Simulations Meet Experiment to Reveal New Insights into DNA Intrinsic Mechanics
[['Binding of DNA to proteins or small molecules is modulated by subtle sequence-dependent variations inherent to the structure and dynamics of free DNA , which facilitate or disfavor the structural fit with cognate partners [1–4] .', 'Given the many DNA targets , a purely experimental characterization of their structure and dynamics is an enormous task .', 'The structural biology of DNA would be greatly helped if one could describe and predict the sequence-dependent intrinsic mechanical and structural preferences of the double helix .', 'That would pave the way to a fuller understanding of DNA malleability in direct and indirect readout .', 'Molecular Dynamics ( MD ) simulations in explicit solvent can potentially explore the properties of any B-DNA sequence of moderate length , considering the extensive sampling afforded by modern computational resources [5 , 6] .', 'However , MD simulations are only as reliable as the underlying energy model , typically treated with a classical force-field .', 'Development of force-fields is complex , requires extensive efforts , and needs precise reference experimental data [7] .', 'This latter requirement has been a complicating factor for DNA , given the paucity of reliable experimental data reflecting the fine structural details of DNA in solution [8–10] .', 'The situation has improved in recent years , especially with respect to the DNA backbone , for which additional experimental information have been gathered from X-ray crystallography and NMR ( see below ) .', 'In response , force-field shortcomings regarding the DNA backbone were addressed , including via QM studies on model compounds [11–13] , motivated by the realization that the backbone is an essential component of the intrinsic mechanical couplings in DNA .', 'Statistical analyses of X-ray structures of free B-DNA have unveiled that , among the five dihedral angles along the phosphate linkage , ε and ζ present bi-modal distributions [14–19] , referred to as BI with ε/ζ:trans/g- and BII with ε/ζ:g-/trans [20 , 21] .', 'In contrast , α , β and γ appear to prefer overwhelmingly one conformation ( α/β/γ:g-/t/g+ ) [14 , 15 , 17 , 19] .', 'Importantly , the BI and BII conformers are associated to distinctive values of the helicoidal parameters , X-disp ( base displacement ) , slide , roll and twist [15 , 16] .', 'In addition , the density of BI or BII phosphate groups in a window of 4 consecutive base pairs is coupled to the groove dimensions [22] .', 'Hence , the modulation of B-DNA shape observed in X-ray structures is associated with the conformation of ε/ζ backbone dihedrals .', 'NMR solution studies echoed these findings and provided additional information about the sequence dependent behavior of the BI and BII populations .', 'In NMR , this equilibrium is reflected by the 31P chemical shifts ( δPs ) [21 , 23] , which can be translated in terms of BII percentages [24 , 25] .', 'Correlations between NMR-measured δPs and internucleotide distances [24 , 26] reflect the coupling between the backbone states and inter base pair parameters observed in X-ray structures .', 'Consistency between NMR and X-ray results extends to the relation between the BII densities and the width of the minor groove , which can also be observed by NMR [27] .', 'In addition , the compilation of a sizeable set of δPs documented the effect of B-DNA sequence on BII propensities [28] , initially inferred from X-ray structures [15 , 16] .', 'Of the 10 unique complementary dinucleotides ( NpN•NpN ) , CpG•CpG , CpA•TpG , GpC•GpC , GpG•CpC are characterized by BII percentages markedly higher than the average ( 21% ) ; ApN•NpT ( N: any base ) and TpA•TpA can be globally considered as BI-rich; GpA•TpC is an intermediate case , with BII percentage only slightly lower than average .', 'These intrinsic sequence-specific BII propensities in solution were summarized on a scale called TRX [28] , by reference to the couplings with Twist , Roll and X-disp .', 'TRX was recently validated further by a large set of δPs collected on new DNA oligomers [27] .', 'This detailed information on DNA in solution offers a precious framework for testing and refining DNA force fields .', 'Thus , the AMBER force fields Parm98 [29] and Parm99 [30] stabilized artefactual α/γ conformations that caused severe distortions in DNA [19 , 31] .', 'Such undesirable