BACKGROUND
dna polymerases are vital enzymes that assist dna replication and maintain the genomic stability of living organisms.
they are grouped into seven main families: a, b, c, d, x, y, and rt.
while dna polymerases from the a, b, c, and d families are replicative, others from the x and y families repair  dna damage or replication errors.
oxidative dna damage, arising from modification of dna by oxygen-derived species, is a frequent type of damaged dna in cells that utilize oxygen  <cit> .
if not accurately repaired, oxidative dna damage can ultimately lead to various human diseases, such as various cancers and premature aging  <cit> .
thus, understanding the mechanism by which dna polymerases process lesions is an important biological challenge.
one of the most common oxidative lesions in the genome is  <dig>  8-dihydro-8-oxoguanine, also called 8-oxoguanine or 8-oxog .
due to oxidation of c <dig> to a carbonyl group, the resulting 8-oxog can adopt a stable syn conformation by rotating 180° around the glycosidic bond when pairing with da, in addition to the regular anti conformation when pairing with dc.
since the 8-oxog:da mispair can introduce g to t transversions, enzymes such as muty in bacteria and ogg <dig> and myh in eukaryotes exist to repair/excise the incorrect bases  <cit> .
a recent crystal structure of muty complexed with 8-oxog  <cit>  reveals the extensive array of hydrogen bonds that allow muty to break the link between such a mispaired adenine  while not affecting correctly paired a:t or g:c units.
the 8-oxog type of dna damage is frequently encountered by dna polymerases, including the repair enzyme dna polymerase β .
kinetic studies  <cit>  have shown that pol β prefers correct insertion  to incorrect insertion  opposite an 8-oxog template.
as in pol β, dctp is also more likely to be incorporated opposite 8-oxog in many other dna polymerases, such as rb <dig>  dpo <dig>  and wild-type t <dig>  <cit> .
furthermore, although datp is less favorably inserted compared to dctp opposite 8-oxog in pol β, the efficiency of datp incorporation opposite 8-oxog is approximately  <dig> -fold higher than opposite dg  <cit> .
in other words, the 8-oxog:datp base pair appears to be treated by pol β like a regular watson-crick base pair  rather than a g:a mispair.
crystallographic structures of various dna polymerase complexes including rb <dig>  t <dig>  bacillus fragment , and dpo <dig> with 8-oxog as the template base at the dna primer/template junction have been resolved  <cit> .
in most structures, the 8-oxog template pairs with dctp in an anti:anti fashion by kinking the template backbone to avoid the steric clash between o <dig> and o5' atoms of 8-oxog.
however, few crystal structures of dna polymerases have captured 8-oxog  pairing with a datp incoming nucleotide.
by mutating an active-site residue  to alanine, brieba et al.
have successfully crystallized the ternary complex of t <dig> dna polymerase with 8-oxog :datp  <cit> .
in the dpo4/dna ternary structure  <cit> , 8-oxog assumes a syn conformation pairing with datp but a second datp nucleotide is also found at the active site dissecting the minor groove.
in the crystal structure of pol β bound to dna with 8-oxog  <cit> , the enzyme is in an open conformation and the adenine base of datp stacks with the template base, both assuming anti conformations.
molecular dynamics simulations of pol β/dna substrate complexes with 8-oxog  <cit>  have shown that the closing conformational pathway of pol β is slowed by datp insertion opposite 8-oxog  but that the closing process is unaffected by dctp opposite 8-oxog.
specifically, unfavorable interactions between the nascent base pair and tyr <dig> on the thumb subdomain cause the adenine base on datp to flip to a syn conformation when 8-oxog:datp is bound to the pol β/dna substrate complex.
to delineate the factors that cause different efficiencies for datp and dctp insertion opposite 8-oxog as well as opposite dg, we apply transition path sampling  simulations to further dissect the closing pathways of pol β associated with 8-oxog and different incoming nucleotides .
we only consider the 8-oxog :dctp   and 8-oxog :datp   conformations here because these two are usually found in a dna duplex.
earlier dynamics simulations also indicate that the anti:anti conformation is less favorable than the syn:anti conformation for the 8-oxog:datp mispair in pol β  <cit> .
the tps method developed by chandler and co-workers  <cit>  can traverse high barriers on the potential energy surface and capture rare events that are not accessible to classical simulations.
tps has been applied to study various systems ranging from clusters of small molecules such as ions, water, peptides and lipids  <cit>  to large complex systems  <cit> .
recently, tps was successfully implemented to study the closing pathways of pol β complex binding g:c and g:a base pairs at the active site  <cit> .
