infectious diseases caused by flaviviruses 
 are major concerns in 
 the public health community , particularly those that are drug - resistant 
 or resistant to antibody - mediated neutralization . however , the basic 
 mechanism by which mutations in antigenic proteins lead to evasion 
 of antibody neutralization is still unclear . in flaviviruses , the 
 envelope protein domain iii ( ed3 )
harbors many of the critical mutations 
 that have been shown to reduce antibody neutralization .
the ed3 forms a classic -sandwich fold that is conserved 
 among flaviviruses ( figure 1a , side view ) . 

e , 
 and f  g form a surface patch that is exposed to the solvent 
 in the viral particle ( figure 1a , top view ) .
structural studies have shown that effective neutralizing monoclonal 
 antibodies ( mabs ) recognize this surface patch with a high degree 
 of shape complementarity .
structural 
 and sequence analysis of the ed3 from different flaviviruses . 
 structural alignment of the ed3 from different flaviviruses : dengue 
 virus types 1 , 2 , 3 and 4 , denv-1 ( pdb 3irc ) , denv-2 ( pdb 1tg8 ) , denv-3 ( pdb 1uzg ) , and denv-4 ( pdb 2h0p ) , respectively ; 
 west nile virus , wnv ( pdb 1s6n ) ; st .
louis encephalitis virus , slev ( pdb 4fg0 ) ; omsk hemorrhagic 
 fever , omsk ( pdb 1z3r ) ; yellow fever virus , yfv ( pdb 2jqm ) ; japanese encephalitis virus , jev ( pdb 1pjw ) ; tick - borne encephalitis , 
 tbe ( pdb 1svb ) .
the rmsd ( all atoms ) among all ed3 structures is between 1 and 
 4  .
-strands are colored in yellow , random coils are 
 colored in green , and a highly conserved hydrophobic core found in 
 most flaviviruses is colored in gray .
the loops de ( cyan ) , bc ( red ) , 
 n - terminus ( blue ) , and fg ( pink ) form a patch of residues that are 
 exposed to the solvent in the context of the intact viral particle .
the figures were rendered using pymol v. 0.97 ( delano scientific 
 llc , san carlos , ca ) .
the sequence alignment shows the amino acids 
 of each solvent - exposed loop and the conserved hydrophobic core .
interestingly , within the large 
 ed3mab interaction surface , 
 a few specific mutations significantly decrease mab binding and reduce 
 neutralization in vivo , depending largely on the type of side chain substitution . in the 
 ed3 of west nile virus ( wnv ) ,
the mutations t332k and t332 m reduced 
 mab binding almost completely ( > 80% reduction compared with wild - type ) .
the mutation t332a partially reduced mab binding ( 50% reduction ) , whereas t332v had no effects in antibody binding .
this broad spectrum of mutational effects on mab binding 
 is also observed in the ed3s of other flaviviruses , such as mutations 
 at positions s331 and d332 in japanese encephalitis virus ( jev ) , a serologically close relative of wnv , or mutations 
 at positions k305 and k307 in dengue virus type 2 ( denv-2 ) , a distant relative of wnv and jev .
moreover , 
 not only mutations within the interaction surface itself 
 prevent mab binding and neutralization , but mutations can occur outside 
 the binding site and influence antibody binding via long - range effects . 

