in recent years , it has become widely 
 accepted that catalytic promiscuity , i.e. , the ability of many enzymes 
 to catalyze the turnover of multiple chemically distinct substrates , 
 plays a key role in the evolution of new functions , allowing for rapid 
 responses to environmental changes .
furthermore , 
 interest in this phenomenon has exploded as it has been increasingly 
 shown to be a powerful tool for gaining knowledge not just into the 
 process of natural functional evolution , but also as a factor that can be exploited in effective artificial 
 enzyme design .
such 
 promiscuity appears to be highly pronounced among many phosphotransferases , 
 such as the recently evolved bacterial phosphotriesterase ( pte ) , serum paraoxonase 1 ( pon1 ) , and members of the alkaline phosphatase ( ap ) superfamily , to name a few examples .
this latter superfamily has additionally 
 played a central role as a model system for understanding enzyme catalytic 
 promiscuity , i.e. , the ability of a given enzyme to catalyze more 
 than one distinct chemical reaction .
the characterized members 
 of the ap superfamily are highly promiscuous 
 hydrolytic enzymes capable of interchangeable cleavage of p  o , 
 s  o , and p  c bonds .
that is , they 
 have been shown to catalyze the hydrolysis of a range of substrates 
 that differ in the nature of their ts solvation and protonation patterns , 
 and thus in their requirements for efficient catalysis ( see discussion 
 in refs ( 1618 ) ) .
furthermore , all known ap superfamily 
 members are metallohydrolases that employ similar catalytic scaffolds , 
 which are comprised of at least one divalent metal ion in their respective 
 active sites ( figure 1 ) .
this metal ion plays 
 an important role in activating the nucleophile , which is generally 
 thought to be an alcohol or alkoxide depending on the particular superfamily 
 member , by increasing the concentration 
 of its active deprotonated form . additionally , while there are a number 
 of similarities between different known members of the superfamily , 
 there are also broad differences in their metal requirements , overall 
 structures , and specific choice of nucleophile , which can in turn 
 be linked to changes in specificity patterns .
despite these differences , a particular hallmark of this superfamily 
 is crosswise - promiscuity , in that the native substrate for one member 
 of the superfamily is often a promiscuous substrate for another , in some cases with high ( and almost comparable ) proficiencies toward 
 both the native and promiscuous substrates . as a result ,
these enzymes provide a perfect 
 showcase to generate a systematic roadmap of the process of functional 
 evolution within an enzyme superfamily , as well as a broader model 
 system for understanding the evolution of phosphohydrolase activity .
an active site comparison of selected members of the ap 
 superfamily . 
 shown here are the active sites of ( a ) rhizobium leguminosarum phosphonate monoesterase ( pdb code 2vqr ) , ( b ) escherichia coli alkaline phosphatase ( 1alk ) , ( c ) pseudomonas aeruginosa arylsulfatase ( 1hdh ) and ( d ) xanthomonas 
 axonopodis nucleotide pyrophosphatase / phosphodiesterase 
 ( 2gsn ) .
the figure highlights the presence of divalent 
 metal ions as well as the conservation of some of the residues surrounding 
 them . among the different superfamily 
 members ,
the name giving member 
 ap as well as the very closely related 
 nucleotide pyrophosphatase / phosphodiesterase ( npp ) have been the subject of extensive scrutiny .
a lesser - studied 
 subset of enzymes that stand out in this superfamily are those classified 
 as phosphonate monoester hydrolases ( pmhs ) , such as the enzymes from rhizobium leguminosarum ( rlpmh ) and burkholderia caryophylli ( bcpmh ) .
these highly 
 promiscuous enzymes efficiently promote the hydrolysis of at least 
 five different substrate classes ( figure 2 ) 
 and stand out in particular as their promiscuous phosphodiesterase 
 activity is almost as efficient as their native phosphonate monoesterase 
 activity ( table s1 ) ; note 
 that the pte activity reported in this work is ambiguous , as discussed 
 in the results and discussion . moreover ,
these 
 pmhs provide the first example of biological pmh activity and are 
 the only currently known enzyme capable of catalyzing the hydrolysis 
 of xenobiotic sulfonate esters by direct s 
note also that both enzymes are large homo tetramers with 56 
 kda subunits and have extremely large binding pockets ( 10 
  20  wide and 15  deep ) .
therefore , one would assume that such enzymes could easily accommodate 
 a range of substrates of different shapes and sizes .
perhaps unsurprisingly , 
 therefore , both pmhs are moderately efficient catalysts for the hydrolysis 
 of the compounds shown in figure 2 ( kcat / km values in 
 the range of 1010 , see table s1 ) and , in the case of rlpmh , apparently only marginally affected by mutations of the key 
 active site residues with presumably multiple catalytic backups present 
 in the active site ( table s2 ) that can 
 take over the role of the mutated residues .
a closely evolutionarily 
 related enzyme in the ap superfamily is 
 the arylsulfatase from pseudomonas aeruginosa ( pas ) ( figure 1c ) .
this enzyme only shares about 27% sequence similarity to rlpmh but has high structural similarity , in that 64% of 
 the residues between the two enzymes structurally align with an rmsd 
 of 2.54  .
this enzyme also has recently 
 been the subject of extensive experimental and 
 computational studies .
both pas and the pmhs 
 contain a mononuclear metal center with distorted octahedral conformation , 
 which is most likely mn in the pmhs and 
 ca in pas .
in addition , 
 all three enzymes use an unusual geminal diol nucleophile ( figure 1 ) , a feature they share with all known sulfatases .
this noncanonical residue is a post - translationally modified 
 cysteine or serine , which is first converted to an aldehyde and then 
 hydrated to give rise to its active form . despite these apparent similarities , the two pmhs and pas have very 
 different specificity patterns .
that is , pmhs are phosphonate monoesterases , 
 while pas is primarily a sulfatase , although all three enzymes have 
 relatively low discrimination between native and promiscuous substrates . in contrast ,
other superfamily members such as ap and npp have dinuclear 
 zinc centers in their catalytic sites ( ap also possesses a third metal 
 ion that appears to play an important role in determining the activity ) and utilize ionized serine or threonine residues 
 as nucleophiles , respectively ( figure 1 ) .
thus , a direct atomic - level comparison between 
 individual ap superfamily members and also related promiscuous phosphatases 
 can provide better and broader understanding of the features that 
 drive selectivity and promiscuity in these highly multifunctional 
 systems .
structure of rlpmh ( pdb i d : 2vqr ) and the corresponding 
 substrates studied in this work . both rlpmh and bcpmh
are dimers of dimers , in 
 which the monomeric units of each dimer communicate with its corresponding 
 oligomeric unit through the c - terminal loop highlighted in this figure 
 ( which is in turn an adaptation from an analogous figure presented 
 in ref ( 12 ) ) .
this 
 loop reaches into the adjacent active site , helping position key catalytic 
 residues .
the substrates studied in this 
 work are phenyl p - nitrophenyl phosphonate ( ppp ) , 
 ethyl p - nitrophenyl phosphate ( pet ) , p - nitrophenyl sulfate ( pns ) , phenyl p - nitrophenyl 
 sulfonate ( pps ) , and the p - nitrophenyl phosphate 
 monoanion ( pnph ) . in the present work , 
 we have performed an extensive number of empirical 
 valence bond ( evb ) simulations ( total simulation 
 time of 4 s ) of both the native and several characterized 
 promiscuous activities of bcpmh and rlpmh , reproducing key experimental observables such as activation 
 barriers , qualitative predictions from the ph - rate profiles for bcpmh activity , and the effect of mutations on rlpmh activity . we demonstrate that , despite 
 their broad promiscuity , the pmhs studied in this work hydrolyze all 
 substrates through a unified mechanism with similar substrate binding 
 positions , transition states , and electrostatic contributions to transition - state 
 stabilization . additionally , we showcase the importance of compensatory 
 and cooperative electrostatic effects , which allow for an electrostatically 
 flexible active site environment that can accommodate a range of substrates 
 with different charge distributions , transition - state geometries , 
 and requirements for efficient catalysis . finally , in order 
 to test whether these observations are general 
 to other members of the superfamily , we provide a detailed comparison 
 of a range of ap superfamily members , in terms of active site shape , 
 volume , and polarity . from this analysis
we find a strong correlation 
 between these properties and both substrate charge preference and 
 number of known promiscuous activities , once again emphasizing the 
 central role of the electrostatic environment of the active site in 
 determining enzyme specificity and promiscuity .
it is commonly accepted 
 that enzymes achieve their tremendous catalytic proficiencies through 
 an exquisite network of interactions that preferentially stabilize 
 their transition states over their ground states , and it has been argued that this is achieved through preorganization 
 of the catalytic residues into an optimal conformation for transition - state 
 stabilization . this has been demonstrated for 
 a wide range of systems through both experimental and computational 
 work .
we illustrate here that while having an optimal electrostatic 
 environment is clearly important to the catalysis of these enzymes 
 toward individual substrates , one should also take into account the 
 cooperativity between these residues , where the effect of the combined 
 electrostatic environment from all relevant residues on the transition 
 state stabilization is greater than the effect of each residue determined 
 individually .
we demonstrate that this cooperativity renders the active 
 site electrostatic environment sufficiently flexible to accommodate 
 a broader range of substrates with different electrostatic needs for 
 efficient catalysis ( without necessarily altering either substrate 
 binding position or enzyme conformation ) .
additionally , our comparative 
 analysis of different alkaline phosphatases shows that the higher 
 the number of polar active side residues , the greater the propensity 
 toward catalytic promiscuity .
this highlights the importance of such 
 cooperative electrostatic interactions as a common feature to functional 
 evolution among members of the ap superfamily , illustrating the power of subtle amino acid substitutions 
 to drive very different solutions for the same chemical problem .
initial structures for both rlpmh and bcpmh ( 1.42 and 2.40  resolution , 
 respectively ) were obtained from the protein data bank ( accession codes 2vqr and 2w8s ) .
as the deposited structure for rlpmh contains only the monomeric unit without the transformation 
 matrix , the structure of the full tetramer was obtained directly from 
 the authors .
potential flips of histidine , 
 asparagine , and glutamine side chains were evaluated using the molprobity 
 server , and those suggested by the software 
 were applied to the structure . in all cases ,
the substrates were placed 
 manually in the active site in such a way to optimize nonbonded interactions 
 between the substrate and nearby amino acid side chains , including 
 charge 
structures for the corresponding q13a , n78a , y105a , t107a , h218a , 
 and k337a variants presented in ref ( 8) were generated by manual truncation of the relevant 
 side chains starting from the wild - type crystal structure , and structures 
 were equilibrated using the same protocol as for the wild - type enzymes 
 in order to allow the active site to adapt to the perturbation introduced .
both pmhs are metalloenzymes with a single metal per active site 
 of the tetramer ( 4 total ) , and the most likely candidate for this 
 role has been identified as being a divalent manganese ion .
we recently presented a set of force - field - independent parameters 
 to describe a range of alkali earth and transition - metal centers based on qvist and warshel s original 
 cationic dummy model , which describes 
 the metal as a delocalized charge spread over a number of dummy atoms 
 placed around the metal center ( in this case six particles in octahedral 
 coordination , as shown in figure s1 ) .
these 
 particles are bonded to the central atom and to each other , and the 
 frame is allowed to freely rotate in its coordination sphere without 
 the need for external constraints or artificial bonds .
we demonstrated that this model also allows one to capture subtle 
 structural effects upon metal substitution without the need for the 
 artificial restraints that need to be imposed in a fully bonded model , 
 while simultaneously capturing key electrostatic properties of the 
 metal center .
we have successfully used our ca model 
 in simulations of the selectivity of pon1 , and the mn model presented in our original paper has been used in the present work to describe 
 the catalytic metal center in the pmhs .
all relevant reactions 
 were simulated in the active sites of both 
 enzyme species and in a 24  water droplet , in order to quantify 
 the catalytic effect of the enzyme compared to background reaction 
 in aqueous solution . to model the reaction in solution , we used truncated 
 residues to model the nucleophile ( acetaldehyde hydrate as a model 
 for the formylglycine ) and the relevant general acids ( ethylamine 
 and ethylimidazole for lys and his , respectively ) . in the enzyme simulations , 

