flavoprotein d - amino acid oxidases reduce o2 to h2o2 in order to regenerate the substrate - reactive oxidized 
 state of their covalently bound flavin cofactors .
flavin oxidation 
 by o2 reduction is slow in free solution because of the 
 requirement for an intermediate step in what would otherwise be a 
 spin - forbidden two - electron transition .
flavoprotein oxidases can speed this reaction up several orders 
 of magnitude , although there does not appear to be a consensus mechanism .
nevertheless , detailed structure - based studies 
 suggest the importance of ( a ) the protein environment near the flavin 
 for possible stabilization of intermediates and ( b ) the protein structure 
 in channeling o2 from solution to the flavin site .
probably the best - characterized flavoprotein 
 oxidase in terms of 
 structure and activity is monomeric sarcosine oxidase ( msox ) , a bacterial enzyme which catalyzes the oxidation of sarcosine ( n - methylglycine ) to produce formaldehyde , glycine , and hydrogen 
 peroxide : msox is a 44 kda two - domain protein 
 consisting 
 of 385 residues containing a single covalently bound flavin adenine 
 dinucleotide ( 8-s - cysteinyl - fad ) whose flavin ring sits at 
 the interface between the so - called catalytic and flavin domains . 

the flavin domain contains a cleft that admits and shelters the cofactor 
 from solution . a major question regarding the o2 reactivity 
 of msox 
 ( and all flavoprotein oxidases )
is the location of o2 activation 
 relative to the flavin ring and surrounding side chains .
the prevaling 
 theory is that the two - electron reduction of o2 passes 
 through a superoxide anion intermediate .
this hypothesis has gained 
 support because there are positively charged side chains near the 
 flavin isoalloxazine ring .
x - ray crystal 
 structures show the lys265 -amino oriented over the si face of the flavin ring with a bridging water linking 
 it to the flavin ring n(5 ) .
lys265 is 
 indeed crucial for o2 reduction : mutations to ala , gln , 
 or met at position 265 result in an 8000-fold decrease in oxygen reactivity , 
 and mutation to arg results in a 250-fold decrease .
it 
 has therefore been proposed that sarocosine oxidation and oxygen reduction 
 may occur on the re and si faces 
 of the flavin ring , respectively , which is consistent 
 with the so - called modified ping - pong mechanism wherein o2 can oxidize fadh before the product imine is 
 released . however , one potential complication 
 with this interpretation is that it is based on structures containing 
 the oxidized flavin , while it is the reduced anionic form , with a 
 protonated n(5 ) and a negative charge on n(1 ) , with which o2 must react .
it is not clear that precise crystallographic arrangement 
 of the lys265 side chain and associated waters is retained with reduced 
 flavin , which leaves unanswered the question as to whether or not 
 this arrangement is a result of flavin oxidation rather than its cause .
a second major question regards how o2 accesses the 
 flavin cavity from the solvent . in the absence of bound substrate , 

there is clearly room for a single o2 to reach the re face of the flavin ring based on the crystal structure . 

however , the modified ping - pong mechanism suggests that o2 may access the flavin while substrate is bound .
the addition of 
 a substrate blocks the channel observed in the static crystal structure , 
 suggesting o2 accesses the cavity through a separate channel . 