the free energy profiles of the g:c and g:a complexes help explain the different efficiencies of the correct and incorrect incorporations by pol β; essentially, a higher overall closing barrier for the mispair, multiple closing pathways in the mispair, and instability of the closed g:a system were identified as crucial factors to explain fidelity, discrimination in pol β's repair cycle.
our present work aims to resolve the complete conformational pathways of pol β associated with an oxidative lesion 8-oxog to advance our understanding of the fidelity mechanism of pol β in processing a lesion.
although we expected energy differences to be small, systematic differences can help interpret biological observations.
in addition, to confirm the role of tyr <dig> in destabilizing the closed conformation of the pol β/dna/8-oxog :datp complex, we perform an md simulation for a y271a mutant of this lesioned mismatch complex before chemistry.
with the bulkier tyr <dig> replaced by alanine, the thumb subdomain of pol β is expected to close faster onto the nascent base pair than in the wild-type simulation  <cit> .
RESULTS
conformational events during thumb closing differ in the 8-oxog:datp and 8-oxog:dctp complexes
by performing tmd simulations on the two 8-oxog complexes, we obtained two initial trajectories that link their open and closed states.
the time courses of side-chain dihedral angle motions and the rmsd of α-helix n are shown in  .
from these plots, we initially identified tentative transition states  for the two pol β 8-oxog complexes.
the existence of these transition states was further confirmed by unconstrained simulations on configurations selected from the tmd trajectory  .
as shown by table  <dig>  both pol β 8-oxog complexes have  <dig> transition states, but variances in the ranges of the associated order parameters occur.
for both complexes, the first and fourth transition states are the same – thumb subdomain closing and phe <dig> flip, respectively.
for the 8-oxog:datp system, the second and third transition states are asp <dig> flip and arg <dig> rotation, while for the 8-oxog:dctp system, transition states  <dig> and  <dig> consist of arg <dig> half-rotation and arg <dig> full-rotation.
the completion of the arg <dig> rotation in two steps resembles the reference nonlesioned g:c complex  <cit> .
however, unlike the subsequent rotation of a single dihedral angle  of arg <dig> in g:c, arg <dig> rotation for 8-oxog:dctp involves conformational changes of the dihedral angle cβ-cγ-cδ-nε from -95° to -150° followed by cγ-cδ-nε-cζ from 100° to 150°.
moreover, the phe <dig> flip  in the 8-oxog:dctp system occurs through a direction opposite to that found for the nonlesioned g:c, where it changes from -70° to 40°.
starting from the physical trajectories linking the open and closed states of the key residues and the thumb subdomain, we pieced the trajectory space of each transition by tps simulations.
this sampling involves generating trajectories connecting the initial and final states of each transition using shooting and shifting algorithms  <cit>  and a monte carlo in the trajectory space  <cit> .
for each transition region we collected  <dig> successful trajectories connecting the initial and final states.
the adequate length of the sampling trajectories is ensured by examining their correlation functions  .
as seen from fig.
<dig>  when the thumb closes , all other residues are still in open states; when asp <dig> flips , arg <dig> and phe <dig> are still unflipped ; similarly, arg <dig> rotates in ts <dig> before phe <dig> flips in ts <dig>
during the transitions of asp <dig> and arg <dig> in the 8-oxog:datp complex, the rmsd values of α-helix n relative to the closed structure are  <dig> – <dig>  Å and  <dig> – <dig>  Å, respectively, and the thumb fully closes prior to ts <dig> .
examining the rmsd of α-helix n  during each transition in the 8-oxog:dctp complex, we determine that the values for ts <dig> to ts <dig> are  <dig> – <dig>  Å,  <dig> – <dig> Å, and  <dig> – <dig>  Å, respectively, smaller than their counterparts in the 8-oxog:datp system.
this suggests that the thumb subdomain closes faster relative to the side-chain motions in the 8-oxog:dctp complex than thumb closing does in the 8-oxog:datp complex.
indeed, md simulations  <cit>  also indicate that the pol β complex approaches the closed state more quickly when it binds the 8-oxog:dctp base pair than the 8-oxog:datp mispair.
free energy profiles of pol β 8-oxog complexes suggest different stability of their closed states
the free energy barriers  for the transition states are estimated using our umbrella sampling protocol "bolas"  <cit>  tailored for tps.
the energetic landscapes of the matched and mismatched 8-oxog complexes in figure  <dig> exhibit different characteristics.
although each system crosses four transition states for closing, the 8-oxog:dctp system must overcome a higher overall conformational barrier arising from ts <dig>  namely the arg <dig> rotation , while the 8-oxog:datp complex passes three energy barriers  with similar magnitudes .
