numerous viruses undergo 
 structural transitions during their life 
 cycles . for many systems a virus receives a signal from the environment 
 which triggers a transition to the next stage in its development . 

these signals can come in the form of a direct interaction ( i.e. , 
 receptor binding ) or through more passive mechanisms , such as changes 
 in ph or ionic strength .
many viruses enter cells and are trafficked 
 through the endosomal system , where they encounter acidic environments 
 ( ph = 4.06.5 ) compared to the extracellular conditions . in certain cases ,
these viruses have evolved 
 to exploit the cellular acidic compartments , where the virus structure 
 responds via spontaneous configurational changes that facilitate the 
 ability to infect the host .
examples of acid - dependent entry mechanisms 
 include influenza , alphaviruses , west nile virus , as well as many other 
 human- and nonhuman - infecting viral species .
the bacteriophage hk97 infects escherichia 
 coli and is a model system for understanding virus 
 maturation , as extensive 
 structural and biophysical data are available .
while in vivo maturation is triggered by dna packaging , in vitro , an analogous structural transition to the capsid 
 can be accomplished in the absence of dna , triggered by acidification 
 ( ph  4 ) .
wild - type hk97 has the 
 unique feature of forming protein catenanes in the mature capsid through 
 a cross - linking reaction between neighboring protein subunits .
while the formation of cross - links 
 renders the maturation transition irreversible , it remains unclear what role the cross - links play in driving 
 the transition .
most striking is the fact that a cross - link deficient 
 mutant ( k169y ) , is capable of undergoing an analogous transformation 
 resulting in a structure which is nearly identical to the wild - type 
 mature capsid in the hexamers but with slightly less protruding pentamers . in vitro ,
closed capsids 
 of hk97 can be assembled 
 by expressing the major capsid protein gp5 .
the shells consist of 
 420 copies of the subunit protein and are arranged into hexamers and 
 pentamers obeying a t = 7 caspar  klug architecture .
this initial structure is know as prohead - i 
 ( p - i ) , but is unstable when coexpressed 
 with the protease gp4 .
the gp4 protease cleaves 102 n - terminal residues 
 from each of the subunit proteins and promotes a structural reorganization , 
 resulting in the spherical particle known as prohead - ii ( p - ii ) .
p - ii 
 is the stage where dna would begin to package , causing the particle 
 to expand and facet , leading to the fully mature head - ii ( h - ii ) structure . 
 in the cross - link
deficient mutant , the final configuration is termed 
 head - i ( h - i ) .
the structural change between p - ii and h - i / ii is very 
 dramatic , involving a 50  radial expansion , morphological changes 
 from spherical to icosahedral , as well as inter- and intrasubunit 
 rearrangements . in both the wild - type and mutant pathways in vitro
earlier work suggested that several intermediate 
 states existed along the pathway , but that view 
 has eroded , and now it is believed there is just a single intermediate 
 state , termed expansion intermediate ( ei ) , which separates p - ii from 
 h - i . a model of 
 ei was constructed by fitting the h - ii coordinates into cryo - electron 
 microscopy ( cryo - em ) maps of the intermediate , which was trapped using 
 low ph conditions . while low ph will 
 initiate the expansion / maturation process in vitro , it is not sufficient to reach the h - i / ii state .
the capsid will 
 only reach the intermediate stage at low ph , and in order to complete 
 the transition , the system must be returned to a neutral ph environment . 

the structures of the different states of hk97 are shown in figure 1a , while the subunit and hexamer structure of p - ii 
 and h - i are presented in b and c , respectively , of figure 1 .
in this work we focus on the transition 
 between p - ii to h - i via 
 ei by examining a low - energy pathway which conserves icosahedral symmetry . 
 while the maturation of hk97 has been studied for many years , both 
 experimentally and theoretically , in previous studies
either only 
 a few states of the pathway have 
 been examined , or if time - resolved methods were employed , the structural 
 resolution has been quite low .
previous studies on the maturation 
 pathway include those employing biochemical methods , small - angle x - ray scattering ( saxs ) , hydrogen / deuterium 
 ( h / h ) exchange , cryo - em , atomic force microscopy ( afm ) , normal - mode 
 analysis ( nma ) , and coarse - grained molecular dynamics using a structure - based potential .
this study provides a higher level of spatial 
 resolution into the maturation process than previous works , through 
 the utilization of all - atom molecular dynamics simulation .
we gain 
 further insight by utilizing constant ph molecular dynamics ( cphmd ) , which allows us to estimate pka s 
 of titratable groups and calculate ph - dependent free energy changes 
 in the stability of the capsid . with these methods we are able to 
 uncover the free energy landscape that governs the dynamics of maturation 
 and understand how that surface is influenced by the chemical perturbation 
 of acidification .
the end points for 
 our pathway calculation were the p - ii ( pdb i d : 3e8k ) and h - i ( pdb i d : 2fs3 ) structures determined 
 by x - ray crystallography . since the h - i structure 
 contains the mutation k169y , this mutation was incorporated into each 
 of the seven subunit proteins in the p - ii asymmetric unit structure 
 using the mutate.pl script from the mmtsb toolset , so that both end points have an equivalent atomic composition . 
 in all molecular simulations in this study
we used the charmm simulation 
 package with the charmm27 force field including the cmap correction term .
the simulation system was the seven protein asymmetric unit , which 
 consisted of a total of 1960 residues and 29911 atoms ; in all energy 
 minimizations and molecular dynamics ( md ) , icosahedral symmetry was 
 enforced on the full capsid , by the rotational symmetry boundary condition 
 method and the image facility in charmm . 

