repeat 
 expansion disorders are caused by mutations in dna where 
 repeats in certain genes become expanded .
once the repeats are transcribed , 
 mrna ( mrna ) folds into a hairpin with repeating internal loop motifs , 
 which can be translated into toxic proteins or sequester proteins 
 and cause disease .
one hypothesis is that formation 
 of non - b - form conformations by the repetitive dna sequences , such 
 as hairpins , is the reason for the expansion during dna replication 
 and repair . in the expansions of cag repeats , which are typically 
 found in the coding regions of mrnas such as huntingtin ( htt ) , androgen 
 receptor ( ar ) , spinocerebellar ataxia ( sca ) , and atrophin-1 ( atn1 ) 
 genes ,
the transcripts are translated into toxic polyglutamine ( polyq ) proteins , resulting in huntington s disease 
 ( hd ) , spinal and bulbar muscular atrophy ( sbma ) , spinocerebellar ataxia 
 type 1 ( sca1 ) , and dentatorubral - pallidoluysian atrophy ( drpla ) , respectively .
furthermore , it has been shown recently that rna cag repeat expansions can sequester proteins and contribute to neurodegeneration .
another genetic disorder , friedreich s ataxia ( frda ) , is 
 caused by expansion of gaa repeats .
a common heritable 
 form of mental retardation , fragile x - associated tremor ataxia syndrome 
 ( fxtas ) , is caused by expansion of the cgg segment from 50 to 200 
 repeats in the 5-untranslated region ( utr ) of the fragile 
 x mental retardation 1 ( fmr1 ) gene .
once the fmr1 gene is transcribed into mrna , the expanded cgg repeats fold into a hairpin structure with repeating 
 11 gg internal loops that sequester and inactivate sam68 protein .
myotonic dystrophy ( dm ) is another genetic disease that is the 
 most common adult - onset form of muscular dystrophy .
dm is a neuromuscular 
 disorder that is characterized by muscle weakness and slow relaxation 
 of muscles after contraction .
it is caused by expansion 
 of ctg and cctg repeats in dna , with ctg leading to 
 myotonic dystrophy type 1 ( dm1 ) and cctg to type 2 ( dm2 ) . in both 
 dm1 and dm2 ,
once the trinucleotide ctg in the 3-utr of the 
 dystrophia myotonica protein kinase ( dmpk ) gene and 
 the tetranucleotide cctg repeats in the zinc - finger 9 ( znf9 ) gene are transcribed , the cug and ccug repeats fold into rna hairpins with repeating 11 
 uu and 22 cu / uc internal loop motifs , respectively , attracting muscleblind - like 1 ( mbnl1 ) or cytoplasmic multiprotein complexes that cause , 
 for example , muscle chloride channel dysfunction and abnormal regulation of insulin receptors . because the expanded rna repeats are in the noncoding regions 
 the diseases are caused by rna gain - of - function . even though the disease mechanisms described 
 above are the most well established ones , expanded rna repeats might 
 play other roles in the cell . as an example , expanded repeats in utrs 
 are translated via a repeat associated non - atg translation .
the crystal structures of model rna molecules 
 containing cug repeats have been determined 
 before by different groups 
 using x - ray diffraction methods .
in addition , an nmr structure 
 of a single copy of the dm1 motif was characterized that displayed 
 an overall a - form structure . even though 
 all these structures show 11 uu internal loops in anti 
anti conformations , large amplitude motions 
 in rna internal loops could not be investigated with the current experimental 
 methods .
the conformations that rna cug repeats 
 adopt upon protein or small molecule binding require a better understanding 
 of these motions .
helical stacking  unstacking and syn  anti transformation of uridines 
 in 11 uu base pairs are two such important large scale motions 
 that have significance in small molecule 
various 
 groups have designed and published small molecules and ligands targeting 
 rna cug repeats , but at present there is no experimental structure available that 
 reports the atomistic details of a small molecule bound to rna cug repeats .
