the question of how 
 to effectively activate o2 for reaction 
 is of great interest in biochemistry and organic and inorganic chemistry 
 ( including materials science ) because the products and byproducts 
 of o2 reactions can be variable and also because o2 often encounters kinetic barriers to the reaction , 
proton 
 transfers , both sequential and concerted , are a major theme in the 
 reaction chemistry of redox - active systems , including many biologically 
 important metalloenzymes .
proton - pumping redox enzymes are functionally 
 essential for energy storage but diverse in their mechanisms and structures , 
 comparing cytochrome c oxidases ( ccos , complex iv ) 
 to cytochrome bc1 centers ( complex iii ) , 
 for example .
two main classes of mechanisms have been proposed 
 for proton pumping 
 in ccos : ( 1 ) a direct mechanism where the chemistry of o2 reduction is directly coupled to proton pumping within the o2 binding dinuclear complex ( dnc ) containing an fe - heme and 
 cu sites ( fe - a3 and cub ) ; ( 2 ) an indirect mechanism 
 where conformational or electrostatic interactions with the surrounding 
 protein , in particular with the neighboring redox donor centers in 
 the enzyme , are required .
our current and past work has centered on 
 potential direct mechanisms for both fundamental and practical reasons . 
 the driving force for proton pumping resides in the metal redox and 
 o2 binding / reduction chemistry of the dnc , so this is clearly 
 a good place to start . by analyzing what the dnc can do with the other 
 relevant sites as simple inputs , we want to identify the distinctive 
 positive features as well as the potential limitations of our models . 

our viewpoint is modular , which simplifies analysis where separability 
 is valid , and reveals its limitations , where predictions prove questionable 
 or false .
our work is an illustration of the theme that while  the 
 map is not the territory 
, to understand 
 the territory , it is best to build and improve the map . following 
 up on our earlier work , we 
 explore how different metal and tyrosine redox and electronic states 

interact with molecular o2 binding to promote proton transfer 
 and proton pumping in the dnc of cco .
the theoretical / computational 
 tools are spin - polarized broken - symmetry density functional theory 
 ( bs - dft ) in conjunction with continuum solvation dielectric modeling 
 for the surrounding protein  solvent environment .
mitochondrial and bacterial respiration are the major sources of 
 functional energy via adenosine triphosphate ( atp ) synthesis in aerobic 
 organisms .
ccos are the terminal electron acceptors in the respiratory chain 
 of mitochondria and many bacteria .
essentially , o2 linked to the metal center is the final sink for electrons from 
 the earlier electron - transfer complexes i  iii and mobile carriers 
 [ ubiquinone ( q ) and cytochrome c]1 there are a number of critical functional requirements for 
 the 
 operation of eq 1 within the dinuclear heme 
 iron  copper complex of cco .
electrons and protons must be taken 
 up at various steps of the catalytic cycle , o2 must be 
 efficiently bound and activated for reaction without releasing oxygen - radical 
 intermediates like superoxide anion o2 or other toxic products [ for example , hydrogen peroxide ( h2o2 ) ] , and protons must be transported to and react with 
 metal - bound o2 and/or its subsequent intermediates .
equation 1 summarizes the relevant net chemical reaction but 
 not the mechanism or the essential coupling to proton pumping .
proton pumps like cco are enzymes coupled to energy transduction 
 machines . beyond the chemistry of eq 1 ,
the free energy of this reaction in cco has to be effectively 
 utilized for proton pumping from the inside ( in ) to the outside ( out ) 
 of the membrane against the electrochemical gradient ( figure 1 ) .
figure 1 is a modified 
 and annotated version of figure 1 in ref ( 2 ) representing the structure of the bacterial b - type 
 enzyme from thermus thermophilus ( tt ) .
cu reaction center 
 ( dnc cu is cub and the corresponding fe is fe - a3 ) are shown .
the dinuclear cu  cu center called cua is shown by two small blue dots .
heme - b , which is the immediate 
 donor of electrons to the dnc fe  cu center , is not shown ; heme - b 
 lies behind heme - a3 in this orientation .
many spectroscopic 
 and kinetic studies show that electrons are donated from cua to heme - b fe and then to the dnc heme - a3 .
further , o2 binding is ordered compared to electron ( e ) transfer , so that typically all four metal redox centers are 1e - reduced before o2 binds to the dnc reaction 
 site between fe - a3 and cub .
schematic ( left ) of cytochrome 
 ba3 with noted functionalities 
 and cartoon of the same ( right ) showing the o2 channel 
 inside the lipid bilayer , the reaction chamber between cu and fe , 
 and the electron- and proton - transfer  pipes  .
n  
 or negative side ( figure 1 , bottom , cytoplasm ) 
 and the outside is the  p  or positive side of the membrane 
 ( figure 1 , top , periplasm ) corresponding to 
 the polarity of the membrane electrochemical gradient .
the detailed 
 mechanism of proton pumping is far from evident , but the overall reaction 
 stoichiometry is2over a full reaction cycle .
some language 
 is useful for bookkeeping : of the ( 4 + n)hin entering the reaction chamber , 4h , called 
  scalar protons  , react with o2 to produce 
 2h2o , while the other nh , 
 called  vector protons  , are pumped across the membrane . 

measurements of n have yielded values near n = 4 for a - type ccos , but lower values near n = 2 have been measured for b- and c - type ccos .
( for example , extrapolating 
 the charge - transfer measurements for the oxidative half of the reaction 
 cycle to the entire oxidative plus reductive reaction cycle for b - type tt ba3 yields n = 2.5 approximately . )
finding accurate experimental values for n is difficult , and significant uncertainties remain . in common with respiratory chain complexes i and iii and ordered sequentially by increasing redox potentials , complex 
 iv links e transfer down the electron - transport 
 chain to proton pumping across the inner membrane of the mitochondria 
 and , analogously , across the plasma membrane in most aerobic bacteria . 

the resultant proton electrochemical gradient , or proton motive force , 
 is utilized for atp synthesis from adenosine diphosphatase ( adp ) plus 
 inorganic phosphate by complex v ( atp synthase ) , which also resides 
 within the same membrane .
the proton electrochemical gradient has 
 a higher positive potential on the outside ( p ) of the membrane and 
 a lower negative potential on the inside ( n ) of the membrane ( matrix 
 side in mitochondria ) .
is largely funneled through the atp synthase active site 
 to generate atp from adp+pi .
as expected from energy conservation , 
 continued proton pumping is required to maintain the membrane potential 
 against the leak and to provide the driving force for atp synthesis . 

alternatively , if the electrochemical gradient is depleted , proton 
 pumping is required to restore the gradient .
the electrochemical potential 
 is the sum of an electrical potential ( voltage ) difference ,  , 
 and a ph difference , ph , across the membrane3where f is the faraday constant . while the 
 reaction inputs and outputs of the respiratory complexes 
 are understood in broad stroke , in no case
is the actual coupled electron 
 redox / proton pumping mechanism understood in even reasonable detail . 