hence, the rate-limiting conformational step in the matched system is arg <dig> rotation, and that in the mismatch can be identified as thumb subdomain closing, since the latter requires the longest time  to cross the same energy barrier compared to asp <dig> flip and arg <dig> rotation.
specifically, the free energy barrier for thumb motions in the mismatched system is higher by  <dig> kbt than that in the matched system, but, because of the size of the error bar, we cannot determine if this finding is significant.
moreover, the closed state of the matched system  is more stable than the mismatched complex  relative to the corresponding open states .
compared with available data for g:c and g:a  <cit> , the closed states of the 8-oxog complexes are slightly less stable than or as stable as g:c  but much more stable than g:a .
thus, the sequence of stability for the 8-oxog and g closed complexes compared to the corresponding open states is: g:c > 8-oxog:dctp > 8-oxog:a > g:a.
based on these free energy values, we compute the rate constants for each transition   and perform stochastic dynamics simulations on the conformational pathways using the gillespie algorithm  <cit>  implemented in the stocks program as done previously  <cit> .
the kinetic networks of the conformational and chemical pathways for the two systems are sketched in fig.
<dig>  the catalytic constants of pol β  in processing the 8-oxog match and mismatched base pairs can be roughly estimated from the stochastic simulations.
for both complexes, we use the same chemical barrier  as that of the regular g:c matched base pair  <cit> , because the steady-state kcat values for datp and dctp incorporation opposite 8-oxog are close to that for dctp opposite dg  <cit> .
the averaged time evolutions of the two systems are plotted in figure  <dig>  indicating how  <dig> complexes evolve in time.
the majority  of the  <dig> starting open 8-oxog:datp complexes converts to the chemical product in  <dig>  s, corresponding to kcat =  <dig>  s- <dig>  while the same amount of product is produced for 8-oxog:dctp in  <dig>  s .
borrowing the experimental values of km for dctp and datp insertions , we derive the catalytic efficiencies  for correct and incorrect insertions as approximately  <dig>  ×  <dig> and  <dig>  ×  <dig> m-1·s- <dig>  respectively.
the ~ <dig> -fold more efficient dctp insertion compared to datp opposite 8-oxog agrees with the experimental data  <cit>  that dctp insertion is 2-fold more efficient.
the role of active-site residue tyr271
our md simulations  <cit>  identified tyr <dig> as a contributor to the thumb's slow closing in the 8-oxog:datp complex, where we found that the incoming datp flips to a syn conformation due to interactions with tyr <dig>  here our monitoring of the interactions between tyr <dig> and the nascent base pair reveals that the binding of datp to the active site of pol β destabilizes the closed thumb conformation.
specifically, the probability distributions of the n-glycosidic bond torsion angle of datp during transition states  <dig> to  <dig> in the 8-oxog:datp system  show that datp changes from anti  to syn conformation  and returns to anti during ts <dig> .
interestingly, during ts <dig>  the thumb subdomain appears more open  than that in ts <dig> .
the repulsion between tyr <dig> and datp thus slows thumb closing when arg <dig> rotates by destabilizing the active site of pol β.
in contrast, transition path sampling simulations did not capture similar changes in the n-glycosidic dihedral angle of dctp in the 8-oxog:dctp system throughout the sampling of all transition states.
to further validate the role of tyr <dig> in destabilizing the pol β 8-oxog complex binding datp, we perform an md simulation on the y271a mutant of the mismatched system.
with tyr <dig> replaced by an alanine, the mutant complex closes quickly in the simulation of the intermediate state.
the final conformations of α-helices n for both wild-type and mutant pol β complexes in figure  <dig>  and corresponding rmsd plots of α-helices n of these complexes relative to the open and closed crystal structures   also clarify the trends.
in the tyr271ala system, datp remains in the anti conformation and the thumb fully closes onto the nascent base pair.
in addition, the conformations of the adenine bases in the wild-type  vs. mutant  complexes in fig.
