biological fe / s clusters are versatile cofactors in enzymes , well known mainly for their ability to act as electron - transfer sites . in the past few years , an increasing number of other fascinating functions of fe / s clusters have been discovered . among those , their use as the source for sulphur atoms in biological radical reactions has been striking with regards to the complex mechanisms of fe / s cluster assembly . as the fe / s cluster is destroyed during this reaction , these enzymes are regarded as suicide enzymes and their respective clusters as substrates rather than cofactors . to date , fe / s clusters have been identified as the source of sulphur atoms in reactions catalysed by four different enzymes belonging to a distinctive class   within the radical s - adenosylmethionine superfamily : biotin synthase ( biob ) , lipoyl synthase ( lipa ) , a transfer rna - methylthiotransferase ( miab )   and a ribosomal methylthiotransferase ( rimo ) . although the latter three enzymes contain [ 4fe4s ] clusters as the assumed sulphur source , biob contains a [ 2fe2s ] cluster which has been shown to be destroyed during catalytic turnover . of the four enzymes , biob is the most extensively investigated and is also the only one whose crystal structure has been solved . a mechanism for its reaction was first published in 2001   and has been closely investigated since ( scheme  1 ) .scheme  1proposed biotin synthase mechanism . adomets - adenosylmethionine the proposed mechanism is supported by the close proximity of the [ 2fe2s ] cluster to the dethiobiotin molecule found in the crystal structure . the closest bridging sulphide of the cluster is situated 4.6   away from c-9 of dethiobiotin , one of the two carbon atoms to which sulphur is attached in the course of the reaction ( fig . sams - adenosylmethionine , dtb dethiobiotin surprisingly , the [ 2fe2s ] cluster carries one strictly conserved arginine ligand in addition to three cysteine ligands typical for fe / s clusters . as arginine is highly exceptional as a ligand coordinating to a metal ion in biological systems , its possible importance has been much discussed since publication of the crystal structure . it has been proposed that it may play electronic , mechanistic or structural roles , possibly related to its bidentate nature or its positive charge in the protonated state . a basic question to be answered is the charge of the arginine guanidine group in the active enzyme . arginine is usually protonated at physiological ph ( the pka in water solution is approximately 12 ) , thereby bearing a positive charge . however , a positively charged guanidine group could not be regarded as a true ligand from a coordination chemist s point of view  for that , it should rather be deprotonated and neutral in biob . this uncertainty is reflected by suggestions of both nh [ 13 , 16 ] and nh2   coordination in the literature . in addition to the protonation issue , the role of the second , non - coordinating nh / nh2 group is to be ascertained . secondary bonding interactions   are conceivable , as well as an involvement of hydrogen bonds with the protein backbone or with the cluster sulphur atoms . furthermore , the crystal structure shows an fefe distance of 3.3   , which is significantly longer than what is found in any other known [ 2fe2s ] clusters ( approximately  2.7   ) . as these issues can not be solved with the published structural data alone , owing to the low resolution of the crystal structure ( 3.4   ) , and the importance of the unusual arginine ligand remains elusive , theoretical methods seem to be a promising strategy to answer the above - mentioned questions . this work focuses on the structural properties of the highly unusual [ 2fe2s ] cluster of biob to improve our understanding of its importance for the enzyme mechanism . the quantum mechanical ( qm)/molecular mechanical ( mm ) calculations were performed with the comqum software program [ 20 , 21 ] utilising turbomole 5.9   for the qm calculations and amber 9   for the mm calculations . the qm calculations were performed using the bp86 functional [ 24 , 25 ] and the def2-sv(p ) basis sets , which have given reasonable results for [ 2fe2s ] clusters in previous calculations [ 18 , 27 ] . for the mm calculations , we used the amber-99 force field [ 28 , 29 ] . for the [ 4fe4s ] cluster and the dethiobiotin and s - adenosylmethionine ligands , we used force - field parameters previously determined in our group [ 3032 ] . in the qm / mm approach , the qm region ( system 1 ) contains the most interesting atoms and is relaxed by qm methods . system 2 consists of the residues closest to the qm system and is optimised by mm calculations . the remaining part of the protein and the surrounding solvent molecules ( system 3 ) are kept fixed at the crystallographic coordinates . in the qm calculations , system 1 is represented by a wavefunction , whereas all the other atoms are represented by an array of partial point charges , one for each atom , taken from mm libraries . thereby , the polarisation of the quantum chemical system by the surroundings is included in a self - consistent manner . when there is a bond between systems 1 and 2 ( a junction ) , the quantum region is truncated by hydrogen atoms , the positions of which are linearly related to the corresponding carbon atoms in the full system ( the hydrogen - link - atom approach ) . to eliminate the non - physical effect of placing point charges on atoms in the mm region bound to junction atoms ( i.e. the closest neighbours of the qm system ) , those charges are zeroed , and the total energy is calculated as\documentclass[12pt]{minimal } 
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				 \begin{document}$$ e_{{{\text{qm}}/{\text{mm } } } } = e_{{{\text{qm}}1 + { \text{ptch } } } } -e_{{{\text{mm}}1 } } + e_{{{\text{mm}}123 } } $ $ \end{document}where eqm1+ptch is the qm energy of system 1 truncated by the hydrogen atoms and embedded in the set of point charges ( but excluding the self - energy of the point charges ) . emm1 is the mm energy of system 1 , still truncated by hydrogen atoms , but without any electrostatic interactions . finally , emm123 is the classical energy of all atoms with normal atoms at the junctions and with the charges of the quantum system set to zero ( to avoid double - counting of the electrostatic interactions ) . by this approach , which is similar to the one used in the oniom method , errors caused by the calculations were based on the crystal structure ( protein data bank code 1r30 ) . as the enzyme was crystallised as a homodimer with little difference in atom positions ( less than 0.1   differences within the [ 2fe2s ] cluster ) , only the a subunit was used for the investigations and only this subunit is discussed . hydrogen atoms were added to the crystal structure and the protein was solvated in a sphere of water molecules with a radius of 36   using the leap module in the amber software suite . the protonation status of all residues was checked by the propka program   and it was concluded that no residues have strongly perturbed pka values ( thus , all arginine and lysine residues , except arg , see below , were considered in their protonated state , whereas all aspartate and glutamate residues were considered in their deprotonated state ) . for the histidine residues , the protonation was decided from a detailed study of the solvent exposure and hydrogen - bond pattern . this procedure led to the following assignment : his and his were protonated on both nitrogen atoms , whereas his was protonated on n only and his was protonated on n only . the [ 4fe4s ] cluster , s - adenosylmethionine and the dethiobiotin molecule found in the crystal structure were all included in the calculations . the total charge of the simulated system was 8 ( neutral arginine ) or 7 ( protonated arginine ) . the positions of the atoms added were optimised by a 90-ps simulated - annealing molecular dynamics simulation , followed by 10,000 steps of conjugate gradient energy minimisation . the temperature was kept constant at 300  k using the berendsen weak - coupling algorithm   with a time constant of 1  ps . the non - bonded cut - off was 15   and the pair list was updated every 50  fs . in the qm / mm calculations , system 1 