many features are known from spectroscopy and kinetics about the chemical 
 mechanism of o2 reduction and subsequent mechanistic steps 
 of the reaction cycle , but there is no current resolution about whether 
 or how proton pumping is directly coupled to the chemistry of o2 reduction at the fe  cu dnc or indirectly coupled through 
 conformational or electrostatic changes in the surrounding protein , 
 particularly involving the nearby redox centers ( the cua homodinuclear and mononuclear fe - heme donor centers ) .
it is possible that the different enzyme classes a1 versus b could 
 have significant differences in their mechanisms ( see the later discussion ) , including whether a direct or indirect 
 mechanism ( or some mixture ) applies .
x - ray crystallographic 
 structures are now available for mitochondrial 
 [ bovine heart ( mt ) ] and several bacterial ccos , including paracoccus denitrificans ( pd ) , rhodobacter spheroides ( rs ; all a1 type ) , 
 and t. thermophilus ( tt ; b type ) the mt structure is by far the most complex , with 
 13 subunits ( 3 encoded by mitochondria and 10 by the nucleus ) . however
, 
 the three mitochondrial subunits ( i  iii ) of mt closely resemble the corresponding subunits in the bacterial enzymes pd and rs , and all are of class aa3 .
the tt enzyme is of a different class ( namely , 
 ba3 ) but still has many similarities in sequence , structure , 
 and mechanism to the other ccos .
the bacterial enzymes are easier 
 to work with than the more complex mt protein and 
 have , therefore , been subjected to studies using systematic mutagenesis 
 of different sites .
our main focus will be on analysis of the tt enzyme , for which fee , stout , and co - workers have obtained 
 high - resolution x - ray structures , including several different mutants , 
 and measured kinetic spectroscopic parameters of many intermediates 
 over the redox and catalytic cycle .
kinetic analysis is enhanced 
 in ba3-type enzymes including tt because 
 the absorption spectrum of heme - b is well - separated from that of heme - a3 in contrast to aa3 ( a type ) enzymes , where the 
 heme - a and -a3 bands overlap .
also , importantly , the tt enzyme has a single input path ( kb path ) for 
 protons into the dinuclear fe  cu center , which simplifies analysis 
 of the proton pathways compared to two paths for a1-type enzymes . 

while the kb path occupies a structurally analogous region 
 compared to the k path in a1 enzymes , the kb path does 
 not contain lysine , in contrast to the k path in a1 .
the biological 
 e - transfer sequence proceeds in one electron ( 1e ) steps 
 from cytochrome c to the dinuclear mixed - valence 
 cua site in subunit ii ( having a 2cu center 
 in the oxidized state and 2cu in the reduced ) , to a mononuclear 
 fe - heme redox center in subunit i ( which in tt is 
 heme - b but in pd , rs , and mt is heme - a ) , and finally to the dinuclear heme - a3fe  cub reaction center , which is also in 
 subunit i and is where o2 binds . the proton entry pathway 
 is simpler in the tt ba3 enzyme , having 
 a single entry pathway called the 
kb path  , 
 compared to two potential entry pathways , called the  k and 
 d paths  , in the class aa3 enzymes .
o2 enters via a well - defined hydrophobic pocket near the dinuclear 
 fe - a3-cub site .
figure 1 ( left ) shows an overall structural model of cco from tt with the inputs and outputs superposed , and figure 1 ( right ) is a cartoon of the reaction chamber with reactants 
 and products . in tt ba3 ,
the subunit i 
 residue ile235 is present ( see figure 1 ) in 
 place of a glutamate residue present in a1-type enzymes , so that the 
 second proton - transfer pathway ( the d or q proton - transfer pathways 
 seen in a1-type enzymes ) is absent in b - type enzymes .
this also eliminates 
 the corresponding path to the  proton loading site  
 as proposed in a - type enzymes .
the significant implication is that 
 the path into the dnc is common to both the scalar and vector protons . 

any subsequent bifurcation of proton flow between the scalar and vector 
 pathways occurs at or after the entry point into the dnc .
also , disruptions in o2 binding and 
 electron- or proton - transfer reactions at cco can lead to an excess 
 of reactive oxygen species including hydroxyl and superoxide radicals . 

these oxygen species can arise directly at cco or can be induced earlier 
 in the electron - transport chain , for example at complexes i and iii , 
 because of a blockage in electron or proton transport at cco .
finally , 
 disruptions in the normal proton - transport pathways may also have 
 damaging effects on the membrane potential and acidity in the matrix 
 or periplasmic space .
understanding the structures , mechanisms , and 
 functions of mitochondrial cco is therefore important for better analysis 
 of genetic and metabolic diseases and cancer and is also relevant 
 to pathologies in aging .
mitochondrial dna is intrinsically subject to elevated mutation 
 frequency possibly because of its proximity to leaky electron - transport 
 chains that produce reactive oxygen species .
the close functional 
 and mechanistic relationship between mitochondrial cco and various 
 bacterial ccos allows for the development of an overview of the catalytic 
 proton - pumping cycle , while variations in the structures and energetics / kinetics 
 can provide insight into the interactions between different redox 
 centers and proton sources .
the a - type enzymes in pd and rs reside in  proteobacteria , some of 
 which were probably ancestors 
 of eukaryotic mitochondria .
b - type enzymes , while simpler in some 
 ways , also show significant variations in different species / genera . 
 further , mutagenesis studies in bacteria provide a good way of examining 
 blockage and inhibition of proton and electron transfer and o2 binding .
there have also been very significant accomplishments 
 in making synthetic analogues of the dnc , and testing the reaction , 
 physical , and spectroscopic properties of these systems .
electron flow in both a1- and b - type 
 ccos has been studied extensively . 

electrons transfer from cytochrome c to cua , then on to heme - a ( or heme - b in a1 and b types , respectively ) , 
 and from there to fe - a3cub .
after o2 binding to the dnc , a number of oxygen - derived 
 intermediates are formed .
a good deal is known about the timing of 
 o2 binding and e transfer by binding 
 co to heme - a3 and then introducing o2 , followed 
 by photolyzing the co in the fully reduced or half - reduced ( mixed - valent ) 
 forms of the bovine and related bacterial enzymes .
because of their considerable structural 
 and functional similarities , 
 a- and b - type enzymes probably have a common mechanism of o2 reduction . using optical spectroscopy to monitor transient kinetics , 
 siletsky et al . and szundi et al .
observed four intermediates for reduction and 
 o2 binding and reactions in tt cytochrome 
 ba3 at the dnc , as shown in figure 2 . to obtain proper timings for kinetics , the reaction of the fully 
 reduced enzyme
is started by photolysis of the reduced fe - a3co adduct of the enzyme in the presence of o2 , 
 and then changes in a wide array of properties are followed from the 
 nanosecond to second time scale . here
the fully reduced enzyme includes 
 the fully reduced state ( r ) of the dnc and the reduced 
 states of heme - b and cua .
concentration of o2 for r  a is 90 m for   9 s , from szundi 
 et al . compounds a , pi ( where pi is likely composed 
 of both pm and pr ) , and o in tt ba3 are similar to their analogues in a1-type enzymes . 
 more broadly , the optical absorption difference spectra of heme - a3 do not clearly report on the oxidation state ( or related 
 chemical / electronic features ) of either cub or the unusual 
 tyrosine called yoh . recently ,
szundi et al . found that the early oxidative steps of the reaction become 
 unreliable with the co photodissociation method because co can then 
 bind to cub , and this inhibits o2 binding to 
 fe - a3 and cub . instead of using co bound to 
 the reduced state r
, they instead utilized a photolabile 
 o2 carrier complex to deliver o2 to the dnc . 

