water - mediated interactions play critical 
 roles in biomolecular 
 recognition processes , such as protein folding and protein  ligand 
 binding . in these processes , hydrophobic regions and apolar molecules are 
 often driven together by the surrounding aqueous solution which has 
 been noted since the famous publication by kauzmann in 1959 . usually , increasing the apolar binding surface area decreases its 
 dissociation constant ( increase the strength of binding ) . during the process of optimizing lead molecules 
 to drug , one of the important strategies for medicinal chemists is 
 to utilize these hydration properties of ligands and receptors . the importance of hydrophobic effects in quantitative 
 structure  activity relationship ( qsar ) has been documented 
 since the first publication of qsar in 1962 . detailed understanding of the hydration properties for each important 
 biological system is important for the rational design of better drugs . theoretical approaches for modeling the hydrophobic effect , 
 such 
 as void volume theories , interpret that the hydrophobic effect is 
 length - scale dependent . at small length scales ( e.g. , solute radius smaller than roughly 
 0.5 nm ) , the solvation of solutes is mainly an entropically driven 
 process in which the water hydrogen bonding network rearranges itself 
 to adapt for the intercalation of solutes . on the other hand , at large 
 length scales , a significant number of water hydrogen bonds around 
 the solute are broken due to the restructuring at extended , relatively 
 flat surfaces of the solutes , resulting into a domination of enthalpic 
 contributions to the solvation process . unlike generic theoretical models with uniform chemical detail , 
 for proteins with both polar and apolar residues , the solute in such 
 a heterogeneous and dynamical environment , water and protein structures 
 are sensitive to the local solute  solvent interface geometry , 
 as well as van der waals ( vdw ) and electrostatic interactions . the 
 coupling between interface geometry and structural polarity is crucial 
 to protein biological function . characterizing the hydration properties 
 surrounding the biomolecules and comparing them with those of bulk 
 water significant progress has been made through the combination of various 
 experiments , theoretical techniques , and models . computer simulations , such as molecular dynamics 
 ( md ) simulation 
 with explicit solvent models , can shed light on the delicate balance 
 among these factors and illustrate the hydrophobic effects associated 
 with ligand molecules and induced polarization . however , one drawback of molecular dynamics 
 simulations is the relatively high computational demand for large 
 systems such as biomolecules . furthermore , the intrinsic fluctuations 
 in all atom md simulations can obscure the underlying intuitive physical 
 pictures . in addition to the explicit solvent simulations , various 
 implicit - solvent models are also developed as efficient alternatives 
 to study the biomolecular hydration behaviors and the values of hydration 
 free energy . to date , most commonly used implicit - solvent models 
 ( e.g. , poisson solvent interfaces 
 ( e.g. , solvent accessible surface ( sas ) , solvent excluded surface 
 ( ses ) , or van der waals ( vdw ) surface ) , in which polar and apolar 
 interactions are assumed to be additive and decoupled . recently , a gaussian - based approach was developed to obtain the 
 distribution of the dielectric constant for a protein in solution . by using the local dielectric constant values , the implicit - solvent models lead to better results than the ones using 
 a uniform dielectric constant . there are also other microscopic theoretical 
 treatments of water without predefined surface and based on the statistical 
 mechanics theory of molecular liquid . the most notable one is the 
 three - dimensional reference interaction site model ( 3d - rism ) . in this model , the solvent distribution function and correlation 
 functions are self - consistently solved with a proper closure relation . it avoids the explicit molecular sampling of instantaneous solvent 
 configurations because it works on average distribution function for 
 the particular atoms . with recent advancement , 3d - rism is able to 
 calculate hydration free energy , equilibrium solvent distributions , 
 and other thermodynamic quantities efficiently for biomolecular systems . the variational implicit - solvent model 
 ( vism ) developed by dzubiella 
 et al . provides a self - consistent description of the molecular 
 solvation with the contributions from the solute solvent interface 
 geometry and van der waals and electrostatic interactions coupled 
 together in a physical based free - energy functional within the purely 
 surface - based implicit - solvent model framework . solvent 
 interface is determined by minimizing the solvation free - energy functional 
 that balances the interface local geometry with various hydration 
 free energy contributions . a similar approach has also been put forward by wei et al . in their model , both theoretical and experimental 
 studies over the past decades 
 showed a complicated picture of hydration behaviors around biomolecules . 
