein surface . a particular 
 aspect of this interaction deals with the precise nature of association 
 geometries and the associated free energetics ; specifically , molecules 
 such as urea , and more so guanidinium cation ( gdm ) , can 
 present several predominant relative orientations to the protein surface 
 through which the interaction is mediated . in general , it is proposed 
 that a dominant interaction of urea with surface groups in protein 
 simulations involves hydrogen bonding with polar side - chain functions , while the unique hydration properties of the gdm support alternative interaction modes involving 
 stacking with side - chain planar and hydrophobic groups . however , we 
 should note that the nature of the relative orientations would be 
 dictated in part by the nature of solvation and hydrophobic effects 
 as they pertain uniquely to each denaturant molecule . understanding 
 of the precise geometrical and associated free energetic properties 
 of denaturant  protein interactions is important as a piece 
 in a more complete understanding of the denaturation process from 
 a molecular perspective . previous studies have shown that cosolvents 
 such as gdm adopt orientations relative to  flat  , 
 model hydrophobic surfaces that are planar . vapor interface , flat hydrophobic plate , and hydrophobic polymer 
 surface . however , there is a lack of 
 direct evidence for similar orientational behavior of gdm upon approaching more complex aqueous protein interfaces . the inherent 
 chemical and topographical heterogeneity of protein surface makes 
 it difficult to find a qualitatively rigorous approach to evaluate 
 the relative orientation between the surface of gdm and 
 the protein . to fill this gap , we apply molecular dynamics simulations 
 investigating the association of gdm cation with a specific 
 protein with a relatively flat surface region consisting of hydrophobic 
 residues . in the context of chemical denaturation via direct association , 
 we ask here about the orientations that gdm and urea adopt 
 when interacting with hydrophobic regions of proteins . the combination 
 of this analysis addresses ideas of direct interaction as well as 
 hydrophobic effects as they pertain to the denaturation process . furthermore , 
 there is sentiment in the literature demonstrating the importance 
 of solvent fluctuations and their relation to what is called the hydrophobic 
 nature of solutes . found that water density 
 near the surfaces of self - assembled monolayers ( sams ) with hydrophobic 
 head groups ( cf3 , ch3 ) shows 
 a poor distinction from that of sams with hydrophilic head groups 
 ( oh , conh2 ) . however , differences arise 
 when considering the fluctuations of water density near the two regions . enhanced fluctuations reflected by the broad probability distributions 
 of water number density are observed around hydrophobic surfaces compared 
 with the bulk solution and hydrophilic surfaces . moreover , the enhanced density fluctuations around hydrophobic surfaces 
 are further characterized by more compressible hydration shells and 
 increased cavity formation , indicating that the 
 nature of hydration shells around hydrophobic surfaces is softer and 
 more flickering than near hydrophilic ones . since the long - ranged 
 solute - induced perturbations of aqueous protein interfaces involve 
 the coupling of local hydration shells of the solutes with distant 
 hydration shells around protein surfaces , the natures of both would 
 affect the extent of induced interfacial fluctuations . it would be 
 interesting to compare the interface height fluctuations as gdm / urea approaches the hydrophobic / hydrophilic protein regions . we note that the interface height fluctuations we are pursuing here 
 are conceptually different from the density fluctuations of refs ( 32 , 33 , 36 , and 37 ) , though both reflect the nature of hydration 
 water around the protein surfaces . it is natural here to investigate 
 the nature of induced fluctuations of the solvent at the protein water 
 interface via consideration of the fluctuations of the height of this 
 interface ( once defined in a well - controlled manner ) upon approach 
 of a denaturant molecule to a hydrophobic protein region as well as 
 when the denaturant resides at very close separation to the protein . the particular protein on which we are focusing in 
 this study is 
 hydrophobin - ii ( hfbii ) , a small protein expressed by filamentous fungi . the protein is known for its ability to form hydrophobic coatings 
 on surfaces and self - assembles into monolayers on hydrophobic / hydrophilic 
 interfaces such as the water / air interface . mapped the effective hydrophobic regions and 
 effective hydrophilic regions of hfbii by considering the density 
 of small probe hydrophobic solutes around each region of the protein . they selected three regions with different hydrophobicity based on 
 this and further monitored the density fluctuations in the vicinity 
 of these regions . their calculation shows that the largest density 
 fluctuations occur around the most hydrophobic region whereas the 
 least density fluctuations are detected around most hydrophilic region . this particular observation suggests hydrophobins as useful candidate 
 proteins for comparing behaviors at hydrophobic and hydrophilic interfaces 
 as denaturant molecules approach . we note that the purpose of this 
 study is to demonstrate the specific denaturant s stability 
 and orientational preference around regions with different hydrophobicity 
 of the protein with implication of the direct interaction as well 
 as hydrophobic effects for the association between denaturant and 
 the protein . the aim of this study does not focus on the denaturation 
 process by these denaturants , so we use the totally fixed protein 
 in the simulation along with quite low concentration of denaturants 
 ( 1 m and an extreme case , single solute ) compared with the significant 
 high concentration ( up to 5 m ) in the actual denaturation experiments . we further emphasize that by using the single solute in this study , 
 it is possible for us to systematically distinguish underlying characters 
 of stability for different species ( gdm and urea ) and 
 orientational preference for different orientations ( parallel and 
 perpendicular relative to the regions of interest ) . ii we discuss 
 the simulation protocols and computational details 
 of the liquid  vapor interface and aqueous protein interfaces . we begin with discussion of potentials 
 of mean force ( pmfs ) and interfacial fluctuations as single gdm / urea cross the aqueous liquid  vapor interface . we 
 consider gdm / urea density distributions around the aqueous 
 hfbii hydrophobic interface in 1.0 m solutions in 
 the second part . we further investigate the pmfs and interfacial fluctuations 
 as single gdm / urea approach this aqueous protein hydrophobic 
 interface , demonstrating the resemblance between liquid vapor 
 interface and hydrophobic protein interface in terms of solute specific 
 effect and orientational preferences . we finish this section by examining 
 single gdm / urea approaching another region , which is considered 
 a hydrophilic patch compared with the hydrophobic region we initially 
 study . all the simulations 
 in this study were performed with md program namd 2.9b3 , using charmm22 all - atom force fields with cmap backbone torsion 
 correction term . simulations of single 
 gdm / urea approaching the liquid  vapor interfaces 
 were performed in the nvt ensemble . the simulation 
 cell was rectangular with dimensions 40   40   
 150  , in which z is the direction normal to 
 the liquid  vapor interface . the system contained one single 
 gdm / urea and 1977 nonpolarizable tip3p water model water molecules . a rigid water geometry is enforced 
 using shake constraints , and an integration 
 time step of 1.0 fs was used . the temperature was kept constant at 
 300 k by applying the langevin friction force scheme with a damping 
 coefficient of 5 ps . a switching distance of 10 
  , nonbonded real - space cutoff of 12  , and pair list generation 
 distance of 14  were used for the van der waals interactions , 
 and the particle mesh ewald ( pme ) method 
 was employed for the calculation of conditionally convergent electrostatic 
 interactions . the grid size of pme in x - dimension 
 is 40 , in y - dimension is 40 , and in z - dimension is 150 ( as close to a 1  grid point separation as 
 possible ) . in order to obtain the pmf for transferring single gdm / urea from bulk aqueous environment to the liquid vapor 
 interface , we define a collective variable , which is based on the 
 cartesian z - component of the separation between the 
 water slab center of mass and single gdm / urea central 
 carbon , describing this pseudochemical reaction path . to enhance sampling 
 of the distribution of configurations where the collective variable 
 holds a particular value , relevant restraint potentials were introduced 
 on the collective variable in order to prevent it from moving outside 
 of the desired range . in this case windows  
 with width 1.0  . in each window , central carbon of single gdm / urea was restrained to z - positions from 
 0 to 30  relative to the water slab center of mass using a harmonic 
 potential urestraint(z ; zrelative , ref ) = /2k(z  zrelative , ref ) with the force constant of 4 
 ( kcal / mol)/ . to consider the orientational dependence 
 of gdm around interface , we further desired to compare 
 the free energetics of single gdm / urea transferring from 
 the bulk with two distinctive orientations : the planar ring of gdm / urea parallel to the liquid  vapor interface and perpendicular 
 to the liquid  vapor interface . here the orientations were defined 
 based on identical definitions from previous publications in which the angle  between the vector normal to the molecular 
 ring and the z - axis was computed . gdm / urea was considered as parallel ( as shown in figure 1a ) and perpendicular ( as shown in figure 1b ) to the liquid we note that for the parallel 
 orientation the normal vector of the molecular ring is along z - direction ; for the perpendicular orientation , the normal 
 vector of the molecular ring can either be along x or along y direction . because of the homogeneous 
 nature of liquid vapor interface and the identical setup in x and y dimensions in the simulation , here 
 we only need to consider one ( when the normal vector is along y direction ) of these two configurations in the perpendicular 
 orientation case . in these two sets of simulations , initially , the 
 parallel and perpendicular configurations of gdm / urea 
 were selected as starting structures , and the orientations were maintained 
 by restraining the directions of central carbon  nitrogen vectors . 