the choice to constrain the system to obey icosahedral symmetry provides 
 a significant ( 60 ) computational advantage , and is justified 
 by a recent study in which the symmetry constraint was not enforced , 
 yet the pathways retained much icosahedral character .
( a ) full capsids : from left to right , prohead - i 
 ( pdb i d : 3p8q ) , prohead - ii ( 3e8k ) , expansion intermediate ( 3ddx ) , head - i ( 2fs3 ) , head - ii ( 1ohg ) .
( b ) subunit structure : the a - subunit of the p - ii 
 and h - i structures are shown , the e - loop ( residues 148181 ) 
 is colored green , the a - loop ( residues 288303 ) is colored 
 red , and the spine helix ( residues 200240 ) is colored blue . 

( c ) hexamer structure of the p - ii and h - i structures are shown with 
 the same secondary structure coloring as in ( b ) .
the initial pathway between the end point structures was 
 built 
 using linear interpolations in both cartesian and internal coordinates , 
 combined with shrinking of the amino acid side chains .
specifically , 
 first backbone atoms were interpolated in the cartesian space , and 
 then side chain atoms were shrunk to half the original size before 
 finally building them onto the interpolated backbone .
this step was 
 followed by short constrained minimization of each bead during which 
 the side chains are restored to their original size .
previously , this 
 approach of building the initial pathway between known end - point states 
 has been shown to produce reasonably low energy paths compared to 
 plain all - atom linear interpolation in cartesian coordinate space .
the initial pathway consisted of 120 structures , 
 spaced in 0.5  increments in rmsd space .
initial energy 
 minimization was performed on each of the structures with a 100 kcal / mol positional restraint on the backbone atoms for 1000 steps 
 with a steepest descent ( sd ) algorithm followed by 2000 steps with 
 an adopted basis newton  raphson ( abnr ) method and using the 
 gbmv implicit solvent model .
starting from 
 this initial minimized pathway , we refined the conformational 
 change pathway using the string method in conjunction with the harmonic fourier beads path interpolation 
 method ( hfb ) implemented in charmm through 
 the trek module .
the string of structures was evolved to yield a minimum 
 energy pathway . during each cycle of hfb refinement ,
the reactive 
 coordinate set ( rcs ) was chosen to be all backbone atoms , which were 
 restrained with a weak ( 1 kcal / mol ) positional 
 restraint . in each cycle of hfb , energy minimization was performed 
 for 500 steps using sd followed by 2000 steps with abnr . following 
 the minimization ,
the string was updated by the generalized gradient - augmented 
 hfb ( gga - hfb ) method in which a harmonic approximation of the energy 
 surface is calculated , and the structures are displaced along the 
 gradient , to allow local energy barriers to be overcome .
the stepping 
 parameter was set to 0.000125 , and 96 basis functions were used to 
 reparameterize the string following the gradient stepping , to keep 
 the beads equally spaced along the pathway .
hfb was performed for 
 132 cycles using the gbmv implicit solvent model , and then an additional 
 68 cycles of hfb were performed using the gbsw implicit solvent model with a salt concentration of 0.1 m. a total 
 of 200 cycles of hfb refinement was performed .
the convergence of 
 the pathway refinement was monitored by energy and structural metrics , 
 as shown in figure 2 . throughout the manuscript 
 we will refer to the 120 structure energy minimized refined pathway 
 as bead 0 through bead 119 .
each structure ( bead ) was aligned with 
 its corresponding bead from the initial path , and the rmsd was calculated 
 over the heavy ( non - hydrogen ) atoms .
the 
 individual bead rmsds , with respect to their corresponding beads in 
 the initial path , are summed over all beads in the path .
the structures from the 
 final ( 200th ) cycle of hfb were then subjected to umbrella sampling 
 md simulations using cphmd to maintain 
 ph 7 conditions and a salt concentration of 0.1 m. the gbsw implicit 
 solvent generalized born model was used 
 during umbrella sampling .
each structure was minimized under these 
 conditions for 500 steps with sd , followed by 500 steps with abnr , 
 while restraining all non - hydrogen atoms with a 10 kcal / mol positional restraint . following the minimization ,
the positional 
 restraints were removed and a center of mass restraint was imposed 
 to keep the structure near a fixed radial value .
the radial restraint 
 was implemented with the charmm cons hmcm command , which restrains 
 the center of mass ( com ) of the atom selection to a reference position . 