α/γ transitions were corrected in the subsequent potential Parmbsc0 [12] .', "First observed by NMR [32 , 33] and then generalized and quantified in the TRX scale [34] , the modulation of CpG BII propensity by the 3'- and 5'-neighbors was qualitatively retrieved by Parmbsc0 [35] .", 'Also , the sensitivity of the BI ↔ BII equilibrium to the type of monovalent cation ( K+ , Na+ ) was demonstrated by NMR [26] .', 'Parmbsc0 simulations do not seem to reproduce this dependence , yet they suggest a mechanism that could explain how K+ and Na+ affect the backbone motions [35] .', 'Concerning the CHARMM family of force-fields , the early thorough systematic calibration of the DNA backbone torsional energetics for CHARMM27 [17 , 36] prevented artefactual α/γ transitions and resulted in a force-field which treats B-DNA robustly [6 , 37 , 38] .', 'Importantly , CHARMM27 , like Parmbsc0 , correctly represent the mechanical coupling between the backbone states and the helical parameters [9 , 38 , 39] .', 'Nevertheless , the remaining shortcomings in Parmbsc0 MDs [5 , 35 , 40 , 41] cannot be ignored , in particular regarding CpG , CpA and TpG that show a systematic deficit in BII with respect to the NMR data [27 , 28 , 32–34 , 42–45] .', 'The CHARMM27 force-field also did not reproduce the experimentally documented BII percentages [9 , 39] .', 'A simulation of the Drew-Dickerson dodecamer with Parmbsc0 [40] and a NMR/modeling study with CHARMM27 [46] also raised the issue of unrealistic BII propensities .', 'In response , two force-fields were recently conceived to improve the DNA backbone representation: Parmbsc0εζOLI [13] , derived from Parmbsc0 - , and CHARMM36 [11] , built on CHARMM27 .', 'Parmbsc0εζOLI and CHARMM36 were developed guided by DNA X-ray structures and a small set of BII percentages extracted from NMR .', 'In initial tests with B-DNA , both force fields notably increased the sampling of the BII form compared to prior potentials [11 , 13] .', 'Since twist and groove shape are coupled to the BI ↔ BII equilibrium , the structural outcome obtained with Parmbsc0εζOLI significantly differs from that yielded by Parmbsc0 [13] .', 'These initial tests are encouraging and call for a more systematic examination of the performance of these potentials , especially in the light of experimental data not used to train the force-fields .', 'The present work exploits a wealth of recent 31P NMR chemical shifts on the DNA backbone motions , to thoroughly evaluate the performance of the Parmbsc0εζOLI and CHARMM36 potentials .', 'These data were collected on four DNA dodecamers [27] , independent of those used to develop those force-fields .', 'Together , the dodecamers cover a 39 bp segment in the 5’ half of sequence 601 , the best artificial sequence at forming nucleosome core particle [47] , which is therefore important to understand how DNA is packaged .', 'The TRX approach [28] combined with the analysis of the 31P chemical shifts of the four dodecamers [27] provides evidence that the intrinsic structural characteristics of the free sequence 601 largely account for its strong affinity for the histone core .', 'In addition to their biological relevance , the 72 dinucleotides ( NpN ) of the four dodecamers behave as expected from the TRX scale regarding the effect of sequence on the BII propensities [27] .', 'These dodecamers and the attending experimental information are therefore ideally suited to evaluate Parmbsc0εζOLI and CHARMM36 , with emphasis on the representation of the BI ↔ BII equilibrium and the coupled helicoidal parameters .', 'Importantly , we show how the improvements brought by these new potentials lead to new insights into DNA structure and dynamics , which are essentially consistent across the two force-fields .', 'The first step was to compare the BII percentages inferred from δP measurements to those generated by MDs .', 'The simulated fine modulation by the sequence is not yet fully satisfactory .', 'For instance the simulated BII populations of some steps , as those of GpC with both force fields , tend to be underestimated .', 'However , Parmbsc0εζOLI and CHARMM36 represent the backbone behavior much more realistically than previous force fields .', 'CHARMM36 in particular shows a very good ability to obtain BII-rich steps .', 'This advance enabled to examine for the first time the conformational combinations corresponding to the states of facing phosphate groups , i . e . BI•BI , BI•BII , BII•BI and BII•BII .', 'We find that the conformational states of the two facing phosphate groups of any complementary dinucleotide are not correlated in either Parmbsc0εζOLI or CHARMM36 simulations .', 'An important practical consequence is that the populations of the combinations of facing phosphates can be easily deduced from the overall individual BII populations inferred experimentally for every phosphate .', 'This approach reveals that the four dodecamers contain a sizable number of steps where BII-containing states , BI•BII , BII•BI and BII•BII , dominate .', 'Such quantification is critical for accurately describing the conformational landscape explored by the complementary dinucleotides , because the backbone combinations are tightly associated with helical parameters , as documented here .', 'Overall , our results deepen our understanding of the intrinsic B-DNA mechanics , which is a key player in the indirect readout of DNA sequences by proteins .'], ['Each of the four dodecamers ( Table 1 ) was simulated with the Parmbsc0εζOLI [13] ( P-MDs ) or CHARMM36 [11] ( C-MDs ) force-field , resulting in a total of 8 MDs .', 'The MDs of Oligo 1 , 2 and 3 were 450ns each , while for Oligo 4 the trajectories were extended to one microsecond .', 'Additional sampling was performed on Oligo 4 since its alternation of BI and BII-rich dinucleotides is especially relevant to test the convergence of backbone dynamics .', 'During the present simulations , the base pairs N2→N11•N14→N23 were stable , with ~99% of Watson-Crick pairing .', 'The root mean square deviations ( RMSDs ) between a regular canonical B-DNA and the simulated snapshots fluctuated around 2 . 6±0 . 6 Å in P-MDs and 2 . 1±0 . 5 Å in C-MDs ( S1 Fig ) .', 'The slightly larger RMSDs for P-MDs versus C-MDs gave the first indication of subtle differences between the force-fields , but one should refrain from interpreting these differences in terms of relative validity of the two force-fields , since canonical B-DNA is a somewhat artificial construct .', 'Then , we examined the five dihedral angles of the phosphodiester backbone , α , β , γ , ε and ζ .', 'In both P- and C-MDs , α/β/γ conform to the canonical g-/trans/g+ pattern observed in free DNA [14 , 15 , 17–19] .', 'The torsions ε and ζ , which undergo correlated motions , define the BI and BII states ( Fig 1 ) .', 'The convergence of the BII populations is of evident relevance , especially to compare simulated BII percentages to their experimental counterpart .', 'Previous analyses of very long trajectories ( up to ~45 μs ) with Parmbsc0 and CHARMM36 showed reasonable convergence of the fast motions ( timescale < 100ns ) on internal parts of DNA oligomers after only ~50ns [5] .', 'A similar conclusion was drawn from μs simulations with Parmbsc0 , using as convergence criteria the average helical and backbone parameters [41] .', 'These previous studies indicate that the timescale of the present MDs should be amply sufficient to investigate the backbone motions .', 'Indeed , our results confirm this expectation , keeping in mind that constraints were applied to the terminal base-pairs to maintain their Watson-Crick base-pairing .', 'A detailed justification of the protocol is given in Materials and Methods .', 'Clearly , the BII population of some phosphates did not converge over the first 50 ns , which may be considered as a reasonable equilibration time .', 'Thus , for each phosphate , convergence was monitored by plotting its BII percentage over increasing trajectory lengths , from 150ns upwards ( S2 Fig ) .', 'For each Oligo treated with Parmbsc0εζOLI or CHARMM36 , convergence of the BII populations was reached within the simulation times , including for phosphates with high BII populations ( S2 Fig ) .', 'An additional test was performed with the MDs of Oligo 4 extended to 1 μs , by comparing the beginning -from 50 to 150ns- and the end -from 900 to 1000ns- of trajectories ( S3 Fig ) .', 'This analysis produced very similar BII percentages on each step of Oligo 4 , with only slight differences ( 8% for the worst case ) on some BII-rich steps .', 'Thus , the first 100ns of production ( from 50 to 150ns ) , while not sufficient to ensure a complete convergence , surprisingly offer a rather good estimation of the backbone behavior , supporting the expectation that the simulations are essentially converged for practical purposes with respect