Structural dynamics of possible late-stage intermediates ... · Structural dynamics of possible...

Structural dynamics of possible late-stageintermediates in folding of quadruplex DNA studiedby molecular simulationsPetr Stadlbauer1 Miroslav Krepl1 Thomas E Cheatham III2 Jaroslav Koca3 and

Jirı Sponer13

1Institute of Biophysics Academy of Sciences of the Czech Republic Kralovopolska 135 612 65 BrnoCzech Republic 2Department of Medicinal Chemistry College of Pharmacy University of Utah Salt Lake CityUT 84124 USA and 3CEITEC ndash Central European Institute of Technology Campus Bohunice Kamenice 5625 00 Brno Czech Republic

Received January 10 2013 Revised April 18 2013 Accepted April 24 2013

ABSTRACT

Explicit solvent molecular dynamics simulationshave been used to complement preceding experi-mental and computational studies of folding ofguanine quadruplexes (G-DNA) We initiate earlystages of unfolding of several G-DNAs by simulatingthem under no-salt conditions and then try to foldthem back using standard excess salt simulationsThere is a significant difference between G-DNAswith all-anti parallel stranded stems and thosewith stems containing mixtures of syn and antiguanosines The most natural rearrangement forall-anti stems is a vertical mutual slippage of thestrands This leads to stems with reduced numbersof tetrads during unfolding and a reduction of strandslippage during refolding The presence of syn nu-cleotides prevents mutual strand slippage there-fore the antiparallel and hybrid quadruplexesinitiate unfolding via separation of the individualstrands The simulations confirm the capability ofG-DNA molecules to adopt numerous stable locallyand globally misfolded structures The key point fora proper individual folding attempt appears to becorrect prior distribution of syn and anti nucleotidesin all four G-strands The results suggest that at thelevel of individual molecules G-DNA folding is anextremely multi-pathway process that is slowed bynumerous misfolding arrangements stabilized onhighly variable timescales

INTRODUCTION

Guanine quadruplex molecules (G-DNA) are the mostimportant non-canonical DNA structures The most

salient feature of G-DNA is the presence of planartetrads of cyclically bound guanines stabilized by mono-valent ions Several consecutive tetrads stack together toform the G-DNA stem with the monovalent ions lining upin its channel The G-DNA molecules can consist of fourtwo or one separate sequences and their stems adoptvarious combinations of parallel and anti-parallel strandorientations Biochemically the most relevant variants arethe single-stranded topologies Monomeric and dimericquadruplexes need single stranded loops to connect theirstrands (1ndash7) G-DNA molecules are versatile and mayadopt numerous topologies which are often sensitive tothe base sequence and the surroundings (8ndash15)

Although the native structures of G-DNA moleculeshave been described by atomistic experiments much lessis known about foldingformation processes of variousquadruplex architectures Contemporary experimentalstudies suggest that quadruplex folding proceeds throughsmall numbers (two to four) of distinct intermediates(1316ndash31) However current experimental techniques tostudy folding have limited resolution which may poten-tially lead to oversimplified atomistic models of foldingand unfolding Some authors have proposed that the keyintermediates may consist of ensembles of isoenergeticstructures (32)

Alternatively at the level of the individual moleculesthe folding processes may include numerous substates andmay consist of diverse individual folding attempts Thenfolding would be a complex multi-pathway process Thishypothesis is supported by recent computational analysisof the spontaneous capture of a single ion by a two-tetradG-DNA stem (33) Even such a simple process as singleion entry into a G-DNA stem is in reality a multi-pathwayprocess with many diverse binding routes Similarly amulti-pathway process has been suggested by computersimulations for folding of small DNA hairpins moleculeswhose folding is undoubtedly much simpler than G-DNA

To whom correspondence should be addressed Tel +420 541 517 133 Fax +420 541 212 179 Email sponerncbrmunicz

7128ndash7143 Nucleic Acids Research 2013 Vol 41 No 14 Published online 21 May 2013doi101093nargkt412

The Author(s) 2013 Published by Oxford University PressThis is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (httpcreativecommonsorglicensesby-nc30) which permits non-commercial re-use distribution and reproduction in any medium provided the original work is properly cited For commercialre-use please contact journalspermissionsoupcom

folding (34) These investigations demonstrate that com-puter simulations can complement experimental studies ofG-DNA folding and unfolding by allowing studies offolding processes (or at least parts of these processes) atthe level of individual molecules with atomistic descriptionand sub-nanosecond time resolution (3536)

In this study we use molecular dynamics (MD) simula-tions to obtain insights into the structures that can bepopulated during the folding process of severalquadruplexes (see later in the text) Clearly the completeprocess of G-DNA folding or unfolding cannot be fullycharacterized by contemporary simulation techniqueswhich only recently reached microsecond timescales forG-DNA (37) In fact unrestrained standard simulationscan only capture dynamics that a real single molecule mayundergo in the simulation timescale when starting fromthe simulation starting structure Nevertheless the lackof complete experimental data justifies computationalstudies of various aspects of G-DNA folding(16183338ndash42) Although all such studies are affectedby specific limitations they provide valuable informationthat is not experimentally accessible When consideringsimulations we need to distinguish studies using unre-strained standard simulations from studies applyingvarious methods to enhance sampling (see later in thetext) Although the enhanced sampling methods allowthe sampling of structural transitions that are not achiev-able during standard simulations they bring additionalapproximations compared with standard simulationswhich need to be considered in the interpretation of thedata

Besides the ion-capture study noted earlier in the text(33) standard simulations were used a decade ago to in-vestigate possible intermediates in the formation ofparallel stranded tetrameric all-anti G-DNA stems (38)The cited authors built up various two three and four-stranded models and investigated their behavior in short(by current standards) 2ndash10 ns simulations followed byfree energy computations They proposed a formationpath from single strand to full stem involving late-stagefour-stranded intermediates with slipped strands and aprogressive reduction of strand slippage This formationpathway may be specific for parallel stranded all-antistems as alternation of syn and anti nucleotides in thestem may prevent easy strand slippage processes (seelater in the text) Recently short 3 ns simulations wereused to support a folding model of intramolecularquadruplexes via a triplex pathway (1618)

Among enhance sampling studies two have analyzedthe disruption of an intramolecular quadruplex bypulling it apart using external forces applied at oppositeends of the molecule (3940) A limitation of such forcedunfolding is that the external forces may qualitativelymodify the unfolding pathway while the ns-timescale(much shorter than in equivalent pulling experiments) ofunfolding may further bias the results (39) More recentlyReplica Exchange Molecular Dynamics (REMD) hasbeen used to probe unfolding properties of a thrombin-binding aptamer (15-TBA) starting from the folded state(41) REMD enhances sampling by simulating differentreplicas of the system at different temperatures (up to

500K or more) and swapping between them TheREMD method introduces some additional approxima-tions compared with standard simulations as the transi-tions occur during unrealistically high temperatures (43)Further true folding of a G-DNA molecule by REMDwould require the simulation to start from entirelyunfolded single strands with different distributions ofsyn and anti nucleotides compared with the foldedG-DNA molecule with a complete loss of the loop struc-tures When starting solely from the folded state (41) con-vergence of the REMD computations cannot be proven(44) In fact converged REMD of even the smallestnucleic acids systems such as RNA tetraloops is stillbeyond contemporary technologies (44) Despite theselimitations REMD simulation from the folded 15-TBAstate (41) has provided valuable insights at least intoearly unfolding and late folding events The ambiguityof the enhanced sampling studies can be demonstratedby comparing the 15-TBA REMD data with meta-dynamics simulations using a specific bias to achieve un-folding (42) The 15-TBA folding mechanisms proposedby REMD (41) and meta-dynamics (42) appear differentIn the present work we try to mimic unfolding of

G-DNA molecules using no-salt simulations where theG-DNA is deprived of the stabilizing ions As explainedlater in the text this approach can be justified by the factthat the likelihood of G-DNA structural rearrangementsis probably increased during periods with reduced bindingof the ions Using the no-salt simulations we try to obtaina spectrum of partially unfolded structures which may berelevant for late stages of the folding We then try to refoldthese structures using standard unbiased excess-salt simu-lations Given the limitations of the enhanced samplingmethods our less ambitious but milder approach is ap-propriate especially as we study more complexquadruplexes than 15-TBA which are beyond the scopeof the enhanced sampling methods We do not quicklyfully unfold or fold the systems but we investigate indetail properties of the G-DNA molecules in proximityto the folded state using conventional simulations andvariations in the environment with no biasing forces orultra-high temperatures Our approach resemblesstopped-flow techniques Starting from the folded struc-ture we first eliminate monovalent ions and afterinitiating unfolding we add the ions back In contrast tothe experimental procedures however the simulations in-vestigate the responses of a single molecule only onmstimescale The change of environment is instantaneousThe advantage is that we see all atomistic details of thestructural developmentsThe studied structures were selected to include stems

with diverse mutual strand orientations and synantipatterns We consider examples of parallel antiparalleland hybrid stems Whether a given stem structure occurswithin a tetramolecular bimolecular or unimolecularcontext is less important as the rearrangements directlyaccessible in the simulation time window are those primar-ily determined by properties of the G-DNA stems andonly secondarily modulated by the loops This is illus-trated by the similarity of stem behavior in simulationsof tetrameric and unimolecular all-parallel all-anti

Nucleic Acids Research 2013 Vol 41 No 14 7129

quadruplexes Even so we study structures with theirnative loops and the simulations thus provide someinsights into the role of the loops However we admitthat full investigation of the role of the loops along thefolding path is not possible owing to simulation timescaleNevertheless our data highlight important factors thatshould be considered when discussing G-DNA foldingpathways at atomistic resolution such as the qualitativedifference in preferred rearrangements of all-anti and syn-anti stems