 in this study , we apply a joint md and vism analysis to gain certain 
 quantitative and qualitative insights into the heterogeneous hydration , 
 the solute most previous studies of hydration behavior 
 focused on either solute geometrical complexity with uniform chemical 
 details or heterogeneous 
 chemical details with a simple domain interface . hua et al . modeled parallel plates consisting of both hydrophobic 
 and hydrophilic particles . they showed 
 that the behavior of water between the two plates strongly depends 
 on the distribution of the hydrophobic and hydrophilic particles on 
 the plates . in the studies presented here , we choose a biologically 
 important and realistic system , the p53/mdm2 protein complex with 
 both geometrical and chemical detail complexities , as an example to 
 investigate hydration properties near complex biomolecular binding 
 sites . the receptor protein mdm2 acts as a negative regulator 
 of the tumor 
 suppressor protein p53 , and loss of the p53 function is observed in 
 50% of human malignancy . to understand 
 the hydration properties of the p53/mdm2 complex during the process 
 of association is very important for the understanding of the p53/mdm2 
 binding mechanism . furthermore , inhibitor design to reactivate p53 
 as tumor suppressor protein will also benefit from this study . this system exhibits a strong hydrophobic character at the p53/mdm2 
 binding interface ( 70% of the residues at the binding interface are 
 apolar ) . however , the edge of the binding pocket is decorated 
 by polar hydrophilic residues . therefore , it provides an excellent 
 example to study the heterogeneous hydration properties in a protein the red color represents charged hydrophilic residues , the pink color 
 represents neutral hydrophilic residues , and the blue color represents 
 hydrophobic residues . in figure 1a , it is apparent 
 that the hydrophobic areas of the two domains are in contact with 
 each other in the bound state . in figure 1b one can 
 clearly see that the binding interfaces are essentially hydrophobic 
 ( blue ) . the domain interface is buried with hydrophobic 
 residues in blue , charged residues in red , and neutral hydrophilic 
 residues in pink . ( b ) two domains of the complex are separated and 
 rotated in such a way that the binding interfaces face the reader . in this work , md simulations and 
 vism calculations are used to 
 study the heterogeneous hydration behaviors around the protein during 
 the p53/mdm2 binding . through md simulations , we construct water density 
 profiles from which we observe high water density solvation shells 
 near the hydrophilic residues and depleted water density regions near 
 the hydrophobic binding pocket of mdm2 . furthermore , we identify a 
 bimodal state for the water occupancy behavior in the binding pocket 
 when the interdomain distance is between 4 and 6  . a solute solvent 
 hydration energy density map is used to illustrate the relation between 
 the water density and the various solute  solvent interactions . 
 as of now , six clinical trials we hope our study can further the understanding of the binding affinity 
 and kinetics between p53 and mdm2 , which eventually could help to 
 design next generation p53/mdm2 inhibitors . the initial structure 
 of the p53/mdm2 complex is taken from the protein data bank ( pdb code : 1ycr.pdb ) . hydrogen atoms 
 are added at ph = 7.0 using the protein preparation workflow in maestro . acetyl ( ace ) and n - methyl amide 
 ( nma ) are incorporated to cap the n- and c - termini , respectively . a series of configurations for the protein complex are produced by 
 separating the two domains along the axis through their geometrical 
 centers . the value of d = 0  
 corresponds to the native crystal structure of the complex . for md simulations , each configuration is then placed in an orthorhombic 
 box with a minimum distance of 10.0  to the boundary of box 
 and hydrated with a pre - equilibrated box of tip3p water using the 
 system builder module of the desmond package . all overlapping 
 solvent molecules are removed , and counterions are added to maintain 
 charge neutrality . for vism calculations , the same input solute 
 structures with partial 
 charges as in the md simulations are used , so that comparisons between 
 explicit and implicit modeling can be made . all 
 molecular dynamics ( md ) simulations are performed using the desmond 
 package . the opls 2005 force field is used to model the protein interactions , and the tip3p model is used for the water . particle - mesh ewald method ( pme ) is used to calculate the long - range electrostatic 
 interactions with grid spacing of 0.8  . van der waals and short - range 
 electrostatic interactions are smoothly truncated at 9.0  . the 
 nose - hoover thermostat is used to maintain 
 the constant simulation temperature and the martina - tobias - klein method is used to control the pressure . the equations 
 of motion are integrated using the multistep respa integrator with an inner time step of 2.0 fs for bonded 
 interactions and nonbonded interactions within the short - range cutoff . an outer time step of 6.0 fs is used for nonbonded interactions beyond 
 the cutoff . periodic boundary conditions are applied . to focus 