one of the main computational difficulties encountered comes from 
 the fact that truncating the 16 c - terminal residues of rlpmh causes the enzyme to lose its tetrameric structure , with a corresponding 
 loss of activity .
this strongly suggests that interactions at the 
 subunit interfaces can be important to catalysis , as can also be observed 
 from the protrusion of the interfacial loop almost into the active 
 site of the adjacent subunit ( see figure 2 ) . 

thus , it is necessary to include the entire ( 2056 amino acid ) tetramer , 
 which creates substantial computational cost . to simplify this 
 problem and reduce computational cost ,
the system 
 was divided into three layers : the evb ( reacting ) atoms , an active 
 region encompassing all residues within a 24  sphere of the 
 reacting atoms centered at the metal center , and an external layer 
 in which the remainder of the system was present , but the atoms were 
 constrained to their crystallographic positions ( as is commonly done 
 in similar studies , see e.g. , refs ( 24 and 45 ) ) .
the simulation sphere encompassing the active region was centered 
 on the catalytic mn ion , and all crystallographic water 
 molecules within 18  of this center were retained in our simulations , 
 with the exception of any crystal waters clashing directly with the 
 substrate once it was placed in the active site .
the solvation sphere 
 was then completed and extended to 24  using tip3p water molecules subjected to the surface constraint 
 all atom solvent ( scaas ) spherical boundary conditions .
a 10 kcalmol harmonic restraint was applied to the outer layer 
 of the active region and associated solvent molecules ( 15% , 3.6  ) , 
 in order to ease the transition between the active and constrained 
 regions , which is why only an 18  of crystallographic water 
 molecules were retained for the simulation .
all forces on the constrained 
 atoms were set to zero , in order to prevent them from distorting the 
 dynamics of the active region .
ionizable residues within 18 
  of the center were ionized during the course of the simulation , 
 leading to a total system charge of 1 ( without including the 
 substrate ) .
the protonation states of histidine side chains were investigated 
 using the molprobity server , propka 3.1 , and by visual inspection .
all other residues , in particular those 
 outside the active region , were set to their neutral form for system 
 stability .
the mn ions in the adjacent monomeric units 
 ( the positions of which were kept constrained ) were removed in order 
 to avoid the presence of residual charge outside the simulation sphere 
 ( we note that the adjacent active sites all fall within the constrained 
 external layer and all surrounding residues are therefore not allowed 
 to move ) . in contrast , the catalytic metal center in the active region 
 was described using a 7-pointed dummy model with distributed charges 
 as described above .
all molecular dynamics ( md ) and evb simulations 
 in this work were 
 conducted using the opls - aa force field implemented in the q simulation package ( version 5.0.6 ) . for the substrate and nucleophile ,
opls - aa compatible 
 force field parameters were generated with macromodel 9.1 ( opls - aa 
 force field , 2001 , schrdinger llc ) .
the only exceptions were the force field parameters for the carbon 
 and oxygen of the deprotonated geminal diol , which were available 
 in the literature and obtained from ref ( 53 ) .
partial charges for the reacting atoms were 
 generated at the hf/6 - 31 g * level of theory using the gaussian 09 simulation 
 package , followed by the standard resp 
 procedure .
all the simulations 
 performed herein used time steps of 1 fs , while the temperatures of 
 the system were regulated using the berendsen thermostat ( with a 100 fs bath relaxation time ) .
the systems 
 were initially heated from 1 to 300 k over a short 80 ps simulation , 
 applying a 200 kcalmol harmonic force constant on the solute atoms to restrain them to 
 their crystallographic positions .
this allowed for the solvent molecules 
 to equilibrate around the protein and the removal of initial contacts 
 due to substrate placement .
the system was then cooled down to 5 k 
 for another 10 ps and then gradually heated to 300 k for 90 ps of 
 simulation time , while the force constants of the harmonic restraint 
 were gradually decreased from 200 to 0.5 kcalmol .
subsequently , a 5 ns equilibration 
 was performed at 300 k for both wild - type and mutant enzyme simulations 
 ( 300 ps for the reference reaction in solution ) using a 0.5 kcalmol position restraint 
 on the substrate atoms , the side chain of the nucleophile , the catalytic 
 metal center , and the side chain of the general acid ( h218 or k337 , 
 depending on the mechanism being considered ) to keep the reacting 
 atoms in place .
an rmsd plot of the active monomer for the wild - type 
 enzyme and each enzyme variant is shown in figures 
 s2 and s3 .
as shown in this figure , due to the fixed excluded 
 region , these systems equilibrated rapidly , with rmsd of < 0.5 
  from the reference crystal structure . after the final equilibration 
 step , we ran an additional 500 ps of molecular dynamics , during which 
 10 snapshots of the whole system were taken every 50 ps to be used 
 as starting points for subsequent evb simulations . finally , although 
 we remained as faithful as possible to a fully nonbonded model for 
 the catalytic metal center , we introduced an angle parameter ( 50 kcalmolrad , equilibrium angle 180 ) 
 between the center of the mn dummy model and the residue 
 d324 ( mn  ometal  ofree , where ometal corresponds to the oxygen atom closest 
 to the mn , and ofree the one not coordinated 
 to it ) , which would otherwise become bidentately coordinate to the 
 metal center and make the active site unstable
as can be seen from 
 the results and discussion , despite the inclusion 
 of this extra parameter , we are able to systematically reproduce the 
 activation energies of both wild - type and mutant forms of these pmhs 
 with different substrates with good agreement to experimental data . our methodology 
 of choice in this work to model chemical reactivity was the evb approach 
 of warshel and co - workers .
this is an empirically - based 
 multiscale valence - bond / molecular mechanics approach that is fast 
 enough to allow for the extensive sampling required to obtain convergent 
 free energies for complex biochemical processes , while having a proven 
 track record as a powerful tool for quantifying and rationalizing 
 the catalytic power of native and mutant enzymes .
all evb calculations were performed using the standard evb free 
 energy perturbation / umbrella sampling ( evb - fep / us ) procedure outlined 
 in refs ( 33 and 57 ) , as implemented 
 in the q simulation package .
the 
 reaction under study was described in terms of two valence bond structures , 
 as illustrated in section s4 of the supporting 
 information .
it should be pointed out that as all atoms in 
 the two valence bond states are treated using the same force field , 
 the only differences between the reacting ( evb ) and nonreacting atoms 
 are the use of morse rather than harmonic potentials to describe bonds 
 that are being broken and formed during the reaction ( see the supporting information ) and the fact that unlike 
 the rest of the protein , the evb atoms do not have a cutoff for calculation 
 of the nonbonded interactions .
all evb - fep / us simulations were performed 
 at 300 k , using 51 mapping windows of 200 ps per window , resulting 