 based on the definition of orientations above , gdm with 
 parallel configuration nitrogen 
 vectors in the plane of xy , with the magnitude along z - direction being zero . therefore , harmonic potentials with 
 force constant k = 1000 ( kcal / mol)/ were applied to keep the magnitudes of z components 
 of two of the three central carbon , we can ensure the parallel orientation 
 of single gdm with respect to the liquid vapor 
 interface . for gdm with perpendicular orientation , all 
 three central carbon nitrogen vectors are in the plane of xz . to maintain this orientation , harmonic potentials with 
 force constant k = 1000 ( kcal / mol)/ were applied to restrain the magnitudes of y components 
 of the carbon these restraint protocols 
 were also applied to single urea molecule by considering only the 
 two central carbon  nitrogen vectors . apart from the orientational 
 restraints , identical choice of collective variable and setup of simulation 
 windows were applied . the total sampling time for each window was 
 15 ns for all the simulations and properties were calculated from 
 all but the initial 1 ns , which was treated as equilibration . ( a ) representative 
 snapshot of single gdm with parallel 
 orientation to the liquid  vapor interface . ( d ) single gdm with parallel 
 orientation to the hfbii protein  solvent interface . ( e ) single 
 gdm with perpendicular y orientation 
 to the hfbii protein ( f ) single gdm with perpendicular x orientation to the 
 hfbii protein  solvent interface . simulations of hfbii in 1.0 m concentration 
 of 
 gdmcl / urea aqueous solutions were performed in the npt ensemble using 
 a cubic cell with a box size 60   60   60 
  . the protein structure was based on the ultrahigh resolution 
 structure of hfbii , with pdb code 2b97 , and it was constructed using charmm - gui . monomer of this hfbii protein , which is composed 
 of 70 residues , was placed in the center of the box and fully solvated 
 with 6481 water molecules , along with 116 pairs of gdmcl or 116 urea 
 molecules . the initial structure of the protein was arranged in a 
 way that its largest hydrophobic patch , consisting of amino acid residues 
 val 18 , leu 19 , leu 21 , ile 22 , val 24 , val 54 , ala 61 , leu 62 , and 
 leu 63 ( the three letters representing the amino acid types and the 
 number representing the position of the amino acid in the primary 
 sequence ) , was nearly perpendicular to the z direction 
 ( further verification is in table s1 of the supporting 
 information ) . the protein was rigidly fixed at the original 
 configuration during the simulation while other system components 
 were unrestrained . temperature was maintained by langevin bath at 
 300 k , and the pressure was kept constant by langevin pressure control 
 at 1 atm . a switching distance of 10  , nonbonded real - space 
 cutoff of 12  , and pair list generation distance of 14  
 were used for the van der waals interactions . for the grid size of 
 pme setup , the values are changed to 60 in all dimensions , corresponding 
 to the cubic simulation cell in this case . six different replicates 
 were applied for each system , and properties were computed based on 
 at least 10 ns of production run for each replicate . a representative 
 snapshot of the simulation system can be found in figure 1c . furthermore , in order to illustrate the 
 molecular details of orientation 
 and free energetics of gdm / urea around protein interfaces , 
 we simulated a system with single gdm / urea approaching 
 the hydrophobic aqueous protein interface with different orientations . we use an identical protein starting structure as in the 1.0 m solution case , with the hydrophobic interface of the protein 
 nearly perpendicular to the z direction . in this 
 way , vapor interface case , the relative 
 orientations between single solute and protein interface can be defined 
 in a straightforward way : when the normal vector of gdm / urea ring is along z direction , the solute is considered 
 to be parallel to the hydrophobic protein interface as shown in figure 1d ; when the normal vector is along y direction ( figure 1e ) or x direction ( figure 1f ) , the solute is considered 
 to be perpendicular to the hydrophobic protein interface . because 
 of the asymmetry of hydrophobic protein interface , differences arise 
 between these two perpendicular configurations . for the convenience 
 of discussion , we denote the orientations in figures 1e and 1f as perpendicular y orientation and perpendicular x orientation , indicating 
 that the normal vector is along y direction and x direction , respectively . here , we note that although the 
 hydrophobic protein patch is commonly considered as flat , it still 
 has some curvature . hence , strictly speaking , speaking of an actual 
 parallel or perpendicular orientation of gdm plane relative 
 to the protein patch is not rigorous . however , in this work , we aimed 
 to study the contrasting hydration properties and surface fluctuations 
 induced by different orientations of gdm ( water - depleted 
 flat faces versus the more strongly water - associated ring ( edge - on ) 
 side of the cation ) with respect to the hydrophobic patch of the protein . 
 therefore , in this convention , parallel orientation simply indicates 
 that gdm has more overlap with the protein patch in terms 
 of their projections to the xy plane , relative to 
 the perpendicular orientation . the whole protein was fixed during 
 the simulation with center of mass located at ( x = 
 0  , y = 0  , z = 0  ) . 
