protein solvation determines to a large 
 extent the physicochemical 
 behavior of proteins , and it is therefore an essential part of their 
 exerted function . in particular , complex formation , which is involved 
 in almost all protein functions , depends on the detailed balance between 
 solvent  solute and solute  solute forces .
too strong 
 solvent  solute forces would impair protein function , while 
 too strong solute  solute forces would lead to unspecific protein 
 aggregation .
protein folds are generally stable 
 under physiological conditions , but changes in the environment can 
 induce unfolding and denaturation .
urea is among the most frequently 
 used denaturants in studies of protein folding and stability .
the 
 effect of cosolvents on proteins has been studied experimentally and 
 theoretically ( for reviews , see refs ( 13 ) ) , but to date the molecular mechanisms and particularly the driving 
 forces of urea - induced protein denaturation are not yet fully understood .
several theoretical studies using molecular dynamics ( md ) on single 
 amino acids , peptides , and proteins have been performed to elucidate 
 the atomic details of the interactions between urea and amino acids , 
 peptides , or proteins .
most simulation studies focused on the energetic components governing 
 the interaction between the proteic solute and the water  urea 
 solvent mixture .
different interaction mechanisms have been suggested , 
 debating whether urea - induced denaturation is driven by polar interactions 
 or by hydrophobic interactions and if these are induced by direct 
 or indirect interactions with the solute atoms , but in the meantime there is sufficient experimental evidence 
 to exclude a urea - induced structural change of water .
a recent experimental study expands thermodynamic data 
 to the spectrum of atoms occurring in proteins with the conclusion that urea interacts favorably , compared 
 to water , with most atom types .
a general consensus attributes a dominant 
 role to van der waals interactions between urea and protein atoms 
 over pure electrostatic contributions .
the hydration shell model explained the solvation terms of small 
 aliphatic hydrocarbons in urea  water mixtures .
an essential 
 term of this model is an enthalpic contribution arising from the van 
 der waals forces between the solute and the cosolvent urea .
however , 
 the model neglected the cavity formation , an integral element of solvent 
 transfer models .
urea does not reduce the free energy of cavity formation ; 
 on the contrary , the strong interaction between urea and water increases 
 the surface tension .
therefore , the replacement of water from the 
 solvation shell around the hydrophobic solute seems not to contribute 
 to the transfer free energy .
also , the 
 hydrogen bond reorganization in the first solvation shell has only 
 a compensatory energetic effect ; i.e. , enthalpic interaction of water 
 with the protein surface is replaced by a gain of entropy in the bulk 
 solvent .
an alternative thermodynamic 
 approach is the solvent exchange model that considers 
 the solute surface as a collection of small interaction sites .
this model is closer in spirit to molecular simulations , because 
 ( i ) system trajectories provide direct information 
 about the urea 
protein interactions and ( ii ) the model allows for the existence of heterogeneous sites ; i.e. , 
 the heterogeneity of the protein surface may be accounted for by the 
 formalism .
a strong interest in protein unfolding and the principles 
 underlying 
 conformational transitions comes from observations that denatured 
 cellular proteins tend to aggregate , a phenomenon that is often associated 
 with a diseased cellular state .
a prominent 
 example of a potentially fatal condition caused by protein misfolding 
 and aggregation is the prion disease that is associated with the formation 
 of aggregates of the prion protein ( prp ) . while the native structure 
 of the globular c - terminus of the cellular prion protein ( prp ) is mostly helical , its amyloid fibrillar 
 aggregates contain -rich conformers ( prp ) .
the details of the conformational transition as well as 
 the structure of the fibrillar aggregates are still elusive . in a 
 quest to determine a minimal set of structural elements that retain 
 the aggregation propensity of the prion protein , the 36-residue fragment 
 h2h3 , comprising the helices h2 and h3 , has been designed . as demonstrated 
 by our previous studies
, h2h3 shows fibrillation , 
 gpi anchoring , and insoluble pk - resistant aggregate formation analogous 
 to prp .