 in 10.2 ns of simulation time for each individual trajectory , sampling 
 over 10 starting conformations per system ( 102 ns per system ) and 
 4 s cumulative simulation time for all systems studied 
 in this work .
all md and evb simulations were performed using a 1 
 fs time step , and long - range effects were treated using the local 
 reaction field ( lrf ) approach . finally , as outlined above , we also modeled the corresponding uncatalyzed 
 reaction for each substrate of interest in this work , as we needed 
 these calculations not only for the calibration of the evb parameters , 
 but also to compare the reactions for different environments .
coordinates 
 for each system were based on the equilibrated enzyme system , but 
 in the absence of the enzyme itself , and the reactions were modeled 
 using the relevant substrate as well as acetaldehyde and protonated 
 ethylamine as models for the nucleophile and the general acid , as 
 described in the initial system setup section . 

all equilibration and evb protocols were the same as for the full 
 enzyme system , with the exception that the background reaction in 
 the absence of the enzyme was only equilibrated for 300 ps rather 
 than 5 ns .
as with the corresponding enzymatic reactions , a weak position 
 restraint of 0.5 kcalmol was placed on all solute atoms ( nucleophile , substrate , 
 and model for general acid ) in order to keep the reacting fragments 
 in the center of the simulation sphere .
this weak restraint is sufficient 
 to keep the nitrogen atom of the general acid within 3.5  of 
 the leaving group oxygen throughout the 300 ps equilibration of the 
 background reaction , in part due to electrostatic interactions between 
 the charge on the general acid and the substrate .
the relevant background 
 reaction was calibrated based on estimations using experimental data , 
 as described in detail in the supporting information .
furthermore , the parameters describing the relative positions of 
 the vb parabolas and the coupling between them were then transferred 
 unchanged to the enzyme in order to be able to quantify 
 and correctly predict the catalytic effect of wild - type and mutant 
 enzymes .
( a ) overlay of the active sites in rlpmh and pas , 
 illustrating conservation of active site structure between the two 
 enzymes .
( b ) a simplified version of the proposed catalytic mechanism 
 for both pmhs considered in this work , based on refs ( 8 and 12 ) . since the catalytic metal is 
 suggested to be mn , which is a hard lewis acid , the nucleophile 
 could be stable as an alkoxide , in agreement with the ph - rate profiles 
 shown in figure s4 .
a unique feature of the pmhs being considered 
 in the present work 
 is that they are the only nonsulfatase enzymes known to date to possess 
 a post - translational modification from a cysteine to an aldehyde ( formylglycine , 
 fgly ) .
the current 
 proposed mechanism for both native and 
 promiscuous pmh activities is shown in figure 3 . in a first step ( i  ii ) ,
hydration 
 of the post - translationally modified aldehyde yields a reactive geminal 
 diol , which can act as a nucleophile .
this geminal diol is activated 
 by the catalytic metal center and exists in its alkoxide form . following 
 substrate binding ( ii  iii ) , this 
 geminal diol then attacks the phosphorus / sulfur center ( iii  iv ) of the relevant substrate ( figure 2 ) to give rise to a hemiacetal intermediate ( iv ) . in the final step ( iv  i )
, this intermediate is hydrolyzed by hemiacetal cleavage to regenerate 
 the aldehyde and yield the final product .
the two pmhs considered 
 in this work show an absolute dependence on divalent metal ions , with 
 the most likely candidate for fulfilling this role being mn , based on experimental data presented in refs ( 8 and 12 ) .
a transition metal would be 
 expected to substantially decrease the pka of the metal - bound nucleophile to yield an alkoxide , as also suggested 
 by the acid limb of the ph - rate profiles shown in figure 2 of ref ( 12 ) ( reproduced as figure s4 ) , which most likely corresponds to 
 the deprotonated nucleophile ( see discussion in ref ( 12 ) ) .
the ph - rate profiles , 
 which are coincidental for all substrates except the phosphate triester , 
 also suggest the involvement of an acid catalyst , most likely either 
 h218 or k337 ( see also figures 3 and s4 ) .
it has 
 been argued that steps iv  i of 
 figure 3 can play an important role in 
 facilitating promiscuity .
specifically , 
 harnessing hemiacetal cleavage allows for a common mechanism irrespective 
 of the functional group used in the intermediate , while simultaneously providing a thermodynamically less 
 challenging route to facilitate c  o cleavage , compared to the 
 repeated cleavage of an extremely stable p(s)o bond .
however , kinetic data on base - catalyzed hemiacetal 
 cleavage in aqueous solution demonstrate that this reaction is extremely 
 fast .
additionally , as all substrates 
 will be broken down by a common mechanism through a common intermediate , 
 the selectivity will be already determined in steps iii  iv , which is also therefore the focus of the 
 present work ( figure 3 ) .
our mechanistic 
 model assumes an anionic nucleophile and general 
 acid catalysis from either k337 or h218 to protonate the departing 
 leaving group . as discussed below , in this work k337
was chosen as 
 the general acid based on empirical pka calculations and experimental data .
that is , the experimental ph - rate 
 profiles suggest a two - pke model , with a pke1 of 7.07.2 
 ( 5.8 for the sulfate monoester ) and a pke2 of 7.58.1 ( see figure s4 ) .
the 
 first pka is likely to correspond to the 
 nucleophile , contributing to catalysis in its deprotonated form as 
 discussed above , and the second pka to 
 the general acid .
the pke2 , which is very 
 close to the pka of around 8 suggested 
 for k337 by propka , led to the choice of this residue as the putative 
 general acid , as also suggested by refs ( 8 and 12 ) .
the only exception to this model 
 is the p - nitrophenyl phosphate monoester , of which 
 the dianionic form will be extremely resistant to attack by an anionic 
 nucleophile ( see ref ( 62 ) ) .
however , the pka of the already basic 
 nonbridging oxygens of this substrate ( pka  5.0 ) is likely to be substantially 
 elevated due to the close proximity of the anionic nucleophile .
this , 
 in turn raises the possibility that this substrate binds as a monoanion , 
 as has already been demonstrated by simulations , for example , for 
 protein tyrosine phosphatase 1b .
note 
 also that , as shown in figure s4 and ref ( 12 ) , the monoanionic sulfate 
 and dianionic phosphate monoesters give rise to very different ph - rate 
 profiles that not only have different slopes but also are shifted 
 by 2 ph units .
thus , we have herein considered a mechanism involving 
 an anionic nucleophile attacking a monoanion phosphate , which yields 
 excellent agreement with experiment as discussed below . calculated 
 and
experimentally derived activation energies for the 
 enzyme - catalyzed reactions of the five substrates studied here by 
 the wild - type forms of ( a ) rlpmh and ( b ) bcpmh . in the present work
we have not examined phosphate triester 
 hydrolysis , 
 which shows a very different kcat / km ph - rate profile to all other substrates studied 
 ( figure s4 ) .
the inverted ph - rate profile 
 observed for this substrate suggests either the involvement of a completely 
 different set of residues or a completely different mechanism of catalysis . 