 a fixed cl ( at x = 0  , y = 0  , z = 15  ) was 
 added as the counterion to neutralize the positive charge in the case 
 of gdm . similar to the liquid vapor interface situation , 
 for calculation of pmf , we use the cartesian z component 
 of the separation between the center of mass of protein and central 
 carbon of single gdm / urea as the collective variable . 
 select configurations of single gdm / urea with parallel , 
 perpendicular y , and perpendicular x orientation were used as starting structures with central carbon 
 of the molecule located at x = 0  and y = 0  . x component and y component of the solute s central carbon were restrained 
 at this original position x = 0  and y = 0  during the simulation using namd s  selectconstraints  
 infrastructure , with sufficiently large force constant k = 1000 ( kcal / mol)/ . vapor interface cases 
 mentioned above . in this case , single gdm / urea will approach 
 the specific spot on the patch ( x = 0  and y = 0  ) with particular orientation while still keeping 
 some rotational degree of freedom by using the normal vector to the 
 molecular ring as rotation axis . we just centered on one specific 
 region on the patch due to the fact that the interface is heterogeneous , 
 resulting in the differences of the extent of inherent interface fluctuations 
 at various locations ( to be discussed further below ) . for a meaningful 
 discussion of the molecule - induced fluctuation ( fluctuation in addition 
 to the level inherent in pure water ) as it approaches the hydrophobic 
 interface , one representative spot with fixed position and unchanged 
 inherent fluctuation had to be defined . for more discussion of the 
 situations of the single solute with other restraint conditions ( totally 
 rigid solute or restrained in a specific sampling volume ) , the reader 
 is referred to the supporting information , section s1 . in this case , along the positive z direction , 49 continuous  windows  with width 0.2 the spans of the windows going 
 from interfacial region to bulk region ( in  ) were [ 15.4:15.6 ] , 
 [ 15.6:15.8 ] , [ 15.8:16.0 ] , ... , [ 24.4:24.6 ] , [ 24.6:24.8 ] , [ 24.8:25.0 ] . 
 in each window , a harmonic restraint potential with force constant 
 of 10 ( other simulation 
 conditions remain the same as that of the system of protein in 1 m concentration of gdmcl / urea aqueous solution . the first 
 2 ns was allowed for equilibration before a total of 20 ns production 
 data was generated for each window . for a complete understanding 
 of the influence of the hydrophobicity 
 of the protein patch on the orientational preference of gdm solute , we considered another system in which single gdm approaches a more hydrophilic protein region which consists of residues 
 asp 25 , cys 26 , lys 27 , thr 28 , ala 58 , asp 59 , and gln 60 . the simulation 
 conditions remained identical except that the protein was posed in 
 a different way in the simulation cell with the selected hydrophilic 
 interface almost perpendicular to the z direction . the window setup ranged from [ 14.0:14.2 ] , [ 14.2:14.4 ] , [ 14.4:14.6 ] 
 .. to [ 24.4:24.6 ] , [ 24.6:24.8 ] , [ 24.8:25.0 ] for a total of 56 windows . it has been previously explored by willard and chandler that one can construct a coarse - grained solvent 
 density field from atomic coordinates in individual snapshots of an 
 md simulation . the interface related to the solvent is defined as 
 a constant density surface for the coarse - grained field in space . specifically , in this work , we are interested in the water  vapor 
 interface and water  protein interface ; we thus use the water 
 oxygen atom as a reference point for constructing coarse - grained interfaces . 
 the oxygen atom in most , including the present , force fields is sufficiently 
 large that its size represents the majority of the size of the model 
 molecule ; thus , using only the water oxygen atom to construct the 
 interfaces is a justifiable approximation . the water oxygen density 
 field is constructed as follows : we set up series of spatial grid 
 points and compute the corresponding coarse - grained densities at space - time 
 point r , t , represented as (r , t ) by eq 1.1where ri(t ) is the 
  ith 
 water oxygen atom s position in space . the summation over all 
 water molecules density contributes to the coarse - grained 
 density at a particular grid point . each oxygen atom s density 
 contribution is coarse - grained via a gaussian function in eq 2.2where r is the magnitude 
 of r ,  is taken as 3.0  , and d stands for dimensionality ( 3 in this case ) . the final d - dimensional density field will be constructed by acquiring each 
 grid point s density . the interface is determined as the ( d  1)-dimensional manifold with a constant value c. differences arise when constructing the liquid thus , we select a cartesian coordinate system to construct 
 the liquid  vapor interface and spherical coordinate system 
 for the protein  water interface . the liquid  vapor interface is constructed by connecting grid points where (x , y , z ) = bulk/2 . this instantaneous surface is denoted as ( ht(x , y ) , at time t ) . we can average these instantaneous surfaces to obtain the mean 
 surface h(x , y). subtracting the mean values from the ht(x , y ) , we obtain ht(x , y ) as 
 surface height and the height fluctuations h(x , y). 
 for the protein  water interface , grid points in space are defined 
 by ( r,, ) and each (  ,  ) 
 coordinate set in the spherical system defines a radial vector . we use 
 a different constant value c = 0.6bulk here compared with the liquid  vapor interface case because 
 this choice results in a more unambiguous construction of a protein  solvent 
 interface . correspondingly , instantaneous protein interface 
 can be expressed as ( ht(, ) ) , 
 mean surface as h(,) , 
 surface height as ht(, ) , 
 and height fluctuation as h(,). this analysis provides a reference context within which 
 to discuss the results at a hydrophobic protein interface later . to 
 first address solute orientational propensities as they vary along 
 the order parameter , we compute orientationally resolved probability 
 distribution profiles along the z - axis as a single 
 gdm / urea approaches the liquid  vapor interface 
 as shown in figure 2a , c . here , in a statistical 
 manner , we consider the probability of the single solute at position z with orientation  , which is defined based on the 
 following eq 3:3where n(z, ) denotes the solute number 
 count at position z with orientation . the 
 numerator represents the number of 
 solutes in a slab from z z/2 to z + z/2 , 
 with select orientation within the range of cos( /2 ) 
 and cos( + /2 ) . the denominator represents the 
 total number of solutes in the slab region z z/2 to z + z/2 ; this is used to normalize the probabilities in the 
 relevant slab whose boundaries along the order parameter are z the limits cos( ) = 1 and cos( ) 
 = 0 represent gdm orientations that are parallel and perpendicular 
 to the liquid  vapor interface , respectively . in bulk region 
 with z < 13  , the probabilities of gdm / urea with different orientations are identical , indicating 
 no orientational preference , while in the interfacial region ( 15  
  z  20  ) , single gdm manifests a higher tendency to adopt the configuration that is parallel 
 to the liquid  vapor interface . this observation is consistent 
 with the result in our previous publication on an identical system 
 using a polarizable force field ( tip4p - fq ) and wernersson et al.s work using 1.1 and 5.3 m gdmcl solutions . single urea also displays 
 a marginal orientational preference for a parallel configuration as 
 well ; urea s propensity for the parallel orientation is lower 
 than that of gdm based on the lower intensity of the corresponding 
 region in figure 2c . we note that this higher 
 probability of parallel orientation of single solute around interfacial 
 region suggests a lower free energy of this configuration relative 
 to the perpendicular . to further explore this difference , we consider 
 potentials of mean force for single gdm / urea from bulk 
 through liquid  vapor interface being restrained at particular 
 orientations as shown in figures 2b and 2d for gdm and urea , respectively . in 
 both panels , black lines represent conditional pmf profiles for single 
 solute with parallel orientation ; blue dashed lines represent conditional 
 pmf profiles for single solute with perpendicular orientation . the 
 orientation - averaged pmf profile ( with no restraints on the orientation ) the weighted histogram analysis method 
 ( wham ) was used for generating the final pmf in all cases . the standard error was estimated by using the 
 block averaging method obtained from each consecutive 0.5 ns time 
 block in the production run of each umbrella sampling window . this 
 selection will ensure the block size was significantly larger than 
 the correlation time in each window . the pmf is defined to be zero 
 when the solute is in the bulk , which is determined by window z = 0  . to better compare the interface stability 
 among different orientations , in the large graph of panels b and d , 
 we emphasized the pmfs around the interfacial region while the entire 
 pmf along the collective variable can be found in the inset . for single 
 gdm , the parallel orientation shows a minimum of roughly 
 0.4 kcal / mol , with uncertainty about 0.1 kcal / mol , prior to 
 the gds at the separation of z = 16.5  , while 
 the perpendicular orientation displays no surface stability at all . overall , when there is no orientational restraint applied on the gdm , as shown by the green line , no surface stability is found 
 near the interface . the pmf is less repulsive in the case with no 
 orientational restraint compared to the perpendicular orientation 
 scenario ; this is consistent considering that it is an average result 
 from the contributions of all possible configurations . the pmf for 
 no orientational restraints ( green dotted line ) shows a slight shoulder 
 around z = 16  , indicating the effect of the 
 parallel orientations . however , since the stability of the parallel 
 orientation is rather small , and configurations differing from the 
 parallel geometry are associated with significantly higher free energies 
 at the interface , the overall effect leads to a pmf displaying no 
 apparent interfacially stable state . for single urea , the parallel 
 orientation pmf shows a slight minimum of 0.04  0.07 kcal / mol . 