the functional form of the restraint energy is , u = k* , where  is the distance 
 been the atom selection ( all backbone atoms ) com and the reference 
 position .
each structure was equilibrated under a high restraint ( 50 
 kcal / mol ) for a minimum of 1.2 ns .
production 
 umbrella sampling was performed for 3.0 ns with a 10 kcal / mol center of mass restraint .
all umbrella sampling simulations 
 were performed at constant volume using a langevin integration scheme 
 coupled to a bath at t = 300 k with a 5.0 ps friction coefficient on all non - hydrogen atoms , and 
 a 2.0 fs time step .
histidine , aspartic acid , and glutamic acid residues 
 protonation states were allowed to fluctuate , via the cphmd implementation . 

a similar 
 approach of combining hfb with cphmd was recently employed to study 
 conformational changes in gpcr rhodopsion .
the production umbrella sampling 
 simulations were used for the potential of mean force ( pmf ) calculations 
 and for estimating pka values . the weighted 
 histogram analysis method ( wham )
was used to 
 construct an unbiased pmf along the radial expansion coordinate , using 
 the code provided by alan grossfield ( http://membrane.urmc.rochester.edu/content/wham ) . from the 3.0 ns of production umbrella sampling data
two separate 
 pmfs were computed , corresponding to the first 1.5 ns and the last 
 1.5 ns of production data .
the pmfs were converged using 60 windows 
 at 10 kcal / mol tolerance ; further reduction of 
 the tolerance criteria did not significantly change the pmfs .
the 
 two pmfs were averaged , and error bars were computed as shown in figure 3 .
potential of mean force for capsid expansion at ph 7 . 
 the radial 
 value of p - ii , pei , ei , and h - i are indicated by the red circle , triangle , 
 square , and diamond , respectively . during cphmd a dynamic variable ,  ,
is propagated according 
 to the extended hamiltonian equations of motions , taking on values between 1 ( fully deprotonated ) and 0 ( fully protonated ) . 
 to determine the pka s of the titrating 
 residues we calculate the fraction of unprotonated ( s ) states by1where n corresponds 
 to  > 0.9 and n corresponds 
 to states with  < 0.1 .
the first 1.2 ns of each umbrella 
 sampling window was discarded , and the remaining data ( minimally 3 
 ns / window ) were used to calculate s. the pka s were then estimated 
 from the generalized henderson 
equation,2where n is the hill coefficient , 
 which is related to the cooperativity between titrating residues . 

we have set n = 1 in our calculations of the pka s , as small deviations from n = 1 have little effect on the resultant free energy changes .
the spine helix 
 kinking angle was 
 calculated by considering the angle between the center of geometry 
 of the backbone atoms for the following three residues : 202 , 209 , 
 and 216 .
the e - loop rotation was calculated by aligning each subunit 
 protein to its corresponding subunit protein in the initial ( p - ii ) 
 state .
the angle was calculated by defining 3 points , one at the base of 
 the e - loop in both the initial and current states ( center of geometry 
 of the set of residues 152154 , 176178 ) , and a point 
 at the tip of the e - loop of the current state ( center of geometry 
 of residues 162169 ) .
we have utilized free energy simulation based methods at constant 
 ph to understand the overall thermodynamics of the expansion / maturation 
 process and also have identified residues that contribute most significantly 
 to both stabilizing the procapsid state and those involved in driving 
 the transition toward the mature state .
we then move 
 on to present and discuss the residues which are most critical to 
 controlling the maturation transition and how these residues are involved 
 in reorganization of specific structural motifs in the capsid .
lastly , 
 we consider the relationship between ph - induced maturation and dna - driven 
 maturation .
we have computed the free energy profile 
 ( pmf ) of hk97 expansion at ph 7 from our umbrella sampling data .
the 
 profile is presented in figure 3 , and at neutral 
 ph the profile is uphill , with a few local minima along the path . 