thus , the structural and thermodynamic properties 
 of 11 uu base pairs in rna cug repeats 
 are of significant interest , since they may provide insight into the 
 conformations that these repeats adopt upon interaction with proteins 
 or small molecules .
we recently analyzed the 
 properties of 11 aa internal loops 
 seen in rna cag repeat expansions .
the crystal 
 structure of a model rna with three cag repeats , 
 r[5uugggc(cag)3gucc]2 , was found to exhibit terminal 11 
 aa base pairs in syn 
the terminal 
 aa base pairs interact with dangling uridine bases , stabilizing the syn  anti conformational state .
the 
 results basically indicated that a dynamic base pair such as 11 
 aa internal loops could transform to another conformation upon interacting 
 with a molecule .
thus , we utilized umbrella sampling md simulations 
 to predict the 2d free energy surface for 11 aa internal loops 
 to investigate the potential stable conformations and transformation 
 pathways . in line with the experimental 
 results ,
anti and syn  anti conformations as global 
 and local minima , respectively . furthermore
, several stable local 
 minima states in both anti  anti and syn  anti conformations 
 were found for 11 aa internal loops .
the results indicated that 
 the stable 11 rna internal loop conformations could be exploited 
 for small molecule binding .
indeed , we analyzed the binding mechanism 
 of a substituted naphthyridine ( c-2 ) to rna 11 uu internal loops , 
 which inhibits binding of mbnl1 to rna cug 
 repeat expansions .
similar results were seen when we analyzed 6-n-5-hexynoate 
 kanamycin alkyne ( k - alkyne ) binding to 22 cu / uc internal loops 
 in rna ccug repeats , which is a lead small 
 molecule targeting rna causing dm2 .
hence , 
 atomistic details of the structure and dynamics of rna internal loops 
 as well as the transformation pathways extracted from the predicted 
 free energy profiles can yield insights that might be used to understand 
 and develop drugs that will target rna repeat expansions .
although 
 there are no structures reported for mbnl1 bound to cug repeats , it is thought that the zinc finger 3 and 4 domains ( zn3/4 ) 
 of mbnl1 have some functional roles in the binding process .
thus , the present investigations could also 
 shed light on this pathogenic interaction . in the present contribution , 

structural and thermodynamic properties 
 of 11 uu rna internal loops are predicted using regular and 
 umbrella sampling md simulations in explicit solvent with an amber 
 force field , which includes a  torsional revision for rna .
we also exploited the discrete path sampling 
 ( dps ) method to investigate the energy landscape of the 11 uu 
 internal loop in rna cug repeats .
three systems 
 were considered : 3cug3syw ( r[5uugggc(cug)3gucc]2 ) , 3cuginf ( r[5c(cug)3g]2 ) , and 1cug ( r[5ccgcugcgg]2 ) . 3cug3syw and 3cuginf were used to predict the dynamic properties of 11 
 uu base pairs .
in particular , 3cuginf was designed 
 to simulate 11 uu rna internal loops in an infinitely long linear 
 rna system , while 3cug3syw is an already solved crystal 
 structure with pdb accession code 3syw .
1cug 
 was designed to predict the 2d free energy surfaces of 11 rna 
 uu internal loops using umbrella sampling md calculations .
similar 
 to our previous rna cag repeat study , one of the reaction coordinates was chosen as 
 the  torsion ( rotation around the glycosidic bond ) in order 
 to mimic the orientation of the uridine base with respect to sugar , 
 while the other reaction coordinate was a pseudotorsion (  ) 
 mimicking base flipping ( base stacking  unstacking ) .
two 2d 
 potentials of mean force ( pmf ) surfaces , ( 1, ) 
 and ( 1,2 ) , were calculated for 
 the 11 uu base pairs .
our results indicate that 11 uu 
 rna internal loops are dynamic and favor the anti  anti conformation but have several local 
 minima in the 2d pmf profiles displaying both anti  anti and syn  anti conformations . the 2d ( 1, ) 
 pmf exhibits three pathways for the syn  anti  anti  anti transformation , one of which dominates in temperature jump md simulations . 