MATERIALS AND METHODS

Initial models

We have used several basic starting structures (Figure 1)Six of them were taken from the Protein Data Bank (PDB)(i) the nuclear magnetic resonance (NMR) solution struc-ture of d[T2(G3T2A)3G3A] (2GKU first frame) (12) a 3+1(hybrid) monomolecular quadruplex with three tetrads (ii)the X-ray structure of d[A(G3T2A)3G3] (1KF1) (45) foldedin a monomolecular parallel quadruplex with three tetrads(iii) the X-ray structure of [d(G4T4G4)]2 (1JPQ) (46)Oxytricha nova telomeric dimeric antiparallel quadruplexwith four tetrads (iv) the X-ray structure of [d(TG4T)]4(352D) (47) forming four consecutive parallel strandedguanine tetrads with thymidines unstructured and bulgedinto space (one disordered thymidine residue was modeled)(v) the structure of RNA parallel quadruplex [r(UG4U)]4(1J8G) (48) forming four G-tetrads complemented byuridines that are bulged out and (vi) the X-ray structureof [d(G4)]4 (3TVB) (49) forming a parallel stranded stemwith the first tetrad all-synAdditional models were prepared manually One was

obtained by deleting all loop residues of 1JPQ so thatonly the four-tetrad antiparallel stem remained Anotherwas prepared from the 352D structure by deleting all theterminal thymidines Further modified structures werederived from 2GKU by slippage of either the first or thelast G-strand by one residue in 50-direction(Supplementary Figure S1) The glycosidic orientation ofguanosines in the slipped strand was adjusted manually toform fully paired tetrads The deoxyguanosine residue thatoccurred above the stem owing to strand slippage wasconsidered with either syn or anti glycosidic torsion ()and two distinct positions with respect to the oppositeloop residue were tested All possible combinations wereconstructed four for each slipped G-strand ie eightin total The molecules were manually built from theinitial NMR structure using the xLEaP module ofAMBER (50)Finally single-stranded d[T2(G3T2A)3G3A] and

d(G2T2G2TGTG2T2G2) (15-TBA sequence) helices werebuilt with helical parameters of B-DNA using the NABmodule of AMBER In some simulations torsions ofselected deoxyguanosines were manually adapted to thesyn region according to the anti and syn deoxyguanosinepattern of the folded quadruplex to facilitate foldingattempts

Water and ionic conditions

Solute molecules were placed in a truncated octahedralbox of TIP3P water molecules (51) with the box borderat least 10 A away from the solute at all points We havecarried out two types of simulations no-salt and excess-salt ones

In no-salt simulations no ions are present while thevirtual continuous plasma neutralizes the system Inother words the system is formally neutral even in theabsence of any counterions as the neutralizing charge isformally distributed over all the particles

Excess salt simulations were carried out with NaCl orKCl at a Na+ or K+ concentration of 03 M and Cl

concentration of 015M AMBER-adapted Aqvist par-ameters for the sodium cation (radius 18680 A and well

Figure 1 Schemes of experimental structures used in our simulations(a) 2GKU (b) 1KF1 (c) 1JPQ and (d) 352D and 1J8G (3TVB has thefirst tetrad in syn) (Deoxy)guanosine residues are depicted by rect-angles Yellow and orange indicate anti and syn conformation respect-ively darker residues are at the back Red lines represent G-DNA WCH hydrogen bonding Black arrows show sugar-phosphate backbone in5030 direction Loops are depicted by thin black curves while flankingresidues are not shown

7130 Nucleic Acids Research 2013 Vol 41 No 14

depth 000277 kcal mol1) (52) and Smith parameters forthe chloride anion (radius 24700 A and well depth0100 kcalmol1) (53) were used in simulations withNaCl The low concentration of NaCl prevents any saltcrystallization (54) Joung and Cheatham parameters forthe potassium cation (radius 1705 A and well depth01936829 kcalmol1) and the chloride anion (radius2513 A and well depth 00355910 kcal mol1) (55) wereused in simulations with KCl The purpose of thiswork was to obtain qualitative insights into possiblefolding intermediates in G-DNA folding therefore thebasic results should not depend on the force fielddetails Solvation and addition of ions were done usingxLEaP

MD simulations

MD simulations were carried out with the parmbsc0 (56)version of the Cornell et al (57) force field In a few simu-lations we also added the parmOL4 modification of the torsion which specifically improves simulation of the synDNA region (58) As we aim to attain qualitative under-standing of G-DNA folding both parmbsc0 andparmbsc0+OL4 force fields are considered close toequivalent for our study Although the OL4 correctionhas been shown to improve structures of simulated G-DNA molecules with syn bases with respect to X-raystructures (58) further testing of this force field is stillrequired OL4 modifies the shape of the syn regionmakes it slightly more stable reduces the barrier for synndash anti transition through the 120 region and increasesthe barrier through the 350 region The essential cor-rection for DNA simulations is the parmbsc0 modification(56) The RNA quadruplex was simulated with theparmbsc0OL3 force field the current AMBER defaultfor RNA (5960) The simulations were performed withthe pmemd module of AMBER 10 except for six per-formed using the CUDA version of AMBER 12 (61ndash63)Periodic boundary conditions were used and electrostaticinteractions were calculated by the particle mesh Ewaldmethod (6465) with the non-bonded cutoff set to 9 AThe SHAKE algorithm (66) was applied to bondsinvolving hydrogen and a 2 fs integration step was usedPressure was held constant at 1 atm and temperature at300 K unless stated otherwise using the Berendsen weak-coupling thermostat (67) Standard equilibration and pro-duction protocols were used trajectories were processedwith the ptraj module of AMBER and visualized in VMD(68)

Simulations of experimental structures

The experimental structures and their reduced modelslacking loops or terminal residues were initially simulatedin no-salt conditions in the absence of any ions The aimof these simulations was to initiate unfoldingAntiparallel quadruplexes were treated at both 300 and350 K because the lower temperature seemed to be insuf-ficient to disrupt the molecules in shorter simulationsThe no-salt simulations were monitored and several rep-resentative or interesting (in our opinion) conformationsfrom each no-salt simulation were chosen to initiate

standard simulations For these simulations severalcations were initially added manually at places with lowelectrostatic potential calculated by CMIP (69) The mol-ecules were then solvated additional ions were added andthe molecules were simulated using standard protocols at300K in excess-salt conditions (see earlier in the text)The simulation lengths were variable based on as-sessment of the simulation behavior (see lsquoResultsrsquosection) For comparison for most systems the no-saltsimulations were repeated in both NaCl and KClsolutions

Simulations of slipped quadruplexes and single-strandedhelices

All eight variants of the slipped hybrid quadruplex(see earlier in the text) were prepared with one ionmanually placed above its terminal tetrad one betweenthe two tetrads and one between the tetrad and the triadresulting from the strand slippage All these variants weresimulated using both NaCl and KCl with parmbsc0 for100 nsAll simulations of the single-stranded helix of

d[T2(G3T2A)3G3A] were run in excess-salt conditionsThe all-anti helix was initially simulated with parmbsc0and the modified helix with some syn-guanosines withparmbsc0+OL4 As the fully expanded single strand islarge and requires a large box the simulation was inter-rupted from time to time (on solute molecule compaction)and the water box size was adjusted to accelerate the simu-lations After 120 ns of the all-anti helix simulation inparmbsc0 two copies of the system were made andsimulated with parmbsc0+OL4 The first was simulatedunchanged whereas in the other the guanosines thatwould be syn in the folded hybrid quadruplex weremanually flipped to the syn region Parmbsc0+OL4 isexpected to sample the conformational space of torsion better than parmbsc0 alone The simulationswere monitored and stopped when no important conform-ational movements were observed for several tens of nsAll simulations of the single-stranded helix of the 15-TBAsequence were run in excess-salt conditions withparmbsc0+OL4 A helix with appropriate syn guanosineswas prepared manually from the all-anti helix Both theall-anti helix and the adapted helix were treated at 300 and350 K for 500 ns (ie 2 ms in total)

Comment on adding internal ions

When using geometries from the no-salt simulations tostart conventional simulations we added cations to theexpected ion-binding sites inside the structures based onelectrostatic potential calculations to accelerate the simu-lations In many cases the added cations were unstableand left the binding sites This may be due to eithergenuine instability of the ion in the binding site or non-optimal binding of the cation in the initial structure Thesimulation may need several nanoseconds to properlyequilibrate the ion-binding site and in some cases theion can be lost during this process An alternativeoption would be to add ions solely to the bulk and thenwait for their spontaneous capture Although spontaneous


capture of ions may occur within the simulation timescalewe applied (7071) it would often take dozens or even 100sof nanoseconds (cf footnote in Supplementary Table S1)(33) Thus we think our approach is justified

RESULTS

All simulations reported here are listed in SupplementaryTables S1ndashS3 The total duration of the simulationsanalyzed in this study is 22 ms

Justification of the no-salt simulations

The main aim of this work was to obtain insights into thetypes of structures that may occur during G-DNA foldingContemporary simulations are insufficiently long tocapture the spontaneous folding or unfolding of G-DNAsystems (see earlier in the text) Indeed folded G-DNAmolecules are so stable that they show no rearrangementsin conventional unbiased simulations in the presence ofions Therefore computational tricks are needed toinitiate unfolding We attempted to unfold the selectedG-DNA molecules by simulating them under no-salt con-ditions (using net-neutralizing plasma see lsquoMaterials andMethodsrsquo section) then investigated structures formedduring the no-salt simulations in standard simulationsTo visualize the difference between the no-salt andstandard simulations we repeated the no-salt simulationsof fully folded quadruplexes in the presence of NaCl andKCl In presence of ions the G-DNA stems are entirelystable (Supplementary Figures S2ndashS6) There is no chanceto see any structural changes of folded G-DNA moleculeson the affordable simulation time scale with exception ofloop dynamics (72)The no-salt simulations can at first sight look unrealis-

tic However destabilization of real quadruplex moleculesand their rearrangements likely occur during periods whenthe molecules are not fully stabilized by complete set oftheir internal ions (333873) The lack of ions in thechannel facilitates strand slippage and strand unbindingprocesses The no-salt simulation can be considered as theextreme such condition and we assume that the rearrange-ments seen during the no-salt simulations may be thoseinherent to the G-DNA molecules The no-salt simula-tions should populate structures that may occur in thelatest stages of the quadruplex foldingformationprocesses The no-salt simulations do not use externalbiasing force or ultra-high temperatures to initiate struc-tural changes The unfolding is initiated just by a changeof the environmentThe force field is not compromised in the no-salt simu-

lations The nucleic acid force field and water modelsare parametrized without considering the ions and areappropriate for any ion conditions In fact the ions areparametrized subsequently to fit the water models (53ndash55)As the positive charge is evenly distributed over all themolecules in the box (including thousands of water mol-ecules) the neutralization procedure has infinitesimallysmall effect on the force field parametersThe no-salt simulation is probably the only option how

to initiate unfolding of G-DNA systems unless we use

some unphysical conditions (temperatures above theboiling point for which the force field is not calibratedin case of REMD simulations or biasing forces in caseof the other sampling-enhancing methods) Simulationscan only show events that a real molecule could experienceon the simulation timescale (presently microseconds)under the simulation conditions In addition realG-DNA molecules are stiff following full binding of theions We suggest that their early unfolding rearrangementsoccur in periods when their stability is temporarilylowered owing to reduction of the number of ionsintegrated in the stem during the genuine processes ofion exchange Thus removal of ions from the channel toinitiate rearrangements in simulations is justifiedHowever we also excluded the bulk ions because in simu-lations with ions in the bulk but not the channel the bulkions would often enter and stabilize the G-DNA stembefore any unfolding rearrangements occurred