we evaluate here the forces acting at the initial stage 
 of urea - induced 
 denaturation on three prp constructs , a stable structure and two h2h3 
 intermediates isolated from misfolding simulations of h2h3 in water .
these two intermediates of h2h3 represent an 
 -rich state h2h3 as an analogue of prp and a -rich state h2h3 as an analogue of prp .
these two conformers 
 have been previously extensively characterized by md simulations , 
 and their role in the assembly of misfolded states has been evaluated .
besides being very different in their secondary 
 structure content , they differ remarkably in their solvent exposure , 
 with the h2h3 state exposing considerably more hydrophobic 
 surface . h2h3 and h2h3 are therefore 
 ideal systems to study the solvation effects .
the solvent forces 
 on h2h3 and h2h3 in pure water 
 and in 4 m aqueous urea solution were analyzed . 

we have previously introduced shannon entropy 
 maps and analyzed the hydration properties of water at the surface 
 of prp , identifying particular loci with different entropies . by studying the effect of urea on folded and 
 intermediate structures , we ( i )
isolate the urea 
 effect on defined conformers from the unfolding process itself and 
 by restraining the protein structure ( ii ) observe 
 the competition of urea and water for protein interaction in the absence 
 of protein dynamics .
it is clear that urea denaturation is induced 
 spontaneously , because 
 protein surface atoms interact stronger with urea than with water . 
 to our knowledge
, no study has yet been directed to the role of solvent 
 forces in the initiation of urea - induced unfolding . here
, the preference 
 of the proteic solute to interact with either urea or water was computed 
 on the basis of atomic force distributions .
shannon entropies of the 
 solvent were computed to illustrate the replacement of water from 
 the solvation shell .
we compare our results of atomic solvation forces 
 to thermodynamic data and observe good correlations , as well as general 
 trends in hydrophobicity scales extracted from molecular dynamics 
 simulations and based on energetical considerations .
three starting structures were 
 used in this study : -rich h2h3 ( h2h3 ) , -rich 
 h2h3 ( h2h3 ) , and the crystal structure of the c - terminal 
 globular domain of prp ( pdb : 1uw3 ) .
h2h3 is a truncated form of the prion protein 
 comprising mainly helices h2 and h3 ( residues 183218 ) .
h2h3 has been shown previously to undergo a conformational transition 
 from an -rich ( h2h3 ) to a -rich ( h2h3 ) conformation .
these two 
 conformations were used here to compare forces on the same sequence 
 in two different folds .
the c - terminal globular domain of prp is used 
 as a native reference protein for the analyses .
the urea model of smith et al . was used in its implementation as molecular 
 building block ' urea ' in this force field .
the temperature was set to 300 k and controlled 
 by weak coupling to a temperature bath with a coupling constant t = 
 0.1 ps .
the non - bonded pair list was updated every time 
 step for pairs within 0.8 nm and every fifth time step for the range 
 0.81.4 nm .
twin - range cutoff radii of 0.8/1.4 nm were used 
 to compute non - bonded interactions .
long - range electrostatic interactions 
 were approximated by a reaction - field force , using a dielectric constant 
 of 54 .
simulations were kept at 0.061020 kj mol nm ( 1 atm ) with a coupling time of p = 0.5 ps and an isothermal compressibility 
 of 5.575  10 ( kj mol nm ) .
initial 
 protein structures h2h3 , h2h3 , 
 and 1uw3 were 
 energy minimized using 100 steps of steepest descent .
energy minimized 
 protein conformations were solvated in a periodic box of 5.2  
 edge length . the minimum solute 
systems were electrostatically neutralized by replacing water 
 molecules with sodium ions to compensate the net charge ( h2h3 , 1 ; 1uw3 , 2 ) of the 
 protein at a neutral ph value .
the neutralized systems were 
 energy minimized using 100 steps of 
 steepest descent , while the protein was harmonically positionally 
 restrained using a force constant of 2.5  10 kj 
 mol nm .