to the BI/BII balance on the 450ns time scale .', 'We recall that the MDs were performed restraining the Watson-Crick hydrogen bonds in the first and last base pairs .', 'We chose this protocol since , with unrestrained MDs , convergence issues were observed in conjunction with fraying events involving larger than expected motions of the terminal regions , consonant with previous reports [5 , 13 , 48] .', 'Since the structural signature of these long-lived fraying events in the unrestrained MDs is not supported by the NMR measurements ( see “Restrained base pairing on the first and last base pairs” in Materials and Methods ) , Watson-Crick pairing restraints of the first and last base pairs were applied in the analyzed MDs .', 'This remedied the convergence concerns otherwise observed in the unrestrained MDs ( see the example of restrained and unrestrained 1 μs P-MDs of Oligo 4 in S4 Fig ) .', 'Importantly , however , the BII percentages calculated on the central part ( N3→N10•N15→N22 ) of the dodecamers are quasi identical ( correlation coefficient of 0 . 98 ) in both restrained and unrestrained MDs .', 'This indicates that the behavior of the internal steps was reproducible in different conditions , another reassuring element concerning the convergence of the simulations presented here .', 'Overall , we observe that the DNA backbone dynamics is essentially converged with MDs of several hundredth ns .', 'This convergence timeframe is realistic considering that the phosphate groups undergo rapid ( nano-picosecond timescale ) conformational exchange according to NMR [49 , 50] .', 'Convergence in terms of sampling of the backbone states allows us to concentrate the following analysis on the influence of the force-fields .', 'In free DNA X-ray structures the distribution of the pseudo-angle ( ε-ζ ) is characterized by two major peaks centered around ( ε-ζ ) = -90° ( BI , ε in trans and ζ in g- ) and ( ε-ζ ) = 90° , ( BII , ε in g- and ζ in trans ) ( S5 Fig ) .', 'Between these two maxima , a region covering ( ε-ζ ) values from -60 to +70° contains phosphate linkages with ε:trans typical of BI and ζ:trans typical of BII .', 'Therefore this region may be considered ambiguous in terms of BI/BII categorization .', 'The separation between BI and BII is commonly set at the minimum of the ( ε-ζ ) distribution , which is close to ( ε-ζ ) = 0 in the X-ray distribution ( S5 Fig ) .', 'BI and BII are thus usually characterized by negative and positive ( ε-ζ ) values , respectively .', 'The pattern observed in the X-ray structures for the ( ε-ζ ) distribution is globally preserved in P-MDs and C-MDs , while influenced by the force-fields ( Fig 2 ) .', 'Thus , the operational definition of the BI and BII states in MDs must be carefully scrutinized , and possibly adapted .', 'In addition to the ( ε-ζ ) histograms , the sugar populations in the south , east and north puckers ( e . g . Oligo 4 sugars in S6 Fig ) were considered , since this criterion is relevant to the definition of BI and BII .', "Indeed , crystallographic and NMR investigations established that BI is tolerant in terms of surrounding 5’ and 3’ sugar puckers , while BII is restricted to south puckers , especially with respect to 5' sugars [15 , 18 , 50] .", 'The ( ε-ζ ) histogram of C-MDs has a minimum at ( ε-ζ ) = 30° , located at a tail of the ε/ζ:trans/trans region ( Fig 2 ) .', "5’ south sugars are observable in both BI and BII regions; 5' east sugars fall in ( ε-ζ ) from -110 to -50° , inside the conventional BI region; 5' north sugars are associated to a larger range of ( ε-ζ ) values , but are suppressed above ( ε-ζ ) = 30° ( Fig 2 ) .", 'This sugar behavior and the minimum of ( ε-ζ ) at 30° offer an analogy with the X-ray observations , such that ( ε-ζ ) = 30° was deemed suitable to separate BI from BII with CHARMM36 .', 'Using instead the conventional cutoff ( ε-ζ = 0 ) to separate BI from BII would not result in a dramatically different description , since the average BII population inferred with ( ε-ζ ) > 0° would only be 4% higher than that based on ( ε-ζ ) > 30° .', 'However , in view of the distribution of 5’ north sugars , the criterion ( ε-ζ ) > 30° was preferred to define BII with CHARMM36 .', 'Incidentally , the present C-MD data confirm the strong association between BII and 5’ south sugars .', 'With Parmbsc0εζOLI , no clear minimum is observed in the ( ε-ζ ) distribution between the BI and BII peaks , which are separated by a flat ( ε-ζ ) distribution ( Fig 2 ) .', 'This intermediate region , centered around ( ε-ζ ) = 0 , contains ε/ζ:trans/trans conformers ( Fig 2 ) , which represent 10% of the snapshots .', 'In absence of a clear minimum in the ( ε-ζ ) distribution , histograms of ε and ζ were considered .', 'This approach was adopted in previous Parmbsc0 trajectories [15 , 18 , 50 , 51] , where the BII linkages were defined relative to the minimum of the distribution .', 'Here , with the minimum of the ζ distribution at ζ = 230° , this approach would designate as BII the range above ( ε-ζ ) = -50° , a strongly negative value .', 'Conversely , the transition from BI to BII would be at ( ε-ζ ) = 40° if chosen to be at the minimum of the ε histogram ( ε = 240° ) .', 'So , the ε and ζ histograms do not provide a coherent definition of BI and BII ranges for P-MDs here .', 'In addition , the sugar dynamical regime is of little help since Parmbsc0εζOLI generates only a few north sugars ( Fig 2 and S6 Fig ) .', 'In absence of any convincing more specific rationale to assign the ε/ζ:trans/trans snapshots to either BI or BII with Parmbsc0εζOLI , we adopted the common BII definition , ( ε-ζ ) > 0° .', 'Such a decision is somewhat arbitrary but the uncertainty it introduces is limited .', 'Indeed , shifting the ( ε-ζ ) dividing value by 20° ( ( ε-ζ ) = -20° or +20° ) only changed the BII population by +/-2% .', 'In sum , BII percentages were extracted using ( ε-ζ ) > 0° for P-MDs and ( ε-ζ ) > +30° for C-MDs throughout this work .', 'These considerations illustrate the difficulty in defining BI and BII unambiguously , in a manner which would be meaningful and transferable across different structural models .', 'It also draws the attention to some differences between Parmbsc0εζOLI and CHARMM36 regarding their representations of sugars and the ( ε-ζ ) distribution .', 'Yet , the following sections show that a consistent overall picture emerges from CHARMM36 and Parmbsc0εζOLI .', 'The four dodecamers studied here correspond to 72 dinucleotide steps , excluding the terminal steps .', 'The corresponding 72 31P chemical shifts ( δPs ) were measured and converted to BII percentages , BII%from NMR , using an empirical procedure based on a calibration involving a comparison of NMR and X-ray structural data [24] ( see also Materials and Methods ) .', 'In this procedure , δPs of pure BI and pure BII states are assumed to be sequence-independent , even if they could be modulated by the dinucleotide sequence , as suggested by a computational study [52] .', 'However , previous studies showed that neglecting subtle sequence effect on δPs of pure BI and pure BII produced reasonable estimations [27 , 53] , for instance with points where BI and BII are expected to be equally populated [27] .', 'Another indication of the protocol reliability is the consistency between the average BII percentage either derived from the average δPs of the 72 steps considered here ( 19% of BII , from δPav = -4 . 20 ppm at 30° ) or inferred from statistics of X-ray structures ( 20% of BII ) [15] .', 'A first test of the force fields is to compare the NMR-inferred and simulated BII populations , averaged on the 72 dinucleotides .', 'The simulated overall average BII percentages are 11% in P-MDS and 18% in C-MDs .', 'Thus , Parmbsc0εζOLI somewhat underestimated the BII populations , as noted before [13] .', 'The excellent agreement of the CHARMM36 value with experiment is an obvious improvement compared to CHARMM27 , which severely underrepresented BII [9 , 11] .', 'That the force fields , in particular CHARMM36 , produce overall BII population commensurate with experimental data is very encouraging , considering that the treatment of the backbone by previous force-fields fell outside the experimental range .', 'Since the dinucleotides have markedly different propensities to populate BII [15 , 27 , 28 , 51 , 53] , reproducing the sequence effects is a more stringent test of the force-fields , examined in the following .', 'A previous dataset of 323 measured δPs has established that the 16 dinucleotides ( NpN steps for a single strand in a duplex context ) composing B-DNA are associated with specific δP values [28] .', 'Since δP translates into a BII propensity it implies that the BI/BII populations are primarily controlled by the dinucleotide sequence [28] .', 'The additional 72 δPs considered here conform to this sequence