no such channels are readily apparent in the msox crystal structures . 
 given that small dissolved gases access protein interiors through 
 relatively small channels ( e.g. , the histidine gate in myoglobin ) , it is plausible that enzymes which utilize gas molecules as reactants 
 may also exhibit such channels . understanding these channels would 
 provide important new structural insight into the biochemistry of 
 flavoprotein oxidases and may even provide clues to the location of 
 the o2 activation site .
both of these questions can 
 be addressed by querying the statistical 
 likelihood of observing an o2 molecule at any position 
 inside the protein . in similar settings ,
this has been approached 
 using analysis of static crystal structures and all - atom molecular 
 dynamics ( md ) simulations , as well as enhanced sampling variants thereof . 
 in all such efforts , an accurate picture of the accessible volume 
 in the protein interior
this is a severe problem in sampling static structures and even in brute - force molecular dynamics ( md ) , especially if one needs enough statistics to map out the entire 
 protein interior .
therefore , enhanced - sampling methods remain an imporant 
 tool for this kind of mapping .
for instance , elber applied the time - dependent 
 hartree approximation to study co diffusion in myoglobin .
applied implicit ligand sampling ( ils ) to study 
 dynamic oxygen access channels in 12/15-lipoxygenase .
recently , a composite method combining temperature - accelerated 
 md , the single - sweep method of free - energy 
 reconstruction , and the string method 
 in collective variables was used to fully 
 map diffusion pathways and adsorption sites for co and water in the interior 
 of myoglobin , including thermodynamic characterization of the pathways .
is well - suited to studying 
 biological systems involving small molecule diffusion ( o2 , co , co2 , etc . ) .
it is applied here on msox to map o2 sites and pathways to the substrate activation site . in particular
, 
 we base our calculations on both substrate - free and inhibitor - bound 
 msox with reduced flavin .
free energy as a function of the cartesian 
 position of the o2 center of mass in a protein - fixed reference 
 frame is determined .
the locations of regions of low free energy are 
 then identified and the string method applied on this free - energy 
 surface to define pathways of minimal free energy connecting these 
 regions .
the result is a network of putative o2 transport 
 pathways and sites within msox .
our results show that o2 can access the active site through several channels , some of which 
 are unexpected .
we observe deep free energy minima for o2 on the re face of reduced flavin , even with the 
 substrate - mimicking inhibitor 2-furoic acid bound , and none on the si face .
we also observed that the locations of the minimum - free 
 energy pathways and low free - energy sites are not strongly sensitive 
 to whether or not the substrate mimic is bound .
the free energy profiles 
 along the paths , however , do depend sensitively on the presence of 
 the substrate mimic : specifically the occurrence of several deep minima 
 along o2 pathways correlates with the inhibitor - bound state . 

this last finding hints at a manifestation of allostery wherein ligand 
 binding alters the transport pathways through a protein , thereby modulating 
 the rate at which a second substrate accesses the active site .
the composite 
 method developed by maragliano et al . in their study of co in myoglobin was employed here to study o2 in 
 msox .
the primary technique in this method is all - atom molecular dynamics 
 ( md ) underlying a particular series of free - energy calculations . before 
 explaining those , a discussion of how the all - atom systems of inhibitor - bound 
 and apo msox were prepared is necessary .
in addition 
 to the protein , this structure contains several crystal waters and 
 the inhibitor 2-furoic acid ( foa ) , the latter of which mimics how 
 the substrate sarcosine binds .
the foa - bound md system was generated 
 by adding hydrogens to the 2gf3 coordinates where needed , solvating in tip3p water , neutralizing with na ions , to generate 
 a box of 33  226 atoms with dimensions 83.8  64.1  
 67.6  .
this initial system was subject to 1000 steps 
 of conjugate gradient minimization followed by 130 ns of npt md equilibration .
the apo system was created by deletion of the foa from this minimized 
 system and subjecting the resulting system to 130 ns of npt equilibration . 

a molecule of o2 was added by mutating one of the crystal 
 waters coordinating lys265 .
this system consisted of 33  221 
 atoms in a box 83.7  64.0  67.5  .
we did not observe 
 spontaneous opening of the so - called active site loop ( residues 5560 ) 
 in the apo equilibration , and all calculations reported here are with 
 this loop in the closed position .
it may exist in either open or closed 
 configurations for apo msox but only closed for ligand - bound msox .
however , spontaneous opening of the fad cleft 
 was observed in the apo equilibration , distinguished by the breakage 
 of a contact between asn41 and arg282 .
the distribution of cc 
 distances for this residue pair is centered at 10  when the 
 cleft is open and 8  when closed . to assess
whether or not this 
 transition altered the ability of o2 to access the flavin 
 cavity , both apo states are considered in subsequent calculations .
molecular dynamics simulations employed periodic boundary conditions , 
 a nonbonded cutoff of 10  , a particle - mesh ewald spacing of 
 2  , rigid bonds , and a time step of 2 fs .
the temperature was 
 held at 310 k using a standard langevin thermostat and 1 bar using 
 a langevin  nos  hoover barostat . finally , because the subsequent free - energy calculations 
 are performed in a protein - fixed coordinate frame , weak positional / rotational 
 restraints were applied .
these consisisted of cartesian harmonic restraints 
 on the c s of residues 25 , 100 , and 370 with 
 a common spring constant of 1 kcal / mol .
we mention in particular 
 that we use the standard neutral charmm force - field model for oxygen 
 which can not model electronic stacking interactions with residues 
 such as phe .
such interactions can have an influence on o2 diffusion in other proteins , and we 
 expect that using methods such as pele which supplement nonbonded interactions with periodic qm / mm calculations 
 could be of some benefit in future refinement of the results presented 
 in this work .
protonation of the flavin was made consistent 
 with its reduced 
 form , fadh .
charmm - style parameters for the adenine 
 and sugar portions of fadh were adapted from existing 
 parameters for nadh .
the flavin ring was parametrized using the amber 
 antechamber procedure with parameters , including charges determined 
 independently using geometry optimization at the b3lyp 6 - 311 g * level 
 using gaussian , translated into charmm - style units .
charmm - style topology and parameter files 
 for fadh and foa are available in the supporting information .
generally , temperature - accelerated 
 md ( tamd ) accelerates the sampling of collective variables ( cv s ) 
 (x ) in an md simulation by tethering them 
 to fictitiously hot auxiliary variables z with high 
 friction  , such that the forces these variables experience 
 approximate negative free - energy gradients on the free - energy surface 
 of the cvs:1here ,  is a spring - constant - like 
 parameter , 
  the artificial friction coefficient ,  
 the inverse of the artificial temperature (   1/kbt , where kb is boltzmann s constant ) , and jz(t ) is white noise with unit variance . in the approach used by maragliano et al . for co in myoglobin , 