these results were verified using dps calculations , which showed that 
 in the dominant kinetic pathway the uridine flips out via the major 
 groove , followed by a rotation around  to produce a syn  anti transformation . in line 
 with previous studies , the 2d ( 1,2 ) pmf as well as regular md simulations displayed 11 uu base 
 pairs in 2 , 1 , and 0 anti  anti hydrogen - bond conformations .
similar to the 11 aa base pairs 
 studied before , a na binding 
 pocket was discovered near the 11 uu base pair , stabilizing 
 the syn  anti conformation . 
 furthermore , md simulations of 3cug3syw showed 22 
 gc / cg regions flanked by 11 uu base pairs to have stable but 
 distorted forms , which indicates flexibility .
the present results 
 reveal atomistic details of the structure and 
 thermodynamics of 11 uu base pairs in rna cug repeat expansions that are inaccessible with current experimental 
 methods .
this insight should help us to design better compounds targeting 
 rna cug repeats in future work .
1cug 
 ( figure 1a ) was employed 
 to predict the 2d free energy surfaces of 11 uu base pairs using 
 umbrella sampling calculations .
3cug3syw ( figure 1b ) was considered 
 to model the structural properties of a crystal structure ( pdb accession 
 code 3syw ) , which has three consecutive cug repeats .
finally , 3cuginf ( figure 1c ) should provide insight into the dynamics 
 of 11 uu base pairs in an infinitely long linear rna system . 

the initial structure of 1cug was built from the already solved 
 nmr structure ( pdb accession code 2l8u ) .
a homology 
 model of 3cuginf was built from the crystal structure 
 data of 3syw(38 ) with uu base pairs in either anti  anti or syn  anti conformations .
two initial structures 
 were created for 3cuginf ; one where all 11 
 uu base pairs were in anti  anti conformations ( 3cuginf / anti  anti ) and another where the middle uu base pair ( u6u17 ) was in syn  anti ( 3cuginf / syn  anti ) .
this was done in order to investigate potential syn  anti  anti  anti transformations . for the initial structure of 3cug3syw ,
data from the crystal structure 3syw(38 ) was used , including dangling uridine residues , which were 
 utilized experimentally to crystallize the system . as shown in figure 1b , the dangling uridine 
 residues were kept in the structure in order to mimic the original 
 system as far as possible . the leap module of amber md package was used to neutralize all the systems with 
 na and/or cl ions and to solvate with tip3p water molecules . in 3cuginf , 10 extra cl and na ions were randomly included in the systems .
the 
 1cug and 3cug3syw were designed to have truncated 
 octahedral boxes , while 3cuginf was designed to have 
 a cubic box that created an infinitely long rna system ( figure 1c ) .
the 1cug , 3cuginf , and 3cug3syw systems had 4025 , 2265 , 
 and 10766 water molecules , respectively .
once equilibrated , these 
 systems had 0.67 , 0.21 , and 0.18 mm na concentrations , 
 respectively .
we also designed another 3cuginf system , 
 which was neutralized with 20 na ions , had the middle 
 uu basepair in syn 
anti conformation , 
 and was solvated with 4333 water molecules to yield a na concentration of 0.24 mm .
two sets of md simulations for this system 
 were run . the amber force field with 
 revised  and / torsional parameters were used in both regular 
 and umbrella sampling md simulations , as these revised parameters 
 have been shown to improve the predictions .
model 
 rna sequences and initial structures used in regular and 
 umbrella sampling md simulations . for illustrative purposes ,
the opaque region of c represents the unit cell , while 
 transparent regions represent the neighboring cells to illustrate 
 the design of the infinitely long rna system .
each system was first 
 minimized and equilibrated in two steps ( see also table s1 ) .
after equilibration , constant pressure dynamics with isotropic positional 
 scaling was used in all the production runs .