the kinetics are then clarified by examining different concentrations 
 of o2 delivered to the dnc .
lifetimes (  = inverse 
 of rate constants r ) from this study are assembled 
 in figure 2 .
these lifetimes differ from those 
 we previously presented based on siletsky s kinetic studies . starting from state r , o2 binding occurs very rapidly ( even at the low effective [ o2 ] = 90 m ) and so does the following formation of ferryloxo 
 states , spectroscopic state pi .
state pi is a combination 
 of electronic / protonation states pm and pr , and because the 
 heme - b fe is also reduced , the very fast e transfer 
 to reduce the tyrosine radical is not detectable in these experiments . 

( the state pm is detected in 
 separate experiments , where the o2 reaction is started 
 from the  mixed - valence state 
, with the dnc being in 
 state r , while the heme - b and cua sites are 
 oxidized . then the cycle stops at pm because of a lack of reducing electrons . )
the cycle depicted 
 in figure 2 omits the next spectroscopically 
 observed intermediate , pii , which 
 corresponds to the timing for e transfer from reduced 
 cua to oxidized heme - b fe , which was the redox center oxidized 
 in the pm  pr transition .
after the heme - b fe is reduced , 
 it is ready to deliver the final electron in the transition pr  o , which 
 is comparatively slow .
end with state o. recent 
 pulse radiolysis experiments have shown 
 a comparatively slow 1e - transfer rate from state o ( reducing agent heme - b fe ) to heme - a3 fe ( iii 
  ii ) , lifetime  = 4800 s , compared to faster 
 e transfer from cua to heme - b ,  
 = 260 s in tt ba3 . therefore , both pr  o and o  r have comparatively slow e transfers .
we have argued in our published work that e transfer from heme - b ( reduced ) 
 to the dnc may be determined by the nature of the oxidant center present 
 on heme - a3 , which is likely to involve both reorganization 
 energy terms and the driving force ( redox potentials ) for different 
 reaction steps . for future reference , we comment briefly on 
 the issue of the electrochemical 
 potential ( load versus no or low load ) in kinetic studies and proton - pumping 
 experiments .
when experiments are conducted 
 in detergents and/or buffers , there is no net directionality ( vectorial 
 character ) to the orientation of the cco proteins in the media , and 
 so there is no net electrochemical potential . for kinetic studies , 
 these types of conditions are often used , and they lead to faster kinetics than those 
 in the presence of an electrochemical potential ( experiments under 
 load ) .
even x - ray crystallographic experiments done in the lipidic 
 cubic phase have no net directionality ( see tiefenbrunn et al . ) because the individual cco proteins are aligned 
 antiparallel in the lipidic cubic phase .
by contrast , experiments 
 designed to measure the proton - pumping stoichiometry or net charge 
 ( q ; e , h ) transfer 
 across the membrane ( usually vesicle experiments ) are set up so that 
 the cco proteins have specific directional alignment with respect 
 to the inside versus outside of the vesicles .
proton - pumping stoichiometry 
 ( vector protons ) is typically determined by running a full or partial 
 cycle and collapsing the electrical potential difference across the 
 vesicle using an ionophore , which does not conduct protons but does 
 conduct some other charged particles .
( for example , valinomycin allows 
 countertransport of k ions when protons are pumped in 
 the cco reaction cycle . ) in that case , ph is measured 
 in the corresponding partial cycle . to measure full charge transfer , 

corresponding to electrons , scalar protons , and vector protons driven 
 against the existing gradient , measurements of the electrical potential 
 change over a partial cycle are obtained . both for proton pumping 
 and net charge transfer , the standing electrochemical potential ( and 
 its electrical component )
( usually , the electrical term dominates 
 eq 3 under physiological conditions in mitochodria 
 and analogously in aerobic bacteria .
so , 
 in practice , most proton - pumping and charge - stoichiometry experiments 
 are under low load
. our dft calculations for the reaction cycle 
 are performed under 
 idealized ph gradient conditions , where we assume that each pumping 
 of a vector proton across the dnc corresponds to transfer from a neutral 
 ph = 7 cytoplasm ( n side ) to an acidic ph = 3 periplasm ( p side ) , 
 and there is no electrical potential gradient , as in the vesicle experiments 
 with an ionophore described above .
this makes bookkeeping for the 
 cost of proton pumping easy because only the vector protons have a 
 cost , which is accounted for as the proton exits from the dnc . by 
 contrast
, a standing electrical potential across the membrane will 
 lead to a pump cost for the vector protons and to a cost for charge 
 transfer for the electrons and scalar protons because these combine 
 in the reaction chamber of the dnc .
the energy accounting here is 
 more complex , and we will defer it to future work . ( for a simple analysis , 
 see siletsky et al . ) however , there is 
 one general observation that is very useful .
if the same energy cost 
 over an entire cycle ( say for pumping four vector protons from ph 
 = 7 to 3 ) is instead distributed over both the vector proton transfers 
 and the scalar proton plus electron transfers as occurs for an electrical 
 potential difference , rather than a ph difference , the charge - transfer 
 cost across the dnc over individual steps is considerably less ( roughly /2 or less because there are q = 8 charges transported across the membrane versus n = 4 vector protons ) .
in our published work ( 2008 ) , we have 
 introduced the first complete catalytic reaction cycle  wheel  
 for the cytochrome ba3 dnc , based on a detailed chemical 
 model supported by large - scale dft calculations .
our work is anchored 
 in several known features of the experimental reaction scheme but 
 goes well beyond what is presently established .
very recently , we 
 have further refined the dft model by examining alternative tautomeric 
 and protonation states .
we emphasize some important general 
 points starting from figure 2.(1 ) electron and proton 
 delivery .
the points of electron entry into the cycle as well 
 as o2 binding are well established , but only four protons 
 are accounted for within this scheme .
these are the scalar protons 
 as in eq 1 , and the vector protons are not included 
 ( see eq 2 ) . on the basis of eq 2 , the optimal proton - pumping ratio is 4h/4e , equivalent to 1h/1e .
typically , experimental proton - pumping ratios are near 1 , but early 
 published measurements with ba3 yielded values of about 
 0.40.5 . in any event , a pumping ratio of 1 requires a proton 
 uptake ratio for hin/1e of 
 ( 4 + n)/4 = 2 .
moreover , under physiological conditions ( and in 
 some experimental setups ) , the pumped protons must be moved against 
 the electrochemical gradient at a cost in g , using the chemical driving force available from the redox / protonation 
 reactions with o2 .
there are critical and distinctive chemical questions raised by 
 the catalytic reaction cycle and the structure / composition of the 
 dnc .
cu bridging peroxo intermediate 
 is likely to form subsequent to the initial oxy complex ( a ) , which has been identified , but the peroxo intermediate(s ) has 
 not been spectroscopically identified .
the peroxo complex is likely 
 to be very short - lived but is clearly 
 essential to the energetics of o  o bond cleavage and for avoidance 
 of a substantial overpotential .
both the energetics and properties 
 of these intermediates are of great interest and are connected to 
 binding modes and protonation states .
( 2b ) there is a 
 unique tyrosine ( yoh in figure 2 ) that 
 is formed from a covalent bond between the tyrosine phenol and a histidine 
 imidazole ring ( residues y237 and h233 in tt ba3 ) .
what is the physical mechanism connecting 
 the redox and chemical bonding cycle to the proton pumping ?
the lack 
 of mobile proton carriers within cco precludes a  redox loop  
 mechanism , but cco pumps protons , nonetheless .
we have already proposed 
 a proton exit channel into the watery surface between subunits i and 
 ii ( see figures 1 and 3 ) . specifically , this involves deprotonation of h376 ( from the positive 
 imidazolium form ) . as an alternative , deprotonation may instead involve 
 a nearby bound water ( probably a hydronium ion ) , which also looks 
 reasonable .
our current working hypothesis is that the dnc complex 
 itself and the kb path conducting protons into the dnc 
 are the major factors driving proton pumping .
we also think that the 
 redox potentials and timing of e transfer from 
 heme - b fe to the dnc play a role , as will be described later .
the 
 central polar plot of the running sum , g , shows the energetic course of catalysis as computed at the 
 level of pw91 .
a combination of electrostatic 
 and large - scale dft calculations 
 with associated energy analysis has been used to examine the proton - pumping 
 mechanism in class a1 ( aa3-type ) enzymes . in a number of papers ,
blomberg 
 and siegbahn have proposed that 1e transfer 
 from the cua center to the mononuclear heme - a drives protonation 
 at a pump - loading site ( pls ) close to a propionate in heme - a3 , as well as protonation of the glutamate ( glu286 in bacterial rs and a homologous glutamate in mitochondria ) .
the glu286 proton then activates 
 proton exit from the pls after 1e transfer from 
 heme - a to the dnc fe site in heme - a3 , with a coupled  chemical  