All re-folding simulations accounting for most of theoverall simulation time in the present study were done inthe presence of ions with no biasing procedure Thereforethe use of no-salt simulations in part of our study shouldnot dramatically compromise the main results

Parallel-stranded intramolecular quadruplex can bere-structured via strand slippage

No-salt simulation of monomolecular intramolecularparallel stranded 1KF1 quadruplex reveals that the mostcommon structural development is vertical strand slippage(Figure 2) This is consistent with a mechanism suggestedfor later stages of the formation of parallel-stranded tetra-meric quadruplex stems (38) Subsequent standard simu-lations initiated with selected intermediates observedalong the no-salt simulation demonstrate that themolecule is capable of quickly restoring the G-DNAstem even when starting from a largely perturbedgeometry (the structure literally collapses to the correctnative arrangement) although this does not occur in allrefolding attempts We have also observed stabilization ofalternative structures with slipped strands

Figure 2 shows the set of structures (marked consecu-tively A to G) observed during the no-salt simulation Thevertical and horizontal lines depict the progressions withtime in the no-salt and subsequent standard simulationsrespectively Consecutive structures in standardsimulations are marked by numbers and are shown indetail in Supplementary Figures S7ndashS14 Structures thatwere subsequently successfully refolded (to a conform-ation with at least two stable tetrads) are shown in greenboxes and others in yellow boxes

In the absence of cations the tetrads became less stableand G-strands were able to slide along each other After20 ns of the no-salt simulation one of the G-strands slidaway completely so that the remaining structure formed atriplex that finally (at 30 ns) converted to a parallelduplex with an additional perpendicular G-strand (a struc-ture nearly identical to molecule G3 SupplementaryFigure S14)

Six conformations (BndashG) from the no-salt simulationwere chosen to start standard NaCl simulations


(Figure 2 and Supplementary Figures S7ndashS14) withcations initially placed inside the stem based on electro-static potential calculations (see lsquoMaterials and Methodsrsquosection) The molecules B and C were simulated twice asthe first simulations did not lead to stable tetradsSimulations starting from structures B C D and Fresulted at least in some runs in stable quadruplexcores B3 C6 C7 D5 D6 and F4 respectively whichwere stable until the end of the simulations (100 ns)Some of them had the native three tetrads whereas the

others had two tetrads with some vertical strand slippageThe simulation of structure D led to fully foldedquadruplex D5 (Supplementary Figure S11) with nocation in the channel but the final structure wassomewhat distorted Thus a new simulation startingfrom the D3 structure with manually placed sodiumcations in the channel was performed which resulted inproperly folded quadruplex D6 We made three attemptsto equilibrate and simulate molecule E all of which wereunsuccessful

Figure 2 Graph (left) of simulations performed on the d[A(G3T2A)3G3] parallel-stranded quadruplex Boxes in the graph mark important con-formations and show their labels The vertical line indicates the unfolding no-salt simulation and the horizontal lines re-folding simulations withexcess-salt conditions Branches from the horizontal lines indicate further simulations from the corresponding structures The numbers in boxes showthe times (ns) when the corresponding structures were observed from the beginning of either the no-salt simulation or excess-salt simulation (exceptthe last numbers in green boxes which show the end of the simulation) The cyan box corresponds to the starting experimental structure Greenboxes represent structures that were successfully refolded (see the text) whereas yellow boxes mark unsuccessful refolding attempts Structuralschemes A-G are visualized as follows deoxyguanosine residues are depicted by rectangles yellow indicates anti conformation orange syn conform-ation and darker residues are at the back Solid red lines represent standard WCH hydrogen bonding and dashed red lines represent any otherhydrogen bonding Black arrows show sugar-phosphate backbone in 5030 orientation Loops are depicted by thin black curves Flanking residuesand ions are not shown The coloring of the edges of the rectangles in the structures indicates residues with approximately the same normal vector oftheir respective base plane the letters below the structures correspond to the labels used in the vertical (no-salt) graph For full structural details seeSupplementary Figures S7ndashS14 and Supplementary Table S4


Spontaneous strand slippage toward the native stemThe most interesting simulation was the one resulting insuccessful refolding of the structure C (SupplementaryFigure S8) which contains only a single tetrad withtriple strand slippage The first refolding attempt failed(Supplementary Figure S9) but in the second attemptthe molecule swiftly slipped back to a structure with twoadjacent strands slipped by one step having two tetradssandwiched by GG pairs at each end (structure C5 inSupplementary Figure S8) After 80 ns the last guanosineof the third G-strand below the two tetrads turned syn(structure C6 in Supplementary Figure S8) This localmisfolding hampered further strand slippage Thus westarted a third simulation from the C5 structure withtwo-strand slippage The molecule captured a secondsodium cation from bulk solvent after 15 ns so that onecation remained inside the two-tetrad stem and an add-itional ion was placed above the upper tetrad After afurther 15 ns the cation placed between the tetrads (theinternal cation) moved below the lower tetrad and theupper cation relocated between the tetrads These move-ments were immediately followed by slippage of thesecond G-strand one step downwards further reducingthe strand slippage to just one slipped strand(Supplementary Figure S15) Thus we obtained a nearlyfully folded stem that would require only one additionalstrand slippage to achieve the native arrangement (struc-ture C7 Supplementary Figure S8) We observed subse-quent dynamics of the two ions between the three bindingsites in the single-slippage stem At 670 ns the originallybound ion (the bottom one) left the system and after50 ns was replaced by a cation captured from the bulksolvent This conformation with two ions did not undergoany changes until the end (2500 ns) of the simulationThe above simulations show the largest spontaneous

rearrangement of a quadruplex toward its native structureseen to date in conventional simulations in which themolecule performed two consecutive strand slippages ona submicrosecond timescale both toward the native stemarrangement In addition this is the second reportedexample of a spontaneous exchange of an initially boundstem ion with the bulk [cf (33)] The simulation supportsthe earlier hypotheses that (i) release of stem-bound ions isusually correlated with binding of incoming ions from thebulk and thus the stem remains stabilized by at least N-1ions (where N is the number of complete tetrads) (3336)and (ii) the strand slippage occurs preferably during theion-exchange events when the energy barrier for strandslippages is reduced (38)Partial folding and unfolding of the G-triplex were

observed in simulation of the molecule G where oneG-strand was found consecutively in perpendicular andparallel positions relative to the remaining G-duplex(Supplementary Figure S14) but at the end of the simu-lation (1000 ns) the structure was completely lostOur simulations did not indicate any significant in-

volvement of loops in the folding or unfolding processin terms of important hydrogen bonding ion binding orinfluence on the direction of strand slippage However theloops might facilitate folding by keeping the G-strands

together and their role may be apparent on longertimescales

In summary the intramolecular parallel-strandedquadruplex shows high potential for strand slippageEven considerably perturbed molecules (Figure 2) havehigh capability to stabilize arrangements with three ortwo fully paired tetrads quickly After forming the two-tetrad stem the parallel quadruplex can rearrangestraightforwardly to a three-tetrad stem on longer time-scales (38) We suggest that structures depicted in Figure 2and Supplementary Figure S7ndashS14 (as well as many otherstructures) could be populated during the latest stages offolding of this quadruplex

Parallel-stranded tetrameric quadruplexes also revealstrand slippage rearrangements

No-salt simulations of all-anti [d(TG4T)]4 (50 ns) and[d(G4)]4 (20 ns) structures revealed a similar unfoldingmechanism In the first few ns the guanine tetradsbecame increasingly perturbed leading to verticalslippage of the individual strands With thymidines twoadjacent strands slipped nearly simultaneously in 50-direc-tion whereas without thymidines we observed slippage ofone strand in 30-direction followed after 3 ns by slippageof the diagonally placed strand in 30-direction This differ-ence is likely incidental and not related to the presence orabsence of the thymidines Meanwhile the remainingtetrads were further perturbed or even disruptedDisruption of the remaining tetrads and previous strandslippage were coupled with rotation of two strands relativeto the other two finally leading to formation of a lsquocross-likersquo molecule (Figure 3) that was stable for the rest of theno-salt simulations The individual rearrangementsdescribed above occurred through series of back-and-forth movements as the molecules usually returned backto the preceding geometry several times before the newone finally stabilized In summary the strands usuallyslip back and forth before slipping permanently forma-tion of the cross-like structure can be partially reversedand the tetrads can be restored for a short time aftertheir initial disruptions Thymidine residues while cer-tainly influencing details of the unfolding (forming basepairs and base stacks with guanines from the disruptedtetrads) do not seem to change the general pathway inwhich the structure unfolds