 on the water behavior around the p53/mdm2 surface , we constrain the 
 protein molecules so that their conformational fluctuations are not 
 convoluted with the process . these constraints will also facilitate 
 the grid - based water density mapping around the protein and inside 
 of the binding pocket and the direct comparison with the vism calculations . the systems are equilibrated with the default protocol provided in 
 desmond . after the equilibration , a 40 ns npt production simulation 
 is performed for each configuration at temperature 300 k and pressure 
 1.01 bar with a 20 kcal/(mol ) harmonic potential 
 restraint on solute atoms , and the simulation trajectories are saved 
 in 4-ps intervals for analysis . the details of vism with the coulomb - field approximation 
 ( cfa ) are described extensively in the previous publications . in short , we optimize the free energy of the solvation system as 
 a functional of all possible solute  solvent interfaces .1where n solute atoms are 
 located at x1 , ... , xn inside m and 
 with point charges q1 , ... , qn , respectively . ( in our system of p53/mdm2 , n = 1688 . ) the first term pvol(m ) is the volumetric part of the energy for 
 creating the solute cavity m with p being the pressure difference between the solvent liquid 
 and solute vapor . the second term is the surface energy , where (x ) is the surface tension given by (x ) = 0(1  2h(x ) ) , where 0 is the constant macroscopic 
 surface tension for a planar solvent liquid  vapor interface 
 which is set as 0.127 kbt /  at 300 k according to the tip3p water simulation . is the first order correction coefficient 
 often termed as the tolman coefficient which is set as 1.0  , and h(x ) is the mean curvature defined as the average 
 of the two principal curvatures . the third term is the energy of the 
 van der waals interaction between the solute atoms and the continuum 
 solvent . the parameter w is the 
 solvent density which is set as bulk water density 0 = 0.0333/ . it is defined by the born 
 cycle as the difference of the energies 
 of two states , where 0 is the vacuum permittivity , 
 m is the relative permittivity 
 of the solute molecule , and w is 
 the relative permittivity of the solvent which are defined by the 
 vism solute solvent interface  by (x ) = m if x  
 m and (x ) = w if x  
 m . now the free energy g[ ] determines the effective boundary force , g[ ] , acting on the vism solute solvent 
 surface  , where  is the variational 
 derivative with respect to the location change of . it is only 
 the normal component of this force that can affect the motion of such 
 a solute we denote by n = n(x ) the unit normal vector at a point x on the solute solvent surface  , pointing from 
 the solute region m to the solvent 
 region m . k = k(x ) is the gaussian curvature , 
 defined as the product 
 of the two principal curvatures , at a point x on . 
 this force will be used as the  normal velocity  in 
 our level - set numerical calculations . to minimize the free - energy 
 functional ( 1 ) , we choose two different 
 types of initial surfaces , a loose and a tight initial surface . both of them enclose all the solute atoms located at x1 , ... , xn . the 
 tight initial surface is defined by the van der waals ( vdw ) surface . the loose initial surface is often set to be a large sphere enclosing 
 all the solute atoms . in this study , it is chosen so that the closest 
 solute atom ( from the vdw sphere edge ) is at least 1.5 water diameters 
 away form the surface . the initial interface can have a very large 
 value of the free energy . it is subsequently moved in the direction 
 of steepest descent of the free energy by the level - set method until 
 a minimum is reached . the starting point of the level - set method is 
 the representation of a surface  using the ( zero ) level - set 
 of a function  = (x ) :  = { x : (x ) = 0}. the motion 
 of a moving surface  = (t ) with t denoting the time is then tracked by the evolution of 
 the level - set function  = (x , t ) whose zero level - set is (t ) at each t. such evolution is determined by the level - set equation3 to study 
 the water density profiles around the p53/mdm2 complex , a lattice 
 with grid size of 0.8  is constructed and tip3p water oxygen 
 atoms from md simulations are assigned to the nearest grid points . to understand the origin of the inhomogeneous water distribution 
 from the solute  solvent interaction perspective , a solute  solvent 
 hydration energy density map is constructed . from this energy density 
 map , we directly identify the hydrophobic and hydrophilic regions 
 around the protein . in this study , we use the vism free energy functional 
 to fulfill this purpose . in principle , the solute solvent hydration 
 energy density map can also be obtained from md results . however , 
 it is much more desirable to calculate the solute solvent hydration 
 energy density from efficient methods than long time md simulations . from the vism solvation free energy functional ( eq 1 ) , the van der waals and electrostatic solvation free energy 
 contributions can be considered as the integration of solute , we define a solute  solvent 