contained the [ 2fe2s ] cluster and the relevant atoms of the four coordinating amino acids ( cys , cys , cys and arg ) and was treated with qm methods . the side chains were included as far as c for the cysteine residues ( replacing c by a hydrogen atom ) and as far as c for the arginine residue ( replacing c by a hydrogen atom ) . thus , it consisted of [ ( ch3s)3(ch3nhch(nh)nh2)fe2s2 ] for the calculations with neutral arginine and [ ( ch3s)3(ch3nhch(nh2)nh2)fe2s2 ] for the calculations with protonated arginine . system 2 included all residues with any atom within 6   of any atom in system 1 and was relaxed with mm methods . system 3 included the remaining protein atoms as well as the water molecules and was kept fixed at the crystallographic coordinates . as both iron atoms of the oxidised [ 2fe2s ] cluster are in the fe high - spin state ( s  =  5/2 ) , two spin states are possible ( the ferromagnetically coupled , f , state , s  =  5 , and the antiferromagnetically coupled , af , state , s  =  0 ) . the af state always had a lower energy than the f state and it is also the one observed experimentally . therefore , all results presented are af energies . to ensure that the qm / mm energy differences are stable , the calculations were in general run forth and back between the relevant states until the energies were stable within 4  kj / mol . similar calculations were also performed on one - electron - reduced clusters , i.e. clusters containing one fe and one fe ion ( net charge of the qm system 1 or 2 , depending on the protonation of the arginine model ) , on two - electron - reduced clusters ( net charge 2 or 3 ) and on clusters with one of the bridging sulphur atoms removed ( the one closest to dethiobiotin ; net charge 0 or 1 , so this is equivalent to removing an s ion and reducing both iron ions to fe ) , in all cases in the af ( s  =  1/2 or s  =  0 ) state . for convenience , all geometry optimisations discussed were started from an initial optimisation with structure 2 ( structure  1 ) . to verify that this is acceptable , we tested to what extent the optimised geometry depends on the starting geometry . in addition , the influence of the spin and oxidation states of the [ 2fe2s ] cluster on structural properties was investigated . these explorative calculations were performed in a vacuum ( i.e. system 1 only ) , starting from the crystal geometry . geometry optimisations for structure 2 in different oxidation states ( fe / fe , fe / fe or fe / fe ) and spin states ( af or f ) showed that the final geometries of the intact clusters , especially the fefe distances and the orientation of the arginine residue , do not depend on the starting geometries . the oxidised af and f states were also tested for the other protonation states ( structures 1 , 3 and 4 ) , with similar results . in all calculations , short fefe distances were found in all cases , although they were slightly longer for the f states ( af : 2.572.65   , f : 2.422.89   ) ; no additional electronic states with larger fefe distances were detected . to verify this observation , the fefe distance was fixed to values between 2.5 and 3.5  ( structure 2 , oxidised , af state ) and the rest of the geometry was optimised . only one energy minimum was found , at approximately 2.6  ( 61  kj / mol more stable than the distance in the crystal structure ) and no evidence for a second minimum close to the crystal structure distance was found.structure  1conceivable coordination modes for arginine in the protonated ( 1 ) or neutral ( 24 ) state as represented in the quantum mechanical system conceivable coordination modes for arginine in the protonated ( 1 ) or neutral ( 24 ) state as represented in the quantum mechanical system similar explorative calculations were performed with the hybrid b3lyp functional [ 38 , 39 ] ( to examine the effect of another functional with exact exchange ) , giving similar results [ eaf    ef  =  20 to 55  kj / mol , d(fefe )  =  2.552.72 ( af ) and 2.702.96   ( f ) and an energy minimum at 2.8   , 36  kj / mol lower than the crystal structure ] . quadrupole splittings were calculated according to\documentclass[12pt]{minimal } 
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				 \begin{document}$$ \updelta e_{\text{q } } = 1/2eqv_{\text{zz } } \left ( { 1 + \eta^{2 } /3 } \right)^{1/2 } $ $ \end{document}where q  =  0.16  b ( 1.6    10  m ) for fe ,   =  ( vxx    vyy)/vzz , with |vxx|  <  |vyy|  <  |vzz| , and 1  mm / s is equivalent to 4.8075    10  ev . we also performed a set of quantum - refinement calculations , using the software program comqum - x . they can be seen as qm / mm calculations in which the structures are restrained towards crystallographic raw data . in comqum - x , the mm program is replaced by the crystallographic refinement program crystallography & nmr system ( cns ) . in crystallographic refinement , the coordinates , b factors , occupancies , etc . are improved by optimising the fit of the observed and calculated structure - factor amplitudes , typically estimated by the residual disagreement , the r factor . because of the limited resolution normally obtained with x - ray diffraction of biomolecules , a mm force field is used to supplement the data for the whole protein . this force field ensures that the bond lengths and angles make chemical sense . in comqum - x , this force field is replaced by more accurate qm calculations for a small , but interesting , part of the protein ( system 1 ) , in a manner completely analogous to the use of quantum mechanics in qm / mm calculations . thus , the comqum - x refinement takes the form of a minimisation using an energy function of the form\documentclass[12pt]{minimal } 
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				 \begin{document}$$ e_{\text{comqum - x } } = e_{{{\text{qm}}1 } } - e_{{{\text{mm}}1 } } + e_{{{\text{mm}}123 } } + w_{\text{a } } e_{\text{x - ray } } $ $ \end{document } here , emm1 and emm123 have the same meaning as in eq .  1 , whereas eqm1 is the energy of the qm system , without any point - charge model of the surroundings . ex - ray is a penalty function , describing how well the model agrees with the experimental x - ray data . we have used the default maximum likelihood refinement target using amplitudes ( mlf ) in cns . wa is a weight factor , which is necessary because ex - ray is in arbitrary units whereas the other terms are in energy units . it should be emphasised that the wa factor is nothing special for quantum refinement . on the contrary , it also has to be set in standard crystallographic refinement ( which is obtained from eq .  3 with eqm1  =  emm1  =  0 ) , although it is rarely discussed . the default behaviour of cns is to determine wa so that the ex - ray and emm123 forces have the same magnitude during a short molecular dynamics simulation , i.e. that the crystallographic raw data and the mm force field have a similar influence on the structure . unfortunately , we encountered convergence problems if we used the default value of wa ( 4.87 ) for some of the structures ( because the crystallographically preferred structure of the [ 2fe2s ] cluster is so poor at this low resolution that it becomes incompatible with the qm calculations ) . therefore , we present results only for the largest value of the wa factor that gave converged structures for all models , viz . the results are qualitatively the same if other values are used , regarding the preferred model and coordination mode of the arginine ligand . following crystallographic custom , no hydrogen atoms were included in the mm region of the comqum - x calculations , because hydrogen atoms are not discernible in the crystal structure . therefore , polarisation of the quantum system by the surrounding protein is not included in comqum - x . finally , it should be noted that the mm force field used in cns ( protein_rep.param , dna - rna_rep.param , water.param and ion.param ) is based on a statistical survey of crystal structures , rather than the energy - based force field in amber and in the qm calculations . therefore , the cns energy has to be weighted by a factor of 1/3 to be comparable with the qm and amber mm energies . the quantum - refinement calculations were based on the same crystal structure as the qm / mm calculations ( but both subunits were