analogously , here the cartesian 
 coordinates of the o2 center of mass are accelerated .
each 
 tamd simulation , or  sweep ,  used the same conditions 
 as did the md equilibrations , with the additional tamd parameters 
 of  = 200 kcal / mol and  = 5 ps .
the goal of tamd is to sample as much of the 
 o2-accessible 
 volume in the protein as possible .
inhibitor bound msox 
 is referred to as  bound msox ,  while apo msox with 
 the asn41arg282 bridge open or closed is  apo - ob msox  
 and  apo - cb msox ,  respectively .
initial sweeps for 
 bound and apo - cb msox were run at ficitious temperatures of 2  
   7 kcal / mol .
three sweeps 
 were run for each discrete fictitious temperature at both the re face near lys265 and below the si face 
 of the flavin ring .
productive sampling was observed between 3 and 
 5 kcal / mol ( see results and discussion ) .
to achieve consistent protein interior volume sampling across the 
 three systems , 1 ns sweeps were initialized from four separate sites 
 within msox , two in each domain .
initial production sweeps were run 
 from two sites in the catalytic domain , the re face 
 near lys265 and below the si face of the flavin ring . 

sites were required in the fad binding domain because regions were 
 accessible to only apo or bound sweeps .
therefore , additional production 
 sweeps were launched from near leu212 and c(5) on fadh but 
 not in the cleft .
for any site , a water was mutated into oxygen from 
 the equilibrated starting structure .
fifty - one sweeps were required for apo - ob , and 64 
 for bound msox .
a total of 151 ns of production sweeps were required 
 to achieve consistent interior volume sampling among all three systems .
the primary output of production sweeps is a dense set of o2 positions both inside and outside the protein .
these sets 
 were culled by beginning with an interior location and including any 
 location not closer than 2.5  to any already - included location . 

each harvested location is referred to as a  center ,  
 and the kth center is indexed as zk .
a total of 262 centers were harvested 
 for apo - cb msox , 355 for apo - ob msox , and 416 for bound msox .
the main idea of single - sweep is to use mean forces computed on 
 a small number of important locations as the basis for reconstruction 
 of a complete analytical free energy as a function of o2 position in the protein .
the md system for the center is run under the 
 tamd protocol with the protein restraints active and the fictitious 
 friction effectively infinite , so the auxiliary variables do not evolve . 

the mean force vector f at center position zk is computed as the following 
 time - average on the atomic trajectory x(t ) as2where t is the number of 
 time increments in the trajectory and  is the collective variable 
 ( instantaneous o2 center of mass ) .
saturation of mean forces 
 was observed to occur in less than 5 ns of md integration using t = 1 fs time - steps .
the reconstructed free energy (z ) is represented analytically 
 as a radial - basis function expansion:3where  is a gaussian 
 with width  , ak is the kth coefficient in the basis - function expansion , 
 and c is an irrelevant constant that adjusts the 
 overall height of (z ) . via 
 standard linear - algebra methods , the fitting parameters ak and 
are determined by minimizing 
 an error function given by4the optimal basis function 
 width (  ) 
 was 2.5  with a relative residual error of approximately 0.66 
 kcal / mol /  for all three configurations .
local minima on each 
 fes are found using multiple - walker steepest - descent 
 minimization . from the final walker locations , a set of local minima 