the magnitude of the free energy change between h - i and p - ii is 150 
 kcal / mol , which at first glance appears to be a tremendous amount 
 of energy .
however , this energy change is for the full capsid , which 
 contains 420 proteins , so on a per protein basis the energy requirement 
 is not that significant .
our estimate of g = 150 kcal / mol appears to underestimate the free energy change as 
 measured by differential scanning calorimetry ( dsc ) at ph = 7.5 ( 250 
 kcal / mol ) , but the sign and order of 
 magnitude are consistent with experiment , and there is a ph difference 
 between our pmf calculation conditions and the experimental measurements 
 ( see discussion below ) .
the radial values of p - ii , ei , and h - i are 
 mapped onto the pmf , and it can be seen that both p - ii and h - i lie 
 in flat regions , while the intermediate lies just past a small bump 
 in a relatively flat region of the landscape .
there are some local 
 minimum free energy states observed around 240  , which may correspond 
 to an early stage intermediate state .
we denote this state around 
 240  and as a putative expansion intermediate ( pei ) , and is 
 also mapped onto the pmf . to validate
that our pathway does 
 pass through the known intermediate state , we performed structural 
 comparisons between our pathway structure and the ei structure .
however , 
 the ei structure is a pseudoatomic model , derived from rigid - body 
 fitting of the h - ii coordinates into a 14  cryo - em map of ei . to compare our pathway structures with ei within 
 the experimental resolution , we computed cross - correlation coefficients 
 ( ccc ) between simulated density maps at 14  resolution , according 
 to3where s and e represent the simulation and experimental 
 maps being compared .
the 
 generation of the maps and rigid - fitting were performed with the situs 
 program , and the ccc computations were 
 performed with the vmd mdff plugin . at 
 the intermediate state region in our landscape ,
we also computed the slope of the pmf 
 to illustrate the intermediate lies just beyond a low - slope region 
 in the landscape , figure 4 . from biochemical 
 and structural experiments we know that maturation will proceed at 
 low ph ; however , it does not go to completion .
so if we 
 consider this to be a three - state process , characterized by two gs , g1 ( p - ii to ei ) and 
 g2 ( ei to h - i ) , we can calculate 
 how these gs are effected when the ph is perturbed 
 away from ph 7 .
equation 4 is a function 
 of the net charge ( q ) difference between states a and b ; r is the gas 
 constant , and t is the temperature . equation 4 can be integrated to give the free energy change 
 as a function of ph,5where 
 the sum is taken over 
 all titrating residues in the ph range of interest ( in our case his , 
 glu , and asp ) .
the reference ph can , in principle , be any number , 
 but we will set ph = 7 , since we have computed a pmf 
 at ph 7 . intermediate validation .
the cross - correlation coefficient between 
 simulated maps of the ei pdb structure and pathway intermediate states 
 is plotted against the left axis .
the location of the ei state from 
 our pathway is marked as a red square .
the slope of the pmf ( figure 3 ) is plotted against the right axis .
we have computed the g curves for 
 both the p - ii to ei transition and the ei to h - i transition ; these 
 curves are shown respectively in a and b of figure 5 . the stability between the states is correctly predicted : 
 the transition from p - ii to ei is more favorable at low ph , while 
 the transition from ei to h - i is more favorable at neutral ph .
these 
 calculations support a ph - stability switch mechanism to control the 
 maturation process .
we have mapped these changes onto our computed 
 pmf at ph 7 to observe how ph modulation alters the expansion free 
 energy landscape , as shown in figure 5c . by 
 lowering the ph the landscape
is tilted , creating a deep well around 
 the ei state . increasing the ph
will then reduce the barrier for reaching 
 the h - i state , becoming nearly flat around ph = 6.5 .
interestingly , 
 the overall g at ph = 7.5 increases compared 
 to g(ph 7 ) .
our prediction of the p - ii to 
 h - i g(ph 7.5 ) = 206 kcal / mol is in closer 
 agreement with the dsc measurement , g(ph 7.5 ) 
 = 250 kcal / mol .
the g for the transition between p - ii and ei ( a ) and for the 
 transition between ei and h - i ( b ) .
( c ) maturation free energy landscape 
 as a function of ph for a simplified three - state surface .
the 
 other curves are generated by considering the three structural regions , 
 p - ii , ei , and h - i as defined by beads 05 , 7579 , and 
 115119 , respectively , and computing the g according to eq 5 , and then adding 
 those differences to the computed pmf at ph 7 .
the g between h - i and ei does not 
 become 
 negative in the range of ph we examined , which is inconsistent with 
 experimental observations . at ph 6.5
the g is 32 kcal / mol , which on a per protein basis is only 0.08 kcal / mol . 
 at the h - i state
we do see the pmf take on a negative slope ( figure 4 ) , and it is possible a deeper minimum exists at 
 a larger radius , which was not sampled in our simulations .
there are 
 a variety of possibilities which could lead to such a discrepancy 
 including the force field , the implicit solvent model , inadequate 
 sampling , or the symmetry constraint . on the basis 
 of the observation of a flat region of the pmf around 240  , 
 and some structural features which display interesting dynamics in 
 this region ( see below ) , we have performed ph stability calculations 
 about this state .
analogous to the calculations in the above section , 
 here examinations of the stability between p - ii , pei ( beads 3035 ) , 
 and ei are made .
we observe the pei state also exhibits stability 
 under low ph conditions , figure 6a , and transition 
 out of the state is favored at higher ph .
we again map the gs onto our ph 7 pmf , but here we also consider points in 
 between each of our states ( p - ii , pei , e - i , h - i ) , to investigate if 
 there are ph - dependent barriers separating the states and to better 
 represent the complexity of the landscape .
these potential barriers 
 were simply chosen as the midpoint ( in bead - space ) between each of 
 the four stable states .
our estimates of the pka values for the 
 titrating residues ( we considered his , glu , and asp ) , give us insights 
 into the most critical interactions controlling the expansion of the 
 capsid . in order to identify which residues have the largest contributions 
 to regulating the structural transition
, we average the pka s over adjacent structures in the pathway and 
 also over identical residues in the hexamer . in effect
we are improving 
 sampling by 30-fold by using 5 adjacent structures from the pathway , 
 and then the 6-fold improvement by averaging over the hexamer subunits . 