considered )   and the corresponding structure factors were downloaded from the protein data bank . calculations were performed with the same qm system as with qm / mm [ ( ch3s)3(ch3nhch(nh12)nh2)fe2s2 ] , as well as a qm system enlarged with a ch3oh model of ser and a ch3nhch(nh2)2 model of arg ( for both the intact oxidised cluster , as well as the one - electron - reduced cluster without one of the bridging sulphide ions ) . the qm method and the quantum mechanical ( qm)/molecular mechanical ( mm ) calculations were performed with the comqum software program [ 20 , 21 ] utilising turbomole 5.9   for the qm calculations and amber 9   for the mm calculations . the qm calculations were performed using the bp86 functional [ 24 , 25 ] and the def2-sv(p ) basis sets , which have given reasonable results for [ 2fe2s ] clusters in previous calculations [ 18 , 27 ] . for the mm calculations , we used the amber-99 force field [ 28 , 29 ] . for the [ 4fe4s ] cluster and the dethiobiotin and s - adenosylmethionine ligands , we used force - field parameters previously determined in our group [ 3032 ] . in the qm / mm approach , the qm region ( system 1 ) contains the most interesting atoms and is relaxed by qm methods . system 2 consists of the residues closest to the qm system and is optimised by mm calculations . the remaining part of the protein and the surrounding solvent molecules ( system 3 ) are kept fixed at the crystallographic coordinates . in the qm calculations , system 1 is represented by a wavefunction , whereas all the other atoms are represented by an array of partial point charges , one for each atom , taken from mm libraries . thereby , the polarisation of the quantum chemical system by the surroundings is included in a self - consistent manner . when there is a bond between systems 1 and 2 ( a junction ) , the quantum region is truncated by hydrogen atoms , the positions of which are linearly related to the corresponding carbon atoms in the full system ( the hydrogen - link - atom approach ) . to eliminate the non - physical effect of placing point charges on atoms in the mm region bound to junction atoms ( i.e. the closest neighbours of the qm system ) , those charges are zeroed , and the total energy is calculated as\documentclass[12pt]{minimal } 
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				 \begin{document}$$ e_{{{\text{qm}}/{\text{mm } } } } = e_{{{\text{qm}}1 + { \text{ptch } } } } -e_{{{\text{mm}}1 } } + e_{{{\text{mm}}123 } } $ $ \end{document}where eqm1+ptch is the qm energy of system 1 truncated by the hydrogen atoms and embedded in the set of point charges ( but excluding the self - energy of the point charges ) . emm1 is the mm energy of system 1 , still truncated by hydrogen atoms , but without any electrostatic interactions . finally , emm123 is the classical energy of all atoms with normal atoms at the junctions and with the charges of the quantum system set to zero ( to avoid double - counting of the electrostatic interactions ) . by this approach , which is similar to the one used in the oniom method , errors caused by the calculations were based on the crystal structure ( protein data bank code 1r30 ) . as the enzyme was crystallised as a homodimer with little difference in atom positions ( less than 0.1   differences within the [ 2fe2s ] cluster ) , only the a subunit was used for the investigations and only this subunit is discussed . hydrogen atoms were added to the crystal structure and the protein was solvated in a sphere of water molecules with a radius of 36   using the leap module in the amber software suite . the protonation status of all residues was checked by the propka program   and it was concluded that no residues have strongly perturbed pka values ( thus , all arginine and lysine residues , except arg , see below , were considered in their protonated state , whereas all aspartate and glutamate residues were considered in their deprotonated state ) . for the histidine residues , the protonation was decided from a detailed study of the solvent exposure and hydrogen - bond pattern . this procedure led to the following assignment : his and his were protonated on both nitrogen atoms , whereas his was protonated on n only and his was protonated on n only . the [ 4fe4s ] cluster , s - adenosylmethionine and the dethiobiotin molecule found in the crystal structure were all included in the calculations . the total charge of the simulated system was 8 ( neutral arginine ) or 7 ( protonated arginine ) . the positions of the atoms added were optimised by a 90-ps simulated - annealing molecular dynamics simulation , followed by 10,000 steps of conjugate gradient energy minimisation . the temperature was kept constant at 300  k using the berendsen weak - coupling algorithm   with a time constant of 1  ps . the non - bonded cut - off was 15   and the pair list was updated every 50  fs . in the qm / mm calculations , system 1 contained the [ 2fe2s ] cluster and the relevant atoms of the four coordinating amino acids ( cys , cys , cys and arg ) and was treated with qm methods . the side chains were included as far as c for the cysteine residues ( replacing c by a hydrogen atom ) and as far as c for the arginine residue ( replacing c by a hydrogen atom ) . thus , it consisted of [ ( ch3s)3(ch3nhch(nh)nh2)fe2s2 ] for the calculations with neutral arginine and [ ( ch3s)3(ch3nhch(nh2)nh2)fe2s2 ] for the calculations with protonated arginine . system 2 included all residues with any atom within 6   of any atom in system 1 and was relaxed with mm methods . system 3 included the remaining protein atoms as well as the water molecules and was kept fixed at the crystallographic coordinates . as both iron atoms of the oxidised [ 2fe2s ] cluster are in the fe high - spin state ( s  =  5/2 ) , two spin states are possible ( the ferromagnetically coupled , f , state , s  =  5 , and the antiferromagnetically coupled , af , state , s  =  0 ) . the af state always had a lower energy than the f state and it is also the one observed experimentally . therefore , all results presented are af energies . to ensure that the qm / mm energy differences are stable , the calculations were in general run forth and back between the relevant states until the energies were stable within 4  kj / mol . similar calculations were also performed on one - electron - reduced clusters , i.e. clusters containing one fe and one fe ion ( net charge of the qm system 1 or 2 , depending on the protonation of the arginine model ) , on two - electron - reduced clusters ( net charge 2 or 3 ) and on clusters with one of the bridging sulphur atoms removed ( the one closest to dethiobiotin ; net charge 0 or 1 , so this is equivalent to removing an s ion and reducing both iron ions to fe ) , in all cases in the af ( s  =  1/2 or s  =  0 ) state . for convenience , all geometry optimisations discussed were started from an initial optimisation with structure 2 ( structure  1 ) . to verify that this is acceptable , we tested to what extent the optimised geometry depends on the starting geometry . in addition , the influence of the spin and oxidation states of the [ 2fe2s ] cluster on structural properties was investigated . these explorative calculations were performed in a vacuum ( i.e. system 1 only ) , starting from the crystal geometry . geometry optimisations for structure 2 in different oxidation states ( fe / fe , fe / fe or fe / fe ) and spin states ( af or f ) showed that the final geometries of the intact clusters , especially the fefe distances and the orientation of the arginine residue , do not depend on the starting geometries . the oxidised af and f states were also tested for the other protonation states ( structures 1 , 3 and 4 ) , with similar results . in all calculations , short fefe distances were found in all cases , although they were slightly longer for the f states ( af : 2.572.65   , f : 2.422.89   ) ; no additional electronic states with larger fefe distances were detected . to verify this observation , the fefe distance was fixed to values between 2.5 and 3.5  ( structure 2 , oxidised , af state ) and the rest of the geometry was optimised . only one energy minimum was found , at approximately 2.6  ( 61  kj / mol more stable than the distance in the crystal structure ) and no evidence for a second minimum close to the crystal structure distance was found.structure  1conceivable coordination modes for arginine in the protonated ( 1 ) or neutral ( 24 ) state as represented in the quantum mechanical system conceivable coordination modes for arginine in the protonated ( 1 ) or neutral ( 24 ) state as represented in the quantum mechanical system similar explorative calculations were performed with the hybrid b3lyp functional [ 38 , 39 ] ( to examine the effect of another functional with exact exchange ) , giving similar results [ eaf    ef  =  20 to 55  kj / mol , d(fefe )  =  2.552.72 ( af ) and 2.702.96   ( f ) and an energy minimum at 2.8   , 36  kj / mol lower than the crystal structure ] . quadrupole splittings were calculated according to\documentclass[12pt]{minimal } 