We attempted two refolding simulations in the presenceof ions The starting geometry for the first was taken fromthe last frame of the no-salt simulation without thymi-dines This structure was heavily perturbed and cross-like (Figure 3) Two Na+ ions were initially placed insidethis structure After a few ns of the simulation a stem wasrestored with diagonally slipped strands three fully stableguanine tetrads (stabilized by the initially placed Na+ions)and fluctuating base pairs at 50 and 30 ends formed byguanines not involved in tetrads owing to the strandslippage (Figure 3) The structure subsequently remainedstable until the end of the 500 ns simulation Initial coord-inates for the second refolding simulation were taken fromthe structure at 85 ns of the [d(TG4T)]4 no-salt simulationAlthough the tetrads were disrupted in this structure and


the strands rotated into the cross-form there was novisible strand slippage (Supplementary Figure S16)After a few ns three stable tetrads formed (stabilized bythe initially placed Na+ ions) However the 50-end tetradwas not restored despite the absence of strand slippageThe 50-terminal guanines sampled many conformationsover the 3 ms trajectory Two guanines formed a stablebase pair whereas the other two mostly interacted withthymine bases preventing completion of the last tetrad(Supplementary Figure S16) The structure thusremained locally misfolded on the 3 ms timescale

The simulations of parallel-stranded tetrameric RNAquadruplex [r(UG4U)]4 show similar trends to simulationsof the DNA tetrameric parallel stem specifically thestrand slippage Details of the simulations are neverthelessdifferent likely reflecting differences in the shapes of theDNA and RNA single strands In the no-salt simulation(at 32 ns) the unfolding begins with perturbations oftetrads followed by slippage of one strand (strand c) in50-direction immediately followed by slippage of anadjacent strand (d) in the same direction Strand c subse-quently slips further away by one step The system adoptsa structure where some base pairing is maintained between

adjacent strands a+b and c+d There is no pairingbetween the diagonally placed strands This resemblesthe cross-form observed in the DNA tetrameric parallelstems although with visibly lesser loss of parallelity(Figure 4) The 20-hydroxyl groups form mainlyintrastrand H-bonds with O40 and O50 atomsInitial coordinates for refolding simulation were taken

from the structure at 40 ns of the no-salt simulation(Figure 5) In this structure one strand was fully andthe adjacent strand partially slipped by one step The in-dividual tetrads especially those at the 30-end were sub-stantially perturbed Two Na+ ions were initially placedinside the structure The partially slipped strand slippedback after 3 ns and the other strand at 17 ns Gradualrestoration of the tetrads was coupled with this processThree tetrads were completed after 17 ns One guaninefrom the 50-end tetrad continued to interact with uridineresidues (preventing completion of the last tetrad) andwas reintegrated into the structure after 36 ns completelyrestoring the quadruplex to its original structure (Figure5) The quadruplex was then entirely stable for the rest ofthe 500 ns simulation The two initially placed Na+ ionsremained in the channel but we did not see the expectedstable incorporation of the third ion into the stem Thismay reflect some remaining minor perturbations of thestructure Nevertheless we observed two consecutive in-stances (at opposite stem ends) of temporary capture andsubsequent loss of the third Na+ ion from the bulk Thetwo internal ions fluctuated between the three availableinter-tetrad cavitiesIn summary it is unlikely that four strands and three

ions simultaneously come together and immediately forma native four-tetrad tetrameric stem Rather the forma-tion process has a multi-pathway nature and includesnumerous diverse formation attempts The most success-ful attempts could result in structures sufficiently close to

Figure 3 (a) Final structure of the parallel all-anti tetrameric [d(G4)]4G-DNA stem forming the cross-like structure in the no-salt unfoldingsimulation (b) The structure at the end of the standard re-foldingsimulation which has a stem with three tetrads and mutual slippageof the diagonally placed strand pairs leading to formation of GG basepairs above and below the stem Strands forming the cross-structure inpart (a) are colored red and yellow the Na+ ions are blue and thebackbone brown (c) Structural scheme of the molecule depicted in(a) (d) Structural scheme of the molecule depicted in (b) For furtherexplanation of the schemes see the legend of Figure 2

Figure 4 Terminal structure of the 190 ns long no-salt simulation ofthe RNA quadruplex [r(UG4U)]4 in which base pairing is maintainedbetween red strands and between yellow strands Yellow strands arethose (strands c and d) that consecutively slipped in the simulationUridines are colored green


the native stem (such as those illustrated in Figure 3 andSupplementary Figure S16) with subsequent rearrange-ments to the final stem We suggest that the structuresshown in Figure 3b and Supplementary Figure S16b rep-resent examples of arrangements that may occur duringthe latest stages of the formation of tetrameric parallelstranded stems These structures can convert to the finalfour-tetrad stem straightforwardly although in mostcases the process would be beyond the present simulationtimescale Our inability to complete the last misfoldedtetrad in the simulation of the [d(TG4T)]4 stem during3 ms is a reminder of the timescale that is sometimesneeded to spontaneously observe even the most trivialG-DNA rearrangements Nevertheless we have observedfull recovery of the RNA quadruplex (Figure 5)

Hybrid form of human telomeric quadruplex

The simulation behavior of G-DNA molecules containingantiparallel strands was strikingly different from that ofparallel-stranded structures The mixture of syn and antiguanines prevents simple strand slippage processesdominating in parallel stranded all-anti systems Anystrand slippage would have to be accompanied with con-certed syn - anti rearrangements Instead the antiparallelquadruplexes show separation of the individual strandsTwo types of movements appeared in our 300 ns no-salt

simulation of the 2GKU structure (Figure 6) During thefirst the groove between the first and last G-strandsslightly opened disrupting hydrogen bonds between thestrands However these minor openings were reversibleand the quadruplex core always quickly reformedSimilar breathing-like motions are needed for passage oflarge cations such as NH4

+ through the quadruplex (74)The other perturbation was much larger with visibleopening of the upper part of the quadruplex propagatingdownward leading to two separated duplexes containingG-strands 1+2 and 3+4 respectively (Figure 6) Thismovement appears to be facilitated by the presence ofthe lateral loop between strands 2 and 3 No splitting of

the structure into duplexes 1+4 and 2+3 was observedbecause such movement may be hindered by the propellerloop between strands 1 and 2 The first separation ofduplexes occurred after 30 ns of the simulation Thenseveral reformations of the bottom tetrad and attemptsto reform the upper tetrads were observed within 10 nsturning the structure into a heavily distorted triplex withstrand 3 separated Although the quadruplex structurewas already almost lost (Figure 7) it suddenly spontan-eously reformed and during a further 150 ns graduallyimproved to an almost precisely folded quadruplex evenin the no-salt conditions (structure Y 227ns)Nevertheless as the simulation further progressed thesecond G-strand completely detached resulting in the for-mation of a triplex of strands 1 3 and 4 Finally a duplexof strands 3+4 remained whereas G-strands 1+2 and theadjacent loops formed a long single-stranded helix We didnot analyze the simulation further as the two ends of themolecule came too close to each other owing to theperiodic boundary condition

Ten representative conformations from the no-saltsimulation (structures QndashZ Figure 7) were chosen tostart standard excess NaCl salt simulations ranging from40 to 500 ns (Supplementary Table S2) The molecule Q

was simulated twice as the first excess-salt simulation didnot lead to any satisfactory structure During the secondattempt the quadruplex almost reformed but no cationswere present in the channel and the core remained slightlyopen After 20 ns two sodium cations were manuallyplaced in the channel Although one of them immediatelyleft the structure improved the core closed and all typicalhydrogen bonds were formed except for a small distortionof the last tetrad where the cation was absent This struc-ture is assumed to have high potential to fully restore on alonger timescale The molecules R and S reformed thequadruplex with two cations in the channel at 2 and12 ns respectively The molecule T reformed properlybut with only one cation Nevertheless it is assumedthat the molecule would obtain the second cation from

Figure 5 (a) Structure after 40 ns of the no-salt simulation of[r(UG4U)]4 (b) The structure resulting after addition of ions whichis fully restored to its typical conformation Guanosines forming theindividual tetrads in the native G-stem are colored mauve red yellowand green Na+ ions are colored blue and the backbone and uridinesbrown

Figure 6 Two types of movements observed during the 300 ns no-saltsimulation of the hybrid 2GKU quadruplex (a) Modest and reversibleopening of the groove between the first and last strands with local lossof direct base pairing (b) Large opening of the quadruplex from theupper part downward The schemes are visualized as in Figure 2 Thered arrows show directions of the movements


the bulk on a longer timescale The molecule V foldedback during the second independent simulation withtwo cations in the channel Although the molecule U

looked visually closer to the initial structure thanmolecule T it lost both sodium cations from the channelin 1 ns Then the structure opened up and was not ableto recover during folding attempts because of stericclashes of loops in the upper part of the structure Thedistorted triplexes of W and X structures were not able toreform the quadruplex in 100 ns However the molecule Ytaken from a later part of the no-salt simulation refoldedimmediately during equilibration Finally the triplexstructure Z lost its first strand and both cations from thechannel binding sites in 100 ns Then the resulting duplexcaptured another cation from the bulk solvent after 50 ns

and the triplex was reformed after a further 30 ns Severalsubsequent exchanges of the triplex-bound cation with thebulk solvent were observed However we did not detectany sign of movement toward the quadruplex stemOne syn-to-anti conversion was observed in the secondG-strand not participating in the triplexIn experiments the type of ion present may affect the

overall free energy balance between different G-DNAfolds at thermodynamic equilibrium (11214) Howeverin the sub-microsecond time window investigated by simu-lations we do not expect large systematic differencesbetween NaCl and KCl simulations as both ionssupport G-DNA folding In the present study we havesimulated neither transitions between different G-DNAfolds nor their equilibrium populations (see lsquoDiscussion

Figure 7 Two graphs (left) showing changes with time of the 2GKU quadruplex in the single no-salt simulation The colors of the boxes indicatewhether the corresponding structure was successfully refolded (green) or not (yellow) in the subsequent KCl and NaCl simulations The conform-ations (right) occurring in this simulation that were used as starts for subsequent NaCl and KCl simulations (except for the ZZ molecule) Forfurther details see Supplementary Table S5 and for further explanation see the legend of Figure 2


and Conclusionsrsquo section) Nevertheless we repeated theNaCl simulations with KCl (Supplementary Table S2)The results were qualitatively similar (Figure 7 left)although some structures were refolded with NaCl butnot with KCl and vice versa However we suggest thatthis does not reflect any major differences between effectsof the Na+ and K+ ions that would be relevant on thesimulation timescale The differences are probablyrandom owing to the stochastic nature of the simulationsIndependent simulations of the same starting structureoften have different trajectories even in otherwiseentirely identical conditions The overall picture (typesof rearrangements) emerging from the NaCl and KClsimulations is consistentIn summary we have observed restoration of the native

stem arrangement of 2GKU in many standard simula-tions The structure was also temporarily restored at227 ns of the no-salt simulation before being ultimatelylost All successful refolding events restored the initialstem structure as it is pre-determined by the distributionof syn and anti guanosines in the strands In some othercases partially refolded structures remained trapped in thesimulations eg structures V and Z formed two correcttetrads in KCl simulations Only one syn-to-anti intercon-version was observed on our simulation timescale in astrand that was unbound from the rest of the structureThus although being far from converged the simulationsdemonstrate that the hybrid 3+1 structure can rearrangethrough multiple individual events by unbinding andbinding of the individual strands The folding clearlyrequires correct alternation of syn and anti nucleotidesin the G-strands Then even visibly perturbed structuresare capable of re-forming the stem spontaneously and theindividual folding attempts are quick