is identified . to find pathways of minimum free energy between any 
 two of these minima , the zero - temperature string method is used .
briefly , for two minima a and b , a line segment 
 connecting them is discretized into n sites , each 
 of which is a walker that is allowed to move according to the local 
 gradient in  subject to a reparameterization 
 step that keeps the site 
the string of sites thus  falls  into 
 a minimum free - energy path ( mfep ) connecting the two minima .
string 
 convergence for this investigation was achieved when the change in 
 free energy between successive calculations was approximately 10 kcal / mol .
figure 1 shows root - mean squared deviation 
 ( rmsd ) traces 
 for each md equilibration , indicating that both systems equilibrate 
 after about 10 ns .
the apo system undergoes slightly larger fluctuations 
 than the inhibitor - bound system , which may stem from the fact that 
 the inhibitor s interactions with the protein suppress certain 
 fluctuations .
as can be seen in the apo rmsd trace , a jump in rmsd 
 occurs at about 50 ns .
this corresponds to the spontaneous opening 
 of the asn41arg282 bridge of the flavin cleft , as illustrated 
 by the renderings in the lower panels of figure 1 .
( upper ) c root - mean squared deviation ( rmsd ) 
 from md simulations of apo and foa - bound msox .
( lower ) images from 
 the apo simulations showing detail of the interaction between asn41 
 and arg282 ; here , 
*  refers to the  closed - bridge  
 state and  * *  to the  open - bridge  state . under normal md , o2 sampling of the protein interior 

figure 2 depicts sampling of o2 locations from 
 1 ns md and 1 ns tamd simulations on bound msox .
this illustrates 
 that tamd provides much more extensive sampling at a fraction of the 
 computational cost of standard md .
the complete sampling provided 
 by tamd in both systems is shown in figure 3 , which depicts the locations of all centers harvested from the tamd 
 sweeps for all three systems .
though the number of centers varies 
 greatly , the vast majority of additional centers occupy the solvent 
 outside the protein but within the 10  cutoff distance for interatomic 
 interactions . as will be shown later , these centers do not impact 
 the pathways within msox .
note that the volume spanned by the set of centers includes 
 many important residues , including the active site loop ( residues 
 5560 ) , lys265 , phe256 , arg49 , cys315 , and both the re and si faces of the flavin ring .
cartoon structures of bound msox showing the 
 location of sampled 
 o2 positions in red .
( left ) 1 ns md trajectory and ( right ) 
 1 ns tamd trajectory with  = 3 kcal / mol .
cartoon structures of msox showing the location 
 of centers harvested 
 from ( a ) apo - cb msox , ( b ) apo - ob msox , and ( c ) bound tamd sweeps .
figure 4 shows running average forces [ eq 2 ] in the three cartesian directions for a representative 
 center .
most of the 1033 individual mean - force calculations required 
 about 1 ns to achieve saturation of the forces .
the calculations that 
 required more than 1 ns saturated within 5 ns . running average forces 
 for one representative center .
the deepest minima observed were on the order of 10 
 kcal / mol , 
 relative to o2 in solvent .
the deepest minima identified 
 were observed to occur at the same locations for all three systems . 