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				 \begin{document}$$ \updelta e_{\text{q } } = 1/2eqv_{\text{zz } } \left ( { 1 + \eta^{2 } /3 } \right)^{1/2 } $ $ \end{document}where q  =  0.16  b ( 1.6    10  m ) for fe ,   =  ( vxx    vyy)/vzz , with |vxx|  <  |vyy|  <  |vzz| , and 1  mm / s is equivalent to 4.8075    10  ev . we also performed a set of quantum - refinement calculations , using the software program comqum - x . they can be seen as qm / mm calculations in which the structures are restrained towards crystallographic raw data . in comqum - x , the mm program is replaced by the crystallographic refinement program crystallography & nmr system ( cns ) . in crystallographic refinement , the coordinates , b factors , occupancies , etc . are improved by optimising the fit of the observed and calculated structure - factor amplitudes , typically estimated by the residual disagreement , the r factor . because of the limited resolution normally obtained with x - ray diffraction of biomolecules , a mm force field is used to supplement the data for the whole protein . this force field ensures that the bond lengths and angles make chemical sense . in comqum - x , this force field is replaced by more accurate qm calculations for a small , but interesting , part of the protein ( system 1 ) , in a manner completely analogous to the use of quantum mechanics in qm / mm calculations . thus , the comqum - x refinement takes the form of a minimisation using an energy function of the form\documentclass[12pt]{minimal } 
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				 \begin{document}$$ e_{\text{comqum - x } } = e_{{{\text{qm}}1 } } - e_{{{\text{mm}}1 } } + e_{{{\text{mm}}123 } } + w_{\text{a } } e_{\text{x - ray } } $ $ \end{document } here , emm1 and emm123 have the same meaning as in eq .  1 , whereas eqm1 is the energy of the qm system , without any point - charge model of the surroundings . ex - ray is a penalty function , describing how well the model agrees with the experimental x - ray data . we have used the default maximum likelihood refinement target using amplitudes ( mlf ) in cns . wa is a weight factor , which is necessary because ex - ray is in arbitrary units whereas the other terms are in energy units . it should be emphasised that the wa factor is nothing special for quantum refinement . on the contrary , it also has to be set in standard crystallographic refinement ( which is obtained from eq .  3 with eqm1  =  emm1  =  0 ) , although it is rarely discussed . the default behaviour of cns is to determine wa so that the ex - ray and emm123 forces have the same magnitude during a short molecular dynamics simulation , i.e. that the crystallographic raw data and the mm force field have a similar influence on the structure . unfortunately , we encountered convergence problems if we used the default value of wa ( 4.87 ) for some of the structures ( because the crystallographically preferred structure of the [ 2fe2s ] cluster is so poor at this low resolution that it becomes incompatible with the qm calculations ) . therefore , we present results only for the largest value of the wa factor that gave converged structures for all models , viz . the results are qualitatively the same if other values are used , regarding the preferred model and coordination mode of the arginine ligand . following crystallographic custom , no hydrogen atoms were included in the mm region of the comqum - x calculations , because hydrogen atoms are not discernible in the crystal structure . therefore , polarisation of the quantum system by the surrounding protein is not included in comqum - x . finally , it should be noted that the mm force field used in cns ( protein_rep.param , dna - rna_rep.param , water.param and ion.param ) is based on a statistical survey of crystal structures , rather than the energy - based force field in amber and in the qm calculations . therefore , the cns energy has to be weighted by a factor of 1/3 to be comparable with the qm and amber mm energies . the quantum - refinement calculations were based on the same crystal structure as the qm / mm calculations ( but both subunits were considered )   and the corresponding structure factors were downloaded from the protein data bank . calculations were performed with the same qm system as with qm / mm [ ( ch3s)3(ch3nhch(nh12)nh2)fe2s2 ] , as well as a qm system enlarged with a ch3oh model of ser and a ch3nhch(nh2)2 model of arg ( for both the intact oxidised cluster , as well as the one - electron - reduced cluster without one of the bridging sulphide ions ) . the qm method and basis sets were the same as in the qm / mm calculations . because of the importance of interactions of the [ 2fe2s ] cluster and its four ligands with the surrounding protein and solvent , a qm / mm approach including the protein environment is the theoretical method of choice . four different structures were studied depending on the protonation state of arg , as is illustrated in structure  1 . in the first ( 1 ) , arg is protonated , and therefore positively charged . in the other three , one of the terminal nh2 groups of arg the three structures differ in whether the deprotonated nh group ( 2 ) or the protonated nh2 group coordinates to iron . in the latter case , the non - coordinating nh group can have the hydrogen atom pointing either towards the cluster ( 3 ) or away from the cluster ( 4 ) . at first glance , the geometry is quite similar in all cases . the fe n distances ( table  1 ) are in a range that agrees with the crystal structure ( 2.4   ) considering its low resolution ( 3.4   ) in all three structures with neutral arginine ( 2 2.05  , 3 2.25   , 4 2.27   ) , as well as in the protonated structure ( 1 2.45   ) . n bond is strongest in 2 , which could be expected as the nh group has an sp - like , nucleophilic lone pair , whereas the p - like lone pair of the nh2 group is involved in  interactions within the guanidine group . nevertheless , the guanidinium group is still in close proximity to the [ 2fe2s ] cluster.fig . 2optimised structures from the quantum mechanical / molecular mechanical calculationstable  1structural parameters from the crystal structure and from the quantum mechanical / molecular mechanical calculationsfe n ( )fefe ( )crystal structure2.40 , 2.353.28 , 3.2412.452.6522.052.6932.252.6342.272.651  +  e3.262.592  +  e2.112.663  +  e3.262.574  +  e3.422.581  +  2e3.192.622  +  2e2.182.683  +  2e3.242.624  +  2e3.232.601    s4.152.542    s2.013.083    s2.142.794    s2.152.74 optimised structures from the quantum mechanical / molecular mechanical calculations structural parameters from the crystal structure and from the quantum mechanical / molecular mechanical calculations recently , di costanzo et al .   