these observations motivated us to address the following questions : 
 what is the nature of epitopes ?
antibody contact region reduce mab binding ? 
 is there a network of interacting residues , wherein mutations perturb 
 distantly positioned regions of the protein ? addressing these 
 questions using high - resolution structures and 
 antibody binding data is challenging and time - consuming , particularly 
 for phylogenetically and serologically related viruses
whose protein 
 antigens typically share a high degree of structural and sequence 
 similarity .
the structures of the ed3 of various flaviviruses , shown 
 in figure 1a , are very similar , making it difficult 
 to identify specific features in each viral protein that may be associated 
 with unique antigenicity .
hence , an alternative approach is needed , 
 and the ed3 of flaviviruses was adopted as a model system . based on 
 increasing experimental evidence highlighting the importance of protein 
 conformational fluctuations in biological function , we hypothesized that epitopes are intrinsically encoded 
 in the thermodynamic properties of the conformational fluctuations 
 of the ed3s .
thus , even if the protein antigens look alike , their 
 thermodynamic properties might differ significantly . to test 
 our hypothesis , we investigated whether mab - resistant mutations 
 affect the conformational fluctuations in the ed3s of two related 
 but serologically distinct flaviviruses , wnv and denv-2 . in this study
, 
 we used an algorithm that allowed us to explore the thermodynamic 
 properties of correlated fluctuations in computer - generated protein 
 ensembles .
our results support a model of evasion of antibody - mediated neutralization 
 that involves changes in the protein s conformational fluctuations 
 and long - range interactions between mutation sites and epitopes .
this 
 study also reveals fundamental thermodynamic properties of residues 
 residing in epitopes that may have general implications for other 
 pathogens .
to investigate the thermodynamic 
 properties of protein fluctuations 
 in the ed3s from wnv and denv-2 , we used the corex algorithm . briefly , corex generates a native state ensemble from the target 
 protein structure ( pdb 1s6n for wnv and 1tg8 for denv-2 ) through the combined unfolding of adjacent 
 groups of residues defined as folding units .
folding units are treated 
 as native - like or as unfolded peptides . within this ensemble
, the 
 free energy of each conformational state , gi , is calculated with a surface - area 
 parametrization that has been validated experimentally . by rewriting gi as an equilibrium constant ( ki ) between the conformer i and the folded state 
 ( ki = exp[gi/(rt ) ] )
, 
 we define the probability ( pi ) of each conformer as1 in eq 1 , q is the sum 
 of all possible states in the ensemble ( partition 
 function ) .
moreover , gi can be resolved into the energetic contributions from each 
 residue in the protein : gi = jn = aagij , which allows the investigation 
 of thermodynamic properties at the residue level . within 
 the ed3 ensembles , we estimated the relative stability of each residue , 
 gf , j , as the ratio 
 of the probability that residue j is in the folded 
 state ( pf , j ) to the probability 
 that the same residue is in the unfolded state ( pu , j):2 from 
 eq 2 , residues 
 with high stability are mostly in the folded state in the ensemble , 
 whereas residues with low stability are mostly in the unfolded state .
we describe pairwise residue interactions in the ed3s as the thermodynamic 
 coupling between two residues j and k. the first step to obtain a quantitative 
 value of the thermodynamic coupling is to evaluate the effect of an 
 energetic perturbation on residue k ( = g ) over the stability 
 of residue j. this is accomplished by recasting eq 2 to consider the folding state of a second residue k. after rewriting eq 2 , we evaluated 
 the effect of g over the stability constant of residue j:3 in eq 3 , the modified 
 residue stability constant ( gf , j ) considers the 
 probabilities of states where residues j and k are both folded ( pf , j|f , k ) , both unfolded ( pu , j|u , k ) , or one in each 
 state ( either pf , j|u , k or pu , j|f , k ) .
thus , an energetic perturbation on residue k (  = exp[g/(rt ) ] ) can have a stabilizing , a destabilizing , or no effect over residue j. this thermodynamic effect can be quantified by subtracting 
 eq 3 from eq 2:4 importantly , this analysis 
 does not 
 require residues j and k to be in 
 close proximity in the primary sequence or in the tertiary structure 
 of the protein .
thus , the value gf , j from 
 eq 4 characterizes long - range effects of residue k over residue j. given that a long - range 
 effect is not a bidirectional phenomenon per se , in this study we define 
 thermodynamic coupling as a bidirectional long - range effect . in other 
 words ,
thermodynamic coupling is the sum of the influence of a perturbation 
 on residue j over residue k ( gf , kpert , j ) and the reciprocal 
 effect , namely , the influence of a perturbation on residue k over residue j ( gf , jpert , k):5 thermodynamic coupling 
 between two residues can be manifested in 
 three ways : positive ( gj , k > 0 ) , negative ( gj , k < 0 ) , 
 and neutral ( gj , k = 0 ) .
positive 
 coupling occurs when stabilization or destabilization of the j residue stabilizes or destabilizes , respectively , the k residue . for negative coupling ,
namely , stabilization of the j residue results in the destabilization of the k residue , and vice versa .
equation 5 provides a quantitative descriptor 
 for long - range interactions between residues in the ed3s . with this 
 analysis
, we can investigate the long - range effects of a mutation 
 by calculating the thermodynamic coupling between residues of mutant 
 proteins ( gj , kmut ) .
a general 
 boltzmann equilibrium process , f(x ) , is defined as6 in eq 6 , f(x ) is the boltzmann 
 factor , x corresponds 
 to the thermodynamic coupling ( gj , k ) , xo is the midpoint of the transition between the two states , 
 and c is a cooperativity constant that describes 
 the sharpness of the transition .
the response of a boltzmann equilibrium 
 process is mathematically obtained by taking the derivative of eq 6 with respect to x:7f(x ) is a peaked function that describes the relationship between gmab and thermodynamic coupling ( gj , k ) shown 
 in figure 6 .
we measured 
 antibody binding to the ed3 from wnv wild - type and the single - site 
 mutants e390d , h396y , l312v , v371i , v338i , and l375i against three 
 type - specific mabs , 5h10 , 5c5 , and 3a3 ( bioreliance corp . ,
rockville , 
 md ) , using published protocols . binding 
 data for other single - site mutant ed3s from wnv or denv-2 used in 
 this study were obtained from the literature ( table 1 ) .
binding data for the ed3 from denv-2 
 against two type - specific mabs , 5h5 and 9f16 , was obtained from hiramatsu 
 et al . , gromowski and barrett , and pitcher et al . for the wnv ed3s k307r , 
 k307e , y329k , 
 y329f , wild - type , a365s , l312a , a369s , k310 t , t330i , t332a , and t332k , 