additionally , bcpmh shows extremely poor activity 
 toward this substrate ( kcat / km of 1.6  10 ms ) , which is actually slower than the corresponding 
 uncatalyzed alkaline hydrolysis of the model substrate paraoxon . taken together
, this suggests that the hydrolytic 
 mechanism of this substrate , if it at all binds in the same active 
 site , is impossible to prove conclusively through calculations due 
 to lack of concrete experimental data . as mentioned before , 
 the reactions examined in this work correspond 
 to the third step ( iii  iv ) of the 
 catalytic cycle shown in figure 3 . since experiments 
 show that the hemiacetal cleavage is a fast step , we focused only 
 on this second step , which is the most chemically challenging step 
 of the cycle , being thus the one related to the measured kinetic parameters . 

figure 4 shows a comparison between our calculated 
 and , where available , experimental activation free energies ( derived 
 from kcat , which provides an upper limit 
 for the reaction rate ) .
, 
 it can be seen that the model used in the present work reproduces 
 the experimental activation free energies within an accuracy of 1.7 
 kcalmol for all substrates .
it has additionally 
 been argued that the pmhs considered in 
 this work can accept both diesters and phosphonates with such high 
 proficiency in the same active site due to similar geometrical and 
 steric demands for the respective substrates and transition states . 
 to probe this further ,
we have examined transition - state geometries 
 for all uncatalyzed and enzyme - catalyzed reactions considered in this 
 work .
table 2 shows a comparison of p(s)o 
 distances to the oxygen atoms of the incoming nucleophile and departing 
 leaving group for all substrates and reactions .
representative transition - state 
 structures in the bcpmh active site are also illustrated 
 in figure 5 . from these results , it can be 
 seen that the pmhs hydrolyze all substrates through a unified mechanism 
 with similar substrate binding positions and transition states . with 
 the exception of the phosphonate
, little change is seen in transition - state 
 geometry upon moving from aqueous solution to the enzyme active sites , 
 in agreement with related experimental work by herschlag and co - workers , as well as theoretical analysis by hou and cui , on alkaline phosphatase . even in the case of 
 the phosphonate ,
the overall transition - state size ( considering the 
 distance between onuc  olg ) stays very 
 similar , and the main change is that the symmetry of the transition 
 states changes , with p  onuc becoming slightly elongated 
 and p  olg slightly compressed compared to the corresponding 
 uncatalyzed reaction .
hence , as suggested in previous works for alkaline phosphatase , we find very little effect on the transition - state 
 geometries of moving to the enzyme active when compared with those 
 obtained through modeling the corresponding uncatalyzed reaction in 
 aqueous solution .
all 
 energies are given in kcalmol and are averages 
 and standard deviations based on 10 individual evb simulations generated 
 from different starting structures , as outlined in the methodology section .
g(expt . ) corresponds to 
 experimental values of the enzyme - catalyzed 
 reaction , based on the kinetic data presented in refs ( 8 and 12 ) .
to locate the origin 
 for the differences in the observed catalytic 
 activity , we have performed a comparison of the electrostatic contributions 
 of individual residues to the hydrolysis of each substrate , calculated 
 using the linear response approximation following previous works ( e.g. , 
 refs ( 66 and 67 ) ; see figure 6 ) .
this analysis shows that , strikingly , despite 
 the calculations of residue interactions being completely independent 
 of each other , with different charge distributions and different transition 
 states , all residues that make substantial electrostatic contributions 
 to the calculated activation barrier are conserved among different 
 substrate .
this is similar to the observations from our previous computational 
 work on the arylsulfatase from pas .
however , 
 although qualitatively similar , there are some key quantitative differences 
 between the different substrates , most notably in the case of d12 , 
 d324 , h325 , and e327 .
while this itself is hardly surprising , considering 
 these are electrostatically quite different substrates , it highlights 
 that the active site pre - organization is not 
perfect  , 
 but rather cooperative electrostatic interactions render this preorganization 
 flexible enough to readily adapt to the electrostatic needs of different 
 substrates ( see also the related discussion of catalytic backups in 
 serum paraoxonase 1 ) . to further 
 explore this observation ,
we have also examined the 
 charge change on the central p / s atom and all atoms bonded to it upon 
 moving from reactant to transition state for the wild - type bcpmh catalyzed hydrolysis of the different substrates studied 
 in the present work .
these atoms were split into three fragments : 
 a central fragment comprising the p / s atom , the nonbridging oxygens 
 of the substrate , and the c atom of the phenyl group of phenyl p - nitrophenyl sulfonate ( pps ) and phenyl p - nitrophenyl phosphonate ( ppp ) connected to the central p / s atom 
 as well as the oxygen atoms of the departing leaving group ( olg ) and attacking nucleophile ( onuc ) as individual 
 fragments ( see table s3 ) .
as the transition 
 states for the reactions studied involve partial bond formation to 
 the nucleophile and leaving group , we have summed up the charges on 
 the central atoms ( p / s , nonbridging oxygens , and carbon ) and treat 
 this as one unit , which we will henceforth refer to as  central 
 fragment  for simplicity .
the schematic for this division is 
 shown in table s3 which also provides absolute 
 charges for each fragment at the reactant and transition states as 
 well as the charge shift upon moving from reactant to transition state . 