fifty - one unique minima were identified for the apo - cb system , 50 
 for apo - ob , and 96 for bound msox .
the bound system was observed to 
 display many more shallow local minima which , as will be shown , had 
 very little effect on the free - energy profiles along the pathways 
 of minimal free energy .
each of the three systems displayed 
 the same two distinct minima 
 on the re face of the flavin ring .
one occurs near 
 flavin atom c(6 ) and the other near n(3 ) ( see figure 5 ) .
these two minima are features of a larger hydrophobic basin 
 bounded by the re face .
lysine residues near the 
 flavin ring have been shown to be important catalytically not only 
 in msox but in histone demethylases lsd1 and lsd2 as well as other 
 systems .
lys265 is directly above c(6 ) , and a local minimum 
 nearby further supports experimental observations .
however , both minima 
 are located on the re face of the ring , suggesting 
 that at least the initial interaction of neutral molecular oxygen 
 with the isoalloxazine ring is a metastable encounter complex with 
 the o2 on the re face .
it may be that 
 the first electron transfer event creates a superoxide anion and the 
 one - electron reduced flavin radical such that the superoxide transits 
 to the end of the lys265 side - chain to the si face , 
 but this would require relative motion of the flavin and arg49 to 
 make room .
the limitation of only considering molecular oxygen in 
 our simulations means we can not directly address the hypothesis that 
 activation and sarcosine oxidation may occur on opposite faces of 
 the flavin ring , as suggested by zhao et al .
the minimum observed by n(3 ) on the flavin ring is close to the 
 inhibitor and not shallow , approximately 67 kcal / mol . on the 
 basis of the location of the substrate - mimicking inhibitor and the 
 presence of an oxygen minima there in the apo systems , this location 
 may be the sarcosine activation site , consistent with experimental 
 results .
( left ) space - filling view of the flavin 
 cofactor ( orange ) and all 
 atoms in hydrophobic residues within 10  of the flavin atoms 
 c(6 ) and n(3 ) .
the crowded si face has little to 
 no room for molecular oxygen to interact with the isoalloxazine ring . 

( right ) rotated view of the same set of atoms as in the left panel , 
 showing the re face of the isoalloxazine ring .
superimposed 
 on this view are isosurfaces of the free energy at 5 kcal / mol 
 ( red ) and 3 kcal / mol ( light blue ) .
two local free - energy minima 
 on the re face are indicated with red arrows .
a 10  grid is 
 overlaid on both panels . for each minimum near the surface , the 
 string method located an mfep to the active site .
the active site 
 is defined as the minimum near n(3 ) on the re face 
 of the flavin ring .
this resulted in four distinct pathways , designated 
 i  iv . with the exception of pathway i
system - specific 
 pathways are referred to using prefixes  apo - cb ,   apo - ob ,  
 or  bound . 
( a ) pathways apo - cb - i , -ii , -iii , and -iv overlaid on 
 the msox 
 structure .
( b ) pathways apo - ob - i , -ii , -iii , and -iv ( c ) pathways 
 bound - i , -ii , -iii , and -iv .
( d ) rotated view ( 180 along of 
 bound pathways to provide a better view of pathways bound - ii and -iv ) . 

pathway i enters msox between 
 the loop connecting f2 with 
 c1 ( residues 3259 ) and the loop connecting c7 
 with c4 ( residues 268289 ) .
these loops form part of 
 the cleft that admits fadh into msox and are seen to open and close 
 in a gate - like fashion in the standard md simulations . inside msox , 
 pathway i passes next to the catalytically active lys265 .
both apo - cb - i 
 and apo - ob - i enter msox this way .
apo - cb - i then passes over the si face of the flavin ring and directly under lys265 when 
 viewing the flavin s si face before terminating 
 at the active site .
it must be stressed that while apo - cb - i passes 
 through what would be the oxygen activation site reported in the literature , no free energy minimum is observed there .
apo - ob - i 
 goes over the cys315 linkage before passing through both minima on 
 the re face and terminating at the active site .
the 
 bound - i string , however , enters msox above the entrance loops .
it 
 then passes between arg49 and lys265 , crossing above the si face and terminating at the active site .
consequently , bound - i passes 
 the loop connecting c(6 ) to c7 ( residues 256264 ) . 
 while apo - ob - i passes through the two distinct minima on the re face of the flavin ring ,
apo - cb - i and bound - i avoid the 
 minima near c(6 ) .
pathways apo - ob - ii , apo - cb - ii , and bound - ii 
 pass through the middle 
 of the gate in pathway i between asn42 and arg282 .
oxygen then travels 
 along the sugar backbone of fadh , entering the binding pocket after 
 passing between the re face of the flavin ring and 
 the loop connecting f9 with f4 ( residues 340350 ) . 

all three paths are geometrically nearly identical and pass through 
 the two distinct minima identified on the re face .
pathways apo - ob - iii , apo - cb - iii , and bound - iii traverse the entire 
 fad binding domain and most of the catalytic domain to arrive at the 
 active site .
the path begins at an entry portal far from the site , 
 bounded by two loops : the first loop connects f8 to f9 
 ( residues 330335 ) and the second f3 to c4 ( residues 
 212219 ) .
the pathways continue past a loop connecting f7 
 to f3 ( residues 199205 ) .
subsequently , oxygen travels 
 along the sugar backbone of the fadh , converging with pathway ii near 
 the flavin ring . as with ii , pathways apo - ob - iii , apo - cb - iii , and 
 bound - iii are geometrically nearly identical and pass through the 
 two distinct minima identified on the re face .
pathways apo - ob - iv , apo - cb - iv , and bound - iv enter msox via passage 
 through the large opening identified as the sarcosine entryway .
all three pass between the active site loop ( residues 
 5560 ) and residues 268272 , part of the loop connecting 
 c7 with c4 , en route to the sarcosine activation site . 