 hydration energy density as4where56 the vdw solute  solvent hydration energy density vdw(x ) and electrostatic solute solvent 
 hydration energy densities elec(x ) are obtained by using the same formula as the individual component 
 of the solvation free energy functional ( i.e. , eq 1 ) in vism without the volume integration . in order to 
 study the aqueous behavior only in the hydrophobic 
 binding pocket of mdm2 , we used the differences between the contracted 
 level - set vism surface with a loose initial surface and the molecular 
 surface to define the binding pocket ( figure 2 ) . binding pocket region is defined by the differences between molecular 
 surface ( green ) and a contracted vism surface with loose initial surface 
 ( red ) . the water 
 density profile is constructed from a 40 ns md simulation with tip3p 
 water . figure 3 shows the cross - section of 
 water density profile across the target protein mdm2 binding pocket 
 when interdomain distance d = 12  . in this 
 figure , the protein complex is represented by its molecular surface 
 with the same color code as figure 1 . the value 
 of the local water density is represented by colors in the legend . white color indicates zero density , blue represents half of the bulk 
 water density , yellow represents the bulk water density , and red represents 
 twice of the bulk water density . ( a ) cross - section of water density profile 
 through the binding 
 pocket based on the md simulation at interdomain distance d = 12  . the molecular surface is represented with 
 the same color code as figure 1 ( blue for hydrophobic 
 residues , red for charged residues , pink for neutral hydrophilic residues ) . the colors in the legend represent the average water density ( range 
 from 0 to 2 and in units of bulk density 0 ) . ( b ) 
 the same cross - section water density profile as ( a ) without showing 
 the protein . it is observed that high 
 density hydration layers are formed around 
 most parts of the solute molecules as shown by the red color . the 
 water density of the hydration layer close to hydrophilic residues 
 ( red molecular surface ) is much higher and more discrete than that 
 near hydrophobic residues ( blue molecular surface ) . when near the 
 convex protein surface , even around the hydrophobic residues , high 
 density and continued hydration layers are observed . when the protein 
 surface is concave and residues are hydrophobic near the binding pocket 
 at the interdomain region , the hydration layers form at the entrance 
 of the pocket away from the molecular surface and water density drops 
 to zero at the bottom of the hydrophobic pocket . these hydration shells 
 behave differently according to local protein surface geometry and 
 chemical details . such a phenomenon as high density layers formed 
 far away from the 
 molecular surface is also observed in several simpler model systems 
 previously and is attributed to the liquid  vapor 
 interface in the hydrophobic binding pocket , and the water density 
 fluctuating between higher than bulk to zero . these behaviors are 
 explained by capillary evaporation and capillary condensation driven 
 by solute  solvent interactions . to understand quantitatively the relations between the hydration 
 water density distribution around the protein and the solute solvent 
 interactions , we analyze and compare the water density profile w(x ) and the solute  solvent 
 hydration energy density vdw+elec(x ) . the solute  solvent interactions contributed hydration energy 
 density consists of vdw and electrostatic components between solute 
 and solvent . details can be found in the theory and 
 methods part . in figure 4a , it 
 shows the cross - section 
 of water density profile w(x ) across the binding pocket with the location of molecular 
 surface ( black line inside ) . the blue color 
 represents vdw+elec(x ) smaller 
 than 0.1 kbt /  . by comparing figure 3a and figure 4b , we find that the high density water layers form 
 at the region with the solute solvent hydration energy density 
 less than 0.1 kbt /  shown as deep blue in figure 4b . solvent 
 hydration energy density ( vdw and electrostatic contributions ) are 
 shown in figure 4c , d , respectively . ( a ) cross - section 
 of water density profile w(x ) ( range from 0 to 2 and in units 
 of bulk density 0 ) through the mdm2 binding pocket , 
 black line inside is the location of molecular surface ( ms ) from md 
 simulations , ( b ) solute  solvent hydration energy density map 
 ( vdw+elec(x ) ) and ( c ) vdw ( vdw(x ) ) , ( d ) electrostatic ( elec(x ) ) ( range from 0.1 to 0.1 and in units 
 of kbt /  ) individual parts derived from vism free energy functional . most hydrophilic areas shown in red in figure 4a originate from the favorable electrostatic solute this is demonstrated in figure 4d where the blue color depicts the strongly attractive solute solvent vdw 
 repulsion ( shown red in figure 4c ) counter - balances 
 the condensation . thus water densities in these solvation shells are 
 much higher near the polar hydrophilic residues . in contrast , the 
 white color at the binding pocket region indicates that the electrostatic 
 contribution is nearly zero , i.e. , an apolar region . the vdw force 
 is the dominant interaction between solute and solvent at this region . 