we compared the pka s between the 
 p - ii state ( beads 04 ) and the ei state ( beads 7579 ) 
 and calculated how those pka differences 
 result in changes in g ( i.e. , g ) at low ph , according to eq 5 .
those 
 residues which have large ( positive or negative ) resultant g , are those residues whose pka changes significantly between p - ii and ei .
pka(p - ii ) ) we refer to having upshifted 
 pka s , and conversely those residues 
 with negative pka s , we 
 refer to as residues with downshifted pka s . in table 1
we present the five 
 residues with the most negative g ( downshifted 
 pka s ) and the five residues with 
 the most positive g ( upshifted pka s ) .
these residues are displayed on 
 the hexamer structure of p - ii in figure 7 . 

what can be immediately recognized is that the residues with down - shifted 
 pka s ( colored red ) exist at the 
 hexamer boundary and are presumably involved in capsomer 
caposmer 
 interactions , while the residues with upshifted pka s are more interior to the hexamer and exist 
 primarily at subunit  subunit interfaces .
those residues which 
 have upshifted pka s have a propensity 
 to protonate and therefore , the interactions which are formed in the 
 p - ii state are likely to be dynamic , whereas those structures which 
 have downshifted pka s are resisting 
 protonation and therefore are more likely to be conserved interactions 
 through the transition .
ph effects on the free energy landscape including 
 pei and potential 
 barrier states .
g for the transition 
 between p - ii and pei ( a ) and for the transition between pei and ei 
 ( b ) .
( c ) maturation free energy landscape as a function of ph for 
 a complex surface .
p - ii , pei , ei , and h - i are considered as well as 
 an intermediate point between each of the states . as we illustrated in figure 7 most of the residues that have large pka downshifts
it 
 is known that hk97 assembles as capsomers ( hexamers and pentamers ) and therefore we might expect that disruption 
 of interactions formed by these residues could have deleterious effects 
 on the assembly process .
asp231 is involved in an intercapsomer salt bridge 
 with lys178 in the p - ii state , as shown in figure 8 , and the single mutation d231l prevents assembly of procapsids .
this interaction is broken in the mature state , 
 but our pathway indicates the interaction is loosely maintained through 
 the ei state . by examining the salt bridge distance between asp231 
 on the a protein ( hexamer ) and k178 on the g protein ( pentamer ) , we 
 see the separation gradually increases until beyond the ei state ( radius 
  255  ) when the separation moves beyond 10  .
the residues from table 1 are 
 shown as green ( most negative g s ) 
 and red ( most positive g s ) 
 are shown as van der waals spheres at the c position of each 
 residue .
another critical set of interactions that are important 
 for capsid 
 assembly and structural stability are those interactions known as 
 the three - fold  staple  .
the staple consists of intercapsomer 
 interactions around three - fold and quasi -three - fold axes , involving 
 two sets of salt - bridging residues ( glu344-arg347 , glu363-arg194 ) , 
 with the orientation shown in figure 9 in the 
 p - ii state .
these interactions are believed to remain fixed through 
 maturation and serve as an anchor point for other structural rearrangements 
 to pivot about .
furthermore , mutation of either 
 of the arg residues or the double mutant e344a / e363a prevent formation 
 of capsids .
our prediction that both e344 and e363 have lower pka s in the ei state , compared to p - ii , 
 is consistent with the capsid requiring these interactions to be maintained .
, parts of four 
 capsomers are shown for the p - ii structure , the three hexamers ( blue , 
 red , cyan ) are surrounding a pentamer ( gray ) .
the salt - bridging residues 
 d231 and k178 are shown in yellow and black , respectively . in the 
 graph below ,
n distance between d231 and k178 for the 
 interaction spanning the hexamer / pentamer interface in the asymmetric 
 unit is plotted for our low energy pathway .
three subunits at a three - fold 
 axis are shown with the salt - bridging residues of the three - fold staple ; 
 coloring of residue side chains is consistent in the three subunits .
we can also explain the role of 
 glu267 in controlling the maturation 
 process , which is another one of the residues we identified with a 
 significant pka downshift between the 
 p - ii and ei states .
some of their interactions are conserved 
 through the pathway , while others form as maturation proceeds .
the 
 salt bridge distances for six of the interactions are shown in figure 10 , and it can be seen that several of the interactions 
 are conserved throughout the path , while others are dynamic and form 
 interactions in the later stages of the pathway .
this behavior seems 
 inconsistent with what was observed in the asp231 interactions , where 
 the interaction was broken in the post ei state .
however in both cases , 
 we would argue that the negative pka is driven by the need to maintain the interaction up to the ei - state , 
 and both glu267 and asp231 exhibit this character . on the other hand , 