again , all type - iv paths are geometrically nearly identical across 
 the three systems . however , since they enter through the substrate 
 access channel and impinge directly on the minimum near n(6 ) , pathway 
 iv does not pass through the minimum near c(6 ) .
none of the 
 pathways pass through a minimum on the si face of 
 the flavin ring before terminating at the sarcosine activation 
 site .
lack of a minimum on the si face of the flavin 
 ring is a concern because as we mentioned previously , it has been 
 suggested that it is the site of oxygen activation .
the tamd trajectories from which centers were harvested 
 sample this region , and several centers at which mean forces were 
 calculated were located on the si face , so if a minimum 
 did exist it would be detected .
to double - check whether such a minimum 
 would occur , an additional center was added on the si face under lys265 , and its mean force was evaluated .
the pmf was 
 reconstructed again for the apo - cb system , and no additional minimum 
 was observed .
however , the minimum near c(6 ) on the re face of the flavin ring is conserved in all three cases .
this suggests 
 that the site may be important to catalysis and possibly be the o2 activation site .
the area within 10  ( the electrostatic 
 cutoff distance ) of 
 c(6 ) encompasses both re face minima and exhibits 
 interesting characteristics .
although the region around the flavin 
 ring is reported as basic , basic residues primarily occur on the si face .
recent work has suggested that oxygen activation sites in flavoenzymes 
 require a nonpolar residue nearby to aid in desolvation , optimize 
 site geometry , and maximize electrostatic effects on molecular oxygen . 

it was therefore suggested that phe256 would be the essential nonpolar 
 residue owing to its proximity to lys265 .
phe256 is well within the cutoff for interactions with oxygen located 
 at the c(6 ) minimum .
the minima near c(6 ) therefore exhibits nearly 
 ideal conditions for oxygen activation : proximity to the catalytic 
 lys265 , multiple nearby nonpolar residues to stabilize the site , and 
 easily accessible by oxygen in all simulations .
the free energy as a function 
 of distance along each mfep can be 
 read directly from the reconstruction .
figure 7 shows the free energies as a function of distance from the sarcosine 
 activation site along each pathway for all 12 pathways identified . 

generally , pathways in the ligand - bound system are lower in free energy 
 than their counterparts in the apo - cb or apo - ob systems .
this generally 
 inhibits transport to the activation site in the bound system as oxygen 
 will tend to stay in the deepest minima .
in contrast , with the ligand 
 unbound , the deep local minima along the pathways attenuate somewhat , 
 which would likely promote transport .
it is not surprising that overall 
 geometrical similarities in pathways exist due to structural similarities 
 among the three systems .
however , the large differences in free energies 
 along these pathways between apo and ligand - bound msox are unexpected
. 
 evidently , ligand binding and unbinding must cause subtle conformational 
 changes which affect oxygen transport .
a deeper analysis of the residues 
 along each pathway reveals the bases for many of these differences .
free energy 
 as a function of distance along each pathway from the 
 activation site for pathways ( a ) apo - cb - i , apo - ob - i , and bound - i ; 
 ( b ) apo - cb - ii , apo - ob - ii , and bound - ii ; ( c ) apo - cb - iii , apo - ob - iii , 
 and bound - iii ; and ( d ) apo - cb - iv , apo - ob - iv , and bound - iv .
apo - cb 
 is shown in green , while apo - ob is shown in blue and bound in red . 