proton transfer close to the reduced fe - a3 site ( the 1e - transfer step modeled is o  e , the first 1e transfer 
 in the o  r 2e reduction ) .
presumably , at other steps of the catalytic reduction 
 o2 binding reaction cycle , some  chemical  
 protons originate from the k channel . in any event , in class b ( ba3-type )
enzymes , there is no d - type proton - transfer pathway , 
 and in tt ba3 , there is an isoleucine 
 ( ile235 ) in a position homologous to glu286 ( see figure 3 in ref ( 35 ) ) .
nonetheless , ba3 enzymes do pump protons , although probably at lower efficiency 
 than aa3.(4 ) proton 
 entry and flow .
therefore , we will focus here on the catalytic 
 reaction cycle , including proton flow into the dnc from the kb path and particularly within the dnc itself .
the vector and 
 scalar protons almost certainly take different paths through the dnc . 
 the currently available high - resolution x - ray structures of tt cytochrome ba3 from fee , 
 stout and collaborators show a much richer 
 array of waters bound to the dnc than that seen in earlier x - ray structures 
 at lower resolution .
( a ) in our earlier paper ( 2008 ) , we 
 constructed the entire catalytic reaction  wheel  for 
 the cytochrome ba3 dnc , employing large - scale dft calculations . 

( b ) on the basis of subsequent work , we have found an improved energy 
 path by modifying the sequence of proton uptake and proton - transfer 
 events and examining alternative proton tautomeric states .
these two 
 sets of models each contain 183189 atoms and are called s1 
 and s2 , for the original and for the newer model encompassing different 
 tautomers for several states .
both models are based on the hunsicker - wang 
 and fee x - ray structure of ba3 .
wang 
 ( pw91 ) exchange - correlation potential for geometry optimization in 
 a dielectric medium with dielectric constant  = 18.5 for the 
 surrounding environment .
then single - point pw91 and b3lyp * calculations 
 are compared over the reaction path .
( c ) for selected parts of the 
 catalytic reaction path , we have now introduced a larger model ( l ) , 
 incorporating additional waters and residues and with greater flexibility 
 in the electronic states described .
the larger model is built based 
 on the high - resolution ( 1.8  ) x - ray structure of tiefenbrunn 
 et al . in the lipidic cubic phase , which 
 has a higher density of water in the protein interior .
as discussed 
 in a recent paper , the observed x - ray 
 structure contains a bound dioxygen species that is probably hydroperoxide . 
 as in the hunsicker - wang and fee ( 2.3  resolution )
x - ray structure , the dnc in the protein is probably radiolytically 
 reduced , but within dft , we can control the oxidation state and the 
 types of bound ligands that are introduced in the calculations .
because of the increased cluster size , we found that the calculations 
 could be performed with fewer geometric constraints .
in particular , 
 only the link atoms at the outside boundary of the quantum cluster 
 were constrained to their positions in the tiefenbrunn x - ray structure , 
 as specified in ref .
the dielectric model is the same as models s1 and s2 , and all use 
 the cosmo solvation model .
the 
 catalytic wheel diagram for the dnc 
 from our new model s2 is presented in figure 3 . from geometry optimization and energy evaluation of 30 different 
 tautomeric / net protonation states ( defined as model sall ) for the 14-step cycle ,
compared to model s1 , if a different tautomer 
 is chosen in s2 , this is indicated by a subscript on the state number , 
 for example , 72 versus 7 . where a proton has been added , this is indicated by an 
 h , so ; for example , 2h compared to 2 and 8h2 compared to 8 indicate 
 both a tautomeric shift and an additional proton added .
figure 3 shows a detailed map of the catalytic reaction 
 cycle for model s2 .
we have augmented the 
 figure by labeling intermediates o , r , a , pm , and pr , which have all been observed spectroscopically . 
 all of these intermediates have approximate counterparts in figure 2 , and the theoretical scheme is supported by detailed 
 dft calculations . most of the spectroscopic intermediates correspond 
 to more than one detailed intermediate in the 14-state reaction cycle . 
 for example , states 13 , 14 , and 1 correspond to experimental intermediate o ; all of these 
 states are fe 
cu species , but they 
 differ with respect to protonation state(s ) or h2o binding . 