binding data against type - specific mabs 5h10 , 5c5 , and 3a3 was obtained 
 with permission from beasley and barrett , volk et al .
for the wnv - ed3s e390d , 
 h396y , l312v , v371i , v338i , and l375i , we measured mab binding against 
 the same three type - specific mabs .
mean thermodynamic 
 coupling of residues 
 in the bc loop ( 328338 ) for wnv and in the fg loop ( 378388 ) 
 for denv-2 .
to obtain 
 thermodynamic information for the ed3s , we used a computer 
 algorithm to generate an ensemble of conformational states around 
 the native structure .
this algorithm 
 models fluctuations in proteins as simultaneous local unfolding reactions 
 throughout the structure of the target protein ( see methods ) .
after generating more than 10 conformational 
 states of the ed3s , we sought to determine whether the ensemble could 
 reveal virus - specific epitopes .
their root - mean - square deviation ( rmsd ) between 
 all atoms is 2.5  ( figures 1b ) , and their 
 sequence similarity is 50% ( figure 1c ) .
hence , these ed3s have high structural similarity and share high 
 sequence identity . the differential 
 effect of 
 mutations in resistance to antibody - mediated neutralization and their 
 limited antigenic relatedness , indicate that the primary epitopes 
 in wnv and denv-2 are distinct .
our previous studies using virus - specific 
 neutralizing antibodies show that mutations at residue t332 generate 
 a resistant phenotype in wnv , whereas mutations at the homologous position in the ed3 from denv-2 , 
 residue s331 , have no significant effect .
conversely , mutations in 
 position k310 in the ed3 from wnv do not generate a resistance phenotype 
 in the virus , whereas mutations in the homologous position in denv-2 
 do ( residue k307 ) ( figure 2a ) .
for example , 
 relative to the wild - type proteins , the mutation t332a in the ed3 
 from wnv decreased antibody binding energy by 10% ( equivalent 
 to a reduction in kd of 5-fold ) , whereas 
 the mutation s331a in denv-2 did not have any effect ( figure 2b ) .
the mutation at position k307 g in denv-2 showed 
 a similar reduction in binding energy and kd , while the mutation k310 t in wnv had no significant effect ( figure 2b ) .
( a ) 
 single - site mutations at homologous positions in the ed3 from denv-2 
 and wnv .
mutation s331a in denv-2 and mutation t332a in wnv are located 
 in the bc loop .
mutations k307 g and k307 t in denv-2 and wnv , respectively , 
 are located in the n - terminal loop .
( b ) effect of the mutations shown 
 in part a on the binding energy to type - specific mabs .
the vertical axis is the ratio of binding energies between mutant 
 and wild - type ed3s .
( c ) residue stability plots ( gf , j ) of the ed3s from wnv ( top ) and denv-2 
 ( bottom ) .
the dashed line represents 
 a threshold that separates residues with low and high stability .
this 
 threshold was obtained by considering the 20% lowest stability 
 from the residue stability distribution .
residues with high stability 
 ( blue ) are mostly located in the core of the protein , whereas residues 
 with low stability ( red ) are solvent exposed .
( d ) linear effect of 
 mutations on the residue stability of the ed3s from wnv and denv-2 . 