all graphs begin with oxygen in the active site and end at the nearest 
 minimum to the protein surface where interactions with the solvent 
 occur .
apo - cb - i and apo - ob - i appear to 
 be the only mfeps affected by cleft 
 opening and closing . when closed , the flavin ring shifts approximately 
 2  in the positive direction normal to the re face , helping to expose the si face .
apo - ob - i in contrast 
 has a si face that is partially blocked by residues 
 4244 .
this slight shift of the flavin ring caused by cleft 
 motion is likely the cause of both the free energy and geometric differences 
 between apo - ob - i and apo - cb - i .
it is interesting to note that when 
 examining bound - i , there were mfeps which caused it to be identical 
 to bound - ii .
since the bound system contains a closed bridge , a mfep 
 similar to apo - cb - i was sought . to have bound - i cross the si face required usage of a different starting point . however , 
 it still passed lys265 approximately where apo - cb - i did .
incidentally , 
 bound - i then failed to pass through the minima near c(6 ) on the re face .
ligand binding may therefore cause the route previously 
 taken by apo - cb - i and apo - ob - i to be adversely affected due to crowding 
 on the re face .
access to and from pathways 
 apo - ii and bound - ii is largely controlled 
 by loops 268289 and 3245 .
initial hypotheses suggested 
 that opening and closing of the cleft would strongly influence the 
 free energy near the end of the mfep .
however , examination of the 
 free energy profiles indicates that opening and closing of the cleft 
 does not influence the energetics significantly .
the largest free 
 energy differences are within the cutoff distance ( 10  ) of the 
 inhibitor .
there are also no other major structural differences between 
 the apo and bound states near the mfeps .
thus , inhibitor binding plays 
 a larger role in influencing energetics along pathway ii than disposition 
 of the cleft . access to apo - cb - iii , apo - ob - iii , and bound - iii 
 is controlled by 
 loops 212219 , 330335 , and f4 .
apo - cb - iii and 
 apo - ob - iii share similar energetics and structurally are nearly identical 
 within the vicinity of the mfep . when compared to bound - iii , several 
 subtle differences become apparent .
one of the controlling loops , 
 212219 , rotates inward , apparently trapping oxygen .
this may 
 be the cause of the deep minima seen approximately 20  along 
 the string .
ligand unbinding is correlated with relaxation of the 
 loop , opening the cavity allowing oxygen to escape .
rotation of this 
 loop may not be caused by ligand binding , however , as it is within 
 the cutoff for interactions with residues 375385 .
they fluctuate greatly over the course of any simulation and interact 
 with loop 212219 .
it is more likely that these interactions 
 are the primary cause of loop shifts resulting in deeper minima .
path iv , which traverses the substrate entryway , bears three mfeps 
 which are nearly identical . for both apo and ligand - bound msox , the 
 active site loop
( residues 5560 ) remains in the closed configuration 
 for the duration of all simulations .
when comparing apo - cb - iv and 
 apo - ob - iv , the energetics are similar except when the mfep is near 
 glu57 .
this places it nearly in van der waals contact with the mfep at the 
 deepest minima near 10  .
apo - ob - iv contains glu57 pointed out 
 toward the solvent . as such , it is further from the mfep .
this may 
 not be the sole cause for the large discrepancy in free energy between 
 the mfeps , but it is the only major structural difference between 
 the two in the region of the mfep .
when compared to bound - iv , there 
 are several differences which must be noted .
tyr55 points away from 
 the channel when bound , yet toward the channel in the apo systems . 

this 
 makes sense because the free energy near glu57 for apo - cb - iv and bound - iv 
 are similar in that region .
it also reinforces the observation that 
 orientation of glu57 affects free energy along the path .
the largest free energy 
 differences occur within the cutoff distance ( 10  ) for interactions 
 with the inhibitor .
therefore , interactions with the inhibitor , as 
 well as shifts in tyr55 and glu57 , result in a path of significantly 
 lower free energy .
the sensitivity observed in the o2 pathway thermodynamics 
 to ligand binding suggests a possible link to the observation that 
 high product concentrations enhance flavoenzyme kinetics .
one interpretation is that positively charged 
 products play the role of stabilizing the superoxide anion for certain 
 flavoenzymes that , unlike msox , lack positively charged side - chains 
 in the vicinity of the flavin ring .
when msox is substrate - bound , many deep local minima 
 for o2 along channels connecting solvent to the re face cavity help it absorb o2 from solution . 

if they were static features of the protein structure , however , these 
 minima would presumably be detrimental for the processing of o2 at the flavin ring .
we see that they in fact are not static 
 but attenuate significantly in apo - msox , meaning that the channels 
 should easily provide access for o2 to the substrate / product - free 
 flavin ring .
a higher substrate concentration would lengthen the time 
 msox spends in a substrate - bound state , sponging o2 from 
 the surrouding solution so that , once product release is initiated , 
 a nearby o2 can readily access the flavin ring and begin 
 the next catalytic cycle .
we are able to identify the structural shifts 
 in backbone segments and side chains that accompany ligand binding 
 to explain how the depths of these minima are allosterically modulated . 