the reference pressure 
 was set to 1 atm with a pressure relaxation time of 2 ps .
an atom - based long - range hard cutoff of 
 8.0  was used .
as described above , two independent md calculations were 
 run on 3cuginf , 3cuginf / anti  anti and 3cuginf / syn  anti , with total md 
 simulation times of 500 and 606 ns , respectively , with a 1 fs time 
 step .
the temperatures of all md simulations were kept at 
 300 k. the pmemd module in amber12 was 
 used to run the md simulations .
the 
 reaction coordinates 
 shown in figure 2 , 
 which we previously utilized to study rna 11 aa base pairs , were used to build the 2d pmf surfaces for rna 
 11 uu internal loops .
two different 2d potential of mean force 
 ( pmf ) surfaces , ( 1 vs  ) and ( 1 vs 2 ) , were calculated for 11 uu 
 base pairs using the model system 1cug ( figure 1a ) .
nucleic acid bases can rotate around 
 glycosidic bonds ( rotation around  torsional angle ) , which 
 are responsible for the syn and anti base orientations with respect to sugar ( figure 2a ) .
while purine residues prefer both syn and anti orientations , pyrimidine residues 
 mostly prefer anti .
hence , one of the reaction coordinates 
 was chosen to be the  torsional rotation .
the second reaction 
 coordinate was chosen to imitate base stacking  unstacking , 
 where the center - of - mass pseudodihedral angle (  ) was defined 
 to mimic this motion ( figure 2b ) . in order to build each 2d pmf surface ,
initial structures 
 with different ( 1, ) and ( 1,2 ) combinations were created for the model system 
 1cug ( see section s1 in the supporting information for the details ) .
reaction coordinates utilized to build the 2d pmf surfaces 
 for 
 rna 11 uu base pairs . in a
, the torsional angle highlighted 
 in red is  ( o4c1n1c2 ) 
 responsible for the syn  anti transformation . in order to investigate the base stacking  
 unstacking , pseudodihedral angles , 1 and 2 , defined by the center - of - masses ( coms ) of four atom groups 
 in b
due to the relatively 
 large energy barriers we did not see any syn  anti transformations in the md simulations of 3cug3syw and 3cuginf ( except for one case , which 
 had low na concentration ) .
thus , we studied the structural 
 properties of 11 uu base pairs with respect to temperature using 
 1cug .
two systems were considered : one where the 11 uu 
 base pair is in an anti  anti conformation (  = 200 and 1 = 40 ) 
 and another where it is in a syn  anti conformation (  = 40 and 1 = 350 ) . 
 for each case , 10 independent md simulations were run where the temperature 
 was increased from 300 to 400 k by 5 k for each 1 ns md time interval . 

once the temperature reached 400 k , another 19 ns md was run in each 
 case .
we should note that this particular calculation is somewhat similar 
 to simulated annealing protocol and was done to force the system to 
 overcome the energy barriers responsible of syn  anti transformation .
because 400 k is higher than the boiling 
 point , a full md would not mean much .
we utilized 
 umbrella sampling md simulations to predict the 1d pmf profiles of 
 a , g , u , and c mononucleosides along the  torsional axis ( figure 2a ) .
the procedure 
 is similar to the umbrella sampling simulations described above , except 
 that only the individual mononucleosides were solvated with 738 tip3p 
 water molecules and simulated .