 considering the uncertainty here , whether parallel orientation of 
 urea shows surface stability or not is debatable . however , we notice 
 that , in contrast to the perpendicular orientation , the parallel orientation 
 is more free energetically favorable , although this trend is not as 
 obvious as the case for gdm . all these pmf results are 
 consistent with the probability distributions of orientations as discussed 
 above . vapor interface may be related to the hydration 
 structure of gdm as previously studied by mason et al . and cooper et al . the hydration around 
 gdm is anisotropic . in the molecular plane , the n h 
 group can serve as hydrogen bond donor , interacting with water molecules as demonstrated in the gas phase , while above 
 or below the planar face , it is inadequate to serve either as hydrogen 
 bond donor or acceptor . vapor interface with parallel orientation , it is 
 easy for desolvation to occur , which is free energetically favorable . 
 for the structurally analogous molecule urea , it still can serve as 
 hydrogen bond donor above or below the planar face , so it is less 
 facile for the parallel urea molecule to desolvate compared with that 
 of gdm . ( b ) pmf of single gdm from bulk transporting 
 through liquid  vapor interface 
 with parallel orientation , perpendicular orientation , and no orientational 
 restraint . ( c ) orientationally resolved probability map of single 
 urea around liquid  vapor interface . ( d ) pmf of single urea 
 from bulk transporting through liquid  vapor interface with 
 parallel orientation , perpendicular orientation , and no orientational 
 restraint . for clarity , in ( b ) and ( d ) , no orientational restraint 
 profiles are shifted by 1 kcal / mol ; perpendicular profiles are shifted 
 by 2 kcal / mol . the gds positions are denoted as orange dashed lines 
 in ( b ) and ( d ) . recent studies have demonstrated 
 an interesting connection between 
 liquid  vapor interfacial stability of chemical species and 
 the extent to which the presence of these molecular species in the 
 vicinity of the interface induces collective fluctuations of the interface 
 in addition to the level inherent in pure water ( absence of the solute ) 
 due to thermal motion ; these studies have focused on monovalent inorganic 
 ions as initial test systems . initially , it is found that the species demonstrating an interfacial 
 stability ( e.g. , i ) as demonstrated by free energy 
 minima in the region of the gds as evaluated via potentials of mean 
 force , appear to enhance liquid vapor interfacial fluctuations , 
 while those that show no interfacial stability ( e.g. , cl ) induce no or lesser extent of fluctuations . the differences in 
 induced interfacial fluctuations by two representative ions , cl and i , has been attributed to these 
 two types of ions presenting distinct hydration shell environments . the nature of the solvent structure 
 around i determines that it is more amenable to 
 inducing fluctuations of the interface as a consequence of a greater 
 disruption of the solvent structure on approach to the interface . 
 inspired by this , we consider that differences in induced interfacial 
 fluctuations should arise as the parallel and perpendicular orientations 
 of gdm approach the liquid vapor interface since 
 these two configurations display distinct hydration shell environments 
 with parallel orientation presenting a more malleable solvent environment 
 and perpendicular orientation showing a more rigid hydration environment 
 due to the more effective hydrogen bonding of water in the plane of 
 the ring . the two orientations are associated with dramatically different 
 free energetic profiles at the liquid  vapor interface . the 
 surface height fluctuations were computed with the protocol of section ii.b . the mean surface height and surface height 
 fluctuation when single gdm resides at the position of z = 14  is shown in figures s1a and s1b of the supporting information . both the mean surface 
 profile and surface height fluctuation profile are radially symmetric , 
 with the largest value at the position where the gdm is 
 just approaching the point ( x = 0 , y = 0 ) . for convenience , we use this representative value h(x = 0 , y = 0) to compare the magnitude of interface fluctuations 
 when the solute is restrained at different z - positions , 
 with the result shown in figure 3 . fluctuation 
 profiles for gdm and urea with distinct orientations are 
 presented in panels a and c , respectively . in the case of pure tip3p 
 water without the existence of solute , the inherent fluctuation for 
 current system size is around 1.32  . using this 
 value as a normalization factor , normalized fluctuation profiles were 
 obtained , presented in panels b and d for gdm and urea , 
 respectively , which will display solute - induced contribution in a 
 direct way . hl2 > 1 indicates the 
 surface 
 height fluctuation is enhanced relative to pure water ; with hl2 < 1 , it denoted that the surface height fluctuation is 
 damped . in the gdm case , the parallel orientation induces 
 a large fluctuation , with the maximum normalized fluctuation value 
 around 2.2 at the location of z = 14  , which 
 is around 3  prior to the position of the free energy minimum . 