performed a survey of metal  guanidine interactions in the cambridge structural database . they found 150 such interactions in 45 different structures , but all except four of these involved a diguanidine moiety chelating a single metal , which is quite different from an arginine  metal coordination . nitrogen distances of 1.842.08  ( average 1.91    0.06  ) , but none of the complexes involved iron . n distance that is similar to what is found in small inorganic metal  guanidine complexes . the survey of di costanzo et al . also involved the only three protein crystal structures with metal  guanidine coordination , viz . biob , an h67r carbonic anhydrase i mutant   and an arginase l - arginine complex . n distance of 2.5  , whereas the zn  n distance in the carbonic anhydrase mutant is 2.1  , i.e. , the only protein structure that has a metal  guanidine bond length similar to the bond length of the small inorganic complexes . di costanzo et al . assumed that the biob structure involved a deprotonated ( neutral ) arginine and did not consider any other possibility . the fefe distance is quite independent of the coordination as well as the protonation state of the arginine group ( 2.632.69  ) and is in perfect agreement with the fefe distances of other [ 2fe2s ] clusters that have been structurally characterised . none of the calculated structures reproduce the long fefe distance found in the biob crystal structure ( 3.243.28  ) . as metal sites are often reduced during x - ray experiments , one- or two - electron - reduced clusters containing fe ions were also optimised , but they do not show any increased fefe distance . the main geometric change upon reduction is the dissociation of the nh2 group ( 1 , 3 , 4 ) . however , when one of the bridging sulphur atoms was removed from the cluster ( and the two iron atoms thereby were reduced ) , the fefe distance increased in the structures with neutral arginine ( 2 3.08   , 3  2.79   , 4 2.74   ) . in this case , only the protonated arginine ( 1 ) dissociates from the iron atom . it is possible that one of the sulphur atoms has been removed from the cluster ( and inserted into dethiobiotin ) in the crystal since the enzyme reaction is started by reduction of the [ 4fe4s ] cluster , which could happen owing to radiation damage during the measurement . it is not possible to decide whether or not there is a sulphur atom in the ( dethio)biotin molecule in the crystal by examination of the electron density map owing to the low resolution . the non - coordinating nh / nh2 group acts as a hydrogen - bond donor in the structures with a proton pointing towards the bridging sulphide ( 1 , 2 , 3 ) . additional hydrogen bonds can be found between arg and four surrounding amino acids ( ser , ser , ser and arg ) . except for ser , which accepts a hydrogen bond from the non - terminal nh group in all cases , thus , the positively charged arg can act as a hydrogen - bond donor towards the bridging sulphide of the [ 2fe2s ] cluster ( 1 , 2 ) or the nh group of arg ( 3 , 4 ) . ser acts as an acceptor towards the nh2 group of arg in all structures and can in addition donate a hydrogen bond towards the bridging sulphide ( 2 , 3 ) , whereas ser can accept hydrogen bonds from the non - coordinating nh2 group of arg ( 1 , 2 ) . in all cases , the arginine acts as a monodentate ligand ; no evidence for secondary bonding interactions was found . of the three structures with a neutral arginine , 2 has the lowest energy , 80 and 88  kj / mol lower than that of structures 3 and 4 , respectively . this shows that coordination by the more nucleophilic nh group is preferred before nh2 coordination . the energy of 1 can not be compared directly because of the additional proton in the system . comparing the protonated structure  ( 1 ) with the best neutral structure ( 2 ) the other relevant distances are similar , as are the hydrogen bonds close to the [ 2fe2s ] cluster . mssbauer parameters of the [ 2fe2s ] cluster in biob have been measured [ 4850 ] , showing a single quadrupole doublet with a quadrupole splitting of eq  =  0.510.53  mm / s . this is quite unexpected , because for a cluster containing two iron atoms with different coordination environments , two doublets would be expected . quadrupole splittings ( eq ) were calculated from the electric field gradients at the position of the iron atoms for the optimised geometries of structures  14 and are presented in table  2.table  2experimental [ 4850 ] and calculated quadrupole splittings ( mm / s)eq ( s4)eq ( s3n)experimental0.530.5310.331.2720.330.5930.451.1440.431.23 experimental [ 4850 ] and calculated quadrupole splittings ( mm / s ) although the quadrupole splittings calculated for the sulphur - coordinated iron atom are roughly the same in all four cases ( 0.330.45  mm / s ) , the other iron atom exhibits very different values depending on the exact coordination mode . although eq is quite large with the nh2 coordinating ( 1 1.27 , 3 1.14 , 4 1.23  mm / s ) , it is relatively small in case of nh coordination ( 2 0.59  mm / s ) . taking into account that calculated quadrupole splittings are usually too low in similar cases   and that the accuracy of calculated eq ( i.e. the amount by which they are lower than experimental values ) seems to depended on the coordination [ 18 , 27 ] , the neutral state with the nh group coordinating ( 2 ) fits the experimental data best . as biological samples usually exhibit weak mssbauer signals owing to their low iron content , especially when another fe / s cluster is present , it seems reasonable that the experimentally found doublet is the sum of two doublets with similar quadrupole splittings . thus , we can conclude that qm / mm calculations predict a neutral arginine with nh coordination ( structure 2 ) . nevertheless , the reason for the experimentally found fefe distance as well as the significance of the unusual arginine ligand remains elusive . we also studied the enzyme by quantum refinement , which is standard crystallographic refinement , using the original experimental structure factors , but replacing the mm force field ( which is used to supplement the crystallographic raw data and give accurate bond lengths and angles ) for the active site by more accurate qm calculations . this will allow us to study what realistic structures of the [ 2fe2s ] site actually fit into the electron density . in particular , we will be able to test what protonation state ( structures  14 ) fits the crystallographic raw data best . two sizes of the qm system were tested ( with or without models of ser and arg ) , as well as models of both the oxidised state with an intact cluster and the two - electron - reduced state with either an intact cluster or one of the bridging sulphur atoms removed . it can be seen that all re - refined structures of the intact cluster give fefe distances ( 2.582.77  ) that are appreciably shorter than in the crystal structure and therefore similar to those obtained in the qm / mm calculations . in the structures without one of the sulphur atoms , the fefe distance is longer ( 2.852.99  ) , but not as long as in the crystal structure . however , it should be noted that both the rfree and residue ( real - space ) r factors are slightly lower for the original crystal structure than for any of the re - refined structures . this indicates a misfit between the crystal structure and the qm systems tested , which may indicate that we still have not yet tested the correct qm system or that the crystal structure is a mixture of several different structures , which is expected if the metal site is reduced during data collection.table  3results of the quantum - refinement calculations with wa  =  0.1fefedistance to fe1 ( )distance to fe2 ( )rfreeresidue reqm1(kj / mol)r1()ns1s2s3s2s3s4s5small qm system , oxidised state , intact cluster  12.583.292.242.212.192.252.222.252.250.30420.23660.80.27  22.692.092.322.232.212.262.222.332.310.30280.19741.60.13  32.692.282.302.202.212.242.232.332.300.30320.21295.30.29 42.692.372.312.182.212.222.242.332.300.30350.213127.10.36large qm system , oxidised state , intact cluster  12.603.342.222.222.182.292.212.232.230.30440.243178.50.91  22.742.102.292.252.202.312.202.312.290.30280.19989.80.20  32.722.332.262.202.212.272.232.312.280.30310.228130.90.31  42.673.182.242.192.172.262.232.282.290.30480.285133.00.87large qm system , reduced state , intact cluster  12.773.552.272.362.172.492.312.282.350.30420.250125.00.65  22.672.092.312.272.242.342.282.382.340.30290.20675.20.11  32.773.082.292.232.212.322.302.332.360.30430.265204.90.96  42.663.252.252.192.332.362.332.332.400.30380.276191.11.03large qm system , without one s atom  12.882.412.232.222.272.272.240.30340.212192.40.26  22.852.062.292.222.242.302.270.30400.196161.60.20  32.992.242.242.202.252.302.260.30300.193195.30.33  42.982.202.252.182.252.322.270.30300.196156.40.14crystal structure re - refined without quantum mechanics  i2.992.332.372.192.102.112.162.192.250.30040.1381.18  ii2.972.332.382.192.132.122.172.192.270.30040.1401.11crystal structure  a3.242.352.322.232.222.222.232.282.300.30030.140244.41.00  