Four-tetrad dimeric antiparallel quadruplex with diagonalloops

The simulations of the [d(G4T4G4)]2 1JPQ quadruplexgive clear hints about the timescales of folding processesof G-DNA molecules and their capability to adoptlong-lasting misfolded structures The molecule wasstable even after 15 ms room-temperature no-salt simula-tion However it slowly degraded in multiple local back-and-forth steps (Figure 8) and in later stages of the no-salt simulation it remained essentially frozen in a locallymisfolded geometry (Figure 9) This is dramatically differ-ent behavior compared with the 2GKU no-salt simula-tion The simulation behavior likely reflects the presenceof four tetrads in this system and stabilizing role of thediagonal loops These structural features extend the time-scale for structural perturbations beyond the capability ofour computer facilities In contrast to the 2GKU struc-ture two diagonal loops present in the [d(G4T4G4)]2quadruplex prevent the stem from opening therefore nosplitting of the stem into duplexes occurs This indicatesthat loop topology may have profound effects on the un-foldingfolding processes at the atomistic level Anattempt to start refolding from the locally misfolded struc-ture proved to be futile demonstrating that the moleculecan adopt highly stable locally misfolded arrangements

Further details can be found in Supplementary Data seealso Supplementary Table S2

Four stranded antiparallel tetrameric stem

No-salt simulation of the stem of 1JPQ without the loopsresulted in disruption of the first and last tetrads within9 ns following equilibration (Supplementary Figure S17)Five independent standard simulations (500 ns in total)using starting structures taken from the first 9 nsshowed that the structure has good potential to refoldat least partially (see Supplementary Figure S17)Further continuation of the no-salt simulation led to sig-nificant distortions of the inner tetrads Two standard

Figure 9 Final structure of the [d(G4T4G4)]2 quadruplex in the 15msno-salt simulation Guanosines forming the consecutive tetrads in thenative G-stem are in blue red yellow and green respectively The sugar-phosphate backbone and thymidines are in brown Five base triads andtheir respective locations in the structure are highlighted Black dotsmark nucleotides in syn conformation The structure remains compactbut the native interactions have been visibly perturbed

Figure 8 Substantial temporary unwinding (unbinding) of one strandfrom the DNA antiparallel [d(G4T4G4)]2 quadruplex structure in theno-salt simulation Guanosines forming the consecutive tetrads in thenative G-stem are in blue red yellow and green respectively Thesugar-phosphate backbone and thymidines are in brown Blackdashed lines represent C10-C10 distances of nucleotides between theunwound strand and the adjacent strand The sketch on the right isshown from a different angle for clarity see the legend of schemes inFigure 2 for further explanation


simulations (60 ns in total) were performed on these struc-tures but they did not show any sign of refolding

Simulations of slipped 2GKU quadruplexes illustrate thepotential for misfolding

We built eight misfolded 2-tetrad structures based on the2GKU quadruplex (see lsquoMaterials and Methodsrsquo section)with single-strand slippage and adequate adjustment ofthe torsions (Supplementary Figure S1) which wesimulated in the presence (separately) of NaCl and KClSignificant loop dynamics were observed in the first nano-seconds of each simulation as the loops were significantlyaffected by the building procedure Increased fluctuationsof the loops also continued during the rest of the simula-tions which could be due to both the misfolded G-stemand inaccurate description of loop torsions caused by theforce field (7576) Although we observed some localdynamics the 16 independent 100 ns simulationsrevealed no sign of dynamics that would indicate capabil-ity of the molecules to move toward the properly foldedquadruplex on any affordable simulation timescale stablemisfolded two-tetrad structures remained in all simula-tions These simulations together with the 1JPQ simula-tions presented earlier in the text highlight the challengesin simulating G-DNA folding A full description can befound in the Supplementary Data

Parallel stranded stem with 50-end tetrad in syn

In all-parallel stems the first (50-end) tetrad may be in synconformation as seen in the X-ray structure of [d(G4)]4(PDB 3TVB) (49) Earlier computations have revealedthat the syn conformation of the terminal tetrad is dueto absence of any upstream nucleotide in the G-strandswhich allows formation of terminal syn-specific 50OHndash N3(G) intrastrand H-bonds (3677) However the50-terminal syn tetrad is also populated as a minorsubstate in (TGnT)4 tetramolecular quadruplexes accord-ing to in-solution NMR data (7879) Thus we carried outno-salt simulation of the [d(G4)]4 3TVB structure whichconfirmed that a mixture of syn and anti guanosines in thestem blocks straightforward strand-slippage movementsExpulsion of one syn guanosine from the 50-terminal syntetrad was followed by additional deformations ultim-ately allowing partial strand-slippage involving exclu-sively the anti guanosines These events were followed bystrand separation leading to a deformed cross-like struc-ture Full details are given in the Supplementary Data andillustrated in Supplementary Figures S18ndashS20

Single-stranded helices

The purpose of the standard simulations of thed[T2(G3T2A)3G3A] and d(G2T2G2TGTG2T2G2) singlestrands was to see if they could suggest at least somesubstates that could form during early stages of the G-DNA folding process These simulations thus complementthe no-salt simulations of folded G-DNA structureswhich aimed to detect possible late intermediates Properfolding of a given final G-DNA architecture requires anappropriate combination of syn and anti guanosines in theindividual strands Thus kinetics of syn$anti transitions

and the relative syn versus anti populations in singlestrands may have dramatic effects on the G-DNAfolding processesOur 300 ns simulations of the d[T2(G3T2A)3G3A]

single strand did not show any development towardquadruplex folding Therefore we did not further extendthese simulations Simulation of the all-anti single strandresulted in formation of an all-anti antiparallel hairpinwith duplex base pairing between the first and secondG-strand after 80 ns The duplex was characterized bypairing between the first and second guanines of eachstrand whereas the third guanine interacted with theloop nucleobases In the context of G-DNA folding thisduplex is clearly a misfolded structure The strands adoptan antiparallel orientation instead of the parallel orienta-tion that would be compatible with the all-anti arrange-ment in G-DNA The structure was stable for theremaining 40 ns of the simulation G15 in the thirdG-strand not involved in the duplex spontaneouslyflipped into syn torsion We then manually flipped thefirst guanine in each strand to syn conformation Thestructure then formed two G-DNA-like WCH GG basepairs and was subsequently stable in the 100 ns simulation(Supplementary Figure S21) However it still did not cor-respond to any G-DNA folding intermediate as the par-ticular synanti pattern (two syn-anti-anti strands) wouldagain require parallel arrangement of the strands corres-ponding to parallel strands in the hybrid structures Thesimulations thus merely illustrate the capability of singlestrands to form numerous intramolecular topologies thatare incompatible with the target G-DNA fold and wouldslow the folding processOur simulations of the d(G2T2G2TGTG2T2G2) single

strand showed somewhat different behavior We againobserved some misfolded hairpins (data not shown)with similar structure to that described earlier in thetext therefore no movement toward folding occurredHowever we also noticed rather frequent syn$anti tran-sitions especially in simulations starting from the all-antihelix The transitions had no site preference and guano-sines could remain in either syn or anti position for periodsof several picoseconds to tens of nanoseconds We thinkthat this was caused by the new force field parmbsc0+OL4 (58) used in this simulation Parmbsc0+OL4 couldprovide a more realistic description of the syn$antikinetics than parmbsc0 alone However we decided topostpone further investigation of single strands to futurestudies as extended analysis would have been beyond thescope of the study The parmbsc0+OL4 force field mightneed more testing especially regarding the energy balancebetween the syn$anti states (ie depths of the syn and antiminima)

DISCUSSION AND CONCLUSIONS

Experimental studies of folding pathways of G-DNA arenot straightforward (16ndash22) Explicit solvent moleculardynamics simulations can give some additional insightsinto selected aspects of the G-DNA foldingformationprocesses owing to their capability to monitor the


development with time of the atomistic structures of theindividual molecules (3338ndash41) However standard unre-strained simulations are limited by the affordable time-scale and by approximations of the simulation forcefields Biased and enhanced-sampling simulations intro-duce additional approximationsThe setup of MD simulations is specific and does not

match that of any existing experiments MD simulation isa technique that investigates the behavior of single mol-ecules assuming some starting geometry on short time-scales Its advantage is the unlimited temporal andcoordinate resolution it affords and hence its ability toreveal unique single-molecule rearrangements at atomisticlevel that are not accessible to experimental techniquesMD is different from ensemble thermodynamics equilib-rium techniques Discussion of differences between experi-mental and simulation setups and guidelines forcomparing simulations with experimental data can befound elsewhere (36) These differences need to be takeninto account when simulation results are interpreted andcombined with experimental knowledgeIn the present study we tried to initiate early stages of

unfolding of several G-DNA architectures by simulatingthem under no-salt conditions In no-salt simulations thesimulated system does not contain any ions and isneutralized by distributing the neutralizing charge overall particles in the solvent box Such simulations couldprovide realistic estimates of natural unfoldingpathways as G-DNA structural rearrangements arelikely accelerated during periods with incomplete bindingof the ions Substates (perturbed structures) occurringduring the no-salt simulations were then furtherinvestigated by standard excess-salt simulations aimingto see if the molecules can fold back to the nativearrangementThe simulations revealed a significant difference