the behavior of these interactions in the post ei state is driven 
 by the relative pka differences between 
 the ei and the h - i , states and here we see the difference between 
 asp231 and glu267 .
while the pka s 
 are very similar for glu267 and asp231 in the p - ii ( 5.21/5.22 ) and 
 the ei ( 4.59/4.68 ) states , their pka s 
 in the h - i state differ significantly .
the pka for asp231 in the h - i state is 4.31 , close to its value in 
 the ei state .
the pka of glu267 is significantly 
 depressed in h - i to 3.53 , which can be viewed as a driving force for 
 the additional salt bridge interactions formed by glu267 as it approaches 
 the h - i state .
the legend 
 indicates 
 which subunits are partnering in the interaction by the letter before 
 the colon ( e.g. , subunit : residue ) .
the residues which have significant upshifts in their pka s we propose are critical for mediating 
 structural reorganization during maturation .
these residues are likely 
 to be involved in salt bridge interactions in the p - ii state , but 
 the change to a low ph causes them to become protonated and breaks 
 the salt bridge , thus allowing for structural plasticity . in this 
 section , we examine how the residues listed in table 1 , with pka upshifts , mediate changes 
 in three structural elements : ( 1 ) unkinking of the spine helix , ( 2 ) 
 rotation of the e - loops , and ( 3 ) forming a symmetric environment at 
 the six - fold axis ( hexamer unskewing ) .
the long spine helix 
 which runs through the p - domain of the subunit protein has a bent 
 ( kinked ) conformation in the p - ii state , figure 1b .
this was somewhat unexpected and it has been proposed that the 
 straightening of the helix plays a significant role in the exothermic 
 nature of the particle expansion .
the spine 
 helix interacts with the e - loop on a neighboring subunit , during maturation 
 many interactions are disrupted between these motifs as the helix 
 twists and straightens and the e - loop undergoes a significant rotation 
 ( more on the e - loop below ) .
a salt bridge interaction between glu153 
 on the e - loop and arg210 on the helix is present in both the p - ii 
 and h - i / ii states ( figure 11a ) , and is proposed 
 to serve as a pivot point for guiding the e - loop into an orientation 
 suitable for forming cross - links
. however , our data indicates there 
 is a transient nature to the glu153-arg210 interaction .
we suggest 
 that the interaction must be destabilized in order for the spine helix 
 to have the flexibility to straighten . as shown in figure 11b , the region of the pathway where glu153-argr210 
 experience a significant separation ( > 5  ) , correlates with 
 significant 
 change in the helix kink angle
. therefore we can understand the large 
 pka upshift of glu153 in the ei state 
 as a driving force for protonating glu153 under low ph conditions 
 to allow for refolding of the spine helix to occur .
the pei state 
 ( 240  ) may gain thermodynamic stability under low ph 
 conditions , because the helix can be free to unkink without the e153-r210 
 salt bridge to restrict its reorganization .
the flexible e - loop 
 region of the subunit protein is a dynamic 
 element that plays a critical role in stabilization of the mature 
 particle . in the wild - type particle isopeptide bonds form between 
 residues lys169 , which is on the e - loop , and asn356 on adjacent subunits . 
 in the p - ii state
the e - loops have an upward pointing orientation 
 ( away from the capsid surface ) , then during maturation the loops rotate 
 by 30 and lie down into the plane of the capsid . owing to the dynamic nature of 
 the e - loop , we observe three of our top five residues with pka upshifts to be along the e - loop : glu153 , glu149 
 and asp173 .
we have observed a contact between glu149 and gln195 on 
 neighboring subunits to be correlated with rotation of the e - loop . 

gln195 is on a short helical segment close to the spine helix , where 
 glu149 is toward the base of the e - loop , figure 12a .
a hydrogen - bonding interaction between glu149 and gln195 
 is possible , but that interaction is likely to be disrupted upon protonation 
 of glu149 .
the separation of glu149 and gln195 allows for the e - loop 
 to rotate and also for the spine helix to move away from the e - loop 
 and accommodate the e - loop in the down position .
the residue separation 
 between glu149 and gln195 and the e - loop rotation are shown in figure 12b and there is strong correlation between the two 
 motions .
the residues glu292 and asp290 are located at the centers 
 of the 
 capsomers , and these residues appear to be mediating the dynamics 
 of organization of the a - loops at the six - fold vertices .
the dynamics 
 at the six - fold axis could also be related to another , more global 
 structural feature , which is the symmetry of the hexamer . in the prohead 
 state
the hexamers adopt an asymmetric , skewed configuration , and as the maturation process proceeds the hexamers  unskew  
 and adopt a six - fold symmetric configuration in the ei and h - i / ii 
 states .
it has been proposed that the relief of the elastic shear 
 stress in the skewed state is a driving force for maturation .
concomitant with the overall hexamer unskewing 
 is the rearrangement of the a - loops from a linear , figure 13a , to a circular / symmetric state , figure 13b , at the 6-fold axis . in the p - ii state ,
glu292-arg294 
 intrasubunit salt bridges are observed in four of the subunits ( b , c , e , f ) . 