the systems were run 
 for 5  10 steps ( 1000 ps ) of md while keeping the 
 solute positionally constrained .
configurations , energies and forces 
 were saved at intervals of 250 steps ( 0.5 ps ) , yielding 2000 conformations per trajectory .
the final urea concentrations were curea(h2h3 ) = 3.8 m , curea(h2h3 ) = 4.5 m , and curea(1uw3 ) = 4.2 m. forces between the following groups of atoms 
 were recorded : protein , ion , water , and urea .
two sets of simulations 
 were performed , ( i ) in pure water ( ii ) and in a urea / water mixture .
since water equilibration around solutes 
 occurs on the time scale of 1020 ps , explicit solvent simulations 
 of 1000 ps are sufficiently long for the pure water simulations to 
 sample representative force distributions .
the urea / water systems 
 equilibrated after about 5 ns , as shown by the radial distribution 
 functions of urea and water in supporting information figure s1 .
simulations of these systems were run for 10 ns , and 
 the last 3 ns were used for the analysis .
given that we estimate the 
 equilibration to occur at approximately 5 ns , we considered 10 ns 
 as sufficiently long to obtain accurate equilibrium solvent properties .
the first 300 ps of the trajectories 
 were excluded from analysis to remove potential equilibration effects . 

the contact coefficient is the contact ratio , the fraction of 
 protein  urea contacts , normalized by the mole ratio of urea:1where
n is the number of 
 contacts , m is the number of molecules , p : u are protein  urea 
 interactions , and p : s are protein(co)solvent ( urea and water ) 
 interactions .
normalized force differences f were computed for protein atoms with at least one contact 
 to urea via2where f denotes 
 the mean force over a specified interval of the trajectory .
rescaled forces were computed for protein atoms with at least one 
 contact to urea via3 statistical values were computed over 
 the last 700 ps of the trajectories 
 using the statistics functions of the gnu scientific library and plotted using the r - project software .
the ability of prp to form fibrils is well 
 recognized , but only 
 recently has the neurotoxic activity been correlated with the formation 
 of soluble oligomeric species .
we have shown that oligomers 
 from the h2h3 subdomain have very similar physicochemical charateristics 
 to those of the entire ovine prp protein .
the formation of these oligomeric 
 species is accompanied by an increase in -sheet ( h2h3 ) content .
we have studied in detail 
 this conformational transition in water by molecular dynamics simulations 
 and have characterized the process of interconversion from an all 
 -helical to a -rich conformer in water . after only 90 
 ns , a -sheet seed forms close to the disulfide bridge ( nucleating 
 at residues v183n184 ) ; later the elongation of this sheet 
 resulted in the refolding of the entire structure to what we call 
 a double--hairpin ( first hairpin , v183t191/i208m216 ; 
 second hairpin , v192t196/q199q203 ) ( figure 1a , b ) .
this conformer was very stable in solution 
 and has been repetitively observed in simulations of oligomer - forming 
 mutants .
we therefore suspect that this is one of the -rich 
 species in solution leading to oligomer formation .
transition from ( a ) the 
 -rich h2h3 to 
 ( b ) the -rich h2h3 conformation .
( c ) c - terminal 
 globular domain of ovine prp ( 1uw3 ) .
the model systems illustrated in figure 1 were selected , because we assume that they are 
 among the species 
 present in the oligomerization pathway .
the comparison of the organization 
 of the urea mixture around these structures can reveal the tendency 
 of denaturants to favor the species that is more prone to forming 
 oligomers . by computing the solvent accessible surface area 
 ( sasa ) calculated 
 by pops and divided into hydrophilic 
 and hydrophobic contributions ( figure 2 )
, one 
 observes the exposure of backbone atoms in the transition from the 
 -rich to the -rich conformer observed in pure water 
 solution ( hydrophobic sasa in yellow , hydrophilic sasa in red ) .
this 
 is intriguing for the study of solvation forces , because one of the 
 postulated effects of urea - induced denaturation is strong interactions 
 with backbone atoms that become exposed .