states not seen spectroscopically , which are testable by energetic 
 calculations and potentially by spectroscopic measurements when these 
 ( or related states ) are isolated .
structures 3 , 6 , 102 , and 13 are detailed 2d maps of the dinuclear fe - a3cub center , while the other states are represented by simple 
 chemical formulas .
a full 3d picture of the fe(o  o)cu bridging peroxo state , intermediate 5 , is shown in figure 4 . by comparison 
 with figure 3 ,
the coordination , covalent , 
 and hydrogen bonds are quite clear in the 2d maps , but the 3d links 
 are distorted ; for example , the heme proprionate side chains are attached 
 to the fe - heme edge . active site structure of compound 5 of ba3 . left : smaller model used in the 2008 calculations . right : larger model used in recent calculations , which is taken from the dnc of the high - resolution 
 ( 1.8  ) x - ray crystal structures ( pdb entry : 3s8 g ) of ba3 cco from tt .
for ease of visualization , these two models are not on the same 
 scale .
the new 14-step cycle differs 
 from the previous one in ( 1 ) having protons 
 enter the reaction path earlier at 
 two steps , 1  2h and 7  8h2 , ( 2 ) retaining 
 water in state 112 compared to 
 state 11 , and ( 3 ) utilizing different proton tautomers , 
 for all of the states where there are subscripts in figure 3 .
( the original tautomers from model s1 are not 
 subscripted . ) by convention , tautomers from model s1 are each tautomer 
 1 ; for example , 6 = 61 . in constructing the intermediates in figure 3
the one 
 exception is state 6 , which is critical to the peroxide 
 cleavage reaction . in our model s2 ,
this is 6 kcal mol higher ( in pw91 ) than the lowest tautomer , 62 , where the special tyrosine ( y237 ) is protonated in 
 place of the peroxide . as we will show later
the outcome of replacing our original 
 reaction path ( model s1 ) with one constructed from the lowest - energy 
 tautomers ( also alternate protonation states ) is shown in figure 5 , comparing parts a and b. the effect is striking . 
 these changes to the previous mechanism result in a substantially 
  smoother  catalytic cycle .
the largest positive free - energy 
 difference g , accounting for successive 
 uphill steps , is lowered to about 20 kcal mol for 
 pw91 in model s2 ( 31 kcal mol in b3lyp * ) , while 
 in the reaction pathway of model s1 for both pw91 and b3lyp * , this 
 value is close to 30 kcal mol .
it is easy to see 
 that both exchange - correlation potentials run in a similar manner 
 for energies over the reaction cycle and that figure 5b shows a more reasonable cycle for both pw91 and b3lyp*. 
 the g values for individual steps are 
 considerably less in all cases ( about 15 kcal mol maximum ) .
accounting for transition states using standard transition 
 state theory will also give barriers larger than those from g steps between intermediates , while concerted processes 
 and/or proton tunneling may well lower the effective barriers .
plots of g ( kcal mol ) along the trajectory 
 from 1 to 14 .
the top panel ( a ) is from 
 the 2008 mechanism ( from table 
 4 for energies ) ; the bottom panel ( b ) 
 represents new work presented here .
solid black circles represent 
 energies obtained from pw91 calculations , while reddish diamonds represent 
 energies obtained from b3lyp * calculations .
the experimental energies 
 from 1  2 and 2  3 are obtained from refs ( 26 ) and ( 44). one protonation step that promotes the catalytic 
 cycle is to add 
 one additional proton to yo in the transition 1  2 to make the state 2h , so that the added proton transfer from the kb path to 
 y237 is effectively concerted with 2e reduction 
 of fe  cu to give fe  cu .
our computed redox potentials for 1  2h are 0.24 v for pw91 and 0.02 v for b3lyp * , versus 
 0.275 v ( experimental average for cu  cu , + 0.34 v , and fe  
 fe , + 0.21 v , for mitochondria ) or 0.314 v using the experimental 
 redox potential for fe  fe for tt ba3 . the corresponding 
 error in g is about 1.63.1 kcal 
 mol for pw91 and about 13.515.5 kcal mol for b3lyp*. in contrast to state 1  2h ( o  r ) , the calculated 
 o2 binding affinity ( for standard state [ o2 ] 
 ( aqueous ) = 1
m ) is much poorer for pw91 than b3lyp * , g = 17 and 10 kcal mol , respectively , versus 8.3 kcal mol experimental 
 for tt ba3 from the reaction kinetics 
 study of szundi et al .
( see also figure 2 ; state 2h  3 , r  a ) .
these few available experimental 
 values are plotted in figure 5b . experimental 
 kinetics work of hallen and nilsson shows 
 that there is no proton uptake when o2 binds ( noting that 
 these are experiments in mitochondria ) , which is consistent with state 2h  3 ( figure 5b ) rather than 2  3 ( figure 5a ) and is correctly represented in pw91 but not 
 b3lyp*. the kb path into the dnc based on tiefenbrunn , 
 fee , 
 and stout s high - resolution x - ray structure is depicted in figure 6 .
all residue 
 side chains are constructed based on the x - ray density map , except 
 for one added water ( center purple ) , which completes the hydrogen - bonding 
 network from glu15(ii ) ( from subunit ii ) to y237 of the dnc and involves 
 a3-roh from the lower heme edge .
the orientation of figure 6 is 180 rotated about the vertical axis with 
 respect to figures 3 and 4 so that the cu site is toward the left ( above y237 ) and fe is toward 
 the right .
figure 6 shows the structure of 
 the kb path for protons into the dnc in tt ba3 .
the glu15(ii ) anion is positioned to accept a proton 
 from the solution ( n side ) and return to a hydrogen - bond alignment . 

then a proton can be readily transferred via a concerted grotthuss - type 
 process ( in common language ,  a 
 bucket brigade mechanism  ) to y237 .
usually we expect that 
 the destination for the proton is y237 , but the 
 geranylgeranyl a3-roh group provides an additional entry 
 point into the complex where an alternative pathway is needed .
structure of 
 the k path in cytochrome ba3 as deduced 
 from a combination of structural and mutational analyses .
the top 
 two residues are actually part of the active site structure per se . 

copyright 2009 national academy of sciences . to examine the physical / chemical 
 forces that drive proton pumping 
 across the dnc
, we now look at the path from state 4 to 5 and include an additional tautomer 52 . compared to state 4 , state 52 has a proton shifted from h282 to h376 
 to form a state with h376h , h282 , and 
 yoh .
the proton - shift distance is much smaller than that directly 
 from state 4 to 5 , and the predicted energy 
 cost is small ( 7 kcal mol for state 4  52 , followed by 5 
 kcal mol for 52  5 , in place of 2 kcal mol for state 4  5 in pw91 ; in b3lyp * , 
 both energy differences are near 2 kcal mol ) . 