b3.282.402.302.262.232.222.232.252.271.17distances between the iron ions and the ligands (  ) are given , as well as the rfree , residue r factors , eqm1 and rqm , which are the differences in the energy and iron  ligand distances of the qm system optimised in the crystal and in a vacuum . four sets of calculations are presented : with the small qm system or with the qm system enlarged by ser and arg , for the oxidised state ( fe2iii ) or for the two - electron - reduced state ( fe2ii ) , and for the intact [ 2fe2s ] cluster or for the cluster with one sulphide ion removed . in addition , the data from the crystal structure ( both subunits ) are presented , as well as a standard crystallographic re - refinement of the [ 2fe2s ] cluster with two different treatments of the fe  s interactions ( see the text ) results of the quantum - refinement calculations with wa  =  0.1 distances between the iron ions and the ligands (  ) are given , as well as the rfree , residue r factors , eqm1 and rqm , which are the differences in the energy and iron  ligand distances of the qm system optimised in the crystal and in a vacuum . four sets of calculations are presented : with the small qm system or with the qm system enlarged by ser and arg , for the oxidised state ( fe2iii ) or for the two - electron - reduced state ( fe2ii ) , and for the intact [ 2fe2s ] cluster or for the cluster with one sulphide ion removed . in addition , the data from the crystal structure ( both subunits ) are presented , as well as a standard crystallographic re - refinement of the [ 2fe2s ] cluster with two different treatments of the fe  s interactions ( see the text ) the structure of the cluster also depends on the details of the refinement protocol . unfortunately , the original publication   does not provide such details and we have not been able to obtain them from the authors . therefore , we tested re - refining the structure of the [ 2fe2s ] cluster with standard crystallography ( i.e. with eqm1  =  emm1  =  0 in eq .  3 ) and with different treatments of the fe  s interactions in the mm force field ( i.e. in the emm123 term ) . as can be seen in table  3 , the results are insensitive to whether fe s bonds are included with zeroed force constants ( the preferred method to allow the site to be determined entirely by the experimental data ; protocol i in table  3 ) or if no fe s bonds are defined ( so that there are van der waals interactions between all iron and sulphur ions ; protocol ii in table  3 ) . this indicates that the default wa factor is so large that the mm force field has only a minor influence on the structure of the [ 2fe2s ] site . however , it can also be seen that the structure of the re - refined [ 2fe2s ] site is quite different from the original crystal structure , showing that details in the refinement still differ . in particular , the fefe distance in our re - refined structure ( 2.972.99   ) is appreciably shorter than in the original crystal structure ( 3.24  ) . the re - refined results are similar to the quantum - refined results with a cluster without one sulphur atom . among the four qm systems tested ( models 14 ) , it is clear that the one with a deprotonated arg and the nh group coordinated to iron ( model 2 ) fits the crystallographic data best for all structures with an intact cluster : it has the lowest rfree and residue ( real - space ) r factors , and it also gives the lowest strain energy ( eqm1 , i.e. the energy difference of the qm system when optimised in the crystal or in a vacuum ) as well as the lowest difference in geometry when optimised in the crystal or in a vacuum ( r1 in table  3 ) . thus , all these four criteria point out the same structure as the best one , showing that the results are conclusive . in particular , it is clear that model 2 fits the crystallographic data appreciably better than the structure with a protonated arg ( model 1 ) . in fact , arg dissociates from iron in the latter model , giving fe  n distances of 3.293.55  , when re - refined with wa <  1 . however , when wa    1 , the fe n distance is shortened to 2.472.26  , showing that the crystal structure prefers shorter values . the two deprotonated models coordinating through the nh2 group ( models 3 and 4 ) give intermediate fits to the crystal structure . figure  3 shows that the quantum - refined structure of model 2 fits the electron density equally well as the original crystal structure , and it also shows the rather poorly defined electron density at this low resolution.fig . 3electron - density omit 2fo    fc maps of the [ 2fe2s ] cluster in the original crystal structure ( left ) and the quantum - refined model 2 ( right ) at the 2.0 level electron - density omit 2fo    fc maps of the [ 2fe2s ] cluster in the original crystal structure ( left ) and the quantum - refined model 2 ( right ) at the 2.0 level for the structure without one of the sulphur atoms , the results are somewhat different . then , the various quality criteria give different results : model 3 gives the lowest rfree and residue r factors , whereas model 4 gives the smallest strain energy and difference in geometry . this is also supported by the higher rfree factor ( 0.3030 ) , compared with the best values obtained for the oxidised models ( 0.3028 ) . however , the difference is not very large , indicating that the crystal structure might actually be a mixture of oxidised and reduced structures . because of the importance of interactions of the [ 2fe2s ] cluster and its four ligands with the surrounding protein and solvent , a qm / mm approach including the protein environment is the theoretical method of choice . four different structures were studied depending on the protonation state of arg , as is illustrated in structure  1 . in the first ( 1 ) , arg is protonated , and therefore positively charged . in the other three , one of the terminal nh2 groups of arg the three structures differ in whether the deprotonated nh group ( 2 ) or the protonated nh2 group coordinates to iron . in the latter case , the non - coordinating nh group can have the hydrogen atom pointing either towards the cluster ( 3 ) or away from the cluster ( 4 ) . at first glance , the geometry is quite similar in all cases . the fe n distances ( table  1 ) are in a range that agrees with the crystal structure ( 2.4   ) considering its low resolution ( 3.4   ) in all three structures with neutral arginine ( 2 2.05  , 3 2.25   , 4 2.27   ) , as well as in the protonated structure ( 1 2.45   ) . n bond is strongest in 2 , which could be expected as the nh group has an sp - like , nucleophilic lone pair , whereas the p - like lone pair of the nh2 group is involved in  interactions within the guanidine group . nevertheless , the guanidinium group is still in close proximity to the [ 2fe2s ] cluster.fig . 2optimised structures from the quantum mechanical / molecular mechanical calculationstable  1structural parameters from the crystal structure and from the quantum mechanical / molecular mechanical calculationsfe n ( )fefe ( )crystal structure2.40 , 2.353.28 , 3.2412.452.6522.052.6932.252.6342.272.651  +  e3.262.592  +  e2.112.663  +  e3.262.574  +  e3.422.581  +  2e3.192.622  +  2e2.182.683  +  2e3.242.624  +  2e3.232.601    s4.152.542    s2.013.083    s2.142.794    s2.152.74 optimised structures from the quantum mechanical / molecular mechanical calculations structural parameters from the crystal structure and from the quantum mechanical / molecular mechanical calculations recently , di costanzo et al .   