these have then in turn been ranked against the measured kcat / km for bcpmh for each substrate . from this table
, 
 it can be seen that while there is little trend in the charge shift 
 on the leaving group oxygen ( which is partially protonated by the 
 general acid ) , there are subtle but clear trends in the partial charges 
 of the nucleophile oxygen and the central fragment .
that is , for the 
 native substrate , ppp , there is a substantial charge shift corresponding 
 to a loss of + 0.2728 au on onuc .
this charge shift gradually 
 decreases across the series , correlated with a reduction in kcat / km . in
parallel 
 to this , for the native substrate , there is a small buildup of negative 
 charge ( 0.0468 au ) on the central fragment , which increases 
 to 0.0884 au for the promiscuous activity with the lowest 
 observed kcat / km ( the sulfate monoester ) .
therefore , there appears 
 to be a correlation between the calculated charge shift at the transition 
 state and the subsequent catalytic efficiency of the enzyme .
this 
 also ties in with experimental observations that other alkaline phosphatases 
 such as ap and npp clearly discriminate on the basis of substrate 
 charge .
the most radical example of such charge discrimination 
 in this superfamily , in fact , is in the arylsulfatase from pseudomonas aeruginosa ( pas ) , where the hydrolysis of large 
 bulky monanionic diesters such as bis - p - nitrophenyl 
 phosphate shows only 100-fold lower values than the monanionic substrate p - nitrophenyl sulfate ( with kcat / km = 4.9  10 ms for the sulfate monoester 
 and 2.5  10 ms for the phosphate diester ) .
in contrast , 
 the dianionic analogue of the sulfate monoester , p - nitrophenyl phosphate , is a much poorer substrate than the sulfate 
 monoester ( kcat / km = 790 ms ) , despite having the same ground - state geometry 
 and similar predicted transition - state geometries to the sulfate monoester . 

even further examples of such charge discrimination have been seen 
 by baxter and co - workers in studies of 
 aluminum and magnesium fluoride transition - state analogues ( tsa ) of 
 phosphoryl transfer enzymes , where they showed clear preference for 
 preserving anionic charge at the expense of tsa geometry over a broad 
 range of ph .
all data are averages and standard 
 deviations over 10 individual simulations as outlined in the methodology section . for an extended version of 
 this table , including both p(s)o and h  n / olg distances , we refer the reader to the table 
 s4 .
representative transition - state 
 structures for the bcpmh catalyzed hydrolysis of 
 ( a ) ppp , ( b ) pet , ( c ) pns , ( d ) pps , and 
 ( e ) pnph .
electrostatic contribution 
 of key residues to the calculated activation 
 barrier for the hydrolysis of the five substrates for wild - type form 
 of bcpmh .
clearly , these enzymes have evolved to provide 
 the key active site 
 interactions that optimally stabilize the transition state for the 
 native reaction , which in turn leads to the observed preference for 
 the native substrate . however , in the electrostatic cooperativity 
 model we present in this work , these interactions are sufficiently 
 flexible to accommodate the electrostatic needs of other substrates , 
 although the same residues can make quantitatively different contributions 
 as shown in figure 6 .
these differences in 
 ability to stabilize different transition states would in turn lead 
 to the selectivity displayed by these enzymes for different substrates .
hollfelder and co - workers have performed a detailed alanine scan of the rlpmh active site residues , testing against both the phosphonatase 
 ( ppp ) and phosphodiesterase ( pet ) activities of the enzyme .
both substrates 
 appear to be highly insensitive to active site single mutations , with 
 the individual substitution of each key active site residue in rlpmh leading to , at worst , a 20-fold reduction 
 in kcat .
an exception to this is modifying 
 the nucleophile to alanine , but even in this extreme case , these enzymes 
 still show some activity . to probe the origin 
 of the seeming resilience of these enzymes to substitution of individual 
 active site residues , we have performed evb calculations to obtain 
 free energy profiles for the chemical step for the hydrolysis of substrates 
 ppp and pet of figure 2 by a range of ala - substituted 
 forms of rlpmh presented in ref ( 8) .
critically , when moving 
 from wild - type to mutants , we used exactly the same 
 parameter set , unchanged , allowing us to in parallel rigorously validate 
 our valence bond model for the reaction mechanism catalyzed by these 
 enzymes and its predictive power ( see the supporting 
 information for theoretical background ) .
the only exception 
 to this is the k337a mutant that has the general acid functionality 
 of k337 removed , and for which we model the reaction as proceeding 
 with h218 as the general acid instead ( for all other calculations , 
 h218 is kept in its neutral form as close proximity to the k337 side 
 chain and the catalytic metal ion will depress its pka ) .
note again that although we have focused on k337 as 
 a putative general acid in this work , due to the agreement between 
 the predicted pka of k337 and the experimental 
 ph - rate profiles as outlined in the previous section , in practice 
 either of these two residues could fulfill the role of general acid .
calculated 
 and experimentally derived activation energies for the rlpmh catalyzed reactions of ( a ) ppp and ( b ) pet . shown 
 here is data both for the reaction catalyzed by the wild - type enzyme 
 as well as several mutant forms of the enzyme .
the data plotted in 
 this figure are presented in table 3 , and the 
 error bars represent standard deviations over 10 independent trajectories .
a comparison between calculated 
 and experimental activation barriers 
 for the hydrolysis of these substrates by each key rlpmh variant is shown in figure 7 with the 
 corresponding energetics presented in table 3 .
it can be seen that we are able to reproduce the experimentally 
 observed effect of all active site mutants ( gwtmut ) to within 
 an average error margin of 1 kcalmol .
the most challenging of these mutations to model is the y105a mutation 
 ( as can also be seen from the large error bar shown in figure 7 ) , as this mutation leads to a larger perturbation 
 in the active site , for example repositioning residues such as t107 
 and y215 .
this results in a larger standard deviation for these calculations 
 in the case of the phenyl phosphonate than in other simulations .
however , 
 the average over 10 trajectories is still in good agreement with experimental 
 results . taken together with our other simulations , this provides 
 support for the quality of our calculations , the suggested mechanism , 
 and our assumption that the group transfer is the key step in determining 
 the specificity .
additionally , an examination of the corresponding 
 p  o distances at the transition state for each variant and 
 substrate shows that , as we move from the background reaction to the 
 enzyme ( table s5 ) , the single mutants in 
 the active site have little effect on the transition - state geometry .
here , we will provide a brief discussion of our simulations of 
 each mutant below and refer the reader to figure 5 for an overview of how each residue interacts with the substrates 
 of interest in the equilibrated wild - type enzyme .
all energies 
 are given in kcalmol and are averages and 
 standard deviations over 10 individual trajectories using different 
 starting conformations , as outlined in the methodology section .
g(expt . ) corresponds to experimental 
 values of the enzyme - catalyzed 
 reaction , based on the kinetic data presented in refs ( 8 and 12 ) .
electrostatic contribution 
 of key residues to the calculated activation 
 barrier for group transfer reactions of ( a ) ppp and ( b ) pet for different rlpmh variants .
as suggested in ref ( 8) , this residue seems to play a key role by holding 
 k337 in place . for the simulations of the q13a variant , we observe 
 that both k337 and h218 are perturbed , and the rms displacement of 
 k337 after equilibration compared to the wild - type enzyme is 0.80 
 and 0.78  for ppp and pet , respectively .
however , the effect 
 of losing this interaction translates to only a 0.4 kcalmol reduction in activation barrier for both substrates 
 both experimentally and from our simulations ( see table 3 ) .
note that , as shown in table s2 , this mutation primarily affects km rather 
 than kcat for both substrates considered 
 here .
n78 is a key active site residue , as it provides 
 a hydrogen - bonding interaction to the nonbridging oxygen of both ppp 
 and pet .
this interaction stabilizes the substrate and also helps 
 to optimally position the substrate in the active site .
loss of this 
 interaction results in a 1.4 kcalmol increase 
 in barrier for both substrates . as
shown in table 3 and figure 7 we are able to reproduce 
 the detrimental effect of the n78a mutant , which is slightly larger 
 for pet than for ppp .
this could be in part due to the presence of 
 the phenyl ring in ppp , which can help to position the substrate in 
 the active site even in the absence of the hydrogen bond from n78 . in the wild - type enzyme
this residue does not 
 directly interact with the nucleophile or the substrate . however , 
 it is part of a hydrogen - bond network that keeps d324 and r61 correctly 
 positioned for catalysis ( figure 1 ) .
it has 
 been experimentally shown that this mutation drastically reduced the 
 kinetic efficiency of the enzyme . as can be seen from table 2 ,
while we are able to reproduce the experimental 
 activation barrier within 1 kcalmol , for 
 both the phosphonate monoester and the phosphate diester , we obtain 
 larger standard deviations for this variant in the case of the phosphonate 
 monoester . in the case of the phosphate diester , upon truncating y105 
 to alanine and equilibrating the system
, we see an increase in the 
 number of water molecules around the nucleophile as well as repositioning 
 of other residues , such as t107 and y215 .
specifically , the interaction 
 between the nucleophile and t107 is broken , and y215 occupies the 
 space left by mutation . in the case of the phosphonate monoester , 
 however , the large hydrophobic phenyl ring of the phosphonate ( compared 
 to the smaller ethyl group in the diester ) blocks water access to 
 the nucleophile and restricts the movement of other residues around 
 it .
t107 is another key active site residue , as it 
 directly interacts with the nucleophile , helping optimally position 
 it for catalysis ( figure 1 ) .
unsurprisingly , 
 truncating this residue to alanine leads to an increase in activation 
 barrier of 1.2 kcalmol for the phosphonate 
 and 1.7 kcalmol for the diester ( a trend 
 we reproduce computationally , see table 3 and 
 figure 7 ) .
this is primarily due to loss of 
 the hydrogen bonding interaction with t107 as well as the resulting 
 subtle repositioning of the nucleophile in the active site .
interestingly , this mutation appears not only 
 to impact the catalytic activity , but also to increase km from 2.8 mm in the wild - type enzyme to 15 and 57 mm 
 in the mutant form for both phosphonate and diester substrates .
it has been argued that this increase in km is due to substrate binding , suggesting that 
 this residue as well as k337 are directly involved in this step .
h218 
 could also play a role as a general acid , due to its close proximity 
 with the leaving group .
however , in its unprotonated form , h218 also 
 plays a key role in positioning k337 for optimal leaving group stabilization 
 ( the distance between n of h218 and k337 is 3.44 
  in the rlpmh crystal structure ) .
the role of k337 is two - fold : it helps to position 
 the substrate in the active site in the michaelis complex ( through 
 a hydrogen bonding interaction to one of the nonbridging oxygens of 
 the substrate ) as well as to stabilize the leaving group upon departure 
 by acting as a general acid and protonating it .
one would expect , 
 then , that mutation of this key residue to alanine would result in 
 a substantial increase in activation barrier . however , the experimentally 
 observed increase is only 0.2 kcalmol for 
 the phosphonate monoester and 0.7 kcalmol for the phosphate diester , which is lower than for example either 
 the n78a or t107a mutations .
this suggests that another positively 
 charged residue is taking up the role of k337 in leaving group stabilization . 