between systems with all-anti parallel stranded stems andstems containing mixtures of syn and anti guanosines Forthe all-anti structures (intramolecular as well as intermo-lecular) the most natural rearrangement is a verticalmutual slippage of the strands (Figure 2) This leads tostems with reduced numbers of tetrads during the initialunfolding and reduction of strand slippage during latestages of folding Additional movements involve variousstrand-separation processes and formation of cross-likestructures (Figure 3) In contrast mutual strand slippageis prevented by alternation of syn and anti nucleotides inthe stem which does not allow viable base pairing aftermutual vertical strand movements Thus in thesequadruplexes separation of strands is the most likelymovement in the first stages of unfolding The alternationof syn and anti nucleotides in a folded G-DNA must havean exact pattern Vertical strand movements would causeheavy distortions in geometry and formation of non-native WCWC and HH GG base pairs Indeed nosuch movements have been noticed in our simulationsFor the human telomeric monomolecular parallel

stranded all-anti quadruplex (Figure 2) we report aconvincing case where the stem is initially almost dis-rupted in no salt-simulation Then in standard simula-tions it spontaneously progresses on sub-microsecond

timescale back from the perturbed structure with triplestrand-slippage and one tetrad to a structure with justone slipped strand having two tetrads and one triadThe back-slippage movement occurs during exchange ofthe bound ion with the bulk when the free energy barrierfor vertical strand movements is likely reduced We reporta case of a full exchange of a stem ion with the bulk andas observed in a recent study by Reshetnikov et al (33)release of the initially bound ion to the bulk is correlatedwith binding of an incoming ion from the bulk This keepsthe quadruplex conveniently stabilized by ions during thewhole exchange Overall our data suggest that strandslippage is likely to participate in late stages of the struc-turing of intramolecular parallel stranded quadruplexesSpecific issues that our simulations have not yet probedare the mechanism and likelihood of the formation ofdouble-chain reversal loops

The results for parallel stranded all-anti four-tetradtetrameric quadruplexes (both DNA and RNA) are con-sistent with the aforementioned data for the intramolecu-lar three-tetrad parallel-stranded quadruplex They alsosupport the formation mechanism suggested a decadeago by Stefl et al (38) These quadruplexes have clearstrand slippage capabilities and tendencies to form cross-like assemblies in the absence of ions (Figures 3ndash5) Thuswe suggest that late stages of tetrameric parallel stem for-mation may involve cation-stabilized four-stranded inter-mediates with various degrees of strand slippage andincomplete numbers of tetrads The slipped strandscould slowly rearrange into a native four-tetrad stem byreduction of strand slippage Such a process is also con-sistent with experimental data (212280ndash82) Similarly tothose of a monomolecular parallel quadruplex the slippedintermediates with tetrads are stable in the presence of thebound ions

Our standard excess salt simulations of the perturbedhybrid 3+1 human telomeric quadruplex structures(Figure 7) demonstrate that these molecules have goodpotential to refold even after substantial structural per-turbations In most cases the refolding occurred as asudden collapse or compaction of the structure towardthe native arrangement Nevertheless all these refoldingattempts used starting structures with native distributionof syn and anti guanosines Thus we further simulated aset of artificially locally misfolded hybrid 3+1 quadru-plexes with a single-strand slippage and adjusted (ienon-native) synanti distribution in the slipped strandThese simulations showed no sign of either unfolding orstructuring toward the native arrangement indicating thateven in the latest stages of folding G-DNA molecules maymassively populate locally misfolded structures with life-times much longer than the presently affordable simula-tion timescale before reaching final thermodynamicequilibrium

Simulation of a parallel-stranded stem with the firsttetrad in syn conformation confirmed that strands inadjacent all-anti tetrads can slide along each otherwhereas steps with alternating syn and anti guanosinessuppress strand-slippage movements

The no-salt simulations of four-tetrad [d(G4T4G4)]2 anti-parallel quadruplex did not achieve large unfolding


although the structure was locally perturbed (Figures 8 and9) The subsequent standard simulations indicate that thefinal structuring of the molecule may be complex processwith numerous micro-rearrangements owing to the cap-ability of the molecule to form numerous non-native inter-actions Such process remains entirely outside the timescaleof contemporary simulations

The simulations provide preliminary insights intomodulation of the stem unfolding pathway by the loopsIn the all-parallel quadruplex 1KF1 with propeller loopsthe G-strands can slide along each other almost freelywith little hindrance from the loops The lateral loop of2GKU enables an opening of the quadruplex (separationof two duplexes) whereas the diagonal loops in the[d(G4T4G4)]2 quadruplex hinder such movement

In many respects our results are consistent with modelsconsidered in previous literature No formation ofquadruplexes via triplex intermediates (161723) wasdirectly observed in our simulations although it wouldbe consistent with the strand separation seen in the no-salt simulations However the process could be morecomplex than previously assumed (161723) as it wouldrequire correct synanti guanosine distribution in all theindividual strands before fourth-strand binding couldoccur (see later in the text) Preliminary simulations (inprogress) indicate that G-strand triplexes once formedwould have lifetimes on ms timescale It is possible thattriplex intermediates may occur during the interconversionbetween various G-DNA folds as a consequence of strand-separation as suggested for example in Figure 6 ofreference (27) Our simulations however do not supportsimple strand-slippage rearrangements (except of the all-anti folds) during such interconversions Changes in thesynanti pattern are likely to occur during periods whenthe guanines do not form complete tetrads ie preferablyin unbound strands Therefore the interconversions mayrequire rather substantial unfolding events along thepathway to allow changes in the synanti patterns totake place

It is not straightforward to comment on thermo-dynamics and kinetics issues based on microsecond scalesimulations Nevertheless the simulations demonstratethat ions stabilize G-DNA stems thermodynamicallyThe molecules typically start to unfold in absence ofions whereas the movement is reversed with adding thesalt The most clearly visualized simulation case is thelarge unfolding and (almost complete) refolding of theparallel-stranded human telomeric quadruplex Howeverions may stabilize many misfolded structures as kinetictraps as they stabilize tetrads in folded as well asmisfolded structures

While the no-salt simulations aimed to reveal possibleintermediates occurring during the latest stages of G-DNA folding we also attempted simulations of singlestrands However these simulations showed no move-ments toward proper G-DNA folding Instead theyindicated that single strands have high capability toadopt misfolded arrangements indicating that folding ofG-DNAs from truly unfolded structures is probablybeyond the simulation timescale even using enhancedsampling methods (see the lsquoIntroductionrsquo section) One

of several issues that need to be addressed in futurestudies is the kinetics of changes in orientation of the nu-cleotides This is important because the molecule musthave an appropriate combination of syn and anti nucleo-tides for folding to a specific G-DNA topology in a singlemolecular event otherwise the likely result will be amisfolded structure This issue is beyond our present com-putational timescale as we observed few changes of orien-tation of the guanines around the glycosidic bond in thewhole study In addition the syn$anti equilibrium andkinetics may be sensitive to the force field parametrizationIt is likely that the folding of G-DNA starts with a pool ofG-tracts with rather random synanti distributions For agiven quadruplex folding sequence with N stem guaninesthere are 2N possibilities of synanti distributions All thesesingle strands attempt folding and in many cases non-native synanti distributions will lead to stable misfoldedstructures A given single strand will only be able to foldcorrectly if it has the native distribution of synanti guano-sines Then it appears that the molecule will often reach anative-like topology by swift fluctuation However evenwith the right synanti distribution at least locallymisfolded structures may form often with long lifetimes(Figure 9) These considerations and the simulationsindicate that some models of G-DNA folding may betoo simplistic as at atomistic level the foldingformationprocesses of individual G-DNA molecules can involvemyriads of routes and diverse folding attempts before afinal thermodynamic equilibrium is reached We suggestthat G-DNA folding is an extremely multi-pathwayprocess that is slowed by numerous misfolding arrange-ments stabilized on highly variable timescales

SUPPLEMENTARY DATA

Supplementary Data are available at NAR OnlineSupplementary Tables 1ndash5 Supplementary Figures 1ndash23and Supplementary Results

FUNDING

European Regional Development Fund project lsquoCEITEC- Central European Institute of Technologyrsquo [CZ1051100020068] Grant Agency of the Czech Republic[P208111822] TEC acknowledges support by NIH[01-GM081411] and NSF [XRAC MCA01S027]Funding for open access charge Grant Agency of theCzech Republic [P208111822]

Conflict of interest statement None declared

REFERENCES

1 BurgeS ParkinsonGN HazelP ToddAK and NeidleS(2006) Quadruplex DNA sequence topology and structureNucleic Acids Res 34 5402ndash5415

2 De CianA LacroixL DouarreC Temime-SmaaliNTrentesauxC RiouJF and MergnyJL (2008) Targetingtelomeres and telomerase Biochimie 90 131ndash155

3 QinY and HurleyLH (2008) Structures folding patterns andfunctions of intramolecular DNA G-quadruplexes found ineukaryotic promoter regions Biochimie 90 1149ndash1171


4 HuppertJL (2008) Four-stranded nucleic acids structurefunction and targeting of G-quadruplexes Chem Soc Rev 371375ndash1384

5 NeidleS (2009) The structures of quadruplex nucleic acids andtheir drug complexes Curr Opin Struct Biol 19 239ndash250

6 HuppertJL (2010) Structure location and interactions ofG-quadruplexes FEBS J 277 3452ndash3458

7 NeidleS (2010) Human telomeric G-quadruplex the currentstatus of telomeric G-quadruplexes as therapeutic targets inhuman cancer FEBS J 277 1118ndash1125

8 HeddiB and PhanAT (2011) Structure of human telomericDNA in crowded solution J Am Chem Soc 133 9824ndash9833

9 SilvaMW (2007) Geometric formalism for DNA quadruplexfolding Chem Eur J 13 9738ndash9745

10 CrnugeljM SketP and PlavecJ (2003) Small change in aG-rich sequence a dramatic change in topology new dimericG-quadruplex folding motif with unique loop orientations J AmChem Soc 125 7866ndash7871

11 PhanAT ModiYS and PatelDJ (2004) Propeller-typeparallel-stranded G-quadruplexes in the human c-myc promoterJ Am Chem Soc 126 8710ndash8716