 in stark contrast , no obvious enhancement of surface fluctuations 
 is associated with perpendicular orientation . these trends are expected 
 considering the distinct hydration structures for the parallel and 
 perpendicular orientation of gdm . the nature of the malleable 
 hydration shell around parallel orientation gdm is similar 
 to that of single , low charge density anions , like i. the solvent structure is more amenable to inducing larger fluctuations 
 due to the fact that it is more easily disrupted as the solute approaches 
 the interface . on the other hand , the perpendicular orientation of 
 gdm showing no interface stability is more like cl , with more rigid solvation structure around the periphery 
 of the ring due to the existence of hydrogen bonding . these results 
 using a nonpolarizable force field are consistent with our previous 
 work using the tip4p - fq polarizable force field , indicating a force field independence of the fundamental , 
 underlying physical origin of this correlative phenomenon . previously , 
 it has been pointed out the importance of considering polarizability 
 in the ion - specific effect . by neglecting the polarizability 
 in the force field , larger anion i may not show 
 significant surface stability , giving a poor distinction with respect 
 to cl . however , our results indicate that in the 
 case of gdm the orientational preference is pronounced 
 enough even in the nonpolarizable force field . in light of this , in 
 the following section for the discussion of gdm around 
 the protein surface we also 
 notice that differences in induced fluctuations also exist in the 
 case of urea with dissimilar orientations . for the parallel orientation , the largest induced normalized fluctuation value is around 1.85 , which 
 is still larger than the fluctuation from perpendicular orientation , 
 1.45 . interestingly , for the parallel orientation , the induced fluctuations 
 from gdm is larger than that from urea , corresponding 
 to gdm s greater free energetic stabilization ; 
 the perpendicular orientations show a reverse trend as the induced 
 fluctuation from gdm is smaller than that from urea , which 
 correlates with the pmf trend that gdm is more repulsive 
 in this case . again , the smaller differences in interfacial stabilization 
 and induced fluctuation between parallel and perpendicular orientation 
 is related to the spatial location of hydrogen bonding network , either 
 below or above the planar face , leading to the closer solvation structure 
 of the parallel oriented and perpendicular oriented urea . overall , 
 the differences in orientational preference around liquid  vapor 
 interface , interfacial stability , and induced fluctuation between 
 gdm and urea may possibly be connected to the efficiency 
 of these two solutes as denaturants via direct interactions with hydrophobic 
 side chains and surface regions of proteins . for a further understanding 
 of this , we attempt to extend this investigation from the ideally 
 hydrophobic aqueous liquid  vapor interface to a somewhat more 
 realistic and more complex aqueous protein hydrophobic interface . ( a ) surface 
 height fluctuation for liquid  vapor interface 
 at ( x = 0 , y = 0 ) as a function 
 of position of single gdm . vapor interface at ( x = 0 , y = 0 ) as a function of position of single 
 gdm . vapor 
 interface at ( x = 0 , y = 0 ) as a 
 function of position of single urea . ( d ) normalized surface height 
 fluctuation for liquid  vapor interface at ( x = 0 , y = 0 ) as a function of position of single 
 urea . before we 
 consider the free energetics of single gdm / urea approaching 
 the hydrophobic protein interfacial region , we provide a general overview 
 of distributions of solute orientation relative to the hydrophobic 
 protein patch . to probe this , generally , we define a sampling volume 
 in the cartesian space corresponding to the hydrophobic patch around 
 the protein . this sampling volume is shown in figure 4a , within the range of 8   x  8  , 8   y  
 8 , and 12   z  25  , roughly 
 including residues val 18 , leu 19 , leu 21 , ile 22 , val 24 , val 54 , 
 ala 61 , leu 62 , and leu 63 . orientationally resolved probability distribution 
 of gdm around this defined region is shown in figure 4b . the probability at position z with orientation  in this case is defined in the same way 
 as that in liquid we note that this marked tendency has previously been noticed in proximity 
 to hydrophobic surface . . found that 
 gdm accumulates in the vicinity of flat hydrophobic plate 
 in a roughly parallel way . also mentioned the gdm has a preference for parallel 
 stacking with the hydrophobic polymer surface from the snapshots of 
 their simulations . here , using a simple approach , we defined the relative 
 orientations between gdm solute and hydrophobic protein 
 surface and showed the orientational preference of gdm around the hydrophobic patch of hfbii . furthermore , we consider 
 orientationally resolved probability distributions of urea in an identical 
 probe volume in figure 4c . parallel oriented 
 urea is also preferred compared with the perpendicular configuration 
 around the hydrophobic protein surface . however , this trend is less 
 intense in the case of urea compared with gdm , which is 
 similar to the situation at the liquid  vapor interface . this 
 is consistent with the previous report that urea , compared with gdm , displays more orientational diversity around hydrophobic 
 plate - like surfaces . so far , we only 
 concentrated on solute distributions around the hydrophobic region 
 of the protein and attempted to connect this with the similar observation 
 around the liquid  vapor interface , which is one model of an 
 ideal hydrophobic interface . a complementary study would be focusing 
 on another distinct region around the protein surface with different 
 hydrophobicity . therefore , we define another sampling volume corresponding 
 to the hydrophilic patch of the protein ( including residues asp 25 , 
 cys 26 , lys 27 , thr 28 , ala 58 , asp 59 , and gln 60 ) in cartesian space 
 within the range of 8   y  
 8  , 8   z  8 , 
 and 12   x  25  . the 
 volume of this sampling region remains the same as that defined for 
 the hydrophobic region , but the position of the probe region in cartesian 
 space is different . in figure 4d is shown the 
 orientationally resolved probability distribution for gdm around this hydrophilic region . overall , no preference for parallel 
 oriented gdm is observed in this case , although this preference 
 can be detected in a small portion of the map with the separation 
 of z = 14  . compared to the orientationally 
 resolved probability maps for gdm around hydrophobic ( panel 
 b ) and hydrophilic area ( panel d ) , it is safe to claim that around 
 more hydrophobic regions there is a stronger tendency for the parallel 
 stacking of gdm with protein surface , which is also been 
 noticed in flat plate systems previously . we note that these general trends are robust as an identical patch 
 with different sampling volume , as defined in the supporting information figures s2 and s3 , further verifying 
 this orientational preference around hydrophobic / hydrophilic regions . ( a ) representative 
 of sampling volume for probing orientational 
 resolved probability of solute around certain region of protein interface . ( b ) orientational resolved probability distribution of gdm around hydrophobic protein interface in 1.0 m gdmcl 
 solution . ( c ) orientational resolved probability distribution of urea 
 around hydrophobic protein interface in 1.0 m urea 
 solution . ( d ) orientational resolved probability distribution of gdm around hydrophilic protein interface in 1.0 m gdmcl solution . the pmf profiles for 
 single gdm / urea approaching the 
 hydrophobic protein surface region are shown in figure 5 . panel a shows the pmf of single gdm with parallel 
 orientation ( solid red line ) , perpendicular y orientation 
 ( dotted green line ) , and perpendicular x orientation 
 ( dashed blue line ) moving toward the hydrophobic patch region from 
 the bulk , which is located at z = 25  in this 
 case . the pmf profiles were generated by postprocessing umbrella sampling 
 md trajectories with wham , and the standard errors were estimated 
 by using the block averaging method obtained from each consecutive 
 0.5 ns time block in the production run of each umbrella sampling 
 window . the parallel configuration gives rise to a pmf minimum of 
 2.85  0.04 kcal / mol as it nears the hydrophobic patch 
 at a separation of z = 15.7  ; a shallow second 
 minimum can be observed at a separation of z = 19 
  . a free energetic barrier can be observed between these two 
 minima , which may be related to the dramatic change of the number 
 of water molecules within the first hydration shell of the solute 
 as shown in figure s4 of the supporting information . 0.04 kcal / mol around z = 17  for the perpendicular y orientation gdm , while for perpendicular x gdm , a monotonically repulsive trend was observed . this difference may be determined by the exact composition and local 
 spatial arrangement of the residues on and near the hydrophobic patch 
 as shown in figures s5a and s5b of the supporting 
 information . when gdm with perpendicular x orientation approaches the patch , there is a repulsive 
 interaction between nh groups of gdm and side chains of 
 residues ile 22 and leu 63 on the patch . more importantly , we notice 
 that compared with pmfs for perpendicular oriented gdm showing marginal or no stability , pmfs for parallel orientation 
 gdm are much more free energetically favorable . this further 
 echoes the result shown in figure 4b , indicating 
 that gdm prefers to associate with the hydrophobic protein 
 patch with its more hydrophobic , easily desolvated , parallel orientation . this preference is explained by england et al . as 
 hydrophobicity - driven stacking interaction in their study using hydrophobic 
 plate . because of the inability of hydrogen bond formation between 
 hydrophobic surface and water molecules , the hydrophobic surface has 
 a stronger tendency to minimize the exposed area in the aqueous environment . 