pattern , validating the notion of dinucleotide-specific BII propensity [27] .', 'Thus , the sequence-dependent BII populations derived from δPs provide a rare opportunity to test the sequence-dependent behavior of DNA force-fields in solution .', 'One notes that adjustments made to Parmbsc0εζOLI and CHARMM36 to increase the BII populations were not tailored depending on the base sequence , in contrast with , for instance , the CMAP approach [54] .', 'In other words , the same backbone force-field parameters are applied to any sequence .', 'Therefore , differences in the backbone behavior during simulations can only be ascribed to intrinsic sequence-dependent properties .', 'To examine whether Parmbsc0εζOLI and CHARMM36 reproduce the effect of sequence on BII populations , the simulated BII percentages were compared to their experimental counterparts , considering the individual phosphates ( BII%from MD versus BII%from NMR , given in S1 Table ) .', 'BII%from MD and BII%from NMR are overall moderately correlated ( Table 2 and S7 Fig ) .', 'The simulated BII percentages of half of the 72 steps ( 53% for both P-MDs and C-MDs ) are within BII%from NMR ±10% , where the 10% interval corresponds to the tolerance allowed around the NMR-based BII percentages ( see Materials and Methods ) .', 'The comparison between BII%from NMR and BII%from MD is shown in Fig 3 for each non-terminal phosphate of the four dodecamers .', 'A more detailed analysis , in particular on the dinucleotides present in several occurrences in the dodecamers , shows that Parmbsc0εζOLI and CHARMM36 correctly reproduce the low or moderate BII%from NMR ( < 20% ) of CpT , GpT , ApC , ApG , ApA and TpT ( Fig 3 and Table 3 for the steps present in several occurrences in the dodecamers ) .', 'However , this overall agreement suffers some shortcomings .', 'The BII population of TpA tends to be either underestimated or overestimated with Parmbsc0εζOLI and CHARMM36 , respectively .', 'GpC steps in BII are quasi systematically underestimated by both force fields , as well as one of the three CpA•TpG in Oligo 4 .', 'Parmbsc0εζOLI generated too low BII percentages on CpC and GpG in Oligo 2 and most CpG ( seven on a total of ten ) .', 'In C-MDs , the representation of CpC , GpG and CpG is reasonable whereas inversions of BII% occurs at two complementary CpG•CpG steps .', 'Indeed , the NMR gives asymmetrical BII percentages for C2pG3•C22pG23 in Oligo 1 , with 79% of BII for C2pG3 and 42% for C22pG23 .', 'C-MD gave the reverse , with 30% and 75% of BII for C2pG3 and C22pG23 , respectively .', 'A similar situation arises for C10pG11•C14pG15 in Oligo 3 .', 'Our results confirm that adjustments specifically aimed at enhancing access to the BII state produce convincing , positive effects , especially perceptible in CHARMM36 .', 'That the increase in simulated BII populations is not distributed uniformly along the sequences ( Fig 3 ) is not trivial since , as noted above , the computational models were not parametrized to reproduce the BII% for specific dinucleotides , but were only adjusted to be generically more permissive to BII .', 'Admittedly , discrepancies still exist between the experimental sequence effect on the BI↔BII equilibrium and Parmbsc0εζOLI or CHARMM36 .', 'However , an essential point is that the simulations are now sufficiently BII-rich to extend the analysis to aspects of the backbone dynamics that eludes experimental approaches .', 'The phosphate groups facing each other across the strands can adopt homogeneous combinations , BI•BI or BII•BII , or hybrid combinations , BI•BII or BII•BI ( denoted here BI•BII|BII•BI , where the vertical bar means logical “or” ) .', 'The populations of these combinations are especially meaningful from the point of view of B-DNA mechanics , because inter base pair parameter values are associated to the conformational states of two facing phosphate linkages [15 , 16 , 24 , 40 , 55–58] , as also addressed below .', 'The behavior of facing phosphate linkages cannot be deduced from δP measurements , which report time and ensemble-averaged BII percentages for individual phosphates .', 'The present simulations offer the opportunity to inspect the dynamic behavior of phosphate linkages in complementary dinucleotides and to estimate possible correlation .', 'Indeed , several steps in C-MDs , in particular CpG•CpG , CpC•GpG and TpA•TpA , adopt the three combinations , BI•BI , BI•BII|BII•BI