 
 torsional angles were incremented by 10 that created 36 umbrella 
 sampling windows for each system .
after minimization and 1 ns equilibration , 
 each window was simulated for 5 ns .
the  torsions in the umbrella 
 sampling md simulations were restrained in a square bottom well with 
 parabolic sides and 30 kcal/(mol rad ) force constants .
the discrete path sampling method ( dps ) has previously been used to study the energy landscapes 
 for a diverse range of atomic and molecular systems . in particular , this approach has proved to be effective in exploring 
 landscapes that feature broken ergodicity , leading to multiple relaxation time scales .
dps is based on geometry 
 optimization techniques and is efficient in sampling  rare 
 event  dynamics , which are typically inaccessible in conventional 
 unbiased simulation methods . in the present work 

we have used dps to explore the energy landscape of the rna cug repeats , to supplement our results from unbiased molecular 
 dynamics and umbrella sampling simulations ( see section s2 in the supporting information for the details ) .
dps simulations were seeded from conformations corresponding to the 
 major basins on the 2d pmf of the single cug repeat , choosing a diverse range of pseudotorsion and  torsion 
 values .
these conformations were locally minimized using a modified 
 version of the lbfgs algorithm , to build 
 an initial database of minima .
geometry optimizations were deemed 
 to have converged when the root - mean - square gradient fell below 10 kcal mol .
connection attempts were made between these minima in a 
 pairwise fashion , starting from the highest energy minimum in the 
 database to the lowest .
once sufficient connections were found , a 
 disconnectivity graph analysis revealed that syn  anti and anti 
anti states of the uridine base pairs were likely to emerge as competing 
 funnels on the energy landscape .
the stationary point databases were 
 further expanded by refining the discrete paths between the syn  anti and anti 
anti end points , using systematic applications 
 of the shortcut barrier and untrap schemes , which have been described 
 in detail in previous work and are available 
 within our pathsample code .
dps simulations 
 were deemed to have converged sufficiently when the rate constants 
 corresponding to the syn 
anti  anti  anti conformational 
 transition were stable to within an order of magnitude . the final 
 stationary point database consisted of 21927 minima and 25467 transition 
 states .
free energies were estimated from the database by employing 
 the harmonic superposition approximation . here , the molecular partition function is approximated as a sum 
 over harmonic vibrational densities of states corresponding to the 
 catchment basins of each minimum .
the ptraj module of amber12 was used 
 for dihedral , root - mean - square deviation ( rmsd ) , 
 and cluster analyses . the weighted histogram analysis method ( wham )
in the wham 
 analysis , the last 1.5 ns data of each umbrella sampling simulation 
 was used , and periodicity was turned on in both dimensions .
x3dna was used to extract global structural properties 
 of 3cug3syw from the md trajectory .
the rate constants corresponding 
 to the conformational transitions between the syn  anti and anti  anti states were calculated from the stationary point database 
 using a graph transformation method , as described in a previous work .
the estimates for the rate constants at 300 
 k were obtained using a self - consistent regrouping scheme , which recursively lumps minima separated by 
 free energy barriers below a threshold into one macrostate .
this is 
 an attractive approach , as the free energy surface then becomes a 
 function of the experimental observation time , due to the lumping 
 of minima separated by low barriers .
furthermore , 
 this method alleviates any bias arising due to the choice of original 
 end points , as they are expanded into ensembles of structures that 
 are assumed to be in local equilibrium on the time scale of the rate - determining 
 step of interest .
the potential 
 and free energy 
 landscapes were visualized in the form of disconnectivity graphs .
the disconnectivity graph provides a powerful yet simple representation 
 of the energy landscapes and is free of potential artifacts that can 
 arise from low dimensional projections onto selected order parameters .
this representation retains all of the kinetic information in the 
 database and thus provides a way to rigorously test the validity of 
 the reaction coordinates employed in our 2d umbrella sampling simulations 
 ( see section s3 in the supporting information for the details ) .