 this can be achieved by the face - on coating by gdm of 
 the surface , which is free energetically favorable . the observed stacking 
 mode of self - association among gdm can also be considered as hydrophobically 
 driven interaction . instead of association with large hydrophobic 
 plate or protein surface , in this case , gdm pairs with 
 another gdm by maximize the overlapping of their hydrophobic 
 planar rings . we further verify this by considering the pmfs of single 
 gdm approaching another gdm with different 
 relative orientations . the details of this can be found in the supporting information , section s2 . in figure 5b , pmf profiles for urea with different orientations 
 moving toward the identical hydrophobic patch are presented . again , 
 parallel oriented urea molecule shows the most free energy stability 
 with a value around 2 kcal / mol compared with the two perpendicular 
 orientations . however , comparing parallel urea association free energy 
 around hydrophobic protein patch with that of parallel gdm , we find that it is less favorable , which is due to the lower hydrophobicity 
 of urea s planar surface as discussed earlier . these behaviors 
 are consistent with the results from orientation distribution maps 
 in figure 4 . ( a ) pmf for single gdm with 
 parallel orientation , perpendicular y and perpendicular x orientation from 
 bulk approaching the hydrophobic protein  solvent interface . ( b ) pmf for single urea with parallel orientation , perpendicular y , and perpendicular x orientation from 
 bulk approaching the hydrophobic protein the stability of a single solute 
 at the protein interface correlates 
 with the induced interfacial fluctuations as the solute approaches . solvent interface was constructed based on the 
 protocol mentioned in section ii.b . a representative 
 average protein solvent interface is shown in figure s1c , and the corresponding height fluctuation is shown 
 in figure s1d . overall , the contour of 
 the mean interface is reasonable considering that the shape of the 
 protein is globular . the magnitude of interface fluctuations can be 
 judged by the color scale in panel d , in which case a single gdm is located at z = 18  right above 
 the position x = 0 , y = 0 . we consider 
 this point as a reference point since it displays the largest induced 
 fluctuations compared with other regions on the protein surface as 
 indicated by the bright ring in figure s1d . to better illustrate the change in interface fluctuation magnitude 
 as single gdm / urea approaches the patch , the induced fluctuation 
 at this reference point , h(x = 0 , y = 0) , as a function 
 of z position of the central carbon of the solute 
 is plotted in figure 6 . in figure 6a , at large separations of the single gdm from the hydrophobic patch region , none of the configurations of 
 gdm solvent 
 interface solely comes from the inherent , thermal fluctuation . as 
 the restrained gdm with distinct orientations approaches 
 the hydrophobic patch , the induced fluctuation profiles exhibit striking 
 differences . parallel - oriented gdm induces large fluctuations 
 of the interface ( 0.95  ) at the separation of z = 18  , which is around 5 times that of the inherent 
 interfacial fluctuation ( 0.19  ) . in the case of 
 perpendicular - orientated gdm , maxima in the fluctuation 
 profiles can also be found at the same separation of z = 18  . however , the extent of the induced interfacial fluctuation 
 is smaller compared with that of the parallel orientation , with perpendicular y giving a value of 0.4  ( 2 times of inherent 
 fluctuation ) and perpendicular x giving a value of 
 0.35  ( 1.8 times of inherent fluctuation ) . vapor interface 
 showing that interfacially stable parallel configurations of gdm induce larger interfacial fluctuations than the perpendicular , 
 less interface - stable orientations of gdm . as expected , 
 parallel orientations urea induces a larger extent of fluctuation 
 ( around 0.75  ) than the perpendicular ones ( around 
 0.45  ) , corresponding to the greater free energy 
 stability of the parallel configurations around the interface shown 
 in figure 5 . comparing the induced fluctuation 
 values between parallel configurations of the two solutes , the more 
 hydrophobic and more surface stable gdm gives a higher 
 level of enhanced fluctuation . these results support the argument 
 that the more hydrophobic nature of the parallel - oriented gdm makes the hydration shell weakly bound and less ordered , 
 so that it has more tendency to break and couple with the hydration 
 water in the vicinity of hydrophobic protein patch region , which will 
 cause a large perturbation of the protein  solvent interface 
 in addition to the level present in pure water . according to the previous 
 studies , this enhanced fluctuation represents an increase 
 of interface entropy , which may contribute to differentially stabilizing 
 configurations where the parallel orientation gdm is closer 
 to the interface compared to other configurations of the solute . ( a ) surface 
 height fluctuation for hydrophobic protein interface 
 at ( x = 0 , y = 0 ) as a function 
 of restrain z position of single gdm with 
 parallel , perpendicular y , and perpendicular x orientation . ( b ) surface height fluctuation for hydrophobic 
 protein interface at ( x = 0 , y = 
 0 ) as a function of restrain z position of single 
 urea with parallel , perpendicular y , and perpendicular x orientation . to close this discussion about induced interfacial fluctuations , one may ask whether the instantaneous coarse - grained 
 interface we construct can artificially pass  through  
 the solute , thus giving rise to artificially large fluctuations . to 
 explore this , we plot the difference  in the z - position of the central carbon of gdm and the z - position of the interface ( zinterface ) as gdm moves toward the protein patch along the z - axis . here , the z - position of the interface 
 is equal to the value of the surface height of the interface at the 
 point ( x = 0 , y = 0 , zinterface ) . > 0 means the interface is between 
 single gdm and the protein patch ; while  = 0 indicates 
 that interface just passes through the gdm ;  < 
 0 implies that the gdm resides between the interface and 
 the protein . we will show that even when all the zinterface values are distributed on one side of the solute 
 with  value constantly being larger or smaller than zero , the 
 distribution of zinterface is not necessarily 
 small . this would suggest that the induced fluctuations are nonartifactual , 
 and the higher fluctuation values are not due to the combination of 
 three different scenarios (  > 0 , = 0 , and < 0 ) . figure 7 displays the values of  and the distributions 
 of  as single gdm is located at three representative 
 positions : z = 16 , 18 , and 19.5  . panels a 
 and d correspond to the parallel configuration ; panels b and e correspond 
 to the perpendicular y configuration ; panels c and 
 f correspond to the perpendicular x configuration . 