<dig> show that, unlike the distorted nascent base pair in the wild-type complex, the 8-oxog:datp base pair in the mutant system becomes co-planar by adopting a hoogsteen conformation .
thus, the adenine base flipping when datp is opposite 8-oxog, as revealed from the tps and md simulations, and the stable datp conformation when tyr <dig> is mutated to ala, confirm that tyr <dig> provides pol β with subtle selectivity for distinguishing datp vs. dctp by destabilizing the active site contents of closed pol β and increasing the conformational barrier for thumb subdomain closing in the mismatch.
discussion and
CONCLUSIONS
we have described the conformational closing profiles of pol β/dna/8-oxog complexes with dctp and datp incoming nucleotides by tps simulations.
both 8-oxog complexes pass four transition states to reach their closed states: two of the four transitions are the same – thumb subdomain closing  and phe <dig> flip  – while the others are different – asp <dig> flip and arg <dig> rotation in the mismatch, and arg <dig> half and full rotations in the match.
importantly, subtle differences in the conformational profiles of the 8-oxog complexes have emerged.
first, the matched system must overcome a higher overall free energy barrier than the mismatched complex , but they can be considered similar due to the size of our error bars.
the higher overall barrier corresponds to a slightly smaller kcat for dctp  vs. datp insertion  opposite 8-oxog.
second, the free energy barrier for thumb closing in the 8-oxog:dctp complex  is slightly higher than the 8-oxog:datp complex , and the increased value in the mismatched system arises from repulsive interactions between tyr <dig> and the nascent base pair.
a probability distribution analysis of the dihedral angle of datp in the mismatched complex shows that the datp base is distorted from an anti to syn conformation as the system traverses transition states  <dig> to  <dig> , with adenine gradually accommodating itself and returning to the anti conformation after the thumb fully closes.
in addition, the tyr271ala mutant simulation for the mismatched complex indicates that thumb can open quickly after the tyr <dig> is replaced with a much less bulky amino acid.
the relative stability of the final closed states compared to the open states emerged as an important factor hampering misincorporation  as suggested by prior tps simulation works.
while the energy differences between the closed and open states in the g:c and g:a complexes without the lesion is dramatic , here we find a smaller but significant difference,  <dig> vs. - <dig> kbt, for 8-oxog:a and 8-oxog:c systems.
significantly, all this information can be now pieced to define a sequence of stability for the closed states of the four complexes relative to their open states: g:c > 8-oxog:dctp > 8-oxog:datp > g:a. this hierarchy directly corresponds to the experimental measurements that indicate both dctp and datp can be incorporated opposite 8-oxog much more efficiently than an incorrect insertion .
particularly, the more stable closed conformation and lower overall conformational energy barrier of pol β associated with 8-oxog:datp lead to much higher efficiency  for datp incorporation opposite 8-oxog than dg.
in addition, the absence of multiple conformational pathways in the 8-oxog:datp system in contrast to g:a might also contribute to the observed higher processing efficiency for the former in pol β.
from our stochastic simulations , we interpret that since the mismatched system spends more time in the open state than the matched system, datp can dissociate from the ternary complex much easier, and this could lower the binding affinity of datp to pol β, resulting a large km value and lower efficiency.
indeed, experiments testing the effects of gapped dna substrates on pol β's fidelity  <cit>  suggest that fidelity is achieved through comparable contributions of the different catalytic constant  and binding affinity  in single nucleotide gap-filling synthesis.
thus, our computed data provide insights into the different binding affinities  of datp and dctp in pol β when 8-oxog is the template base.
unlike the pol β/dna substrate complex with a g:c nascent base pair, both matched and mismatched 8-oxog complexes do not have ion-rearrangement step in their closing pathways .
the critical distances for metal-ion binding are larger than the ideal values required for the nucleotidyl-transfer reaction   in both 8-oxog complexes.
these deviations suggest that these systems must go through more subtle rearrangements  prior to the chemical reaction  <cit> .
the existence of additional free energy barriers for the subtle rearrangements is also reflected in the larger catalytic constants  for the matched and mismatched 8-oxog complexes computed using the chemical barrier of a g:c base pair than their corresponding experimental values .
the additional pre-chemistry checkpoints  following conformational steps might account for the overestimated kcat values.
in summary, transition path sampling suggests that, when processing the 8-oxog lesion, pol β differentiates the incoming nucleotides dctp and datp through altered conformational barriers, closed-state stability, and the requisite active-site geometry before the chemical reaction.
particularly, residue tyr <dig> hampers the thumb subdomain closing of the 8-oxog:datp complex and provides subtle selectivity for pol β to discriminate dctp against datp.