the top panel shows the residue stability plot of the wild - type ed3 
 from wnv (  ) and the resistant mutation t332k (  ) .
the 
 amino acids perturbed by the mutation correspond to residues in the 
 bc loop ( red , dotted square ) .
the bottom panel shows the residue stability 
 plot for the wild - type ed3 (  ) and the resistant mutant k388 g 
 from denv-2 (  ) .
the effect of the mutation is concentrated 
 to residues in the fg loop ( red , dotted square ) .
the top panel 
 displays the destabilizing effect of the mutation k307r ( blue arrowhead ) 
 in wnv .
the affected residues due to the k307r mutation correspond 
 to the bc loop ( red , dotted box ) .
g 
 in denv-2 , which is located in a structurally homologous position 
 to k307 in wnv , had destabilizing effects over residues in the fg 
 loop ( bottom panel ) . to test whether the differential effect of mutations between the 
 ed3 of wnv and denv-2 on antibody binding were due to differences 
 in the conformational ensembles and their sensitivity to mutations
, 
 we characterized the stability ( eq 2 in methods ) of each residue in the ensemble of the 
 wild - type ed3s .
then , we determined what amino acids were thermodynamically 
 perturbed ( stabilized or destabilized ) by resistant and nonresistant 
 mutations previously described in wnv and denv-2 ( column 1 in table 1 ) .
the plot gf , j vs amino acid position of the wild - type 
 ed3s is shown in figure 2c .
the bottom panel shows the values for denv-2 , plotted 
 as gf , j to resemble a mirror image between the two residue stability profiles . 

this mirror image suggests that the analysis of the residue stability 
 captures both the structural and the sequence similarities between 
 these two protein antigens .
as expected from the ed3 structures , highly 
 stable amino acids are found in the protein cores , while those with 
 low stability are located in solvent - exposed structures or random 
 coils ( figure 2c , structures ) .
not expected , 
 however , were the two distinct effects that resistant mutations had 
 on the residue stability constants .
the first effect was the perturbation 
 of the stability constant of residues near the mutation sites or 
this linear effect was observed in residues 328338 
 for resistant mutations in wnv such as t330i , t332a , and t332 k and 
 ( figure 2d , top ) .
resistant mutations in denv-2 
 such as e383 g or k388 g had linear effects over the stability of residues 
 378388 ( figure 2d , bottom ) .
conformational 
 effects  , wherein the effect of the resistant mutations was 
 not localized to nearby residues in the primary sequence .
for example , 
 mutations in the n - terminal loop , such as k307r in wnv and k305 g in 
 denv-2 , destabilized residues in the bc loop ( 328338 ) for 
 wnv and in the fg loop ( 378388 ) for denv-2 ( figure 2e , top and bottom , respectively ) .
noteworthy , the 
 bc and fg loops have been identified as major mab - neutralizing epitopes 
 in wnv and denv-2 , respectively .
to better 
 understand the basis for mutational effects over the bc and fg loops , 
 we sought to identify the thermodynamic properties of these loops 
 that distinguish them from other structural elements in the ed3s . 
 to address this
, we determined the correlated thermodynamic fluctuations , 
 or thermodynamic coupling , between residues in the ed3 ensembles . 

thermodynamic coupling ( defined as gj , k , eq 5 in methods ) applies even if two residues 
 are distantly positioned in the protein structure , allowing the characterization of long - range residue networks in 
 the ed3 . to experimentally validate the analysis of thermodynamic 
 coupling , we compared calculated long - range mutational effects between 
 distantly positioned residues in the ed3 from wnv with previously 
 published experimental data .
specifically , 
 we correlated the effect of the single - site mutations k310 t , t332a , 
 and t332k on the solvent accessibility and dynamics of the single 
 tryptophan residue w397 , which is located 2 nm away from the 
 mutation sites in the ed3 structure . the 
 mutations k310 t , t332a , and t332k linearly increased the solvent - accessibility 
 and dynamics of w397 , which correlated very well with the linear increase 
 of our calculated long - range mutational effects ( r = 0.98 ) ( figure 3a ) .
the agreement 
 between experimental and calculated data demonstrates that analysis 
 of the thermodynamic coupling captures long - range interactions between 
 residues in ed3 .
these published results are consistent with those 
 from molecular dynamics simulations ( gottipati , dodson and lee , in 
 preparation ) .
( a ) 
 long - range 
 mutational effect on the solvent accessibility and protein dynamics 
 near the single tryptophan residue in the ed3 from wnv ( w397 ) .
data were obtained 
 with permission from maillard et al .. the values of gw397mutation were calculated using 
 eq 4 in methods .
the 
 structure on the right side displays the position of the mutation 
 sites and w397 .
( b ) thermodynamic coupling ( eq 5 in methods ) between each residue pair in 
 the ed3 from wnv . the color scaling represents the thermodynamic coupling 
 between each residue pair , from 3 kcal / mol ( purple / blue color ) 
 to 3 kcal / mol ( orange / red color ) .
the blue and black squares 
 highlight distantly positioned residues that share high positive thermodynamic 
 coupling . ( c )
data is rendered identically as in panel b. we determined the 
 entire set of long - range 
 interactions in the ed3 by calculating the pairwise thermodynamic 
 coupling in the wild - type protein ( gj , kwt ) .
the plot of gj , kwt forms an n  n matrix that describes the thermodynamic coupling at the 
 residue level , where n is the total number of amino 
 acids in the structure .
we rendered the values of gj , kwt in a color map ( figure 3b , c ) , wherein amino acids with positive thermodynamic 
 coupling are in red , residues that manifest negative thermodynamic 
 coupling are in blue , and residues that are not thermodynamically 
 coupled are in green .
the results of gj , kwt for wnv , shown in figure 3b , reveal several features .
first , the algorithm captures 
 the expected local perturbations to nearby residues , as delineated 
 by the positive thermodynamic coupling running in diagonal from the 
 lower left to the upper right of figure 3b . 