state 5 is then generated by shifting a proton in 52 from neutral y237 ( yoh ) to h282 to form yo , h282h . in figure 7 , the structures of these states are presented with 
 the dipole moment vectors superimposed in red and the magnitudes labeled 
 [  in debye ( d ) units ] . because dipole moment vectors are oriented 
 from negative to positive , it is clearly seen that the proton shifts 
 strongly reorient the very large dipole moment vector from 4  52  5 , so that state 4 is almost oppositely aligned 
 to state 5 .
the corresponding electrostatic potential 
 becomes more positive in the vicinity of h376h , or alternatively 
 in the nearby water cluster ( top of figures 3 and 4 ) .
the following proton entering via 
 the kb path ends in state 6 ( see figure 3 ) , but the proton entry state is tautomer 62 ( fe  o  o  cu , yoh ) .
state 62 is 6 kcal mol below 
 state 6 in pw91 , so the path 5  62  6 has energy 
 differences ( 8.7 and + 6 kcal mol ) .
after 
 proton entry in state 62 , the 
 proton shift to form the hydroperoxide in state 6 produces 
 an increase in the dipole moment magnitude of about 13 d , in a direction 
 similar to that in state 5 , again enhancing the electrostatic 
 potential near h376 . as shown in figures 3 and 5b , the energy difference 6  72 is only mildly endergonic ( 11 kcal 
 mol in pw91 ; pumping against an assumed proton 
 gradient from the ph = 7 n side to the ph = 3 p side , equivalent to 
 5.5 kcal mol ) .
these three structures 
 are overall neutral . as expected on physical grounds , reducing cu  
 cu in the preceding step 1  2 increases the proton affinity of the covalently linked y327h233 
 pair bonded to cu ( g = 11.4 
 kcal mol for pw91 for 2  2h , so g is lowered for 14  2h to 11.1 kcal mol compared to that for 14  2 , + 22.5 
 kcal mol ) .
this is also consistent with the experimental 
 observation that o2 binding is not ph - dependent because 
 that proton enters earlier at state 2h .
after o2 binding and formation of a peroxo - type bridge 
 and higher fe and cu oxidation states , ( fe , fe ) and cu , we expect that cu would acidify 
 y237h233 ( i.e. , the yoh site ) via through - bond interactions 
 with cu .
 yo(h282h ) , where 
 g = 8.7  2.7 and 6.5 
  3.7 kcal mol for pw91 and b3lyp * , respectively 
 ( average , range ) .
this average and range is based on our calculations 
 for the tautomers of seven different states ( 5 , 6 , 9 , 10 , 11 , 13 , and 14 ; figure 3 ) , 
 which are all cu species . from figures 5b and 3 ,
it is evident that 
 the entire pathway from states 3  92 has only low - energy 
 barriers , at least judging from the energy differences between these 
 intermediates , and the overall pathway is highly exergonic , which 
 is consistent with the rapid rate observed from states a  pr ( observed as pi ) .
the e transfer 
 from heme - b ( fe ) to the tyrosine radical pm  pr is clearly very fast , faster than 5 s from experiment 
 ( figure 2 ) , and the earlier  true peroxo 
  intermediates are not observed ( figure 3 ) .
the calculated g value for 8h2  92 is 23 kcal mol ( corresponding 
 to a redox potential of about + 1.22 v ; we assume that the redox potential 
 of the donor is near that of cytochrome c , about 
 0.22 v ) .
if the proton coming in must go to y237 first , then g for tautomer 91 is more positive , 10.4 kcal mol ( redox 
 potential of about + 0.67 versus she ) .
however , this is still quite 
 exergonic . for the next redox step , from state 112 to 12
, g is again 
 very negative , 21 kcal mol ( redox potential 
 of + 1.12 v versus she ) .
there are two coupled protonations assumed 
 here , and it is assumed that e transfer from heme - b 
 fe is to cu  cu . if state 12 is skipped in favor of state 13 , so that e transfer goes from heme - b fe to heme - a3 fe 
 fe  fe directly , the predicted 
 g value is almost the same .
the 
 corresponding spectral state changes of the dnc are pr  f and pr  o for reduction 
 at cu and fe , respectively . as is seen in figure 2 ,
the transition from pr  o is observed to go fairly slowly , and pr  f 
 is not directly observed .
cu is , however , not a good spectroscopic 
 reporter using optical difference spectroscopy , and spectral analysis 
 is focused on heme - a3 fe .
typically , the state f is not seen in the normal reaction cycle of cco but can 
 be generated by binding h2o2 to the reduced 
 state r ( fe and cu ) in the dnc . 

this shortcircuits the normal catalytic cycle , and the intermediate 
 state f slowly changes back to state o ( resting oxidized ) . in any event , the comparative 
 slowness of the observed pr  o transition may well be a consequence of the coupled proton 
 transfers and associated proton rearrangement .
( all calculations above 
 are with pw91 , unless noted otherwise . ) in tables 1 and 2 ( see also figure 4 , right ) , 
 we present structures and energies for 
 a number of states of the large model .
we focus on two arcs with olyp 
 potential , one encompassing the  true peroxo  states 
 ( 4  5  6 ) , 
 table 1 , and the second covering the last 1e reduction ending in the resting state o ( 112  12  13  14  1 ;
pr  f  o ) , table 2 . the size of the quantum cluster is increased to 205207 
 atoms by adding structural waters observed in the tiefenbrunn x - ray 
 structure and a glycine fragment that hydrogen bonds to internal waters 
 near the reaction site .
the larger size of the cluster allows us to 
 model the reaction geometries with less constraints .
cu 
 distance is no longer constrained to x - ray geometries as in work by 
 fee et al .
also , 
 the olyp potential used typically has a better balance in describing 
 the relative energies of different site spin states for fe and typically 
 yields more accurate spin coupling energies between transition - metal 
 sites compared to pw91 . in work by fee
( 2008 ) , we employed parallel spin on ( ferromagnetic coupling , f ) 
 fe and cu sites for ease of computation and kept the observed experimental 
 site spins over the reaction cycle .
by contrast , the newer calculations 
 take account of both f and af ( antiferromagnetic ) alignment of the 
 site spins , and different possible site spins as well ( see table 1 ) , and our recent paper . note that structure 4 of the larger model here does not have the water molecule 
 above 
 his376 .
the energies given in the af - coupled 
 states are broken - symmetry state energies .
the calculated properties given here include 
 energies ( e , offset by 28000 kcal mol ) , s expectation values , 
 net charges of the cluster ( q ) , the mulliken net 
 spin polarizations for the fe , cu , o1 , and o2 atoms , and the key geometric 
 data ( distances in angstroms ) .
f stands for ferromagnetic coupling 
 and af for antiferromagnetic coupling . in the following notes , ls 
 represents low spin and
is represents intermediate spin . formally adding two protons to state 112 , one on the h282 side chain and another one on fe = o
this is tautomer 1 ( t1 ) of 112_2h with lower energy ( see footnote d for tautomer 2 ) . 