as discussed above , the role of general acid could be fulfilled by 
 either k337 or h218 , and in absence of the close proximity of the 
 k337 positive charge upon mutation ( the distance between the n of h218 and the nitrogen of k337 is 3.44  in 
 the wild - type crystal structure ) , one 
 would presume that h218 is more likely to be protonated than in the 
 wild - type .
therefore , we tested modeling h218 as a general acid , demonstrating 
 that this in fact provides activation barriers in very good agreement 
 with experiment ( table 3 ) , suggesting that 
 in the absence of k337 , h218 takes up the role of this residue in 
 leaving group stabilization ( either through hydrogen - bonding / charge 
so far , we have not yet discussed the details of the proton transfer 
 to the leaving group from either k337 or h218 . in the present work , 

we have used a two - state valence bond model to describe this process , 
 as outlined in the methodology section . in 
 our model , for both the lysine- and histidine - catalyzed mechanisms 
 ( wild - type and k337a mutants , respectively ) , the group transfer and 
 proton transfer reactions take place in a single , concerted but slightly 
 asynchronous reaction step ( figures s5 and s6 
 and table s4s6 ) . as seen from these figures and
associated 
 table , when the general acid is modeled as being k337 , the transition 
 state is dominated by the group transfer reaction , with the proton 
 transfer reaction taking place very slightly after the group transfer . 

this would tie in with the fact that the p - nitrophenol 
 leaving group is sufficiently basic to not a priori need protonation to depart . in the case of h218 as the general acid 
 ( in the k337a mutant ) , the proton transfer becomes more concerted 
 with the group transfer reaction ( figure s6 ) .
this would be in agreement with our previous dft study of the 
 hydrolysis of phosphate and sulfate monoesters , in which we carefully examined all proton transfer steps 
 involved and demonstrated that they either immediately precede or 
 succeed the group transfer step , but along the same reaction coordinate 
 ( without the need for discrete intermediates ) .
such a model also agrees 
 with high - level qm / mm calculations of the phosphoryl transfer reaction 
 catalyzed by dutpase , which show a similar 
 coupling between proton transfer and group transfer reactions , suggesting 
 that a two - state vb model is adequate for capturing the key features 
 of the relevant reaction mechanisms , and this is also borne out by 
 the agreement with the experimental data .
finally , a comparison 
 of the electrostatic contributions of individual 
 residues to catalysis for both substrates and all variants ( figure 8) shows that , as with the wild - type reactions , changes 
 in activity correspond to cooperative electrostatic effects , where 
 the active site residues are able to compensate the absence of key 
 active site residues and stabilize the transition state of different 
 substrates .
this effect was also seen in our previous computational 
 studies of the evolutionarily related pas and has also been alluded to in other recent works . a similar phenomenon has been observed in experimental studies of 
 serum paraoxonase 1 , suggesting that 
 such electrostatic flexibility is a feature of multiple enzymes that 
 catalyze phosphoryl transfer .
although our data strongly point toward electrostatic 
 cooperativity 
 as the origin for the observed selectivity and promiscuity among members 
 of this superfamily , it is important to also examine other possible 
 origins of this effect . before proceeding further in this discussion , 

it is worth mentioning that there are several different ways to define 
 this concept , that range from an enzyme 
 performing distinct chemistry using a similar set of residues and 
 the same mechanism to cases where different sites of an enzyme are 
 used to perform different chemical reactions ( a form of  protein 
 moonlighting  ) .
common to all these definitions , however , is 
 the fact that promiscuity can be regarded simply as a converse of 
 specificity , in that a highly specific enzyme would 
 only be able to perform a single chemical reaction , whereas a catalytically promiscuous enzyme would be able to perform 
 multiple distinct chemical reactions .
in addition , 
 while the enzymes studied in the present work are multifunctional , 
 with very high proficiencies for both phosphonate monoester and phosphodiester 
 hydrolysis , they nevertheless show high selectivity and an order of 
 preference between these and other promiscuous reactions that they 
 catalyze ( see table s1 ) .
therefore , in 
 the present discussion , we will use  specificity  as 
 a converse to promiscuity ( i.e. , referring to the number of reactions 
 the enzyme catalyzes ) and  selectivity  to indicate 
 the discrimination between different reactions catalyzed by the same 
 enzyme . an important point to take into account in the present 
 work is 
 that , with the exception of the monoesters , the reactivity of the 
 substrates examined herein is substantially lower by several orders 
 of magnitude under neutral conditions than at high ph ( see table s1 ) .
therefore , it is plausible to consider 
 that a part of the broad substrate specificity might result because 
 the enhanced reactivity of the active site nucleophile by the catalytic 
 metal center already provides substantial rate accelerations for a 
 broad range of substrates .
this would be consistent with the small 
 effects of < 10-fold ( on kcat ) on the 
 enzymatic activity of the mutation of they key residues that interact 
 with the substrate oxygens , specifically n78 and k337 .
however , while having an activated nucleophile is clearly 
 important for the overall activity toward different substrate , this 
 in itself is not fully sufficient to describe the observed promiscuity , 
 as there are clear variations in rate acceleration between the different 
 substrates , even when considering the alkaline reaction as the relevant 
 reference state for the uncatalyzed reaction ( see values presented 
 in table s1 )
. additionally , as discussed 
 and demonstrated in several of our previous 
 works , despite the 
 superficial similarities between the different transition states involved 
 ( substitution of p for s , adding or removing functional groups ) , they 
 have very different charge distributions and thus solvation patterns , 
 leading to very different requirements for efficient catalysis .
this 
 can also be seen in both the quantitative differences in the residue 
 contributions shown in figure 6 , and the fact 
 that although multifunctional , bcpmh ( for which more 
 kinetic data is available with different substrates , see table s1 and ref ( 12 ) ) shows up to 25,000-fold differences 
 in kcat / km values toward different substrates .
these range from 0.59 ms for the sulfate monoester 
 to 1.5  10 ms for the phosphonate monoester . following from this , there is also 
 large sensitivity among alkaline phosphatases to the nature of the 
 leaving group .
for example , in the case of bcpmh , 
 simply changing the leaving group to phenol substantially reduces 
 the catalytic activity for all substrates by up to 350-fold ( in terms 
 of kcat / km ) . in the case of ap , for which linear free energy relationships 
 do exist , these also show moderate - to - strong leaving group dependence 
 ( see , e.g. , refs ( 22 , 79 , and 80 ) ) . in particular , reported literature values 
 for the ap - facilitated hydrolysis of sulfate monoesters phosphorothioates , 
 phosphate monoesters and phosphate diesters all show steep leaving 
 group dependence , with lg values in the range from 
 0.76 to 0.95 . therefore , although the transition states are superficially very 
 similar , the enzyme is actually highly selective between the different 
 substrates and leaving groups . as these enzymes are all metalloenzymes , 
 the catalytic metal center 
 plays a major role in substrate positioning in all cases , guiding 
 the ultimate orientation of the electrophile relative to the nucleophile . 