 dna polymerases are vital enzymes that assist dna replication and maintain the genomic stability of living organisms. they are grouped into seven main families: a, b, c, d, x, y, and rt. while dna polymerases from the a, b, c, and d families are replicative, others from the x and y families repair dna damage or replication errors. oxidative dna damage, arising from modification of dna by oxygen-derived species, is a frequent type of damaged dna in cells that utilize oxygen. if not accurately repaired, oxidative dna damage can ultimately lead to various human diseases, such as various cancers and premature aging. thus, understanding the mechanism by which dna polymerases process lesions is an important biological challenge. one of the most common oxidative lesions in the genome is 8-dihydro-8-oxoguanine, also called 8-oxoguanine or 8-oxog. due to oxidation of c to a carbonyl group, the resulting 8-oxog can adopt a stable syn conformation by rotating 180° around the glycosidic bond when pairing with da, in addition to the regular anti conformation when pairing with dc. since the 8-oxog:da mispair can introduce g to t transversions, enzymes such as muty in bacteria and ogg and myh in eukaryotes exist to repair/excise the incorrect bases. a recent crystal structure of muty complexed with 8-oxog reveals the extensive array of hydrogen bonds that allow muty to break the link between such a mispaired adenine while not affecting correctly paired a:t or g:c units. the 8-oxog type of dna damage is frequently encountered by dna polymerases, including the repair enzyme dna polymerase β. kinetic studies have shown that pol β prefers correct insertion to incorrect insertion opposite an 8-oxog template. as in pol β, dctp is also more likely to be incorporated opposite 8-oxog in many other dna polymerases, such as rb dpo and wild-type t. furthermore, although datp is less favorably inserted compared to dctp opposite 8-oxog in pol β, the efficiency of datp incorporation opposite 8-oxog is approximately -fold higher than opposite dg. in other words, the 8-oxog:datp base pair appears to be treated by pol β like a regular watson-crick base pair rather than a g:a mispair. crystallographic structures of various dna polymerase complexes including rb t bacillus fragment, and dpo with 8-oxog as the template base at the dna primer/template junction have been resolved. in most structures, the 8-oxog template pairs with dctp in an anti:anti fashion by kinking the template backbone to avoid the steric clash between o and o5' atoms of 8-oxog. however, few crystal structures of dna polymerases have captured 8-oxog pairing with a datp incoming nucleotide. by mutating an active-site residue to alanine, brieba et al. have successfully crystallized the ternary complex of t dna polymerase with 8-oxog:datp. in the dpo4/dna ternary structure, 8-oxog assumes a syn conformation pairing with datp but a second datp nucleotide is also found at the active site dissecting the minor groove. in the crystal structure of pol β bound to dna with 8-oxog, the enzyme is in an open conformation and the adenine base of datp stacks with the template base, both assuming anti conformations. molecular dynamics simulations of pol β/dna substrate complexes with 8-oxog have shown that the closing conformational pathway of pol β is slowed by datp insertion opposite 8-oxog but that the closing process is unaffected by dctp opposite 8-oxog. specifically, unfavorable interactions between the nascent base pair and tyr on the thumb subdomain cause the adenine base on datp to flip to a syn conformation when 8-oxog:datp is bound to the pol β/dna substrate complex. to delineate the factors that cause different efficiencies for datp and dctp insertion opposite 8-oxog as well as opposite dg, we apply transition path sampling simulations to further dissect the closing pathways of pol β associated with 8-oxog and different incoming nucleotides. we only consider the 8-oxog:dctp and 8-oxog:datp conformations here because these two are usually found in a dna duplex. earlier dynamics simulations also indicate that the anti:anti conformation is less favorable than the syn:anti conformation for the 8-oxog:datp mispair in pol β. the tps method developed by chandler and co-workers can traverse high barriers on the potential energy surface and capture rare events that are not accessible to classical simulations. tps has been applied to study various systems ranging from clusters of small molecules such as ions, water, peptides and lipids to large complex systems. recently, tps was successfully implemented to study the closing pathways of pol β complex binding g:c and g:a base pairs at the active site. the free energy profiles of the g:c and g:a complexes help explain the different efficiencies of the correct and incorrect incorporations by pol β; essentially, a higher overall closing barrier for the mispair, multiple closing pathways in the mispair, and instability of the closed g:a system were identified as crucial factors to explain fidelity, discrimination in pol β's repair cycle. our present work aims to resolve the complete conformational pathways of pol β associated with an oxidative lesion 8-oxog to advance our understanding of the fidelity mechanism of pol β in processing a lesion. although we expected energy differences to be small, systematic differences can help interpret biological observations. in addition, to confirm the role of tyr in destabilizing the closed conformation of the pol β/dna/8-oxog:datp complex, we perform an md simulation for a y271a mutant of this lesioned mismatch complex before chemistry. with the bulkier tyr replaced by alanine, the thumb subdomain of pol β is expected to close faster onto the nascent base pair than in the wild-type simulation.  