the only region in which 
 the -rich conformer exposes more hydrophobic surface is observed 
 in the stretch 198204 , which corresponds to the loop connecting 
 the two helices .
this loop becomes quite buried in the -rich 
 conformer , forming a minimal core between the two aforementioned hairpins .
solvent - accessible 
 surface areas ( in  ) of the 
 prion protein conformers h2h3 ( blue ) and h2h3 ( red ) .
the bars are divided into hydrophobic ( light 
 colors ) and hydrophilic ( dark colors ) contributions . in denaturant - induced 
 unfolding experiments ,
the number of denaturant molecules bound to 
 the protein can be derived from the depression of the transition temperature , 
 and thermodynamic parameters can broken down into increments per contact . in computational 
 studies ,
this type of information is directly accessible if one defines 
 a contact distance threshold ( here 3.5  ) between protein atoms 
 and ( co)solvent atoms .
the relative preference of protein surface 
 atoms to bind to either the cosolvent ( urea ) or the solvent ( water ) 
 can be expressed by the contact coefficient , which is the fraction of contacts to a given cosolvent normalized 
 by the mole fraction of the cosolvent in the mixture . a contact coefficient 
 above 1 indicates a favored contact to the cosolvent and below 1 , 
 a disfavored contact . in figure 3 , the normalized 
 force difference between the protein 
hydrophobic c atoms 
 show the strongest preference for urea , and their force difference 
 is positive ; i.e. , protein  urea forces are stronger than protein  water 
 forces for hydrophobic atoms .
the polar amide atoms n and o have a 
 preference for urea contacts , but the interaction forces with urea 
 are on average lower than those with water .
polar oh and charged o and n atoms show the highest preference 
 and force differences for water
. the normalized force differences 
 between protein  urea and protein  water interactions 
 in figure 3 follow a hydrophobicity scale . 

urea 
 and protein  water interactions per atom type 
 as a function of the contact coefficient . 

the linear fit through all data points 
 ( solid line ) has a regression coefficient of r = 0.6 , exclusion of the outlier 
solvent forces on individual protein atoms are cumulative ; i.e. , 
 the recorded forces originate from interactions with one to several 
 ( co)solvent atoms and molecules .
the effect of denaturants is concentration 
 dependent , because the number of interactions and therefore the cumulative 
 solvation forces increase with the mole ratio .
the concentration effect 
 can be compensated computationally by a scaling of the solvation forces 
 with the contact ratio ( eq 3 ) .
this creates 
 a useful theoretical scenario , in which solvent and cosolvent form 
 an equal number of contacts with the protein , and therefore the forces 
 are represented on a symmetric basis .
a detailed picture of 
 this scenario is obtained from a plot of the force distributions . 

the quantile  quantile ( q  q ) plots in figure 4 provide a graphical summary of the differences 
 between the force distributions .
q plots , while increased frequencies in one distribution 
  bend the curve toward that dimension .
the axes show 
 the scaled forces fc of protein  urea 
 versus protein 
it is apparent that 
 almost all atom types favor urea interactions compared to water interactions , 
 with the exception of  hydroxyl o and partially 
carboxylate o and  amide 
 n establish particularly strong forces with urea , while forces 
 on  amide o are moderate .
the increased backbone exposure 
 of h2h3 compared to h2h3 is notable 
 in the relatively large forces on the backbone atoms 
amide 
 n and  amide o. the surface interaction potentials 
 ( in units 10 m  ) determined by guinn et al .
however , 
 the potentials  aromatic c 8.9 and  amide 
 o 8.7 were not reproduced by our simulations , possibly 
 because the exposure of these atoms was significantly higher in the 
 model compounds of the thermodynamic study than in the protein folds 
 used here .
the mean forces ( not scaled ) , contacts , and contact ratios 
 are tabulated in table 1 .
interaction forces normalized by the contact ratio 
 between h2h3 and urea ( fcp : u ) compared to h2h3 and water ( fcp : w ) . shown
are the force distributions of selected types of atoms as 
 q  q plot .