performed a survey of metal  guanidine interactions in the cambridge structural database . they found 150 such interactions in 45 different structures , but all except four of these involved a diguanidine moiety chelating a single metal , which is quite different from an arginine  metal coordination . nitrogen distances of 1.842.08  ( average 1.91    0.06  ) , but none of the complexes involved iron . n distance that is similar to what is found in small inorganic metal  guanidine complexes . the survey of di costanzo et al . also involved the only three protein crystal structures with metal  guanidine coordination , viz . biob , an h67r carbonic anhydrase i mutant   and an arginase l - arginine complex . n distance of 2.5  , whereas the zn  n distance in the carbonic anhydrase mutant is 2.1  , i.e. , the only protein structure that has a metal  guanidine bond length similar to the bond length of the small inorganic complexes . di costanzo et al . assumed that the biob structure involved a deprotonated ( neutral ) arginine and did not consider any other possibility . the fefe distance is quite independent of the coordination as well as the protonation state of the arginine group ( 2.632.69  ) and is in perfect agreement with the fefe distances of other [ 2fe2s ] clusters that have been structurally characterised . none of the calculated structures reproduce the long fefe distance found in the biob crystal structure ( 3.243.28  ) . as metal sites are often reduced during x - ray experiments , one- or two - electron - reduced clusters containing fe ions were also optimised , but they do not show any increased fefe distance . the main geometric change upon reduction is the dissociation of the nh2 group ( 1 , 3 , 4 ) . however , when one of the bridging sulphur atoms was removed from the cluster ( and the two iron atoms thereby were reduced ) , the fefe distance increased in the structures with neutral arginine ( 2 3.08   , 3  2.79   , 4 2.74   ) . in this case , only the protonated arginine ( 1 ) dissociates from the iron atom . it is possible that one of the sulphur atoms has been removed from the cluster ( and inserted into dethiobiotin ) in the crystal since the enzyme reaction is started by reduction of the [ 4fe4s ] cluster , which could happen owing to radiation damage during the measurement . it is not possible to decide whether or not there is a sulphur atom in the ( dethio)biotin molecule in the crystal by examination of the electron density map owing to the low resolution . the non - coordinating nh / nh2 group acts as a hydrogen - bond donor in the structures with a proton pointing towards the bridging sulphide ( 1 , 2 , 3 ) . additional hydrogen bonds can be found between arg and four surrounding amino acids ( ser , ser , ser and arg ) . except for ser , which accepts a hydrogen bond from the non - terminal nh group in all cases , thus , the positively charged arg can act as a hydrogen - bond donor towards the bridging sulphide of the [ 2fe2s ] cluster ( 1 , 2 ) or the nh group of arg ( 3 , 4 ) . ser acts as an acceptor towards the nh2 group of arg in all structures and can in addition donate a hydrogen bond towards the bridging sulphide ( 2 , 3 ) , whereas ser can accept hydrogen bonds from the non - coordinating nh2 group of arg ( 1 , 2 ) . in all cases , the arginine acts as a monodentate ligand ; no evidence for secondary bonding interactions was found . of the three structures with a neutral arginine , 2 has the lowest energy , 80 and 88  kj / mol lower than that of structures 3 and 4 , respectively . this shows that coordination by the more nucleophilic nh group is preferred before nh2 coordination . the energy of 1 can not be compared directly because of the additional proton in the system . comparing the protonated structure  ( 1 ) with the best neutral structure ( 2 ) the other relevant distances are similar , as are the hydrogen bonds close to the [ 2fe2s ] cluster . mssbauer parameters of the [ 2fe2s ] cluster in biob have been measured [ 4850 ] , showing a single quadrupole doublet with a quadrupole splitting of eq  =  0.510.53  mm / s . this is quite unexpected , because for a cluster containing two iron atoms with different coordination environments , two doublets would be expected . quadrupole splittings ( eq ) were calculated from the electric field gradients at the position of the iron atoms for the optimised geometries of structures  14 and are presented in table  2.table  2experimental [ 4850 ] and calculated quadrupole splittings ( mm / s)eq ( s4)eq ( s3n)experimental0.530.5310.331.2720.330.5930.451.1440.431.23 experimental [ 4850 ] and calculated quadrupole splittings ( mm / s ) although the quadrupole splittings calculated for the sulphur - coordinated iron atom are roughly the same in all four cases ( 0.330.45  mm / s ) , the other iron atom exhibits very different values depending on the exact coordination mode . although eq is quite large with the nh2 coordinating ( 1 1.27 , 3 1.14 , 4 1.23  mm / s ) , it is relatively small in case of nh coordination ( 2 0.59  mm / s ) . taking into account that calculated quadrupole splittings are usually too low in similar cases   and that the accuracy of calculated eq ( i.e. the amount by which they are lower than experimental values ) seems to depended on the coordination [ 18 , 27 ] , the neutral state with the nh group coordinating ( 2 ) fits the experimental data best . as biological samples usually exhibit weak mssbauer signals owing to their low iron content , especially when another fe / s cluster is present , it seems reasonable that the experimentally found doublet is the sum of two doublets with similar quadrupole splittings . thus , we can conclude that qm / mm calculations predict a neutral arginine with nh coordination ( structure 2 ) . nevertheless , the reason for the experimentally found fefe distance as well as the significance of the unusual arginine ligand remains elusive . we also studied the enzyme by quantum refinement , which is standard crystallographic refinement , using the original experimental structure factors , but replacing the mm force field ( which is used to supplement the crystallographic raw data and give accurate bond lengths and angles ) for the active site by more accurate qm calculations . this will allow us to study what realistic structures of the [ 2fe2s ] site actually fit into the electron density . in particular , we will be able to test what protonation state ( structures  14 ) fits the crystallographic raw data best . two sizes of the qm system were tested ( with or without models of ser and arg ) , as well as models of both the oxidised state with an intact cluster and the two - electron - reduced state with either an intact cluster or one of the bridging sulphur atoms removed . it can be seen that all re - refined structures of the intact cluster give fefe distances ( 2.582.77  ) that are appreciably shorter than in the crystal structure and therefore similar to those obtained in the qm / mm calculations . in the structures without one of the sulphur atoms , the fefe distance is longer ( 2.852.99  ) , but not as long as in the crystal structure . however , it should be noted that both the rfree and residue ( real - space ) r factors are slightly lower for the original crystal structure than for any of the re - refined structures . this indicates a misfit between the crystal structure and the qm systems tested , which may indicate that we still have not yet tested the correct qm system or that the crystal structure is a mixture of several different structures , which is expected if the metal site is reduced during data collection.table  3results of the quantum - refinement calculations with wa  =  0.1fefedistance to fe1 ( )distance to fe2 ( )rfreeresidue reqm1(kj / mol)r1()ns1s2s3s2s3s4s5small qm system , oxidised state , intact cluster  12.583.292.242.212.192.252.222.252.250.30420.23660.80.27  22.692.092.322.232.212.262.222.332.310.30280.19741.60.13  32.692.282.302.202.212.242.232.332.300.30320.21295.30.29 42.692.372.312.182.212.222.242.332.300.30350.213127.10.36large qm system , oxidised state , intact cluster  12.603.342.222.222.182.292.212.232.230.30440.243178.50.91  22.742.102.292.252.202.312.202.312.290.30280.19989.80.20  32.722.332.262.202.212.272.232.312.280.30310.228130.90.31  42.673.182.242.192.172.262.232.282.290.30480.285133.00.87large qm system , reduced state , intact cluster  12.773.552.272.362.172.492.312.282.350.30420.250125.00.65  22.672.092.312.272.242.342.282.382.340.30290.20675.20.11  32.773.082.292.232.212.322.302.332.360.30430.265204.90.96  42.663.252.252.192.332.362.332.332.400.30380.276191.11.03large qm system , without one s atom  12.882.412.232.222.272.272.240.30340.212192.40.26  22.852.062.292.222.242.302.270.30400.196161.60.20  32.992.242.242.202.252.302.260.30300.193195.30.33  42.982.202.252.182.252.322.270.30300.196156.40.14crystal structure re - refined without quantum mechanics  i2.992.332.372.192.102.112.162.192.250.30040.1381.18  ii2.972.332.382.192.132.122.172.192.270.30040.1401.11crystal structure  a3.242.352.322.232.222.222.232.282.300.30030.140244.41.00  