conformational events during thumb closing differ in the 8-oxog:datp and 8-oxog:dctp complexes by performing tmd simulations on the two 8-oxog complexes, we obtained two initial trajectories that link their open and closed states. the time courses of side-chain dihedral angle motions and the rmsd of α-helix n are shown in. from these plots, we initially identified tentative transition states for the two pol β 8-oxog complexes. the existence of these transition states was further confirmed by unconstrained simulations on configurations selected from the tmd trajectory. as shown by table both pol β 8-oxog complexes have transition states, but variances in the ranges of the associated order parameters occur. for both complexes, the first and fourth transition states are the same – thumb subdomain closing and phe flip, respectively. for the 8-oxog:datp system, the second and third transition states are asp flip and arg rotation, while for the 8-oxog:dctp system, transition states and consist of arg half-rotation and arg full-rotation. the completion of the arg rotation in two steps resembles the reference nonlesioned g:c complex. however, unlike the subsequent rotation of a single dihedral angle of arg in g:c, arg rotation for 8-oxog:dctp involves conformational changes of the dihedral angle cβ-cγ-cδ-nε from -95° to -150° followed by cγ-cδ-nε-cζ from 100° to 150°. moreover, the phe flip in the 8-oxog:dctp system occurs through a direction opposite to that found for the nonlesioned g:c, where it changes from -70° to 40°. starting from the physical trajectories linking the open and closed states of the key residues and the thumb subdomain, we pieced the trajectory space of each transition by tps simulations. this sampling involves generating trajectories connecting the initial and final states of each transition using shooting and shifting algorithms and a monte carlo in the trajectory space. for each transition region we collected successful trajectories connecting the initial and final states. the adequate length of the sampling trajectories is ensured by examining their correlation functions. as seen from fig. when the thumb closes, all other residues are still in open states; when asp flips, arg and phe are still unflipped; similarly, arg rotates in ts before phe flips in ts during the transitions of asp and arg in the 8-oxog:datp complex, the rmsd values of α-helix n relative to the closed structure are – Å and – Å, respectively, and the thumb fully closes prior to ts. examining the rmsd of α-helix n during each transition in the 8-oxog:dctp complex, we determine that the values for ts to ts are – Å, – Å, and – Å, respectively, smaller than their counterparts in the 8-oxog:datp system. this suggests that the thumb subdomain closes faster relative to the side-chain motions in the 8-oxog:dctp complex than thumb closing does in the 8-oxog:datp complex. indeed, md simulations also indicate that the pol β complex approaches the closed state more quickly when it binds the 8-oxog:dctp base pair than the 8-oxog:datp mispair. free energy profiles of pol β 8-oxog complexes suggest different stability of their closed states the free energy barriers for the transition states are estimated using our umbrella sampling protocol "bolas" tailored for tps. the energetic landscapes of the matched and mismatched 8-oxog complexes in figure exhibit different characteristics. although each system crosses four transition states for closing, the 8-oxog:dctp system must overcome a higher overall conformational barrier arising from ts namely the arg rotation, while the 8-oxog:datp complex passes three energy barriers with similar magnitudes. hence, the rate-limiting conformational step in the matched system is arg rotation, and that in the mismatch can be identified as thumb subdomain closing, since the latter requires the longest time to cross the same energy barrier compared to asp flip and arg rotation. specifically, the free energy barrier for thumb motions in the mismatched system is higher by kbt than that in the matched system, but, because of the size of the error bar, we cannot determine if this finding is significant. moreover, the closed state of the matched system is more stable than the mismatched complex relative to the corresponding open states. compared with available data for g:c and g:a, the closed states of the 8-oxog complexes are slightly less stable than or as stable as g:c but much more stable than g:a. thus, the sequence of stability for the 8-oxog and g closed complexes compared to the corresponding open states is: g:c > 8-oxog:dctp > 8-oxog:a > g:a. based on these free energy values, we compute the rate constants for each transition and perform stochastic dynamics simulations on the conformational pathways using the gillespie algorithm implemented in the stocks program as done previously. the kinetic networks of the conformational and chemical pathways for the two systems are sketched in fig. the catalytic constants of pol β in processing the 8-oxog match and mismatched base pairs can be roughly estimated from the stochastic simulations. for both complexes, we use the same chemical barrier as that of the regular g:c matched base pair, because the steady-state kcat values for datp and dctp incorporation opposite 8-oxog are close to that for dctp opposite dg. the averaged time evolutions of the two systems are plotted in figure indicating how complexes