, 
 we found that the md trajectories for 3cug3syw and 
 3cuginf show stable 11 uu base pairs both in anti  anti and syn  anti conformations . except for one case 
 ( 3cuginf with low na concentration ) , 
 no syn 
this result was attributed to the high energy barriers observed in 
 umbrella sampling and dps calculations , which predicted three syn 
temperature 
 jump md simulations were performed , which revealed that one of the 
 pathways predicted by umbrella sampling and dps calculations dominates 
 the syn 
we use different colors to represent each stable 11 uu base 
 pair conformation to highlight the transformations ( figure 3 ) .
conformational states 
 of 11 uu base pairs seen in md trajectories 
 of 3cug3syw and 3cuginf .
color notation 
 was used to represent each state to make visualization of rmsd plots 
 ( vide infra ) easier .
black ( a ) , red ( b ) , and cyan ( c ) represent anti  anti conformations with 2 , 
 1 , and 0 hydrogen - bond .
green ( d ) , blue ( e ) , yellow ( f ) , and orange 
 ( g ) are used for syn 
anti uu conformations , the system is symmetric . as a result , 
 there are two conformations each in a and b representing the same 
 state .
the initial 
 structure of 3cug3syw solved by x - ray diffraction 
 with 2.20  resolution is shown in figure 1b .
the system 
 contains three consecutive rna cug repeats 
 with two dangling uridines which were included experimentally to facilitate 
 crystallization .
we analyzed the global structural properties of 3cug3syw and compared them to the published crystal structure . 

furthermore , the conformational preference of each 11 uu base 
 pair , as well as the 22 cg / gc base pairs flanked by two neighboring 
 11 uu base pairs ( figure 4 ) , along with the dynamics of dangling uridines , were analyzed .
rmsd s ( in  ) of u8u33 , g9c10/g31c32 , u11u30 , g12c13/g28c29 , and u14u27 are plotted 
 with respect to the stable conformations shown in figures 3 and 5 .
anti conformations with stable forms represented by black , 
 red , and cyan ( figure 3a  c , and movie s1 ) . in the rmsd 
 analysis of the 11 uu base pairs ( u8u33 ,
u11u30 , and u14u27 ) , 
 conformational states with rmsd greater than 1  represent symmetry 
 related versions of the states .
as noted in figure 3 , uu base pairs in states colored black and 
 red have two identical conformations representing 2 and 1 hydrogen - bond 
 states , respectively .
the plots were created in this form to display 
 the transformations of 11 uu base pairs during the trajectory . 

note also that the stable gc / cg conformation represented by magenta 
 only forms when the flanking 11 uu base pairs are both in the 
 2 hydrogen - bond and opposite symmetry states ( black ) ( see movie s2 ) .
the main difference between the 3syw crystal structure and the 3cug3syw structure is that the former 
 is an almost frozen system while the latter is a system equilibrated 
 at 300 k and thus includes dynamics .
the minor ( mgw ) and major groove 
 widths ( mgw ) in the crystal structure of 3syw are around 15 and 16  , respectively 
 ( figure s1 ) .
analysis of the md trajectory 
 shows that the mgw fluctuates around the crystal structure value ( figure s1 ) , which is globally in an a - form conformation . 
 on the other hand
the expanded mgw suggests that the inclusion of 11 
 uu internal loops gives flexibility to the system . to understand the 
 flexibility of each region in the rna duplex
, we analyzed the rmsd 
 of 3cug3syw with respect 
 to the crystal structure . in the analysis ,
the sequence was broken 
 down into 2 and 5 base pair segments so that we could investigate 
 which regions in the rna were responsible for the flexible behavior 
 ( figure s2 ) .
the results show that the 
 regions including uu base pairs are more flexible than the other regions 
 in 3syw ( figure s2 ) .
globally , the central region , which 
 includes 3 cug repeats , is more flexible than 
 the terminal regions , which includes watson  crick gc and wobble 
 gu base pairs ( figure s2 ) . this result 

is expected because individual fluctuations of 11 uu internal 
 loops will accumulate and yield global flexible regions as seen in 3syw .
it is noteworthy , 
 however , that the overexpanded mgw might be a force field artifact . 

even though it is known that rna internal loops introduce flexibility 
 into the system , the overexpanded mgw might be due to an improper 
 description of base stacking and/or backbone torsions .
cluster analyses of 
 the md trajectory show three unique anti  anti conformations for the 11 uu base pairs , in line 
 with the previous experimental results , which represent 2 , 1 , and 0 hydrogen - bond states , colored black , 
 red , and cyan , respectively , in the rmsd plots ( figures 3 and 4 ) . during the 
 1 s md simulation
anti  anti  anti transformations numerous times ( figure 4 and movie s1 ) . 