this is further facilitated by the involvement of a number of key 
 residues that are strategically positioned to assist in overall substrate 
 positioning , which for the pmhs studied here are n78 , h218 , and k337 . 

these residues primarily interact with the leaving group or nonbridging 
 oxygens of the relevant substrates and keep the electrophile in similar 
 positions relative to the nucleophile for different substrates and 
 electrophiles .
however , due to the large binding pocket ( 10 
  20  wide and 15  deep ) , there is extensive space to accommodate variations 
 in binding conformations of spectator and leaving groups , which in 
 turn would facilitate the accommodation of a broader range of substrates 
 shapes .
such substrate repositioning through diversity in placement 
 of leaving and spectator groups would therefore also play a role in 
 determining the resulting overall catalytic efficiency and promiscuity . 

this is in line with our computational evidence , which highlights 
 the importance of cooperative electrostatic interactions , brought 
 about by active site plasticity , in accommodating a range of different 
 substrates . tying in with this ,
if plasticity is important for 
 facilitating 
 promiscuity in these enzymes , one can ask whether flexibility would 
 be reduced for catalysis by enzymes that show high specificity for 
 their physiological substrates . a classical set of proteins where 
 rigidity is very important in ligand binding specificity vs promiscuity 
 are the periplasmic binding proteins , as illustrated by the structure 
 of the cellulose - binding protein from thermotoga maritima .
this protein has a bipartite active 
 site , comprised of a solvent excluded region involved in highly specific 
 ligand binding and is adjacent to a second and more flexible solvent - filled 
 cavity in which semi - specific ligand binding occurs .
detailed studies 
 of these systems as well as exploration of the role of water molecules 
 have provided important insight into how the interplay between flexibility 
 and rigidity allows both specificity and promiscuity to be encoded 
 into a single binding site , moving beyond a single highly specific 
 and fixed protein scaffold .
other examples of highly specific 
 enzymes that show comparably 
  rigid  active sites ( in the substrate - bound conformation ) 
 are orotidine 5-monophosphate decarboxylase and -phosphoglucomutase , among others .
these enzymes can exist in more than one conformational 
 form and undergo ligand - gated conformational changes , engulfing their 
 substrates upon ligand binding .
however , once the substrate is bound , 
 crucial tight binding hydrogen - bonding networks are involved in keeping 
 the key catalytic residues in place , and , for example , truncation 
 of various functional groups on the respective substrates can lead 
 to tremendous reductions in catalytic activity due to the loss of 
 key stabilizing interactions ( see , for example , richards  substrate - in - pieces  