second , there is positive and negative thermodynamic coupling between 
 several groups of residues that are distantly positioned in the tertiary 
 structure , indicating that there is a complex long - range interaction 
 network between residues that is encoded in the native state ensemble 
 of the ed3 .
third , there appears to be a grid of high coupling that 
 connects distal regions of the protein .
particularly pronounced among 
 these regions are residues 375 through 384 , which are thermodynamically 
 coupled with the entire ed3 .
the relatively high coupling between 
 these sites and the rest of the protein indicates a high mutual susceptibility 
 to perturbations that will likely affect other residues .
when residues 
 375384 are mapped onto the ed3 structure , it is clear that 
 they are part of a highly conserved hydrophobic core of this family 
 of viral protein domains ( figure 1 , -strand 
 colored in gray ) .
similar analysis 
 of the thermodynamic 
 coupling in ed3 from denv-2 also showed positive thermodynamic coupling 
 between distant residues , as well as a conserved core of hydrophobic 
 residues that are thermodynamically coupled with the entire protein 
 antigen ( residues 370379 ) ( figure 3c ) . residues 370379 in ed3 from denv-2 and residues 375384 
 in ed3 from wnv
altogether , these analyses show that the ed3s 
 do not behave as rigid structures but rather as conformational ensembles 
 that are capable of transmitting long - range effects between even distant 
 residues . against this backdrop of global coupling between 
 core residues
, 
 we sought to determine the effect of mutations on the residue networks 
 of the ed3s .
we investigated how single - site mutations in wnv and 
 denv-2 perturb the pattern of thermodynamic coupling observed in the 
 wild - type ed3s ( figure 3b , c , respectively ) . 

our goal was to identify the unique thermodynamic features of mutations 
 that confer resistance to antibody - mediated neutralization compared 
 with those that do not .
we analyzed the thermodynamic coupling of 
 a panel of resistant and nonresistant mutations of wnv and denv-2 
 ( table 1 ) .
for the mutants analyzed , the general 
 pattern of thermodynamic coupling was qualitatively similar to that 
 of the wild - type ed3s ( gj , kmut  gj , kwt ) .
the similarity between gj , kwt and gj , kmut for both wnv and denv-2 ( figure 4 ) indicates that the overall energetic hierarchy 
 of states ( i.e. , what states are most stable ) of the ed3s is thermodynamically 
 robust and that single mutations do not disrupt the basic networks 
 of long - range interactions between residues . despite these similarities , 
 however , important differences were revealed by subtracting the values 
 of thermodynamic coupling of the wild - type ed3 , gj , kwt , from those of the mutant , gj , kmut ( figure 5 ) .
gj , kwt , quantifies the relative impact of each mutation 
 on the coupling network in each ed3 and reflects the response of the 
 ensemble to a resistant or nonresistant mutation .
thermodynamic coupling 
 of single site mutants of the ed3 from wnv 
 and denv-2 ( a ) thermodynamic coupling observed for the wnv wild - type 
 ed3 and for a representative mutant .
( b ) thermodynamic coupling from 
 denv-2 wild - type ed3 and a representative mutant .
( a ) effect of mutations on the thermodynamic coupling of 
 the ed3 from wnv .
resistant mutations such as k307r ( middle ) decreased the thermodynamic 
 coupling of residues 328338 .
the mutation t332k , another resistant 
 mutation , increased the thermodynamic coupling of residues 328338 . 

mutations that do not confer resistance against antibody neutralization , 
 such as the k310 t mutation , did not have any large effect on the thermodynamic 
 coupling of residues 328338 .
( b ) effect of mutations on the 
 thermodynamic coupling of the ed3 from denv-2 .
nonresistant mutations such as i379v did not significantly 
 affect any other part of the protein .
gj , kwt for resistant mutations in the ed3 from wnv 
 revealed three striking features ( figure 5a ) . 

first , the effect of the mutation on the thermodynamic coupling was 
 localized mainly to residues 328338 , that is , the bc loop , 
 the major neutralizing epitope in the ed3 of wnv .
second , depending 
 on the type and position of the mutation , we observed two distinct 
 effects on the thermodynamic coupling of residues 328338 . 