( a ) h2h3 , ( b ) h2h3 , and ( c ) 1uw3 .
data points above the diagonal line indicate a preferred interaction 
 with urea , below a preferred interaction with water .
fc : mean force per contact  standard deviation 
 in units kj mol nm .
entropic solvation effects 
 are as important as the enthalpic force contributions discussed in 
 the previous section . as urea replaces water in the first solvation 
 shell , water gains entropy , but the reorganization of hydrogen bonds 
 is an endothermic process .
therefore , the water replacement has been 
 refuted as a driving force ( gibbs energy change ) of denaturation .
the solvent entropy in simulated systems can 
 be approximated by the shannon entropy h of the solvent .
the atom occupancy within cells of a virtual 
 grid were recorded along the simulation and transformed into an entropy hper grid cell ( for details , 
 see the methods ) .
the orange distributions show the values of grid cells close 
 to the protein surface ( 00.25  distance ) ; the blue distributions 
 show the values of the second solvation shell ( 0.50.75  
 distance ) .
the differences between the orange and blue distributions 
 illustrate that the h values are a sensitive 
 measure of local atom fluctuations , although the resolution of the 
 grid cells is limited ( here 2.0  ) to provide a sufficiently 
 diverse cell occupancy , because each additional atom contributes to 
 the shannon term .
water mixtures ( hugc ) and pure water 
 ( hwgc ) are given as q 
q plots in the right column of figure 5 , the color code representing the same distance 
 ranges as in the left column .
the entropy distributions of the bulk 
 are about the same for protein  urea mixtures and pure water , 
 with the exception of the lower entropy range of the h2h3 system .
h2h3 shows a reduction , compared 
 to the pure water system , of the number of water molecules in the 
 urea / water mixture in the entropy range of 0.40.7 , which indicates 
 a loss of low entropy water molecules in the solvation shell of the 
 protein .
h2h3 exposes the largest fraction of hydrophobic 
 surface area among the three prion conformers , and this entropic effect 
 is most likely due to the replacement of water by urea at the protein 
 surface .
this effect is not detectable in the urea / water mixture systems 
 of the helical proteins h2h3 and 1uw3 .
however , all urea / water 
 systems show an increase , compared to the pure water system , in the 
 number of water molecules in the entropy range 0.71.2 , which 
 is caused by the presence of urea in the solvation shell and the concurring 
 reduction of solvent mobility .
shannon entropy distributions of the solvent 
 around prion conformers 
 h2h3 ( a , b ) , h2h3 ( c , d ) , and 1uw3 ( e , f ) .
distributions 
 are divided into grid cells close to ( 00.25  , orange ) 
 and far from ( 0.50.75  , blue ) the protein surface .
right : q  q 
 plots of the shannon entropy distributions of the solvent environment 
 of water ( hwgc ) and urea ( hcgc ) atoms .
urea does not replace water molecules that 
 are tightly bound to the protein surface and therefore create a low 
 entropy environment .
urea replaces water molecules at protein surface 
 locations where the bound solvent water fluctuates . the water 
urea 
 shannon entropy maps are shown as isosurfaces in figure 6 for both h2h3 and h2h3 .
these maps highlight the structural and dynamical properties of 
 the solvent mixture around the molecules .
high entropy solvents close 
 to the protein surface are visible as locations where the contour 
 map touches the protein .
these are sites that are prone to ( water ) 
 desolvation by exchange with cosolvents like urea that form stronger 
 interactions with these sites . for the h2h3 -rich conformer
, 
 the loop between the two helices shows a high entropy environment , 
 and urea molecules interact closely with the backbone . for both conformers
, 
 one can observe clustering of urea molecules at exposed amide n atoms 
 ( blue space - filling spheres ) , in agreement with observations in the 
 atomic force analysis , where amide n atoms gave rise to the largest 
 scaled forces in water urea mixtures .