the a and d subunits are the central subunits in the linear orientation 
 of a - loops in the p - ii state , and the glu292-arg294 interaction is 
 not observed in these subunits .
however , the energy minimized initial 
 state of the pathway displays intersubunit interactions between asp290-arg294 
 between the a and d subunits .
therefore we propose the abrogation 
 of glu292-arg294 and asp290-arg294 interactions to be critical for 
 allowing reorientation of the a - loops and obtaining a symmetric hexamer 
 in the ei and h - i / ii states .
h / h exchange has shown that 
 the a - loops in ei and h - i are more protected than p - ii and there is 
 little change between the ei and h - i states .
we have computed contact maps for structures in our pathway corresponding 
 to the p - ii ( bead 0 ) , ei ( bead 76 ) and h - i ( bead 119 ) states , shown 
 in figure 13 c  e , respectively .
the 
 a - loop contact maps of the structures in our pathway are consistent 
 with the h / h data , showing very similar maps between ei 
 and h - i .
both the ei and h - i maps display more contacts between neighboring 
 subunits , compared to p - ii , and display a - f subunit contacts which 
 are not present in p - ii . spine helix bending .
( a ) the spine helix of 
 the f - subunit is shown 
 in the bent configuration from p - ii ( blue ) and the straight configuration 
 in h - i , also shown are the e - loops from the a - subunit ( p - ii in red , 
 h - i in orange ) .
the salt - bridging residues e153 on the e - loop and 
 r210 on the helix are drawn as sticks .
n distance 
 between e153 and r210 for the interaction spanning subunits a and 
 f is plotted along the left axis .
the spine helix bending for the 
 f subunit is plotted along the right axis .
structural averaging was 
 performed on both the distance and bending data by computing a running 
 average over five adjacent structures in the pathway .
a ) the d - subunit is shown for the initial 
 ( blue ) 
 and final ( cyan ) conformations from the pathway .
the structures were 
 aligned using residues 200300 in the d subunit . also shown 
 in red
the residues 
 e149 ( gray ) on the d - subunit and q195 ( green ) on the c - subunit are 
 shown .
( b ) the e - loop rotation and the minimum distance between e149 
 and q195 on adjacent subunits are shown .
both the e - loop rotation 
 and e-149-q195 distances are averaged over the six hexamer subunits .
this study 
 is focused on understanding the in vitro , ph - induced 
 maturation pathway of hk97 .
however , it is tantalizing to try to relate 
 these thermodynamic calculations to the in vivo process , 
 which is driven by dna - packaging into the capsid shell .
while it is 
 well established that bacteriophage capsids are extraordinarily robust 
 nanoshells and their packaging machinery is likely the most powerful motor 
 in biology , we contend that the structural changes to the capsid proteins contain 
 significant contributions from the response to the changing chemical 
 environment and do not arise solely from mechanical stress . for phages , 

this view is supported by the fact the maturation - related conformational 
 changes in hk97 can be generated in the absence of dna , that increased 
 divalent cation concentrations weaken the mechanical response to nanoindentation 
 in dna - filled phage  , and that 
 theoretical calculations which have predicted that electrostatic energies 
 are dominant to dna - bending energies in fully packaged phage capsids .
we postulate that the large negative charge density that packaged 
 dna introduces into the capsid , will cause negatively charged residues 
 to protonate to reduce the charge  charge repulsion .
this effect 
 mimics low ph by increasing the pka s 
 of those residues . the degree
to which the pka s are increased should be a function of the amount 
 of genome packaged .
therefore , at the p - ii state , when only a small 
 fraction of the genome is packaged , we expect the effect to be considerably 
 less than in the fully packaged mature h - i(i ) state .
( a ) the a - loop orientation 
 from the p - ii crystal structure ( 3e8k ) , the four salt bridges between 
 e292-r294 are numbered .
d290 residues are colored purple , e292 residues 
 are colored pink , and r294 is cyan .
the coloring of the subunits is 
 as follows , a - blue , b - red , c - gray , d - orange , e - yellow , f - olive .
( b ) 
 the a - loop orientation in the h - i crystal structure ( 2fs3 ) , same coloring 
 as in ( a ) .
( c  e ) contact maps for the structures from our energy 
 minimized pathway . contacts were computed by calculating the separation 
 between the center of geometry of the side chains of residues 288306 . 
 a contact was considered to be formed if the separation was less than 
 8  . the maps were computed for states representative of the 
 p - ii state ( bead 0 , shown in c ) , the ei state ( bead 76 , shown in d ) 
 and the h - i state ( bead 119 , shown in e ) . given our assertion that dna packaging will have a less significant 
 effect on upshifting the acidic residue pka s in the p - ii state compared to h - i(i ) , we can estimate how 
 significantly dna must perturb the pka s to make maturation favorable at physiological ( neutral ) 
 ph .
this calculation can be formulated by invoking a thermodynamic 
 cycle , as described in figure 14a .
we know 
 from our pmf calculation gmat - ph = 206 kcal / mol at ph= 7.5 , and we can calculate the electrostatic 
 component of the free energy change in the capsid due to dna packaging , 
 as6where pkai * is the pka of residue i in the presence of packaged 
 dna .
we assume that the pka s in 
 the presence of dna are just a perturbation away from our calculated 
 pka s , pkai * = pkai + . the 
 dna - induced maturation free energy is then7and we can calculate 
 gmat  dna for varying ratios 
 of the pka perturbation , (p - ii)/(h - i ) . 