mutations at position t330 and t332 increased the magnitude of thermodynamic 
 coupling ( positive effects ) , while mutations at position k307 decreased 
 the degree of thermodynamic coupling ( negative effects ) ( figure 5a , center and right ) .
third , residues 328338 
 become thermodynamically coupled with the rest of the amino acids 
 in ed3 . this last observation indicates that the effect of a resistant 
 mutation is not limited to nearby residues .
thus , the ability of a 
 mab to neutralize a virus can be impaired by a single mutation , even 
 if that mutation is outside of the mab binding site . the analysis 
 of mutations that have no effect on mab neutralization resistance 
 in wnv ( e.g. , k310 t ) revealed minimal changes in the thermodynamic coupling over residues 
 328338 or other regions in the ed3 ( figure 5a , left ) .
gj , kwt for denv-2 also revealed positive 
 or negative 
 effects on the thermodynamic coupling for mutations that confer resistance 
 to neutralization ( figure 5b ) .
however , and 
 most interestingly , the effects of the mutations were concentrated 
 on residues in the fg loop of the ed3 structure ( residues 378388 ) , 
 the major epitope in denv-2 ( figure 5b , center 
 and right ) remarkably , resistant mutations such as k305 g and k307 g 
 had a negative effect on the thermodynamic coupling of the fg loop 
 despite being located outside of the affected area . moreover ,
residues 
 378388 became thermodynamically coupled to the rest of amino 
 acids in ed3 , underscoring again the long - range effects of the resistant 
 mutations on the thermodynamic properties of the protein antigen .
since the calculations in this study are based on the thermodynamics 
 of protein fluctuations , these results indicate 
 that resistant mutations in ed3 change the conformational dynamics 
 of specific loops that correspond to the primary epitopes in the protein 
 antigens .
moreover , the positive 
 and negative coupling effects on these loops are observed exclusively 
 in mutations that confer antibody resistance .
in the present study , we used an experimentally 
 validated ensemble model to investigate the 
 molecular mechanism by which single - site mutations in wnv and denv-2 
 lead to evasion of antibody - mediated neutralization .
our approach 
 successfully identified the location of the primary epitopes in the 
 ed3s of wnv and denv-2 , despite the high structural and sequence similarity 
 between the two protein antigens .
thus , even if two viral proteins 
 share high sequence and structural stability , the response of the 
 ensemble to mutations is unique . equally important
is that the ensemble - based 
 thermodynamic analysis used in this study reveals a previously unidentified 
 relationship between mutational susceptibility and epitope location , 
 a relationship that could prove useful for a priori identification of specific primary epitopes in different viruses .
we observed that evasion of neutralization 
 and decrease in mab binding was caused by mutations that triggered 
 changes in the conformational fluctuations of the epitopes .
based 
 on this observation , we sought to establish a quantitative relationship 
 between changes in the conformational fluctuations and mab binding . 