or BII•BII ( Table 4 and Fig 4 ) .', 'In P-MDs , BI•BI and BI•BII|BII•BI are also frequently observed , but the BII•BII populations are almost inexistent ( Table 4 ) , consistent with Parmbsc0εζOLI generating fewer BII conformers than CHARMM36 .', 'Fig 5 illustrates the statistics of the transitions between the facing phosphate combinations for steps that adopt BII•BII in both P-MDs and C-MDs .', 'The same result holds for any other complementary step investigated here in which the facing phosphates undergo BI ↔ BII transitions .', 'With both force fields , the large majority of the transitions between BI•BI , BI•BII|BII•BI and BII•BII involves only one of the two facing phosphates ( BI•BI ↔ BI•BII or BII•BI; BI•BII or BII•BI ↔ BII•BII ) .', 'BI•BII|BII•BI ↔ BII•BII are infrequent in P-MDs , the BII•BII state being poorly populated .', 'In both P-MDs and C-MDs , the simultaneous transitions of two phosphate states ( BI•BII ↔ BII•BI; BI•BI ↔ BII•BII ) are very rare , representing at most 5% of the total number of transitions ( Fig 5 ) .', 'The populations of BI•BI , BI•BII|BII•BI and BII•BII can be addressed with simple elements from probability theory , summarized here before comparison to the MD data .', 'Pi ( BII ) is the probability that phosphate i is in BII , the complementary event has probability Pi ( BI ) = 1 –Pi ( BII ) .', 'The states of facing phosphate pairs i , j are characterized by pair probability distributions , Pi , j ( BI•BI ) , Pi , j ( BI•BII ) , Pi , j ( BII•BI ) and Pi , j ( BII•BII ) .', 'Because the facing phosphate groups are either BI or BII , the probabilities satisfy the relations:', 'Pi , j ( BI•BI ) +\xa0Pi , j ( BI•BII ) =\xa0Pi ( BI )', 'Pi , j ( BI•BI ) +\xa0Pi , j ( BII•BI ) =\xa0Pj ( BI )', 'Pi , j ( BII•BI ) +\xa0Pi , j ( BII•BII ) =\xa0Pi ( BII )', 'Pi , j ( BI•BII ) +\xa0Pi , j ( BII•BII ) =\xa0Pj ( BII )', 'Summing the last two equations gives:', '[Pi , j ( BII•BI ) +\xa0Pi , j ( BI•BII ) ]\xa0+\xa02\xa0Pi , j ( BII•BII ) =\xa0[Pi ( BII ) +\xa0Pj ( BII ) ]', '( 1 )', 'The first term on the left in ( 1 ) is the probability of BI•BII|BII•BI , Pi , j ( BII•BI|BI•BII ) .', 'Note that here Pi , j ( BII•BI|BI•BII ) does not denote a conditional probability , but simply the probability of states BII•BI or BI•BII .', 'So Eq 1 is equivalent to', 'Pi , j ( BII•BI|BI•BII ) +\xa02\xa0Pi , j ( BII•BII ) =\xa0Pi ( BII ) +\xa0Pj ( BII ) .', '( 2 )', 'Eq 2 is general , as it follows directly from the definitions and it does not rely on any assumption about the independence ( correlation ) of facing phosphate groups .', 'One now examines the case when the states of the two facing phosphate groups are independent of each other .', "Then , the pair probabilities factorize: Pi , j ( b•b' ) = Pi ( b ) Pj ( b' ) , where b and b’ stand for any of the phosphate states .", 'In particular , we have', 'Pi , j ( BII•BII ) =\xa0Pi ( BII ) Pj ( BII )', '( 3 )', 'Pi , j ( BII•BI|BI•BII ) =\xa0Pi ( BII ) +\xa0Pj ( BII ) −\xa02Pi ( BII ) Pj ( BII ) .', '( 4 )', 'Eq 4 follows from Eqs ( 2 ) and ( 3 ) and from the relations: Pi ( BI ) = 1- Pi ( BII ) and Pj ( BI ) = 1- Pj ( BII ) .', 'Eqs 3 and 4 mean that , under the assumption of statistical independence of the two individual facing phosphates , the knowledge of the single phosphate probabilities Pi ( BII ) and Pj ( BII ) is sufficient to find the probabilities of BII•BI|BI•BII , BII•BII , and then also of BI•BI by using equation:', 'Pi , j ( BI•BI ) =\xa01–\xa0[Pi , j ( BII•BI|BI•BII ) +\xa0Pi , j ( BII•BII ) ] .', 'The next step was to test the possibility of uncorrelated facing phosphates against data collected from the MDs .', 'Thus , Pi , j ( BII•BI|BI•BII ) , Pi , j ( BII•BII ) , Pi ( BII ) and Pj ( BII ) were evaluated as the proportions of these states in the MD trajectories; Pi , j ( BII•BI|BI•BII ) was compared to [Pi ( BII ) + Pj ( BII ) −2Pi ( BII ) Pj ( BII ) ] in P-MDs and C-MDs; Pi , j ( BII•BII ) was compared to [Pi ( BII ) Pj ( BII ) ] in C-MDs only , since they generate sizable BII•BII populations in contrast with P-MDs .', 'The agreement between the compared quantities is clearly visible in Fig 6 , with correlation coefficients of 0 . 