evolve in time. the majority of the starting open 8-oxog:datp complexes converts to the chemical product in s, corresponding to kcat = s- while the same amount of product is produced for 8-oxog:dctp in s. borrowing the experimental values of km for dctp and datp insertions, we derive the catalytic efficiencies for correct and incorrect insertions as approximately × and × m-1·s- respectively. the ~ -fold more efficient dctp insertion compared to datp opposite 8-oxog agrees with the experimental data that dctp insertion is 2-fold more efficient. the role of active-site residue tyr271 our md simulations identified tyr as a contributor to the thumb's slow closing in the 8-oxog:datp complex, where we found that the incoming datp flips to a syn conformation due to interactions with tyr here our monitoring of the interactions between tyr and the nascent base pair reveals that the binding of datp to the active site of pol β destabilizes the closed thumb conformation. specifically, the probability distributions of the n-glycosidic bond torsion angle of datp during transition states to in the 8-oxog:datp system show that datp changes from anti to syn conformation and returns to anti during ts. interestingly, during ts the thumb subdomain appears more open than that in ts. the repulsion between tyr and datp thus slows thumb closing when arg rotates by destabilizing the active site of pol β. in contrast, transition path sampling simulations did not capture similar changes in the n-glycosidic dihedral angle of dctp in the 8-oxog:dctp system throughout the sampling of all transition states. to further validate the role of tyr in destabilizing the pol β 8-oxog complex binding datp, we perform an md simulation on the y271a mutant of the mismatched system. with tyr replaced by an alanine, the mutant complex closes quickly in the simulation of the intermediate state. the final conformations of α-helices n for both wild-type and mutant pol β complexes in figure and corresponding rmsd plots of α-helices n of these complexes relative to the open and closed crystal structures also clarify the trends. in the tyr271ala system, datp remains in the anti conformation and the thumb fully closes onto the nascent base pair. in addition, the conformations of the adenine bases in the wild-type vs. mutant complexes in fig. show that, unlike the distorted nascent base pair in the wild-type complex, the 8-oxog:datp base pair in the mutant system becomes co-planar by adopting a hoogsteen conformation. thus, the adenine base flipping when datp is opposite 8-oxog, as revealed from the tps and md simulations, and the stable datp conformation when tyr is mutated to ala, confirm that tyr provides pol β with subtle selectivity for distinguishing datp vs. dctp by destabilizing the active site contents of closed pol β and increasing the conformational barrier for thumb subdomain closing in the mismatch. discussion and  we have described the conformational closing profiles of pol β/dna/8-oxog complexes with dctp and datp incoming nucleotides by tps simulations. both 8-oxog complexes pass four transition states to reach their closed states: two of the four transitions are the same – thumb subdomain closing and phe flip – while the others are different – asp flip and arg rotation in the mismatch, and arg half and full rotations in the match. importantly, subtle differences in the conformational profiles of the 8-oxog complexes have emerged. first, the matched system must overcome a higher overall free energy barrier than the mismatched complex, but they can be considered similar due to the size of our error bars. the higher overall barrier corresponds to a slightly smaller kcat for dctp vs. datp insertion opposite 8-oxog. second, the free energy barrier for thumb closing in the 8-oxog:dctp complex is slightly higher than the 8-oxog:datp complex, and the increased value in the mismatched system arises from repulsive interactions between tyr and the nascent base pair. a probability distribution analysis of the dihedral angle of datp in the mismatched complex shows that the datp base is distorted from an anti to syn conformation as the system traverses transition states to, with adenine gradually accommodating itself and returning to the anti conformation after the thumb fully closes. in addition, the tyr271ala mutant simulation for the mismatched complex indicates that thumb can open quickly after the tyr is replaced with a much less bulky amino acid. the relative stability of the final closed states compared to the open states emerged as an important factor hampering misincorporation as suggested by prior tps simulation works. while the energy differences between the closed and open states in the g:c and g:a complexes without the lesion is dramatic, here we find a smaller but significant difference, vs. - kbt, for 8-oxog:a and 8-oxog:c systems. significantly, all this information can be now pieced to define a sequence of stability for the closed states of the four complexes relative to their open states: g:c > 8-oxog:dctp > 8-oxog:datp > g:a. this hierarchy directly corresponds to the experimental measurements that indicate both dctp and datp can be incorporated opposite 8-oxog much more efficiently than an incorrect insertion. particularly, the more stable closed conformation and lower overall conformational energy barrier of pol β associated with 8-oxog:datp lead to much higher efficiency for datp incorporation opposite 8-oxog than dg. in addition, the absence of multiple conformational pathways in the 8-oxog:datp system in contrast to g:a might also contribute to