what is observed , 
 is that relatively slight perturbations to h - i ( < 0.3 pka units ) , are sufficient to make maturation favorable , 
 when there is minimal perturbation to the pka s in p - ii , which we expect to be the case .
furthermore , 
 that at high perturbation ratios ( 0.8 ) , maturation still becomes favorable 
 around (h - i ) = 0.6 .
these calculations have assumed that the 
 perturbation is uniform to all residues , which is a naive assumption . 

it is more realistic to expect a distance - dependent effect ; those 
 residues close to the dna will experience larger perturbations than 
 those on the external surface ; nonetheless , these calculations provide 
 a back - of - the - envelope estimation , and serve to demonstrate a feasible 
 connection between the in vitro and in vivo processes .
( a ) the free energy change of 
 dna - induced 
 maturation can be related to the free energy change of ph - induced 
 maturation through a thermodynamic cycle .
( b ) gmat  dna is plotted against the pka perturbation (  ) to h - i .
each of the different 
 colored trends represents a different ratio of the perturbation between 
 p - ii and h - i , (p - ii)/(h - i ) , ranging from equal effect , 
 ratio = 1.0 ( blue line ) , to no effect on p - ii , ratio = 0 ( yellow line ) .
we 
 have performed an extensive study investigating how local chemical 
 perturbations are linked to massive global conformational changes 
 in a virus capsid .
we have computed the free energy landscape for 
 the expansion and maturation of the hk97 capsid , which is in reasonably 
 good agreement with known thermodynamic parameters for this process . 
 by computing the pka s of titrating 
 residues
, we were able to demonstrate a ph - stability switch is occurring 
 around the intermediate state , where expansion is favored at low ph 
 in the initial stage of the pathway and then is favored at higher 
 ph in the latter stage .
we have also examined those residues 
 which display the largest 
 pka shifts between the initial and intermediate 
 state . by examining the local environment of these residues and their 
 relation to secondary structural elements in the subunit , we identified 
 residues which have downshifted pka s 
 as being critical for the capsid integrity .
conversely , those residues 
 with significant pka upshifts are related 
 to dynamic elements in the capsid which undergo structural reorganization 
 during maturation .
lastly , we considered how changes in the electrostatic 
 environment caused by dna packaging should be sufficient to drive 
 conformational changes in the capsid .
the methods employed in 
 this study combined constant ph md with 
 pathway refinement methods and free energy calculations , representing 
 a coalescence of state - of - the - art techniques with extensive simulations . 

the agreement of our computations with experimental data from structural , 
 h / h , and thermodynamic sources indicates the robustness 
 of our approach and its applicability to other ph - mediated viral processes . 

hk97 is a well - studied model system and provides a rich system to 
 demonstrate our ability to predict which residues are  gate - keepers  
 for conformational changes .
furthermore , the methods and approach 
 we have described have the potential to open new avenues for combating 
 viral infections , as many viruses undergo a ph - dependent change during 
 their life cycles .
 many 
 viruses undergo large - scale conformational changes during 
 their life cycles . 
 blocking the transition from one stage of the life 
 cycle to the next is an attractive strategy for the development of 
 antiviral compounds . in this work , 
 we have constructed an icosahedrally 
 symmetric , low - energy pathway for the maturation transition of bacteriophage 
 hk97 . by conducting constant - ph molecular dynamics simulations on 
 this pathway , 
 we identify which residues are contributing most significantly 
 to shifting the stability between the states along the pathway under 
 differing ph conditions . 
 we further analyze these data to establish 
 the connection between critical residues and important structural 
 motifs which undergo reorganization during maturation . 
 we go on to 
 show how dna packaging can induce spontaneous reorganization of the 
 capsid during maturation . 
Introduction
Materials and Methods
Results and Discussion
Conclusions