it is worth pointing out that the ils simulations of o2 in 12/15-lipoxygenase by saam et al .
show that binding the ligand arachidonic acid closes one o2 diffusion channel but opens another .
our work on msox shows that 
 ligand binding can act more subtly by altering pathway thermodynamics 
 without completely shutting them off .
it is not clear from this 
 work whether or not msox is special in 
 displaying ligand - dependent  cryptic  allosteric sites 
 for o2 .
but the ability of proteins to display otherwise 
 hidden secondary binding sites upon binding of a primary partner molecule 
 is certainly gaining attention .
for example , recent analysis of long 
 all - atom md simulations by bowman and geissler clearly illustrate 
 the existence of cryptic sites for small molecules in a variety of 
 proteins .
our work suggests that the 
 single - sweep approach is also a viable choice of methods for discovering 
 such sites .
the composite 
 method of maragliano et al . has been 
 used to map pathways and sites relevant for o2 transport 
 in msox as well as to gain a better understanding of the impact of 
 substrate binding on these pathways .
we observe two o2 binding 
 sites near the reduced flavin ring on the re face , 
 suggesting that o2 reduction is at least initiated on the 
 same side of the flavin ring on which sarcosine oxidation occurs . 
 generally , we observed that multiple plausible pathways exist by which 
 o2 can access the sites in the re face 
 cavity , regardless of whether or not the substrate - mimicking inhibitor 
 2-furoic acid is bound .
these pathways are geometrically similar in 
 the three different systems examined ( apo , bound , and apo with an 
 open flavin cleft ) but show marked differences in their free energies 
 between ligand - bound and unbound states .
these differences manifest 
 in the appearance of free - energy minima separate from the flavin cavity 
 and the protein surface .
we show that fluctuations in relative loop 
 placements and side - chain orientations among the three systems explain 
 the appearance of these cryptic minima .
this may point to a mechanism 
 of allostery by which transport of small molecule reactants is dependent 
 upon large - molecule ligand binding similar to that seen in 12/15-lipoxygenase .
the presence of deep minima along each pathway 
 that attenuate with ligand unbinding also suggests a sort of organic 
  pump  that ensures o2 is able to reach the 
 substrate activation site in msox rapidly to begin a new catalytic 
 cycle . nevertheless , the identification of important residues and 
 loops in the models presented should serve to guide experiments aimed 
 at elucidating small - molecule transport pathways in msox .
a detailed 
 investigation into transport rates along each pathway is the next 
 step and can be determined using techniques such as milestoning .
it has also been 
 used to study myoglobin , characterizing multiple pathways for co diffusion . 

this composite method may be adapted to study many biological systems , 
 including other flavoenzyme oxidases ( gox , tsox , hsox , etc . )
 monomeric 
 sarcosine oxidase ( msox ) is a flavoprotein d - amino acid 
 oxidase with reported sarcosine and oxygen activation sites on the re and si faces of the flavin ring , respectively . 
 
 o2 transport routes to the catalytic interior are not well 
 understood and are difficult to ascertain solely from msox crystal 
 structures . a composite free - energy method known as 
 single - sweep is 
 used to map and thermodynamically characterize oxygen sites and routes 
 leading to the catalytically active lys265 from the protein surface . 
 
 the result is a network of pathways and free energies within msox 
 illustrating that oxygen can access two free - energy minima on the re face of the reduced flavin from four separate solvent 
 portals . 
 no such minimum is observed on the si face . 
 
 the pathways are geometrically similar for three major states of the 
 enzyme : ( 1 ) apo with a closed flavin cleft , ( 2 ) apo with an open flavin 
 cleft , and ( 3 ) inhibitor - bound with a closed flavin cleft . 
 interestingly , 
 free energies along these transport pathways display significantly 
 deeper minima when the substrate - mimicking inhibitor 2-furoic acid 
 is bound at the sarcosine site , even at locations far from this site . 
 
 this suggests a substrate - dependent allosteric modulation of the kinetics 
 of o2 transport from the solvent to the active site . 
Introduction
Methods
Results
and Discussion