h282h , y237 ) , and fe  ohh2o  cu(h376h , h282h , y237 ) .
this 
 is the second tautomer ( t2 ) of state 112_2h with higher energy .
this is formal state 12 + h2o , where h2o is scalar water on cu .
note 
 that in this larger model 
 no water molecule is added on the top of h376 .
spin projection 
 corrections are : 1.3 , 0.3 kcal 
 mol for 14_h2o ( af ) and 1_h2o ( af ) . in tables 1 and 2 ,
simple redox potentials without coupled protonation events can 
 be calculated with the equation4where the absolute standard hydrogen 
 electrode 
 energy value is taken as e(she ) = 4.34 
 ev = 100.1 kcal mol and eox and ered are the energies 
 of the oxidized and reduced states .
e(she ) 
 corresponds to the best measured solvation free energy of a proton 
 gsolv = 264.0 kcal mol , where the ionization threshold energy of a free 
 electron is taken as 0 , with no account of electron entropy ( see the appendix and references therein ) . similarly , gdeprot can be computed from adf energies ; we 
 take a typical e(zpe ) ( zpe = zero - point energy ) 
 for deprotonation of hydroxyl oxygen as about 8.7 kcal mol , and this gives the protonation energy correction 
 for single proton addition as 4.5 kcal mol at ph = 7 ( see the appendix , table a3 ) .
this is a dft correction , 2.9 kcal mol plus an empirical correction ( 1.6 kcal mol ) , to the adf energy differences e(ha ) 
e(a ) , from table 1 . for different tautomers in tables 1 and 2 ,
energy differences are directly 
 meaningful without correction , assuming only that e(zpe ) cancels for deprotonation / protonation . in table 1
, we include the small spin projection energy corrections 
 from the broken symmetry ( af ) to the proper pure spin singlet states , 
 in parentheses . from table 1 , state 4 , and ref ( 37 ) , 1e reduction of state 4 is very unfavorable , 
 redox potential e = 0.73 v vs she , 
 so cytochrome c ( or heme - b ) can not further reduce 
 the fe(o 
protonation of state 6 at the tyrosine 
 anion ( y237 ) is very unfavorable ( gprot = 7.2 kcal mol , about 
 5.3 ph units more acid than ph = 7 ) , which is important because the 
 tyrosine anion is well adapted to become a radical after 1e transfer to fe(ooh)cu , which would be suppressed if the neutral tyrosine ( yoh ) 
 were very stable .
the reaction pathway 4  52  5  62  6 has g = + 5.1 , 6.8 , 4.1 , and + 6.5 kcal mol and is similar to the energy profile for the smaller 
 model s2 . the protonation free energy for
5  62 4.1 kcal mol includes an empirical correction ( see the appendix , table a3 ) .
structurally , it is clear that 
 the hydroperoxide in state 6 is very important for breaking 
 the o  o bond because the activated af state has an o  o 
 distance of 1.49  .
the calculated f - coupled state 6 has an even longer o  o bond , 1.53  , and is only 4.3 
 kcal mol above af .
even more importantly , the 
 cu  o2 ( bond to hydroperoxo o atom ) bond is significantly shorter 
 in the f state , 2.35  compared to 2.66  in the af state , 
 and is on the path to a cu 
o1 bond is also close to that 
 expected for ferryl oxo in both f and af . also , the charged a3 rohoy hydrogen bond 
 is very short , oo = 2.83  in state 5 , and still short in state 6 but much longer for all 
 states with neutral tyr 
this is entirely consistent 
 with what we saw in ref ( 37 ) , where the x - ray structure of tiefenbrunn was proposed to have a charged a3 roh bond . 

turning now to the reaction pathway for the final e transfer pr  o , it is clear that obtaining fe  oh would be facilitated by having a nearby proton , but 
 in the earlier small model ( s2 ; figure 3 ) , 
 we proposed that h2o exited the reaction pocket directly 
 between fe and cu at this stage .
instead , we now retain this scalar 
 h2o in states 12_h2o , 13_h2o , 14_h2o , and 1_h2o ( f and o ) . in place of state 112 in figure 3 , we now add 
 2h to form two tautomeric states ( the first two lines 
 in table 2 ) . we find that the addition of these 
 two protons is very favorable and
these two states are related by a proton shift from y237 
 ( yoh ) to replace the proton shifted from h2o  cu to fe = o .
our calculations indicate that 
 to some extent an electron may accompany this proton transfer onto 
 the fe , but this state is a resonance mixture of valence isomers . 

the proton - shifted tautomer 112_2h ( tautomer 1 ; table 2 , line 1 ) is lower in energy than 112_2h ( tautomer 2 ) by about 5 kcal mol , while upon 
 1e reduction , the cu state is predicted 
 to be lower , by about 4 kcal mol ( 0.17 ev ) .
the 
 corresponding redox potential is about 0.57 v ( reduction of cu ) or 
 0.40 v ( reduction of fe ) .
the actual reduction process may not follow 
 the lowest energies because it is favorable to preserve the proton 
 shift to form fe  oh once this is formed . 

further , kinetic measurements of farver , fee , and co - workers implicate total reorganization energies in the 
 range of 1.01.5 ev for e transfer between 
 heme - b and heme - a3 fe .
both the driving force and the reorganization 
 energies then are important for the timing of e transfer .
the fe  ohh2o  cu state ( 13_h2o ) will provide 
 a focal point for the 
 last part of the reaction cycle ( second arc ) extending from 112_2h  13_h2o  14_h2o  1_h2o . in figure 8 , we present the energy profile from the last 1e reduction to the last proton pumping as assumed within 
 the model cycle to the final reset to the initial state 1 .
we also compare the energetic pathway with one where the scalar 
 h2o on cu has dissociated ( figure 9 ) .
however , the presence of h2o on 
 cu facilitates proton transfer between cu  h2o and fe = o or fe  oh . further , there 
 is recent x - ray structural evidence for two waters or oh  h2o between fe and cu in the resting state o. we do find 
 that g(h2o dissociation ) = 9 
 kcal mol ( olyp ) , favoring dissociation , and less , 
 0.6 kcal mol ( pw91 ) and + 3.2 kcal mol ( b3lyp * ) , but based on the active site structure , 
 kinetic trapping for the cu - bound h2o is likely . 