to this end , for each ed3 mutant , we plotted the thermodynamic coupling 
 of the residues in the epitope ( gepitope ) and their corresponding binding energies to mabs ( gmab = rt ln[keq ] , where keq is 
 the equilibrium binding constant ) .
figure 6a shows the mean thermodynamic 
 coupling of residues in the bc loop for wnv and their respective mab 
 binding energies , gmabwnv ( figure 6a , 
 red squares ) . in the same figure , we included the plot for denv-2 , 
 but with the values of mean thermodynamic coupling of residues in 
 the fg loop and their respective mab binding energies , gmabdenv2 ( figure 6 , blue circles ) .
qualitatively , 
 the two plots in figure 6a have a similar shape , 
 following a peaked function . moreover , figure 6a shows that for both viruses mutations that significantly decrease 
 the mab binding energy ( i.e. , low binding constants ) also exerted 
 the largest changes in the thermodynamic coupling of epitope residues 
 ( i.e. , gepitopemutant > gepitopewild - type or gepitopemutant < gepitopewild - type ) .
the conserved effect of mutations in both ed3s suggests similar 
 thermodynamic principles in the mechanism of evasion of antibody - mediated 
 neutralization .
( a ) the correlation between thermodynamic coupling and binding energy 
 to mabs follows a peaked function .
the values for this figure were 
 obtained by averaging the thermodynamic coupling of the residues in 
 the ed3s that reside in the bc loop for wnv ( red symbols ) or in the 
 fg loop for denv-2 ( blue symbols ) .
the black line is a fit of the 
 response of a boltzmann equilibrium process ( eq 7 in methods ) .
( b ) changes in the response 
 of the boltzmann fit using decreasing cooperativity values ( c = 6.5 in brown , c = 4.0 in green , c = 2.0 in dark brown , and c = 1 in orange ) . the simplest model that describes 
 the peaked function shown in 
 figure 6 is the response of a boltzmann ( equilibrium ) 
 process between two thermodynamic states ( eq 7 in methods ) . often in biophysics
, a boltzmann 
 process is described for folded / unfolded , bound / unbound , or active / inactive 
 transitions in a protein . in this study
, however , the boltzmann process 
 represents a transition between low and high thermodynamic coupling 
 states in the epitope of the ed3s .
we interpret these thermodynamic 
 coupling states as states of lower or higher fluctuations in the epitope 
 relative to wild - type . by using eq 7 to fit 
 the data in figure 6a
, we determined the midpoint 
 of the transition ( xo = 2.3 kcal / mol ) 
 and a cooperativity factor , c , that describes the 
 sharpness of the transition between the two states .
we obtained 
 a value of c = 6.5 , which reflects a sharp transition 
 between states .
the high degree of cooperativity implies that mutations 
 that generate small changes in the thermodynamic coupling of the epitope 
 result in a large reduction in the binding energy to a mab .
this is 
 clearly seen in figure 6a wherein changes in 
 the thermodynamic coupling of the epitope as small as 0.3 kcal / mol 
 result in a  12 kcal / mol change in binding energy 
 ( equivalent to 10- and 100-fold decrease in mab binding affinity ) . to illustrate the biological relevance of a high 
 degree of cooperativity characterizing the transition between thermodynamic 
 coupling states , we systematically reduced c in eq 7 and recorded the changes in the shape of the peaked 
 function observed in figure 6a .
when we reduced 
 the value of c from 6.5 to 1 , the height of the peaked 
 function was significantly reduced ( figure 6b ) .
this decrease in height implies that even if a mutation in ed3 
 generates a large change in the thermodynamic coupling of the epitope , 
 the reduction in the mab binding affinity will be very small .
we also 
 observed that the peaked function broadens as the value of c decreases .
this broadening effect indicates that a mutation 
 in ed3 loses efficacy in reducing mab binding affinity even for large 
 changes in thermodynamic coupling .
in fact , for a change of 0.3 
 kcal / mol in the thermodynamic coupling and a c = 
 2 , the reduction in mab binding affinity is only 25% . when c = 1 , the expected change in mab binding affinity is negligible . 

a phenotype that evades neutralization in wnv and denv-2 is clearly 
 observed when the mab binding affinity is reduced 10-fold or more 
 relative to wt . in order to decrease the mab binding affinity 10-fold 

when c = 2 , the change in thermodynamic coupling 
 in the epitope needs to be as high as 1.52.0 kcal / mol .
thermodynamic 
 perturbations of 1.52.0 kcal / mol will likely lead to global 
 protein unfolding and render the viral particle nonviable .
our 
 analysis is logical from a biological point of view because mutations 
 that result in severe changes in the stability of the protein antigen 
 will be selected against .
instead , mutations that generate small changes 
 in the thermodynamic coupling of residues in the epitope would be 
 evolutionarily advantageous and provide the virus with an advantage 
 over neutralizing antibodies without jeopardizing the structural integrity , 
 fold , global stability of the protein antigen , or viability of the 
 infectious virion .
because of the fundamental thermodynamic nature 
 of our analysis , we foresee that the strategy to generate resistance 
 to antibody binding described here may be applicable to other pathogens .
previous studies have proposed that epitopes are predominantly 
 located in flexible regions of a protein antigen .
our studies , however , provide 
 a thermodynamic foundation for the role of protein flexibility in 
 escape mutants .
we found that resistant mutations increase or decrease 
 the flexibility of the epitope by tuning up or down the degree of 
 thermodynamic coupling between the site of mutation and the epitope . 