the observed higher processing efficiency for the former in pol β. from our stochastic simulations, we interpret that since the mismatched system spends more time in the open state than the matched system, datp can dissociate from the ternary complex much easier, and this could lower the binding affinity of datp to pol β, resulting a large km value and lower efficiency. indeed, experiments testing the effects of gapped dna substrates on pol β's fidelity suggest that fidelity is achieved through comparable contributions of the different catalytic constant and binding affinity in single nucleotide gap-filling synthesis. thus, our computed data provide insights into the different binding affinities of datp and dctp in pol β when 8-oxog is the template base. unlike the pol β/dna substrate complex with a g:c nascent base pair, both matched and mismatched 8-oxog complexes do not have ion-rearrangement step in their closing pathways. the critical distances for metal-ion binding are larger than the ideal values required for the nucleotidyl-transfer reaction in both 8-oxog complexes. these deviations suggest that these systems must go through more subtle rearrangements prior to the chemical reaction. the existence of additional free energy barriers for the subtle rearrangements is also reflected in the larger catalytic constants for the matched and mismatched 8-oxog complexes computed using the chemical barrier of a g:c base pair than their corresponding experimental values. the additional pre-chemistry checkpoints following conformational steps might account for the overestimated kcat values. in summary, transition path sampling suggests that, when processing the 8-oxog lesion, pol β differentiates the incoming nucleotides dctp and datp through altered conformational barriers, closed-state stability, and the requisite active-site geometry before the chemical reaction. particularly, residue tyr hampers the thumb subdomain closing of the 8-oxog:datp complex and provides subtle selectivity for pol β to discriminate dctp against datp. 
8-oxoguanine is a common oxidative lesion frequently encountered by dna polymerases such as the repair enzyme dna polymerase β. these results suggest that the lower insertion efficiency for datp compared to dctp opposite 8-oxog is caused by a less stable closed-form of pol β, destabilized by unfavorable interactions between tyr and the mispair. our study offers atomic details of the complexes at different states, in addition to helping interpret the different insertion efficiencies of datp and dctp opposite 8-oxog and g. in particular, the closed-to-open state stability difference in each system establishes a hierarchy of stability as g:c > 8-oxog:c > 8-oxog:a > g:a, corresponding to - - kbt, respectively. to interpret in atomic and energetic detail how pol β processes 8-oxog, we apply transition path sampling to delineate closing pathways of pol β 8-oxog complexes with dctp and datp incoming nucleotides and compare the results to those of the nonlesioned g:dctp and g:datpanalogues. network models based on the calculated rate constants in each pathway indicate that the closed species are more populated than the open species for 8-oxog:dctp, whereas the opposite is true for 8-oxog:datp. this stability of the closed vs. open form can also explain the higher insertion efficiency for 8-oxog:datp compared to the nonlesioned g:datp pair, which also has a higher overall conformational barrier. our analyses show that the closing pathways of the 8-oxog complexes are different from one another and from the nonlesioned analogues in terms of the individual transition states along each pathway, associated energies, and the stability of each pathway's closed state relative to the corresponding open state.
 8-oxoguanine is a common oxidative lesion frequently encountered by dna polymerases such as the repair enzyme dna polymerase β. to interpret in atomic and energetic detail how pol β processes 8-oxog, we apply transition path sampling to delineate closing pathways of pol β 8-oxog complexes with dctp and datp incoming nucleotides and compare the results to those of the nonlesioned g:dctp and g:datpanalogues.  our analyses show that the closing pathways of the 8-oxog complexes are different from one another and from the nonlesioned analogues in terms of the individual transition states along each pathway, associated energies, and the stability of each pathway's closed state relative to the corresponding open state. in particular, the closed-to-open state stability difference in each system establishes a hierarchy of stability as g:c > 8-oxog:c > 8-oxog:a > g:a, corresponding to - - kbt, respectively. this hierarchy of closed state stability parallels the experimentally observed processing efficiencies for the four pairs. network models based on the calculated rate constants in each pathway indicate that the closed species are more populated than the open species for 8-oxog:dctp, whereas the opposite is true for 8-oxog:datp.  these results suggest that the lower insertion efficiency for datp compared to dctp opposite 8-oxog is caused by a less stable closed-form of pol β, destabilized by unfavorable interactions between tyr and the mispair. this stability of the closed vs. open form can also explain the higher insertion efficiency for 8-oxog:datp compared to the nonlesioned g:datp pair, which also has a higher overall conformational barrier. our study offers atomic details of the complexes at different states, in addition to helping interpret the different insertion efficiencies of datp and dctp opposite 8-oxog and g. 