b3.282.402.302.262.232.222.232.252.271.17distances between the iron ions and the ligands (  ) are given , as well as the rfree , residue r factors , eqm1 and rqm , which are the differences in the energy and iron  ligand distances of the qm system optimised in the crystal and in a vacuum . four sets of calculations are presented : with the small qm system or with the qm system enlarged by ser and arg , for the oxidised state ( fe2iii ) or for the two - electron - reduced state ( fe2ii ) , and for the intact [ 2fe2s ] cluster or for the cluster with one sulphide ion removed . in addition , the data from the crystal structure ( both subunits ) are presented , as well as a standard crystallographic re - refinement of the [ 2fe2s ] cluster with two different treatments of the fe  s interactions ( see the text ) results of the quantum - refinement calculations with wa  =  0.1 distances between the iron ions and the ligands (  ) are given , as well as the rfree , residue r factors , eqm1 and rqm , which are the differences in the energy and iron  ligand distances of the qm system optimised in the crystal and in a vacuum . four sets of calculations are presented : with the small qm system or with the qm system enlarged by ser and arg , for the oxidised state ( fe2iii ) or for the two - electron - reduced state ( fe2ii ) , and for the intact [ 2fe2s ] cluster or for the cluster with one sulphide ion removed . in addition , the data from the crystal structure ( both subunits ) are presented , as well as a standard crystallographic re - refinement of the [ 2fe2s ] cluster with two different treatments of the fe  s interactions ( see the text ) the structure of the cluster also depends on the details of the refinement protocol . unfortunately , the original publication   does not provide such details and we have not been able to obtain them from the authors . therefore , we tested re - refining the structure of the [ 2fe2s ] cluster with standard crystallography ( i.e. with eqm1  =  emm1  =  0 in eq .  3 ) and with different treatments of the fe  s interactions in the mm force field ( i.e. in the emm123 term ) . as can be seen in table  3 , the results are insensitive to whether fe s bonds are included with zeroed force constants ( the preferred method to allow the site to be determined entirely by the experimental data ; protocol i in table  3 ) or if no fe s bonds are defined ( so that there are van der waals interactions between all iron and sulphur ions ; protocol ii in table  3 ) . this indicates that the default wa factor is so large that the mm force field has only a minor influence on the structure of the [ 2fe2s ] site . however , it can also be seen that the structure of the re - refined [ 2fe2s ] site is quite different from the original crystal structure , showing that details in the refinement still differ . in particular , the fefe distance in our re - refined structure ( 2.972.99   ) is appreciably shorter than in the original crystal structure ( 3.24  ) . the re - refined results are similar to the quantum - refined results with a cluster without one sulphur atom . among the four qm systems tested ( models 14 ) , it is clear that the one with a deprotonated arg and the nh group coordinated to iron ( model 2 ) fits the crystallographic data best for all structures with an intact cluster : it has the lowest rfree and residue ( real - space ) r factors , and it also gives the lowest strain energy ( eqm1 , i.e. the energy difference of the qm system when optimised in the crystal or in a vacuum ) as well as the lowest difference in geometry when optimised in the crystal or in a vacuum ( r1 in table  3 ) . thus , all these four criteria point out the same structure as the best one , showing that the results are conclusive . in particular , it is clear that model 2 fits the crystallographic data appreciably better than the structure with a protonated arg ( model 1 ) . when re - refined with wa  <  1 . however , when wa    1 , the fe n distance is shortened to 2.472.26  , showing that the crystal structure prefers shorter values . the two deprotonated models coordinating through the nh2 group ( models 3 and 4 ) give intermediate fits to the crystal structure . figure  3 shows that the quantum - refined structure of model 2 fits the electron density equally well as the original crystal structure , and it also shows the rather poorly defined electron density at this low resolution.fig . 3electron - density omit 2fo    fc maps of the [ 2fe2s ] cluster in the original crystal structure ( left ) and the quantum - refined model 2 ( right ) at the 2.0 level electron - density omit 2fo    fc maps of the [ 2fe2s ] cluster in the original crystal structure ( left ) and the quantum - refined model 2 ( right ) at the 2.0 level for the structure without one of the sulphur atoms , the results are somewhat different . then , the various quality criteria give different results : model 3 gives the lowest rfree and residue r factors , whereas model 4 gives the smallest strain energy and difference in geometry . this is also supported by the higher rfree factor ( 0.3030 ) , compared with the best values obtained for the oxidised models ( 0.3028 ) . however , the difference is not very large , indicating that the crystal structure might actually be a mixture of oxidised and reduced structures . we have studied the structure of biob with both quantum - refinement and qm / mm methods . this gave us the opportunity to interpret the crystal structure as much as its low resolution ( 3.4  ) allows us . first , it is quite clear that the arg ligand is deprotonated in the crystal structure , because such structures fit the crystallographic raw data best . likewise , both the qm / mm energies and the quantum refinement strongly indicate that it is more favourable for the deprotonated arg to coordinate to iron via the deprotonated nh group , rather than by the nh2 group , even if hydrogen bonds with the surrounding residues are considered . these conclusions are supported by calculated mssbauer parameters which also fit the experimental data best for this coordination mode . finally , it also seems clear that the fefe distance in the [ 2fe2s ] cluster is not as long as the initial report on the crystal structure indicated . instead , it is most likely similar to what is found in all normal [ 2fe2s ] clusters , i.e. approximately 2.7  . the reason for the long bond in the crystal structure may either be the low resolution or that the structure is a mixture of different states of the [ 2fe2s ] cluster , e.g. caused by a successive reduction of the cluster during data collection . clearly , more accurate structural data are needed , as well as further theoretical investigations of the reaction intermediates , which should help to understand this fascinating enzyme .
biotin synthase was the first example of what is now regarded as a distinctive enzyme class within the radical s - adenosylmethionine superfamily , the members of which use fe / s clusters as the sulphur source in radical sulphur insertion reactions . 
 the crystal structure showed that this enzyme contains a [ 2fe2s ] cluster with a highly unusual arginine ligand , besides three normal cysteine ligands . 
 however , the crystal structure is at such a low resolution that neither the exact coordination mode nor the role of this exceptional ligand has been elucidated yet , although it has been shown that it is not essential for enzyme activity . 
 we have used quantum refinement of the crystal structure and combined quantum mechanical and molecular mechanical calculations to explore possible coordination modes and their influences on cluster properties . 
 the investigations show that the protonation state of the arginine ligand has little influence on cluster geometry , so even a positively charged guanidinium moiety would be in close proximity to the iron atom . 
 nevertheless , the crystallised enzyme most probably contains a deprotonated ( neutral ) arginine coordinating via the nh group . 
 furthermore , the fefe distance seems to be independent of the coordination mode and is in perfect agreement with distances in other structurally characterised [ 2fe2s ] clusters . 
 the exceptionally large fefe distance found in the crystal structure could not be reproduced .