the modulation of thermodynamic coupling may occur via linear effects 
 ( mutations in the epitope ) or by conformational effects ( mutations 
 in neighboring structures of the epitope ) .
these long - range mutational 
 effects probably originate in the redistribution of conformational 
 states within the ensemble of the ed3s and not through a direct mechanical pathway that evokes a static 
 view of proteins .
we envision that long - range interactions between 
 residues residing in the epitopes and other amino acids may provide 
 additional mutation sites in the virus to increase antigenic variations 
 that allow the virus to go undetected by the host immune system .
altogether , the application of an ensemble - based description of protein 
 fluctuations quantitatively explains the effect of mutations in evasion 
 of antibody neutralization .
ensemble - based descriptions of the equilibrium 
 have been successfully used to describe the mechanism of allosteric 
 regulation in other protein systems ( i.e. , dhfr and camp receptor 
 protein ) .
thus , changes in the subpopulations of the native state 
 ensemble ( due to mutation , ligand binding , or protein  protein 
 interactions ) seem to be a general strategy that nature uses to regulate 
 biological function , including escape from antibody binding .
the parallel observations for wnv and denv-2 allowed us to establish 
 a unified mechanism of antibody - mediated neutralization for these 
 two viruses .
this mechanism correlates subtle changes in the conformational 
 fluctuations in the epitope ( described as thermodynamic coupling ) 
 and large defects in antibody binding affinity .
the consequence of 
 such correlation is that the virus is efficiently undetected by neutralizing 
 antibodies without global unfolding of the viral protein .
viruses 
 have evolved many strategies to survive neutralizing antibodies , including 
 the disruption of interaction surfaces between the epitope and the 
 antibody ( steric hindrance ) . here
, we describe the role of 
 protein conformational fluctuations and how mutations inside or outside 
 the epitope lead to evasion to antibody neutralization ( figure 7 ) .
. a static view of the mechanism of antibody resistance involves steric 
 hindrance of tight antibody 
antigen interactions due to mutations 
 in the epitope ( i.e. , at position t332 , green arrowhead ) . alternatively , 
 but not exclusively , mutations in the viral epitope ( red arrowhead ) 
 may lead to changes in the conformational dynamics of the protein 
 antigen to prevent antibody binding . moreover , we found that mutations 
 not located in the primary epitope ( the bc loop in wnv ) that are thermodynamically 
 coupled can also lead to antibody neutralization resistance via conformational 
 effects ( black arrowhead ) . in this figure ,
antibody neutralization 
 is a central component of the immune response 
 against viruses , as antibodies reduce viral infectivity by preventing 
 cell entry and tissue dissemination .
a large effort is being invested 
 in identifying epitopes in proteins from these and other flaviviruses . correctly identifying 
 the epitopes
is very important , since it will allow the development 
 of new and efficient therapies ( i.e. , therapeutic antibodies ) , or the identification 
 of target sites for small molecules to bind and inactivate viral proteins . 
 without a priori information on the epitopes ,
our 
 studies revealed a previously unidentified relationship between mutational 
 susceptibility of the ensemble and epitope location .
thus , an important 
 and fundamental question arises : what is an epitope ? from a functional perspective , an epitope has been identified by 
 mutations that decrease antibody - binding affinity and generate a neutralization - resistant 
 phenotype in a virus . from a structural point of view , epitopes have 
 been assigned as residues that are part of an interaction surface 
 between the protein antigen and the antibody . in this study , we add 
 a dimension to the identification of an epitope based on the fundamental 
 thermodynamic property of correlated fluctuations in the protein ensemble . 

we propose that the combination of functional data , high - resolution 
 structures , and thermodynamic information should allow a more accurate 
 identification of the key residues responsible for the generation 
 of evasion to antibody - mediated neutralization of viruses or other 
 pathogens .
 mutations 
 in the epitopes of antigenic proteins can confer viral 
 resistance to antibody - mediated neutralization . however , the fundamental 
 properties that characterize epitope residues and how mutations affect 
 antibody binding to alter virus susceptibility to neutralization remain 
 largely unknown . to address these questions , we used an ensemble - based 
 algorithm to characterize the effects of mutations on the thermodynamics 
 of protein conformational fluctuations . 
 we applied this method to 
 the envelope protein domain iii ( ed3 ) of two medically important flaviviruses : 
 west nile and dengue 2 . 
 we determined an intimate relationship between 
 the susceptibility of a residue to thermodynamic perturbations and 
 epitope location . 
 this relationship allows the successful identification 
 of the primary epitopes in each ed3 , despite their high sequence and 
 structural similarity . 
 mutations that allow the ed3 to evade detection 
 by the antibody either increase or decrease conformational fluctuations 
 of the epitopes through local effects or long - range interactions . 
 
 spatially distant interactions originate in the redistribution of 
 conformations of the ed3 ensembles , not through a mechanically connected 
 array of contiguous amino acids . 
 these results reconcile previous 
 observations of evasion of neutralization by mutations at a distance 
 from the epitopes . finally , we established a quantitative correlation 
 between subtle changes in the conformational fluctuations of the epitope 
 and large defects in antibody binding affinity . 
 this correlation suggests 
 that mutations that allow viral growth , while reducing neutralization , 
 do not generate significant structural changes and underscores the 
 importance of protein fluctuations and long - range interactions in 
 the mechanism of antibody - mediated neutralization resistance . 
Introduction
Methods
Results
Discussion
Conclusions