 the lack of strong competition between attractive and repulsive solute solvent 
 interactions leads to a lower water density solvation shell minimizing 
 the surface energy and the high density hydration layers form far 
 from the molecular surface at this concave region . the comparison 
 between water density distribution from extensive md simulations and 
 the hydration energy density from vism free energy functional shows 
 that we can qualitatively identify the hydrophobic and hydrophilic 
 regions from the solute solvent hydration energy density map 
 without extra - simulations and it can be achieved in minutes just based 
 on the information of 3d protein structure . solvent 
 interactions in a free energy functional and is solved self - consistently . in the following study , we investigate the interplay between solute  solvent 
 interactions and the solute solvent interface geometry by numeric 
 minimization of the vism free energy functional ( i.e. , eq 1 ) with respect to the solute figure 5 shows the superposition of equilibrium 
 vism surfaces from both loose and tight initial surfaces with the water density profile and the solute the two 
 equilibrium vism surfaces correspond to two stable states of solvation 
 and are the results of the complex relations between polar , apolar , 
 and surface energy contributions to the hydration process . when superimposing 
 the equilibrium vism surfaces on the md water density profile w(x ) in figure 5a , we find that most part of the vism surface corresponds 
 to the high density hydration shell regardless of the initial conditions 
 except for the interdomain region . in figure 5b solvent 
 hydration energy density map vdw+elec(x ) to show the relation between water density and solute water density profile ( range from 0 to 2 and 
 in units of bulk density 
 0 ) ( a ) from md simulations and solute solvent 
 hydration energy density map ( range from 0.1 to 0.1 and in 
 units of kbt /  ) ( b ) from vism free energy functional are superimposing with 
 the equilibrium vism surfaces ( depicted by the thick orange  white  blue 
 lines ) which are obtained from loose and tight initial surfaces , respectively . furthermore , in figure 6a , it shows the 
 average water density ( in units of average bulk water density 0 ) vs the signed distance to the p53/mdm2 equilibrium vism 
 surface ( a tight initial surface was used here ) . a negative value 
 represents the distance to the equilibrium vism surface from inside 
 and vice versa . the water density peak at zero suggests that the equilibrium 
 vism surface is largely located at the first hydration shell and the 
 water density vanishes to nearly zero inside the vism surface ( < 1.4 
  ) . however , in the mdm2 binding pocket , the vism surface captures 
 the high energy density shell much further away from molecular surface 
 ( figure 5b ) . comparing md results with vism 
 surfaces , we can identify the delicate hydration balance for hydrophobic 
 and hydrophilic effects near protein surfaces with both geometrical 
 and chemical complexities . we find vism is able to properly describe 
 hydrophobic binding pockets which are of ultimate interest in most 
 cases . in contrast , traditional implicit - solvent models based on predetermined 
 surfaces , such as pbsa , are only able to account for the geometrical 
 shape defined by the vdw radii . solvent 
 hydration energy density map vdw+elec(x ) ( black line ) and the individual components vdwc(x ) ( green line ) and elec(x ) ( red line ) as a function of signed distance to the equilibrium 
 vism surface . by comparison of these two figures , one can see that 
 the solute  solvent interactions are essentially the main driving 
 forces for the formation of high density hydration layer . ( a ) water density 
 profile w(x ) ( in 
 units of average bulk water density 0 ) in 1d obtained 
 from the md simulation vs the distance to the vism 
 surface of a tight initial . ( b ) solute  solvent hydration energy 
 density and individual components from the vism free energy functional 
 vs the distance to the vism surfaces obtained by a tight initial surface . a negative distance represents the distance from the vism surface 
 to the solute direction , and a positive value represents the other 
 way . , it 
 takes about a week on average for 40 ns md simulation with 8 cpus 
 in parallel for each configuration . in contrast , it takes about 1 
 h for tight initial surface and 3 to 4 h for loose initial surface 
 with single cpu processor for the same configuration in md simulations . the calculation speed of vism strongly depends on the initial surfaces 
 and convergence threshold . we are working on speeding 
 up the vism calculation through numerical algorithm improvement , better 
 initial conditions , and parallelization . interesting hydration behaviors happen inside 
 of the hydrophobic mdm2 binding pocket . in the following study , we 
 define the region of mdm2 binding pocket as the area between the molecular 
 surface and a contracted vism surface from a loose initial surface 
 of mdm2 ( details in methods of analysis section ) . in figure 7a , it shows the water density distribution inside 
 of the binding pocket of mdm2 . in this figure , the blue color represents 
 density lower than half of the average bulk density 0 and the red color represents regions with water density 1.5 times 
 higher than the average bulk density 0 . when the 
 transactivation domain of p53 binds to mdm2 , the key residue l26 occupies 
 the left region in the figure , w23 occupies the middle , and f19 occupies 
 the right . the left pocket is formed by hydrophobic residues ile99 , 
 leu57 , and leu54 . the middle one is formed by val75 , leu57 , ile61 , 
 val93 , and ile99 , and the right pocket is formed by val93 , val75 , 
 and il61 . in figure 7a , we find three isolated 
 high water density regions in the p53-l26 binding pocket , four high 
 water density regions in the w23 binding pocket , and two high water 
 density regions in the f19 binding pocket . these high density 
 regions will be occupied by the three p53 residues when they bind . 