12 LuuKN PhanAT KuryavyiV LacroixL and PatelDJ(2006) Structure of the human telomere in K+ solution anintramolecular (3+1) G-quadruplex scaffold J Am Chem Soc128 9963ndash9970

13 PhanAT KuryavyiV and PatelDJ (2006) DNA architecturefrom G to Z Curr Opin Struct Biol 16 288ndash298

14 DaiJX CarverM and YangDZ (2008) Polymorphismof human telomeric quadruplex structures Biochimie 901172ndash1183

15 AmbrusA ChenD DaiJX BialisT JonesRA andYangDZ (2006) Human telomeric sequence forms a hybrid-typeintramolecular G-quadruplex structure with mixed parallelantiparallel strands in potassium solution Nucleic Acids Res 342723ndash2735

16 MashimoT YagiH SannoheY RajendranA andSugiyamaH (2010) Folding pathways of human telomeric type-1and type-2 G-quadruplex structures J Am Chem Soc 13214910ndash14918

17 BoncinaM LahJ PrislanI and VesnaverG (2012) Energeticbasis of human telomeric DNA folding into G-quadruplexstructures J Am Chem Soc 134 9657ndash9663

18 KoiralaD MashimoT SannoheY YuZB MaoHB andSugiyamaH (2012) Intramolecular folding in three tandemguanine repeats of human telomeric DNA Chem Commun 482006ndash2008

19 GrayRD and ChairesJB (2012) Isothermal folding ofG-quadruplexes Methods 57 47ndash55

20 MergnyJL PhanAT and LacroixL (1998) FollowingG-quartet formation by UV-spectroscopy FEBS Lett 43574ndash78

21 RosuF GabelicaV PonceletH and De PauwE (2010)Tetramolecular G-quadruplex formation pathways studied byelectrospray mass spectrometry Nucleic Acids Res 385217ndash5225

22 BardinC and LeroyJL (2008) The formation pathway oftetramolecular G-quadruplexes Nucleic Acids Res 36 477ndash488

23 GrayRD BuscagliaR and ChairesJB (2012) Populatedintermediates in the thermal unfolding of the human telomericquadruplex J Am Chem Soc 134 16834ndash16844

24 GrayRD LiJ and ChairesJB (2009) Energetics and kineticsof a conformational switch in G-Quadruplex DNA J PhysChem B 113 2676ndash2683

25 YingLM GreenJJ LiHT KlenermanD andBalasubramanianS (2003) Studies on the structure and dynamicsof the human telomeric G-quadruplex by single-moleculefluorescence resonance energy transfer Proc Natl Acad SciUSA 100 14629ndash14634

26 GreenJJ LadameS YingLM KlenermanD andBalasubramanianS (2006) Investigating a quadruplex-ligandinteraction by unfolding kinetics J Am Chem Soc 1289809ndash9812

27 ZhangZJ DaiJX VeliathE JonesRA and YangDZ(2010) Structure of a two-G-tetrad intramolecular G-quadruplex

formed by a variant human telomeric sequence in K+ solutioninsights into the interconversion of human telomericG-quadruplex structures Nucleic Acids Res 38 1009ndash1021

28 LeeJY OkumusB KimDS and HaTJ (2005) Extremeconformational diversity in human telomeric DNA Proc NatlAcad Sci USA 102 18938ndash18943

29 HardinCC PerryAG and WhiteK (2001) Thermodynamicand kinetic characterization of the dissociation and assembly ofquadruplex nucleic acids Biopolymers 56 147ndash194

30 OlsenCM GmeinerWH and MarkyLA (2006) Unfolding ofG-quadruplexes energetic and ion and water contributions ofG-quartet stacking J Phys Chem B 110 6962ndash6969

31 ZhangAYQ and BalasubramanianS (2012) The Kinetics andFolding Pathways of Intramolecular G-Quadruplex Nucleic AcidsJ Am Chem Soc 134 19297ndash19308

32 GrayRD and ChairesJB (2008) Kinetics and mechanism ofK(+)- and Na(+)-induced folding of models of human telomericDNA into G-quadruplex structures Nucleic Acids Res 364191ndash4203

33 ReshetnikovRV SponerJ RassokhinaOI KopylovAMTsvetkovPO MakarovAA and GolovinAV (2011) Cationbinding to 15-TBA quadruplex DNA is a multiple-pathwaycation-dependent process Nucleic Acids Res 39 9789ndash9802

34 PortellaG and OrozcoM (2010) Multiple routes to characterizethe folding of a small DNA hairpin Angew Chem Int EdEngl 49 7673ndash7676

35 SponerJ and SpackovaN (2007) Molecular dynamicssimulations and their application to four-stranded DNAMethods 43 278ndash290

36 SponerJ CangXH and CheathamTE (2012) Moleculardynamics simulations of G-DNA and perspectives on thesimulation of nucleic acid structures Methods 57 25ndash39

37 ReshetnikovR GolovinA SpiridonovaV KopylovA andSponerJ (2010) Structural dynamics of thrombin-binding DNAaptamer d(GGTTGGTGTGGTTGG) quadruplex DNA studiedby large-scale explicit solvent simulations J Chem TheoryComput 6 3003ndash3014

38 SteflR CheathamTE SpackovaN FadrnaE BergerIKocaJ and SponerJ (2003) Formation pathways of a guanine-quadruplex DNA revealed by molecular dynamics andthermodynamic analysis of the substates Biophys J 851787ndash1804

39 LiH CaoEH and GislerT (2009) Force-induced unfolding ofhuman telomeric G-quadruplex a steered molecular dynamicssimulation study Biochem Biophys Res Commun 379 70ndash75

40 YangC JangS and PakY (2011) Multiple stepwise pattern forpotential of mean force in unfolding the thrombin bindingaptamer in complex with Sr2+ J Chem Phys 135 225104

41 KimE YangC and PakY (2012) Free-energy landscape of athrombin-binding DNA aptamer in aqueous environmentJ Chem Theory Comput 8 4845ndash4851

42 LimongelliV De TitoS CerofoliniL FragaiM PaganoBTrottaR CosconatiS MarinelliL NovellinoE BertiniI et al(2013) The G-Triplex DNA Angew Chem Int Ed Engl 522269ndash2273

43 BeckDAC WhiteGWN and DaggettV (2007) Exploring theenergy landscape of protein folding using replica-exchange andconventional molecular dynamics simulations J Struct Biol157 514ndash523

44 KuhrovaP BanasP BestRB SponerJ and OtyepkaM(2013) Computer folding of RNA tetraloops Are we there yetJ Chem Theory Comput 9 1461ndash1468

45 ParkinsonGN LeeMPH and NeidleS (2002) Crystalstructure of parallel quadruplexes from human telomeric DNANature 417 876ndash880

46 HaiderS ParkinsonGN and NeidleS (2002) Crystal structureof the potassium form of an Oxytricha nova G-quadruplexJ Mol Biol 320 189ndash200

47 PhillipsK DauterZ MurchieAIH LilleyDMJ and LuisiB(1997) The crystal structure of a parallel-stranded guaninetetraplex at 095 angstrom resolution J Mol Biol 273 171ndash182

48 DengJP XiongY and SundaralingamM (2001) X-ray analysisof an RNA tetraplex (UGGGGU)(4) with divalent Sr2+ ions at


subatomic resolution (061 angstrom) Proc Natl Acad Sci USA98 13665ndash13670

49 ClarkGR PytelPD and SquireCJ (2012) The high-resolutioncrystal structure of a parallel intermolecular DNA G-4quadruplexdrug complex employing syn glycosyl linkages NucleicAcids Res 40 5731ndash5738

50 CaseDA DardenTA CheathamTE III SimmerlingCLWangJ DukeRE LuoR CrowleyM WalkerRCZhangW et al (2008) AMBER 10 University of California SanFrancisco CA

51 JorgensenWL ChandrasekharJ MaduraJD ImpeyRW andKleinML (1983) Comparison of simle potential functions forsimulating liquid water J Chem Phys 79 926ndash935

52 AqvistJ (1990) Ion water interaction potentials derived fromfree-energy perturbation simulations J Phys Chem 948021ndash8024

53 SmithDE and DangLX (1994) Computer simulations of NaClassociation in polarizable water J Chem Phys 100 3757ndash3766

54 AuffingerP CheathamTE and VaianaAC (2007) Spontaneousformation of KCl aggregates in biomolecular simulations a forcefield issue J Chem Theory Comput 3 1851ndash1859

55 JoungIS and CheathamTE (2008) Determination of alkali andhalide monovalent ion parameters for use in explicitly solvatedbiomolecular simulations J Phys Chem B 112 9020ndash9041

56 PerezA MarchanI SvozilD SponerJ CheathamTELaughtonCA and OrozcoM (2007) Refinenement of theAMBER force field for nucleic acids improving the descriptionof alphagamma conformers Biophys J 92 3817ndash3829

57 CornellWD CieplakP BaylyCI GouldIR MerzKMFergusonDM SpellmeyerDC FoxT CaldwellJW andKollmanPA (1995) A second generation force field for thesimulation of proteins nucleic acids and organic moleculesJ Am Chem Soc 117 5179ndash5197

58 KreplM ZgarbovaM StadlbauerP OtyepkaM BanasPKocaJ CheathamTE JureckaP and SponerJ (2012)Reference simulations of noncanonical nucleic acids with differentchi variants of the AMBER force field quadruplex DNAquadruplex RNA and Z-DNA J Chem Theory Comput 82506ndash2520

59 BanasP HollasD ZgarbovaM JureckaP OrozcoMCheathamTE SponerJ and OtyepkaM (2010) Performance ofmolecular mechanics force fields for RNA simulations stability ofUUCG and GNRA hairpins J Chem Theory Comput 63836ndash3849

60 ZgarbovaM OtyepkaM SponerJ MladekA BanasPCheathamTE and JureckaP (2011) Refinement of the Cornellet al nucleic acids force field based on reference quantumchemical calculations of glycosidic torsion profiles J ChemTheory Comput 7 2886ndash2902

61 CaseDA DardenTA CheathamTE III SimmerlingCLWangJ DukeRE LuoR WalkerRC ZhangWMerzKMR et al (2012) AMBER 12 University of CaliforniaSan Francisco CA