two waters are probably released after 2e reduction 
 of state 1_h2o  2h ( o  r ) with a lowering 
 of the free energy .
plots of g ( kcal mol ) relative to state 13_h2o along the trajectory 
 from 112_2h ( lower 
 energy tautomer 1 ) to 1_h2o in the cycle with 
 the scalar water on cu .
the pw91 and b3lyp * energies 
 were obtained for the smaller model ( see table s2 in the supporting information , si ) .
olyp calculations 
 were performed on the larger models ( tables 2 and a3 ) .
plots of g ( kcal mol ) relative to state 13 along the trajectory 
 from 112_2h to 1 in the cycle without the scalar water on cu .
the pw91 and b3lyp * energies were obtained for the smaller model 
 ( see tables s2 and s3 in the si ) .
olyp 
 calculations were performed on the larger models ( tables 3 and a3 ) .
the calculated properties given here include 
 energies ( e in kcal mol ) , s expectation values , net charges of the cluster 
 ( q ) , and the mulliken net spin polarizations for 
 fe and cu sites .
note that in this larger model no 
 water molecule is added on the top of h376 .
returning to the energy profiles in figure 8 , the calculated g values for 1_h2o relative to state 13_h2o are + 14.0 and 
 + 15.6 kcal mol for the large olyp model ( without 
 and with the empirical deprotonation correction ) and + 19.0 and + 18.3 
 kcal mol for pw91 and b3lyp*. in figure 9 , the corresponding energies are + 13.6 , + 15.2 , + 21.2 , 
 and + 14.8 kcal mol for olyp , olypcorr , pw91 , and b3lyp*. these are not high energy differences for proton 
 pumping considering that a + 5.5 kcal mol pumping 
 cost ( for ph = 7  ph = 3 ) is included . in light of the experimental structural , kinetics , 
 and mutagenesis data for ba3 from tt , 
 the idea that there is a largely common pathway for scalar and vector 
 protons and that this derives from the kb pathway should 
 not be surprising .
the 
 first , mentioned earlier ( see figure 6 ) , is 
 at a3-roh and the adjacent tyr237 .
this bifurcation point 
 is mainly utilized as needed to bypass tyr237 when it is in a radical 
 state , and a proton needs to be passed on , especially a chemical proton 
 entering the reaction chamber between fe and cu at that stage .
the 
 other bifurcation point , which we think is much more common in the 
 reaction path , occurs at his282 . from this location
, a proton on his282 
 ( neutral ) can move onto a cu - bound hydroxo or peroxo 
 ( scalar proton ) , with the different tautomers being close in energy 
 from our dft calculations . alternatively
, a vector proton can move 
 onto the exit position ( pls ) and proceed on the exit pathway . specifically , 
 starting with his282 , a proton enters typically 
 from tyr237 to generate his282 neutral .
this will weaken the hydrogen 
 bond to threonine ( t302 ) , allowing its side chain to rotate and deposit 
 a proton on his376 or more probably in the nearby water pool ( see 
 figure 4 , large model , right ) .
( this location 
 is near propionate a , as previously proposed for the pls location . ) 
 above his376 in figures 3 and 4 is an asp287arg225 salt bridge .
indicate that asp287 is probably important for 
 efficient proton pumping ; these results are still incomplete , and 
 only one mutation has been examined for arg225 , which is so far inconclusive . 

we propose that the asp287arg225 salt bridge is potentially 
 a simple electrostatic switch or gate , which could be opened by a 
 strongly positive electrostatic potential nearby , for example , by 
 having a proton in the adjacent water pool .
arg salt bridge could be paid when the proton 
 enters the water pool or during transit .
also , the local electric 
 field of this proton ( and from the surrounding charge distribution ) 
 possibly acts in opposition to the long - range electric field from 
 the membrane potential .
on the basis of our earlier work on the catalytic cycle of the 
 cytochrome ba3 dnc , we have found an improved reaction 
 path by modifying the sequence of proton uptake and proton - transfer 
 events and examining alternative tautomeric states .
the new 14-step 
 reaction cycle results in a much  smoother  energy pathway 
 for the catalytic reaction cycle , comparing parts a and b of figure 5 with lower barriers between intermediates .
the 
 entire pathway from state 3  92 has low - energy barriers and proceeds downhill . 

we have also tracked the dft - calculated dipole moments of peroxo and 
 hydroperoxo intermediates after o2 binding ( figure 7 ) .
here we find that there are very substantial 
 changes in the magnitude and direction of the dipole moment of the 
 dnc with tautomeric shifts , and a progressive increase in the positive 
 electrostatic potential near his376 ( in addition to that due to protonation 
 of his376 itself ) .
we then constructed large model structures and 
 evaluated geometries and energies ( olyp potential ) for two arcs of 
 the cycle , one for  true peroxo  states 4  5  6 and the other for 
 the last 1e reduction from state 112  1 ( spectroscopic 
 states pr  o ) .
important results from these dft calculations are presented in 
 figures 8 and 9 and 
 tables 2 and 3 .
we have 
 tested the effect of keeping the scalar water bound to cu in state 112 through the remainder 
 of the catalytic cycle both for the large model ( olyp potential ) and 
 for the smaller model ( pw91 and b3lyp * ) potentials .
the energy profiles 
 in both figures 8 and 9 are similar , but the water on cu facilitates protonation 
 of fe - oxo .
the energy barriers for the final proton - pumping step 13  1 are about 1516 kcal mol for olyp , large model , and somewhat higher for b3lyp * 
 ( 1518 kcal mol for b3lyp * , small model ) 
 and for pw91 ( 1921 kcal mol ) . these results 
 include an assumed 5.5 kcal mol cost for proton 
 pumping at one step .
further , we discuss a potential proton exit pathway 
 involving breaking of an asp 
the exiting proton 
 would be carried or transferred via a water pool from inside to outside . 

earlier on the vector proton pathway , we have proposed that his282 
 and thr302 play an important role .
there are many important 
 issues still to be understood in the reaction 
 cycle and proton - pumping mechanism of cco both in ba3 class 
 enzymes and more broadly including also aa3 enzymes ( bacterial 
 and mitochondrial ) .
we have not yet addressed the kinetics in detail , 
 including transition states , effects of sequence differences , and 
 mutational effects .
more needs to be done to integrate 
 the kb path and the other redox centers into the models 
 presented here .
the scalar water exit pathway is also essential for 
 proper analysis . in general , however , we expect that the structural 
 and energetic maps of the reaction cycle in the dnc that we have generated 
 will contribute to a better representation of the coupling of electron 
 and proton transfer to proton pumping in cco .
 after 
 a summary of the problem of coupling electron and proton 
 transfer to proton pumping in cytochrome c oxidase , 
 we present the results of our earlier and recent density functional 
 theory calculations for the dinuclear fe - a3cub reaction center in this enzyme . 
 a specific catalytic reaction 
 wheel diagram is constructed from the calculations , based on the structures 
 and relative energies of the intermediate states of the reaction cycle . 
 a larger family of tautomers / protonation states is generated compared 
 to our earlier work , and a new lowest - energy pathway is proposed . 
 
 the entire reaction cycle is calculated for the new smaller model 
 ( about 185190 atoms ) , and two selected arcs of the wheel are 
 chosen for calculations using a larger model ( about 205 atoms ) . 
 we 
 compare the structural and redox energetics and protonation calculations 
 with available experimental data . 
 the reaction cycle map that we have 
 built is positioned for further improvement and testing against experiment . 
Introduction
Biochemical Background
Electron Flow within CcO
Reaction Cycle
of the DNC in CcO
Objectives of the Theoretical/Computational
Cycle
Models and Methods: Catalytic Wheel
Catalytic Reaction Cycle Results and Discussion
Conclusions