 in figure 7b , we show vdw+elec(x ) inside of the binding pocket , the blue color 
 represents hydration energy density lower than 0.1 kbt /  indicating 
 hydrophilic regions , the red color represents energy density higher 
 than + 0.1 kbt /  indicating hydrophobic regions , and the white color represents 
 the zero hydration energy density level . when p53 binds to this pocket 
 and water molecules are replaced by ligand atoms , a substantial amount 
 of entropy can be gained by occupying the red high water density with 
 ordered water regions ( red in figure 7a ) . enthalpic 
 gain is more pronounced at the blue region where water molecules are 
 relatively close to the surface of the protein . in figure 7b , this figure illustrates that the low vdw+elec(x ) regions locate near the critical 
 binding regions for the three p53 key residues . ( a ) water density profile 
 inside of the mdm2 binding pocket from 
 md simulations with p53 peptide absence . the entrance of the binding 
 pocket is at the front and the bottom is at the back . in part a , the 
 blue color represents density lower than 0.50 and 
 the red color represents density higher than 1.50 . ( b ) solute  solvent hydration energy density map vdw+elec(x ) from vism free energy functional 
 inside of the binding pocket . in part b , the blue color represents 
 the value lower than 0.1 kbt /  , the red color represents values higher 
 than + 0.1 kbt /  , and the white color represents the zero energy level . in figure 8a , we show the distribution of 
 water densities inside of the binding pocket in a range of interdomain 
 distances from 4 to 12  . in this figure , when the interdomain 
 distance is larger than 6  , the water density inside of the 
 cavity has a one - state distribution , and the peaks are located around 
 0.50.60 . when the interdomain distance 
 decreases to 5  , an interesting two - state water density profile 
 emerges with peaks at 0.20 and 0.50 . they correspond to partially dry and wet states for this pocket . 
 as the interdomain distance decreases further to 4  , the water 
 density profile peaks at zero , corresponding to a completely dry state . ( a ) water 
 density distribution inside of the binding pocket obtained 
 from md simulations when different interdomain distances range from 
 4 to 12  . blue line represents the bulk water distribution in 
 the same volume as d = 12  . ( b ) normalized 
 autocorrelation function ( acf ) cnn(t ) of occupancy fluctuations in the pocket 
 with the p53/mdm2 interdomain distance increasing from 4 to 12  . the blue line represents the bulk water autocorrelation in the same 
 volume as d = 12  . in figure 8b , we show the water occupancy 
 autocorrelation function ( acf ) , cnn(t ) = n(t)n(0)/n. 
 bulk water acf is shown with the blue line as a comparison . in the recent work of setny et al . , a more than 1 order of magnitude shift in time 
 scale for the acf in a purely hydrophobic pocket was reported . here , 
 we find that the acf of occupancy fluctuation in the mdm2 binding 
 pocket depends on the interdomain distances . a very long correlation 
 time exists for a particular interdomain distance . when the separation deviates from there , the correlation 
 time reduces quickly . in the case of p53/mdm2 , the distance is around 
 5  . when the interdomain distance is larger than that value , 
 the binding pocket begins to get flooded by bulk water giving shorter 
 correlation times . when the interdomain distance is smaller than 5 
  , the water also fluctuates faster . under this condition , the 
 waters inside the pocket prefer to evacuate the binding site quickly . 