studies of these systems that quantify the contribution of different 
 parts of the substrate to binding and catalysis ) .
yet another example 
 is a recent study of the evolution of -lactamases from their 
 promiscuous ancestral variants to their modern specific counterparts 
 ( such as tem-1 -lactamase ) .
this 
 work demonstrates that , within these enzymes , evolution from a generalist 
 to a specialist enzyme is coupled to a loss of conformational flexibility .
finally , as pointed out by a reviewer , it should be noted out that 
 the experimental work on which the present study is based was performed using nonphysiological substrates , where the leaving 
 group is the weakly basic nitrophenoxide anion ( as the physiological 
 substrate has not been identified ) . the 
 relatively small requirement for stabilizing negative charge at weakly 
 basic anions will in turn increase the contribution of the enhanced 
 reactivity of the active site nucleophile to the total rate accelerations 
 outlined in table s1 , facilitating the 
 turnover of a broader range of substrates .
as discussed in the introduction , the phenomenon 
 of catalytic promiscuity appears to be common among members of the 
 ap superfamily .
although the members 
 of this family ( which include ap , npp , pmh , and pas ) have diverged 
 considerably , they still share considerable similarities in active 
 site architecture and key catalytic residues , as highlighted in figure 1 and discussed in ref ( 15 ) . in the present work ,
we have performed a detailed 
 computational study of the hydrolysis of a range of substrates by 
 two pmh , demonstrating the key role of cooperative electrostatic interactions 
 at the pmh active site .
moreover , there is no significant conformational 
 change in the active site alongside the reaction coordinate when comparing 
 the different reactions studied .
this suggests an important role for 
 electrostatic rather than conformational active site plasticity in facilitating the observed promiscuity 
 in these enzymes . in order to examine this effect ,
we have studied 
 the geometry of the active site cavity for different members of the 
 ap superfamily , using the fpocket 2 software package .
we have inspected several members of this superfamily , 
 as well as related promiscuous phosphatases , in the search for a possible 
 correlation between the physical properties of the different active 
 sites and their corresponding catalytic promiscuity .
the corresponding 
 results are summarized in figure 9 and tables s7 and s8 . from this data , it can be seen 
 that when comparing different ap superfamily members , clear trends 
 emerge with respect to the active site volumes and the number of activities 
 that have been reported for each enzyme to date . specifically , according to this 
 analysis , pockets with a larger polar surface allow the enzyme to 
 exploit distinct residue conformations to create an optimal electrostatic 
 environment and accommodate different transition states .
in addition 
 to this , the large volume of the different pockets would allow for 
 the accommodation of a more diverse range of substrates , which can 
 then be hydrolyzed through cooperative enzyme  substrate electrostatic 
 interactions in the corresponding active sites . through this 
 comparison ,
we find that ap , npp , and the pmhs have 
 the largest active site volumes and polar solvent accessible surface 
 areas ( sasas ) , mostly due to the width of their active sites .
tying 
 in with this , the arylsulfatases and other members of the superfamily 
 have comparably smaller and narrower pockets .
interestingly , this 
 can be directly correlated to the number of reported activities in 
 the literature ( figure 9 and table s7 ) where ap has both the largest and most accessible 
 active site as well as the highest number of reported activities .
this is closely followed by npp and the 
 pmhs , with five clear activities each ( not including the anomalous 
 pte activity of bcpmh for reasons outlined above ) . 
 finally , a blast search with rlpmh against known 
 protein structures yielded the related alkaline phosphatase , pas , 
 as the protein with the highest sequence identity . as can be seen from figure 9 , upon 
 moving from the pmhs to pas ,
the active site starts to reduce in volume 
 to give a much narrower pocket , in line with the lower number of reported 
 activities for pas .
the remaining enzymes all have 
 smaller active site volumes compared to ap , npp , and pmh , and all 
 of them , according to braunschweig enzyme database , have so far been reported to have only one activity each . 
 when this observation is combined with
the similar mechanisms and 
 highly polar active site residues that members of this superfamily 
 possess ( figure 10 ) as well as with the experimental 
 evidence for the existence of catalytic backups in pon1 , this strongly suggests that the cooperative 
 electrostatic flexibility observed in pmh and related enzymes is a 
 common feature for evolution in the ap superfamily as well as related 
 phosphotransferases .
one limitation of this analysis , however , 
 is that while we consider 
 the total number of characterized activities , it neither takes into 
 account the possibility of further as - yet uncharacterized activities 
 in these enzymes nor the relative proficiency of these enzymes toward 
 their promiscuous substrates .
for example , even though ap has the 
 highest number of known activities among the enzymes we examine , only 
 two of those six activities ( phosphate and phosphothioate monoester 
 hydrolysis ) are particularly proficient with kcat / km values of 3.3  10 and 2.0  10 ms , while the other activities can have kcat / km values as low as 10 ms .
however , clearly , a very high number of polar 
 residues in the active site , as shown in figure 10 and table s7 , as well as very 
 large active sites , would allow for the presence of multiple distinct 
 catalytic backups and a shifting electrostatic field upon substrate 
 binding that can accommodate substrates of other shapes and charge 
 distributions .
additionally , it is of course useful to consider not 
 only the total binding interactions available for transition - state 
 stabilization but also the binding interactions that are actually 
 needed to account for a given observed enzymatic rate acceleration , 
 because nonspecificity will be favored whenever these total possible 
 interactions greatly exceed the number of required interactions . for 
 example , in the case of phosphate monoester hydrolysis , strong interactions 
 between the enzyme and heavily charged reacting phosphate may be more 
 than sufficient to account for the enzymatic rate acceleration .
this 
 would favor a lack of specificity for the leaving group and , perhaps , 
 also floppiness in transition - state binding , provided there is no 
 strict requirement of the precise placement of enzymatic side chains 
 around the phosphate .
in contrast , there may be a greater requirement 
 for precision in the binding of the less highly charged transition 
 state for sulfate monoester hydrolysis , which would also tie in with 
 the experimental observation that pas , a native sulfatase , is a more 
 proficient phosphatase than the corresponding phosphatases in the 
 ap superfamily are sulfatases .
correlation 
 between the number of known catalytically activities 
 ( in parentheses ) and the total volume and sasa for several members 
 of the ap superfamily .
surface representation of the active sites of ( a ) burkholderia caryophylli pmh , ( b ) escherichia coli ap , ( c ) pas , and ( d ) xanthomonas axonopodis npp ( pdb ids : 2w8s , 1alk , 1hdh , and 2gsn , respectively ) , 
 displaying the polar character inside the pocket .
( b ) and ( d ) show 
 a strong presence of negatively charged residues ( red ) near the metal 
 site . for both ( a ) and ( c ) , there are more apolar residues present 
 ( white ) , although bcpmh still has a larger number 
 of polar residues in its active site , mostly due to the very large 
 size of the binding pocket
this would be supported by our observed correlation between 
 larger 
 active site volume / polar sasa and a great number of activities and 
 is in sharp contrast to enzymes such as orotidine 5-monophosphate 
 decarboxylase , which is highly selective for the decarboxylation of 
 orotidine monophosphate , because the enzyme makes use of every possible 
 interaction with omp in the stabilization of the decarboxylation state .
interestingly , there appears to be also some 
 sort of correlation between tertiary structure and the number of reported 
 activities , in that the enzymes with the highest number of characterized 
 activities shown in figure 9 , namely ap , npp , 
 and pmh , are dimers and a tetramer , respectively , whereas all other 
 enzymes are monomeric .
one would assume that having a large number 
 of polar residues in the active site would result in electrostatic 
 strain that would have to be compensated elsewhere in the structure , 
 which could potentially be correlated to the oligomeric states of 
 these proteins .
overall , however , the clear correlation between increased 
 promiscuity and a larger active site volume and sasa highlights the 
 crucial importance of substrate charge and active site electrostatics 
 in facilitated selectivity and evolution among these highly promiscuous 
 enzymes .
in the present work , we have 
 performed a detailed evb study of 
 both the native and several promiscuous activities of two pmh , bcpmh and rlpmh , as well as rlpmh variants with mutations in key active site residues .
our calculations 
 can reproduce key experimental observables such as experimentally 
 observed activation barriers for the wild - type reactions of all substrates 
 and qualitative mechanistic predictions based on examining ph - rate 
 profiles as well as energetic trends upon mutation of key active - site 
 residues in rlpmh .
we demonstrate that despite their 
 broad promiscuity , both pmhs studied in this work hydrolyze all five 
 chemically distinct substrates through a unified mechanism , binding 
 substrates in similar positions and without the need for any significant 
 local or global conformational changes .
additionally , we demonstrate 
 that the apparent resilience of these enzymes to active site mutations 
 as well as the overall promiscuity is due to compensatory electrostatic 
 effects from different residues , allowing enough flexibility in the 
 electrostatic environment of the active site to accommodate multiple 
 substrates with distinct transition states and charge distributions . 

finally , we provide a detailed structural and physical comparison 
 of a range of highly promiscuous members of the ap superfamily .
these results demonstrate the strong correlation between the structural 
 and electrostatic features of these enzyme s active sites and 
 the corresponding variations in both substrate charge preference and 
 the number of known promiscuous activities .
this further supports 
 our hypothesis by strongly suggesting that active site shape , size , 
 and more critically number of polar residues available can be directly 
 correlated the ability to accommodate increasing numbers of promiscuous 
 activities .
our simulations and comparative analysis therefore highlight 
 the importance of cooperative electrostatic interactions and an electrostatically 
 flexible active site as a common feature in the evolution of promiscuous 
 side reactions among members of the ap superfamily . in the present 
 work
we demonstrate that , in addition to the electrostatic preorganization 
 originally suggested by warshel in 1978 , the active site can also electrostatically reorganize to accommodate 
 the needs of different substrates .
this provides a classical example 
 of protein flexibility allowing the reaction to occur , as these enzymes 
 do not know in advance what substrate is going to bind .
rather , they 
 adjust their active site environment to a given substrate after the 
 binding step . these insights , in turn ,
helps us not only to understand 
 protein evolution within a superfamily at the molecular level but 
 also highlights a concrete feature that can be manipulated in targeted 
 artificial enzyme design .
 it 
 is becoming widely accepted that catalytic promiscuity , i.e. , 
 the ability of a single enzyme to catalyze the turnover of multiple , 
 chemically distinct substrates , plays a key role in the evolution 
 of new enzyme functions . in this context , the members of the alkaline 
 phosphatase superfamily have been extensively studied as model systems 
 in order to understand the phenomenon of enzyme multifunctionality . 
 in the present work , we model 
 the selectivity of two multiply promiscuous 
 members of this superfamily , namely the phosphonate monoester hydrolases 
 from burkholderia caryophylli and rhizobium leguminosarum . 
 we have performed extensive 
 simulations of the enzymatic reaction of both wild - type enzymes and 
 several experimentally characterized mutants . 
 our computational models 
 are in agreement with key experimental observables , such as the observed 
 activities of the wild - type enzymes , qualitative interpretations of 
 experimental ph - rate profiles , and activity trends among several active 
 site mutants . in all cases the substrates of interest bind to the 
 enzyme in similar conformations , with largely unperturbed transition 
 states from their corresponding analogues in aqueous solution . 
 examination 
 of transition - state geometries and the contribution of individual 
 residues to the calculated activation barriers suggest that the broad 
 promiscuity of these enzymes arises from cooperative electrostatic 
 interactions in the active site , allowing each enzyme to adapt to 
 the electrostatic needs of different substrates . by comparing the 
 structural and electrostatic features of several alkaline phosphatases 
 , 
 we suggest that this phenomenon is a generalized feature driving selectivity 
 and promiscuity within this superfamily and can be in turn used for 
 artificial enzyme design . 
Introduction
Methodology
Results and Discussion
Examining Other Plausible
Contributions to the Observed Selectivity
and Promiscuity
Implications for Evolution
in the Alkaline Phosphatase Superfamily
Overview and Conclusions