99 .', 'That is , the distribution of BII steps between the BI•BII|BII•BI and BII•BII combinations in complementary dinucleotide matches Eqs 3 and 4 very well .', 'Thus , the conformational states of the facing phosphates are statistically independent of each other .', 'In sum , the ability of both Parmbsc0εζOLI and CHARMM36 to generate phosphates visiting BII enabled to gain new insights into their dynamics and populations .', 'Thus , simultaneous transitions of two facing phosphate groups are very rare .', 'The two force-fields unambiguously support the notion of statistical independence of the conformational states of individual , facing phosphates .', 'This means that the populations of the three combinations of facing phosphates can be simply expressed from the BII propensities of individual phosphate groups , in particular from experimental data , as developed in the next section .', 'Considering that the notion of uncorrelated facing phosphate is convincing , the probabilities of states BI•BII|BII•BI and BII•BII were calculated using Eqs 3 and 4 , respectively , and equating Pi ( BII ) and Pj ( BII ) to Pi from NMR ( BII ) and Pj from NMR ( BII ) ( equivalent to BII%from NMR given in S1 Table ) .', 'This has the advantage to use the experimental data directly ( δP-derived BII percentages ) to quantify the phosphate states , bypassing the limitations in the simulated estimates of the phosphate state populations .', 'The resulting experimentally inferred BI•BII|BII•BI and BII•BII populations along the four dodecamers are shown in Fig 7 and the values are given in S2 Table .', 'According to this approach , most CpG•CpG and GpC•GpC , as well as the only CpC•GpG , are characterized by high percentages ( 45% and more ) of BI•BII|BII•BI ( Fig 7 ) .', 'CpG•CpG in Oligos 1 and 3 , CpC•GpG in Oligo2 and CpA•TpG in Oligo 4 are in addition more than 20% in BII•BII ( Fig 7 ) .', 'Overall , BI•BI is
['Introduction', 'Results', 'Discussion', 'Materials and Methods']
['The accurate prediction of the structure and dynamics of DNA remains a major challenge in computational biology due to the dearth of precise experimental information on DNA free in solution and limitations in the DNA force-fields underpinning the simulations .', 'A new generation of force-fields has been developed to better represent the sequence-dependent B-DNA intrinsic mechanics , in particular with respect to the BI ↔ BII backbone equilibrium , which is essential to understand the B-DNA properties .', 'Here , the performance of MD simulations with the newly updated force-fields Parmbsc0εζOLI and CHARMM36 was tested against a large ensemble of recent NMR data collected on four DNA dodecamers involved in nucleosome positioning .', 'We find impressive progress towards a coherent , realistic representation of B-DNA in solution , despite residual shortcomings .', 'This improved representation allows new and deeper interpretation of the experimental observables , including regarding the behavior of facing phosphate groups in complementary dinucleotides , and their modulation by the sequence .', 'It also provides the opportunity to extensively revisit and refine the coupling between backbone states and inter base pair parameters , which emerges as a common theme across all the complementary dinucleotides .', 'In sum , the global agreement between simulations and experiment reveals new aspects of intrinsic DNA mechanics , a key component of DNA-protein recognition .']
['The ability to simulate computationally the structure and dynamics of biomolecules is a major goal of structural biology .', 'Such simulations require the calculation of the forces and energy of the system , typically with extensively parametrized functions called “force-fields” .', 'Developing reliable force-fields has been very challenging for DNA , mainly because the simulations have to reproduce subtle , complex , sequence-dependent differences that also remain difficult to capture experimentally in solution .', 'Here , we take advantage of an extensive set of recent experimental ( NMR ) data gathered on selected DNA oligomers to test the performance of a new generation of force-fields for DNA simulations .', 'Our results demonstrate impressive progress towards more realistic simulations of DNA .', 'The agreement between experiment and simulations is now good enough to incite further interpretation of the experimental observables and yield new original insights into the intrinsic DNA mechanics .', 'In sum , this work shows that reliable DNA simulations provide a much finer understanding of the structural and dynamical B-DNA behavior , which will be essential to account for DNA recognition by proteins .']
[]