 at a separation of z = 18  , where the gdm induces a large interfacial fluctuation , we observe that 
  is always larger than zero for all the three cases , indicating 
 that the interfaces will always reside between the protein and the 
 solute , so there is no artifact where the surface passes through the 
 solute . the same applies to the situation that gdm is 
 located at z = 19.5  as indicated by the blue 
 line . although at the separation of z = 16  
 there are some  values less than zero , at this point the interfacial 
 fluctuation is suppressed by the presence of the solute . this suggests 
 further that enhanced fluctuations are not influenced by the interface 
 fluctuating on both sides of the solute . furthermore , at closer separations 
 of gdm and the protein  water interface , the meaning 
 of the local interface becomes ambiguous perhaps , but this is not 
 a serious issue as the major differences in interface effects occur 
 well before the solute arrives at the interface . an additional point 
 worth addressing is that at a separation of z = 18 
  we observe that the parallel configuration of gdm exhibits a wider distribution of  values as shown in the 
 panel d green line . this is consistent with the earlier result of 
 figure 6a that parallel orientations of gdm induce larger fluctuations of hydrophobic protein solvent 
 interface compared to the perpendicular ones . in a recent study , patel 
 et al . discussed that water near hydrophobic surfaces can be described 
 as being near a phase transition characterized by enhanced fluctuations 
 in relevant order parameters . the relevant order 
 parameter is solvent density in their work , the distribution of which 
 varies from unimodal ( when two hydrophobic interfaces are far apart ) 
 to bimodal at separations where the volume between surfaces fluctuations 
 between wet and dry states to unimodal once the intersolute space 
 is completely dry ( post - dewetting transition ) . in this work , as solutes 
 approach the hydrophobic surface as a perturbation to the interfacial 
 water , a different order parameter based on the interfacial height 
 is considered . ideally , this interfacial height should display the 
 same signatures of bimodal distribution as the solute reside at the 
 position that induces the largest surface fluctuation . from previous 
 discussion since zgdm is almost constant ( this is the fixed position of the solute ) , the 
 distribution profiles of  and zinterface should be identical except the shift along the x - axis . a fat tail in the distribution profile in figure 7d is observed as the solute is located at a separation 
 of z = 18  , which is near the position of largest 
 fluctuation . furthermore , the distribution profiles of  for 
 gdm with parallel orientation at the separation of z = 17.5  and z = 17.7  are 
 shown in figure 8a . interestingly , at the exact 
 separation where solute induces the largest fluctuation , z = 17.7  , a prominent bimodal distribution is observed , which 
 is consistent with the view that at this position , there would be 
 transitions between a  wet  and  dry  
 region between the solute and the protein  water interface . figure 8b shows the log probability of  
 versus  , analogous to figure 3c in patel et al . the present probability distributions for the 
 interface position recapitulate the results of patel et al . in a rather 
 dramatic fashion . this further speaks to the notion that water near 
 hydrophobic interfaces , even on the smaller scales of specific regions 
 of biomolecules , is poised close to phase transitions , which upon 
 perturbation by external potentials ( in this case , a solute approaching 
 the interface and perturbing the solvent density near the protein 
 surface as a consequence of the nature of the solute s hydration 
 shell ) undergoes a transition . ( a  c ) differences 
 between single gdm position 
 and surface position ( surface position is defined by the surface height 
 at position x = 0 , y = 0 )  
 for gdm with different restrained orientations locating 
 at various positions : ( a ) parallel orientation , ( b ) perpendicular y orientation , and ( c ) perpendicular x orientation . ( d  f ) probability distributions of  for gdm with different restrained orientations locating at various positions : 
 ( d ) parallel orientation , ( e ) perpendicular y orientation , 
 and ( f ) perpendicular x orientation . ( a ) probability distributions of  for gdm with 
 parallel restrained orientation locating at various positions close 
 to the peak of largest fluctuation . ( b ) probability distributions 
 ( log scale ) of  for gdm with parallel restrained 
 orientation locating at various positions close to the peak of largest 
 fluctuation . finally , we consider 
 pmfs of single gdm approaching 
 a hydrophilic region on the protein surface . figure 9a shows the pmf profiles of a single gdm approaching 
 the hydrophilic protein patch with parallel orientation ( red ) , perpendicular y orientation ( green ) , and perpendicular x orientation ( blue ) . a slight free energy stabilization is observed 
 in all the cases , which may due to the electrostatic interaction between 
 the nh group of gdm and side chain of hydrophilic 
 residues ( like asp 25 ) on the patch as shown in figure s5c of the supporting information . however , compared with 
 the free energy of gdm with most favorable parallel configuration 
 approaching the hydrophobic protein region ( 3  0.15 
 kcal / mol ) , the free energetic advantages from gdm with 
 all three configurations approaching the hydrophilic patch are quite 
 small ( around 0.5  0.15 kcal / mol ) . furthermore , all 
 three configurations show little to no difference in free energy , 
 suggesting that the orientational preference of gdm around 
 certain types of surfaces is highly dependent on the effective hydrophobicity 
 of the region , with significant orientational preference of gdm occurring around the more hydrophobic surface regions . furthermore , 
 the induced interfacial fluctuation profiles of single gdm with these distinct orientations approaching this hydrophilic region 
 are shown in figure 9b . previously , we have 
 reported that for the protein in pure water regions with different 
 hydrophobicity will display dissimilar inherent interface height fluctuations . the larger magnitude of fluctuations are related 
 to the malleable nature of the water and facile cavity formation around 
 hydrophobic patches . when gdm is located far from the patch , in all three cases , an inherent fluctuation 
 value of 0.07 is detected , which is lower compared 
 with the inherent fluctuation value around hydrophobic protein region 
 0.18  . as gdm moves closer to the hydrophilic 
 interface , both parallel and perpendicular orientation have an inappreciable 
 effect on hydrophilic interfacial fluctuations . although parallel 
 configuration may induce a little larger fluctuation compared with 
 the perpendicular one , the difference is quite small , around 0.02 
  . such negligible differences in inducing fluctuations 
 among these configurations corresponds to the marginal differences 
 of free energies around hydrophilic interface . ( a ) pmf for single gdm with parallel , perpendicular y , and perpendicular x orientation from 
 bulk approaching the hydrophilic protein  solvent interface . ( b ) surface height fluctuation for hydrophilic protein interface at 
 ( x = 0 , y = 0 ) as a function of 
 restrain z position of single gdm with 
 parallel , perpendicular y , and perpendicular x orientation . ( a ) gdm number density map around hfbii protein ( hydrophobic 
 side ) . ( b ) gdm number density map around 
 hfbii protein ( opposite side ) . ( c ) representation of hydrophobic protein 
 patch of hfbii with orange highlighting each hydrophobic residue on 
 the patch . in this article , we continue to explore and 
 demonstrate a connection 
 between interfacial stability and induced interfacial fluctuations 
 as interfacially stable solutes approach ostensibly hydrophobic aqueous the context in which we consider the present work is relevant 