 interestingly but not surprisingly , when around d = 5  , the drying and wetting processes compete and result 
 in long correlation times ( 400 ps ) . as a result , a bimodal 
 distribution with two peaks at 0.20 and 0.50 arises at this distance as shown in figure 7a with population ratio of 0.41/0.59 which is obtained by 
 gaussian distribution fitting of the bimodal density probability . in order to interpret the population of dry and wet states in 40 
 ns md simulation at certain distance , we artificially define the dry 
 state as the pocket water density smaller than 0.20 and the wet state as pocket water density larger than 0.50 . figure 9 shows the water density 
 profile by averaging md frames which are selected by the dry ( a ) and 
 wet ( b ) state criteria . in figure 8a , a water 
 depleted dry region is observed in the interdomain region which is 
 flooded in figure 8b . during the 40 ns simulation , 
 we find 19% frames in which the pocket water density is smaller than 
 0.20 and 24% frames with larger than 0.50 pocket water density . in this interdomain distance , ( a ) water density profile 
 by averaging md trajectories in which 
 the binding pocket water density is less than 0.20 . ( b ) water density profile by averaging md trajectories in which 
 the binding pocket water density is larger than 0.50 . figures are for the p53/mdm2 at an interdomain distance of 
 5  . in figure 10 , we also calculated the relative 
 population of dry and wet states for different interdomain distances 
 ranging from 4 to 12  . from these p53/mdm2md simulations , we 
 find that the binding pocket will prefer a flooded wet state when 
 the interdomain distance is larger than 6  and a depleted dry 
 state when the interdomain distance is smaller than 4  . the 
 interesting dry  wet transition likely takes place when the 
 p53/mdm2 interdomain distance is between 4 and 6  . the dehydration 
 at the hydrophobic interface has profound implications to the kinetics 
 of p53/mdm2 binding . mdm2 has positively 
 charged residues ( k51 and h73 ) at the edge of the binding pocket , 
 and p53 transactivation domain ( tad ) has two corresponding negatively 
 charged partners ( e17 and e28 ) . the electrostatic interactions help 
 to orientate ligand and receptor during binding . however , schon et 
 al . , showed that the association rate 
 of p53/mdm2 was independent of the ionic strength and the truncation 
 of e17 and e28 did not reduce the binding affinity . on the basis of 
 these results , they hypothesized that the binding of p53/mdm2 is dominated 
 by the dehydration of the hydrophobic interface , hydrophobic interactions , 
 and interface rearrangement while electrostatic contribution is less 
 pronounced . probability of having 
 a dry and wet pocket when interdomain distances 
 ranging from 4 to 12  in md simulations . water density smaller 
 than 0.20 for dry pocket ( blue line ) and larger 
 than 0.50 for wet pocket ( red line ) . in the current study , the binding process of the 
 p53 transactivation 
 domain ( tad ) and mdm2 is modeled by conformational constrained protein 
 domains . although the p53 tad has been shown as predominantly disordered 
 before binding in solution , a high percentage 
 of -helical secondary structure is required for stable binding 
 with mdm2 . the high affinity of stapled p53 peptide also demonstrates 
 that preorganization of tad is beneficial to the binding . therefore , the current frozen conformational modeling system can 
 provide important insights to the binding process from the hydration 
 perspective . it should be noted that the static protein 
 simulations and analysis can not capture every aspect of the actual 
 binding process , such as the long relaxation time for the pocket water 
 due to large scale protein conformational dynamics . the coupling of protein dynamics to the surrounding 
 water dynamics is of immense interest , and a completed picture will 
 be undoubtedly much more complex than that presented in this study . in summary , we have studied the aqueous behavior 
 around the p53/mdm2 
 complex in detail using md simulations and vism calculations . we show 
 that water density is significantly lower in regions near the concave 
 hydrophobic binding pocket and the hydrophobic ligand residues . near 
 the hydrophobic cavity , the first solvation layer forms at the entrance 
 of the pocket . the water density drops from higher than bulk to zero 
 at the pocket bottom . the water in the hydrophobic binding pocket 
 behaves like the liquid  vapor interface and the water density 
 fluctuates between high and low values . in addition , we show 
 that the local water density is correlated 
 with the local solute  solvent hydration energy density . the 
 interplay among polar , apolar , and geometric factors forms the energy 
 minimum at the solute  solvent interface . inside of the hydrophobic 
 binding cavity , the averaged water density is lower than the bulk , 
 and water molecules are heterogeneously distributed inside the pocket . the water occupancy in the concave binding pocket fluctuates between 
 dry and wet states as a function of interdomain distance . this fluctuation 
 has important implications to the kinetics of the p53/mdm2 binding 
 process . as one of the most studied tumor proliferation pathways , 
 detailed 
 molecular binding mechanism and kinetics are of ultimate interest 
 for developing therapeutics for activating p53 . although it is generally 
 known for the hydrophobic nature of binding , we illustrate that the 
 balance of hydrophobicity , shape , and polarity plays a key role in 
 hydration . numerous successful drugs have also demonstrated that balanced 
 hydrophilic and hydrophobic properties are critical for drug development . our results hopefully can provide a rational 
 strategy to the design of new drugs with balanced hydrophobic and 