62 GotzAW WilliamsonMJ XuD PooleD Le GrandS andWalkerRC (2012) Routine microsecond molecular dynamicssimulations with AMBER on GPUs 1 Generalized BornJ Chem Theory Comput 8 1542ndash1555

63 Le GrandS GotzAW and WalkerRC (2013) SPFP speedwithout compromisemdashA mixed precision model for GPUaccelerated molecular dynamics simulations Comput PhysCommun 184 374ndash380

64 DardenT YorkD and PedersenL (1993) Particle mesh Ewald -an Nlog(N) method for Ewald sums in large systems J ChemPhys 98 10089ndash10092

65 EssmannU PereraL BerkowitzML DardenT LeeH andPedersenLG (1995) A smooth particle mesh Ewald methodJ Chem Phys 103 8577ndash8593

66 RyckaertJP CiccottiG and BerendsenHJC (1977) Numericalintegration of cartesian equations of motion of a system withconstraints - Molecular dynamics of N-alkans J Comput Phys23 327ndash341

67 BerendsenHJC PostmaJPM VangunsterenWF DinolaAand HaakJR (1984) Molecular-dynamics with coupling to anexternal bath J Chem Phys 81 3684ndash3690

68 HumphreyW DalkeA and SchultenK (1996) VMD visualmolecular dynamics J Mol Graph 14 33ndash38

69 GelpıJL KalkoSG BarrilX CireraJ de La CruzXLuqueFJ and OrozcoM (2001) Classical molecular interactionpotentials improved setup procedure in molecular dynamicssimulations of proteins Proteins 45 428ndash437

70 SpackovaN BergerI and SponerJ (2001) Structural dynamicsand cation interactions of DNA quadruplex molecules containingmixed guaninecytosine quartets revealed by large-scale MDsimulations J Am Chem Soc 123 3295ndash3307

71 CavallariM CalzolariA GarbesiA and Di FeliceR (2006)Stability and migration of metal ions in G4-wires by moleculardynamics simulations J Phys Chem B 110 26337ndash26348

72 IslamB SgobbaM LaughtonC OrozcoM SponerJNeidleS and HaiderS (2013) Conformational dynamics of thehuman propeller telomeric DNA quadruplex on a microsecondtime scale Nucleic Acids Res 41 2723ndash2735

73 SpackovaN BergerI and SponerJ (1999) Nanosecondmolecular dynamics simulations of parallel and antiparallelguanine quadruplex DNA molecules J Am Chem Soc 1215519ndash5534

74 PodbevsekP HudNV and PlavecJ (2007) NMR evaluation ofammonium ion movement within a unimolecular G-quadruplex insolution Nucleic Acids Res 35 2554ndash2563

75 FadrnaE SpackovaN SteflR KocaJ CheathamTE andSponerJ (2004) Molecular dynamics simulations of guaninequadruplex loops advances and force field limitations BiophysJ 87 227ndash242

76 FadrnaE SpackovaN SarzynskaJ KocaJ OrozcoMCheathamTE KulinskiT and SponerJ (2009) Single strandedloops of quadruplex DNA as key benchmark for testing nucleicacids force fields J Chem Theory Comput 5 2514ndash2530

77 CangXH SponerJ and CheathamTE (2011) Explaining thevaried glycosidic conformational G-tract length and sequencepreferences for anti-parallel G-quadruplexes Nucleic Acids Res39 4499ndash4512

78 SketP VirgilioA EspositoV GaleoneA and PlavecJ (2012)Strand directionality affects cation binding and movement withintetramolecular G-quadruplexes Nucleic Acids Res 4011047ndash11057

79 SketP and PlavecJ (2010) Tetramolecular DNA quadruplexes insolution insights into structural diversity and cation movementJ Am Chem Soc 132 12724ndash12732

80 WyattJR DavisPW and FreierSM (1996) Kinetics ofG-quartet-mediated tetramer formation Biochemistry 358002ndash8008

81 MergnyJL De CianA GhelabA SaccaB and LacroixL(2005) Kinetics of tetramolecular quadruplexes Nucleic AcidsRes 33 81ndash94

82 GrosJ RosuF AmraneS De CianA GabelicaV LacroixLand MergnyJL (2007) Guanines are a quartetrsquos best friendimpact of base substitutions on the kinetics and stability oftetramolecular quadruplexes Nucleic Acids Res 353064ndash3075


folding (34) These investigations demonstrate that com-puter simulations can complement experimental studies ofG-DNA folding and unfolding by allowing studies offolding processes (or at least parts of these processes) atthe level of individual molecules with atomistic descriptionand sub-nanosecond time resolution (3536)

In this study we use molecular dynamics (MD) simula-tions to obtain insights into the structures that can bepopulated during the folding process of severalquadruplexes (see later in the text) Clearly the completeprocess of G-DNA folding or unfolding cannot be fullycharacterized by contemporary simulation techniqueswhich only recently reached microsecond timescales forG-DNA (37) In fact unrestrained standard simulationscan only capture dynamics that a real single molecule mayundergo in the simulation timescale when starting fromthe simulation starting structure Nevertheless the lackof complete experimental data justifies computationalstudies of various aspects of G-DNA folding(16183338ndash42) Although all such studies are affectedby specific limitations they provide valuable informationthat is not experimentally accessible When consideringsimulations we need to distinguish studies using unre-strained standard simulations from studies applyingvarious methods to enhance sampling (see later in thetext) Although the enhanced sampling methods allowthe sampling of structural transitions that are not achiev-able during standard simulations they bring additionalapproximations compared with standard simulationswhich need to be considered in the interpretation of thedata

Besides the ion-capture study noted earlier in the text(33) standard simulations were used a decade ago to in-vestigate possible intermediates in the formation ofparallel stranded tetrameric all-anti G-DNA stems (38)The cited authors built up various two three and four-stranded models and investigated their behavior in short(by current standards) 2ndash10 ns simulations followed byfree energy computations They proposed a formationpath from single strand to full stem involving late-stagefour-stranded intermediates with slipped strands and aprogressive reduction of strand slippage This formationpathway may be specific for parallel stranded all-antistems as alternation of syn and anti nucleotides in thestem may prevent easy strand slippage processes (seelater in the text) Recently short 3 ns simulations wereused to support a folding model of intramolecularquadruplexes via a triplex pathway (1618)

Among enhance sampling studies two have analyzedthe disruption of an intramolecular quadruplex bypulling it apart using external forces applied at oppositeends of the molecule (3940) A limitation of such forcedunfolding is that the external forces may qualitativelymodify the unfolding pathway while the ns-timescale(much shorter than in equivalent pulling experiments) ofunfolding may further bias the results (39) More recentlyReplica Exchange Molecular Dynamics (REMD) hasbeen used to probe unfolding properties of a thrombin-binding aptamer (15-TBA) starting from the folded state(41) REMD enhances sampling by simulating differentreplicas of the system at different temperatures (up to

500K or more) and swapping between them TheREMD method introduces some additional approxima-tions compared with standard simulations as the transi-tions occur during unrealistically high temperatures (43)Further true folding of a G-DNA molecule by REMDwould require the simulation to start from entirelyunfolded single strands with different distributions ofsyn and anti nucleotides compared with the foldedG-DNA molecule with a complete loss of the loop struc-tures When starting solely from the folded state (41) con-vergence of the REMD computations cannot be proven(44) In fact converged REMD of even the smallestnucleic acids systems such as RNA tetraloops is stillbeyond contemporary technologies (44) Despite theselimitations REMD simulation from the folded 15-TBAstate (41) has provided valuable insights at least intoearly unfolding and late folding events The ambiguityof the enhanced sampling studies can be demonstratedby comparing the 15-TBA REMD data with meta-dynamics simulations using a specific bias to achieve un-folding (42) The 15-TBA folding mechanisms proposedby REMD (41) and meta-dynamics (42) appear differentIn the present work we try to mimic unfolding of

G-DNA molecules using no-salt simulations where theG-DNA is deprived of the stabilizing ions As explainedlater in the text this approach can be justified by the factthat the likelihood of G-DNA structural rearrangementsis probably increased during periods with reduced bindingof the ions Using the no-salt simulations we try to obtaina spectrum of partially unfolded structures which may berelevant for late stages of the folding We then try to refoldthese structures using standard unbiased excess-salt simu-lations Given the limitations of the enhanced samplingmethods our less ambitious but milder approach is ap-propriate especially as we study more complexquadruplexes than 15-TBA which are beyond the scopeof the enhanced sampling methods We do not quicklyfully unfold or fold the systems but we investigate indetail properties of the G-DNA molecules in proximityto the folded state using conventional simulations andvariations in the environment with no biasing forces orultra-high temperatures Our approach resemblesstopped-flow techniques Starting from the folded struc-ture we first eliminate monovalent ions and afterinitiating unfolding we add the ions back In contrast tothe experimental procedures however the simulations in-vestigate the responses of a single molecule only onmstimescale The change of environment is instantaneousThe advantage is that we see all atomistic details of thestructural developmentsThe studied structures were selected to include stems

with diverse mutual strand orientations and synantipatterns We consider examples of parallel antiparalleland hybrid stems Whether a given stem structure occurswithin a tetramolecular bimolecular or unimolecularcontext is less important as the rearrangements directlyaccessible in the simulation time window are those primar-ily determined by properties of the G-DNA stems andonly secondarily modulated by the loops This is illus-trated by the similarity of stem behavior in simulationsof tetrameric and unimolecular all-parallel all-anti




Initial models












MD simulations












RESULTS






























































































SUPPLEMENTARY DATA


FUNDING



REFERENCES


























































































Initial models












MD simulations












RESULTS






























































































SUPPLEMENTARY DATA


FUNDING



REFERENCES

























































































MD simulations












RESULTS






























































































SUPPLEMENTARY DATA


FUNDING



REFERENCES

























































































RESULTS






























































































SUPPLEMENTARY DATA


FUNDING



REFERENCES







































































































































































SUPPLEMENTARY DATA


FUNDING



REFERENCES
























































































Structural dynamics of possible late-stage intermediates ... · Structural dynamics of possible...

Documents

Transcript of Structural dynamics of possible late-stage intermediates ... · Structural dynamics of possible...