 for discussion of the nature of direct chemical interactions between 
 typical chemical denaturants of proteins , gdm and urea , 
 specifically at hydrophobic regions of a model protein , hfbii . our 
 calculations of potentials of mean force indicate that gdm and urea exhibit nontrivial stability at the aqueous  hydrophobe 
 interface as indicated by figure 5 . furthermore , 
 we observe a richer subdivision of the contributions to the total 
 free energy arising from two relative orientations of the solute that 
 we have chosen to study : the parallel and perpendicular orientations 
 as defined relative to the surface of the protein . though the protein 
 surface is not quite parallel to the axis chosen as our order parameter 
 for calculations of potentials of mean force , the selected definitions , 
 we feel , suffice for the current purposes . with respect to the orientation - free 
 energy correlation , our calculations indicate that the orientations 
 of both solutes in which the solute is parallel to the interface are 
 associated with stronger free energy minima compared to configurations 
 where the solutes approach in a perpendicular orientation . these two 
 orientations appear to envelope the total free energy profiles ( though 
 we can not say with certainty what contributions intermediate orientations 
 would offer ; however , we stress that in this study our aim is to demonstrate 
 the self - consistency of the free energy profiles computed via the 
 potentials of mean force with the orientation probability densities 
 determined from free , solute - unrestrained md simulations of the solutes 
 in solution with the protein ) . furthermore , we find that the correlative 
 behavior between solute orientation and free energy stability ( using 
 the current force field combinations for water , solute , protein , and 
 ions ) mimics that observed at the aqueous liquid  vapor interface 
 ( figures 2 and 4 , probability 
 distribution maps ) . our results for both the protein  water 
 interface and the pure liquid  vapor interface are in agreement 
 with previous studies . recent simulations have 
 highlighted the unique nature of hydrophobic 
 interfaces as it relates to the fluctuations induced in solvent density 
 vicinal to the interface ( refer to garde et al.s work ) . hydrophobe 
 interfaces as simpler atomic species ( monovalent ions ) and slightly 
 more complicated molecular species approach such interfaces . both 
 these approaches ostensibly define a further characteristic property 
 associated with hydrophobic solutes ( and perhaps the hydrophobic effect 
 in general ) . the present calculations indicate that associated with 
 interfacial stability of the chosen chemical denaturants is an induced 
 fluctuation of the interface upon approach of the solute to the interface . we stress that the induced fluctuations of the interface formed between 
 the hydrophobic region of the protein and solvent occur before the 
 solute resides directly at the interface . this is an important detail , 
 as it speaks to the somewhat long - ranged nature of the effects generated 
 by certain solutes prior to any direct interaction being realized . 
 that solutes can affect an interface from a distance is a subtle though 
 non - negligible effect we suggest . moreover , the present results suggest 
 that denaturant orientations that are parallel to the interface ( vis -  - vis , 
 display interfacial stability ) are the orientations that induce the 
 largest fluctuations of the interface ( and hence the solvent density ) . the relation between solute orientation and induced fluctuations is 
 related to the nature of the solvation shells of the solute presented 
 toward the interface upon approach of the solute . in the case of gdm approaching the interface in a parallel orientation , the 
 solvation shell presented is a more  malleable  one , 
 where the solvent is more labile and free to rearrange . this leads 
 to greater solvent density fluctuations and hence higher interfacial 
 induced fluctuations . in the case of the perpendicular orientations 
 of gdm and urea , the tighter hydrogen bonding patterns 
 of water ( as demonstrated in previous studies ) create a more rigid , well - defined solvation shell that is not easily 
 disrupted . this translates to lower solvent density fluctuations and 
 hence lower induced fluctuations ( or even suppression of interfacial 
 fluctuations ) . the present results are thus consistent with recent 
 work and provides yet another example of the relation of hydrophobic 
 effect , solvent fluctuations , and interfacial stability . this relationship 
 appears to be common across a series of atomic and molecular species 
 as well as encompassing charged , polar , and nonpolar characteristics 
 of the solutes considered . these observations suggest that molecular 
 ions , such as gdm , as well as polar molecules with heterogeneous 
 charge distributions ( at least in the context of empirical molecular 
 mechanics force fields ) inherently have built into them regions of 
 high and low charge density . the dependence of local solvation structure 
 on this heterogeneous ( or asymmetric ) charge density is to a large 
 extent involved in determining the propensities of the modalities 
 involved in specific association of molecules with specific types 
 of interfaces . observations based on classical simulations as well 
 as recent dft - based calculations thus 
 suggest an intriguing fundamental underlying theme . these ideas call 
 for further study regarding specific details about the nature of the 
 relationship between fluctuations , degree of solute hydrophobicity , 
 solute solvation / hydration shell properties , and interfacial stability . finally , figure 10 shows the number density 
 of gdm molecules in the vicinity of the canonical hydrophobic 
 region of hfbii as well as on the side opposite to this hydrophobic 
 patch ( the opposite side not being hydrophobic to any significant 
 extent ) . our analysis of simulation data from 1 m gdm solutions 
 with no restraints demonstrates a propensity for the gdm to the hydrophobic region .
the notion of direct interaction 
 between denaturing cosolvent and 
 protein residues has been proposed in dialogue relevant to molecular 
 mechanisms of protein denaturation . here 
 we consider the correlation 
 between free energetic stability and induced fluctuations of an aqueous 
 hydrophobic 
 interface between a model hydrophobically associating protein , hfbii , 
 and two common protein denaturants , guanidinium cation ( gdm+ ) and urea . 
 we compute potentials of mean force along an order parameter 
 that brings the solute molecule close to the known hydrophobic region 
 of the protein . 
 we assess potentials of mean force for different relative 
 orientations between the protein and denaturant molecule . 
 we find 
 that in both cases of guanidinium cation and urea relative orientations 
 of the denaturant molecule that are parallel to the local protein 
 water 
 interface exhibit greater stability compared to edge - on or perpendicular 
 orientations . 
 this behavior has been observed for guanidinium / methylguanidinium 
 cations at the liquid  vapor interface of water , and thus the 
 present results further corroborate earlier findings . further analysis 
 of the induced fluctuations of the aqueous  hydrophobic interface 
 upon approach of the denaturant molecule indicates that the parallel 
 orientation , displaying a greater stability at the interface , also 
 induces larger fluctuations of the interface compared to the perpendicular 
 orientations . 
 the correlation of interfacial stability and induced 
 interface fluctuation is a recurring theme for interface - stable solutes 
 at hydrophobic interfaces . 
 moreover , observed correlations between 
 interface stability and induced fluctuations recapitulate connections 
 to local hydration structure and patterns around solutes as evidenced 
 by experiment ( cooper et al . , j. phys 
 . chem . 
 a2014 , 118 , 5657 . ) and high - level ab initio / dft calculations ( baer 
 et al . , faraday discuss2013 , 160 , 89 ) .