 polar properties and taking advantage of the bimodal solvation process 
 in the p53/mdm2 complex . for instance , one can optimize molecules 
 that minimize the probability of bimodal solvation to gain fast onset 
 kinetics . this study also illustrates the physical connection 
 between the 
 newly developed vism model and explicit water simulations . the vism 
 surface mostly corresponds to the first high water density shell around 
 the protein . in a protein binding site with complex geometry and charge 
 distributions , it often defines the interface where bulk waters are 
 greatly perturbed by the protein residues . in the case of the mdm2 
 binding site , it encloses the region that has 40% less water than 
 the surrounding bulk . there have been many attempts to locate 
 hot spots for water on 
 the protein surface to find the potential binding sites , from both 
 explicit and implicit - solvent aspects . the kinetics of hydration sites ( both drying and 
 wetting processes ) strongly depends on the protein surface geometrical 
 and physiochemical properties . for instance , the water molecules can 
 be trapped and take a longer time to escape in deep and polar cavities 
 than the ones in shallow hydrophobic areas . the variety of protein 
 surfaces leads to relatively broad distributions of thermodynamics 
 properties for hydration sites . in explicit solvent md simulation 
 studies , pure water solvents as well as mixed solvents are used to 
 investigate the solvation of protein  ligand binding sites . correct hydration site predictions are only 
 possible if the bound solvent molecules can be exchanged at a reasonably 
 faster speed relative to the simulation time scale . have 
 studied the exchange frequency by counting all the occurrences of 
 solute  solvent contacts for eight proteins including p53 peptide 
 and mdm2 . they have shown that solvent 
 interaction withthe p53 binding site is mostly short - lived ( up to 
 9 ns at most ) . beuming et al . have produced 
 consistent convergence in the hydration site - free energies across 
 a broad range of targets in their internal studies with 5.0 kcal / mol harmonic restraint and 2 ns production simulations . of course , sufficient sampling is not always 
 warranted in every system by md simulation . for example , water molecule 
 permeation through the na / glucose cotransporter ( sglt1 ) under equilibrium 
 require hundreds of nanosecond simulations due to cotransporting partners , 
 long transporting channel , and protein conformational change . in p53/mdm2 , sampling is less problematic as 
 the pocket is relatively shallow so that the time scale to reach equilibrium 
 hydration is shorter than sglt1 . although an extremely long kinetic 
 trap for water can not be completely ruled out , we believe that 40 
 ns production md simulation after equilibration provides us sufficient 
 hydration information for this particular system . all our calculations 
 are based on the constrained protein surfaces 
 to emphasize the role of water fluctuations during the hydration processes . it is similar to the early bagchi - zewail model . on the basis 
 of their theoretical models , they revealed that the hydration dynamics 
 directly relate to the water residence time near this protein surface . the hydration dynamics at the protein surface was characterized by 
 two time scales , an ultrafast bulk like time scale followed by a slow 
 one 10 times longer . the fast time scale arises mainly due to the 
 reorientation and translation of hydrating water . it indicates that the 
 water response is not qualitatively modified by a constrained protein . although the constrained protein surface limits rearrangements of 
 local water networks , it does not alter the hydration dynamics qualitatively . of course , protein flexibility is still required 
 to observe the slow component . in the current static model , important 
 hydration effects , such as the different relaxation time scales for 
 the pocket water due to the protein chemical and geometrical environment , 
 the fluctuations between bound and bulk water , can be captured . it 
 has also been shown that constrained protein simulations facilitate 
 the grid mapping of water density . incorporating 
 protein full flexibility will undoubtedly offer a richer and more 
 complex picture of actual water behaviors around protein . we are actively 
 pursuing this direction and hope to report our results in a future 
 publication .
water - mediated 
 interactions play critical roles in biomolecular 
 recognition processes . explicit solvent molecular dynamics ( md ) simulations 
 and the variational implicit - solvent model ( vism ) are used to study 
 those hydration properties during binding for the biologically important 
 p53/mdm2 complex . 
 unlike simple model solutes , in such a realistic 
 and heterogeneous solute  solvent system with both geometrical 
 and chemical complexity , the local water distribution sensitively 
 depends on nearby amino acid properties and the geometric shape of 
 the protein . 
 we show that the vism can accurately describe the locations 
 of high and low density solvation shells identified by the md simulations 
 and can explain them by a local coupling balance of solvent  solute 
 interaction potentials and curvature . in particular , capillary transitions 
 between local dry and wet hydration states in the binding pocket 
 are 
 captured for interdomain distance between 4 to 6  , right at 
 the onset of binding . 
 the underlying physical connection between geometry 
 and polarity is illustrated and quantified . 
 our study offers a microscopic 
 and physical insight into the heterogeneous hydration behavior of 
 the biologically highly relevant p53/mdm2 system and demonstrates 
 the fundamental importance of hydrophobic effects for biological binding 
 processes . 
 we hope our study can help to establish new design rules 
 for drugs and medical substances .