shannon entropy of the solvent surrounding 
 ( a ) h2h3 and ( b ) h2h3 illustrated 
 as isosurface in wire 
 mesh rendering .
solvation forces are a sensitive measure 
 to gauge the solution 
 properties of protein atoms in urea  water mixtures .
the individual 
 preferences to interact with urea or water follow a hydrophobicity 
 scale in a similar trend as force field energies of amino acid analogues .
the comparison of the scaled forces showed largely 
 agreement with data of surface interaction potentials .
particularly strong force differences were observed for 
  carboxylate o and  amide n atoms .
the 
 direct comparison of urea and water forces on the protein was performed 
 on rescaled forces to compensate for the dependence of the solvation 
 forces on the urea concentration .
solvent species appear in two forms : 
 occupying a site and as a solution component .
 this has implications 
 for the relative weights of the contributions to the solvation force 
 of the ( co)solvent components . in the direct comparison of the force 
 distributions of the protein  urea and protein
 water 
 interactions ( figure 4 ) , the forces were scaled 
 by the inverse of the contact ratio , but not additionally by the mole 
 fraction as in the contact coefficient . therefore the interacting 
 solvent components were viewed as  occupying a site , 
 which reflects the fact that the relative concentrations of urea and 
 water are different close to the protein surface compared to in solution , 
 as has been shown by radial distribution functions here and in previous 
 studies .
the urea molecules close to the protein 
 surface remained largely 
 outside the first water solvation shell , except at locations where 
 the solvent entropy is relatively high .
it was noted earlier for the 1uw3 molecule in pure water that surface sites surrounded 
 by high entropy water molecules are likely to be structural defects 
 or interaction sites , because of the low energetic cost of desolvation .
one of these sites , the loop between the two 
 helices , is also an apparent interaction site in the h2h3 -rich 
 conformer : it is surrounded by high entropy solvent , and urea molecules 
 bind to the backbone amide n atoms .
the use of other cosolvents 
 like fluorinated derivatives in the 
 stabilization of folded and unfolded species of prpc has been explored 
 in experimental and theoretical approaches . generally , 
 a stabilization of helical structure is observed in these solvents . 

hexafluoro-2-propanol has been shown to affect the ultrastructure 
 of prp amyloid and to decrease the -sheet content as well as 
 prion infectivity .
in contrast , 1,1,1-trifluoro-2-propanol does not 
 inactivate prion infectivity but alters the morphology of the rods 
 and abolishes congo red binding .
protein simulations in urea  water 
 mixtures provide a rich 
 source of information about solvation effects that can be used to 
 detect potential structural defects and interaction sites .
the solvent interaction forces of individual 
 atom types could be converted to solvation parameters and embedded 
 in an implicit solvation model for urea  water mixtures .
another , 
 more challenging , perspective is the combination of the observed surface 
 site interactions in md simulations with a thermodynamic site model .
 solvation forces are crucial determinants in the equilibrium 
 between 
 the folded and unfolded state of proteins . 
 particularly interesting 
 are the solvent forces of denaturing solvent mixtures on folded and 
 misfolded states of proteins involved in neurodegeneration . 
 the c - terminal 
 globular domain of the ovine prion protein ( 1uw3 ) and its analogue 
 h2h3 in the -rich and -rich conformation were used as 
 model structures to study the solvation forces in 4 m aqueous urea 
 using molecular dynamics . 
 the model structures display very different 
 secondary structures and solvent exposures . 
 most protein atoms favor 
 interactions with urea over interactions with water . 
 the force difference 
 between protein  urea and protein  water interactions 
 correlates with hydrophobicity ; i.e. , urea interacts preferentially 
 with hydrophobic atoms , in agreement with results from solvent transfer 
 experiments . 
 solvent shannon entropy maps illustrate the mobility 
 gradient of the urea  water mixture from the first solvation 
 shell to the bulk . 
 single urea molecules replace water in the first 
 solvation shell preferably at locations of relatively high solvent 
 entropy . 