hydrogen - bond analyses indicate that the 11 uu base pairs populate 
 the 2 , 1 , and 0 hydrogen - bond states with probabilities 43% , 41% , 
 and 16% , respectively .
furthermore , in the regions where the 22 
 gc / cg base - pairs are in canonical watson  crick forms the black 
  red transformations are very fast because the conformational 
 states are very similar to each other ( figures 3a , b and 4 ) .
the 0 
 hydrogen - bond state ( cyan ) seems to act like an intermediate state 
 and is less stable than to the 1 ( red ) and 2 ( black ) hydrogen - bond 
 states .
hence , the dynamic behavior of the 11 uu base pairs 
 yields flexible regions in the rna structure described above ( figure s2 ) .
the structure of 3cug3syw ( figure 1b ) is not as rigid as an infinitely 
 long rna .
thus , the effects of its flexibility will appear in weak 
 regions of 3cug3syw .
the 11 uu base pairs will 
 be the first to acquire this flexibility , as noted above .
the next 
 weakest regions are 22 gc / cg base - pairs flanked by these uu 
 base - pairs . even though the gc base pairs in these regions are in 
 watson 
crick forms , they will not be as rigid as in regular 
 rna stem regions due to the flanking uu base pairs .
indeed , our 
 analysis shows that 22 gc / cg regions flanked by uu base - pairs 
 are flexible and can have a stable noncanonical conformation ( figures 4 and 5c and movie s2 ) . in the rmsd analysis 
 of g9c10/g31c32 and
g12c13/g28c29 the magenta color 
 represents this stable noncanonical conformation ( figure 5c ) , which persists for as long 
 as 200 ns , as is apparent during 420 and 610 ns intervals in the md 
 simulation ( magenta color in figure 4 ) .
note , however , that this stable noncanonical gc / cg 
 conformation only forms when the flanking 11 uu base pairs are 
 both in stable 2 hydrogen - bond and opposite symmetry states ( black ) 
 ( figure 4 and movie s2 ) . in this noncanonical gc / cg form
, each 
 gc base pair loses two watson  crick hydrogen - bonds , while forming 
 an attractive electrostatic interaction between the nh2 group of guanine and the 2-oh group of the ribose 
 of its watson 
the results indicate that if the flanking 
 base pairs ( in this case the 11 uu ) transform to energetically 
 favorable states they can distort the repeating 22 gc / cg regions 
 ( movie s2 ) .
this particular phenomenon 
 is one of the reasons why we observe an overexpanded mgw in the md 
 trajectory ( figure s1 ) . as described above , 
 the particular distorted gc / cg conformation shown in figure 5 forms when the flanking uu 
 base pairs are in 2 hydrogen - bond states ( figure 4 ) .
the overexpression of the 2 hydrogen - bond 
 states might be a force field artifact , which could indirectly cause 
 the overexpanded mgw we observed ( figure s1 ) .
therefore , caution is required when analyzing the results , even 
 though we are using an improved rna force field .
( b ) one of the gc base pairs is distorted and loses a hydrogen - bond . 
 in this form
, the nh2 group of guanine forms an 
 attractive electrostatic interaction with the 2-oh group of 
 cytidine .
( c ) both gc base pairs are distorted and lose one hydrogen - bond 
 each .
both gc base pair conformations are in the distorted gc form 
 described in b. the distortions happen only when the flanking 11 
 uu base pairs are both in the 2 hydrogen - bond but opposite symmetry 
 states ( see movie s2 ) . as noted 
 above
, the rna sequence shown in figure 1b includes dangling uridines , which were 
 used experimentally to help crystallize the system .
the initial conformations of the dangling uridine ends 
 are shown in figures 1b and 6a .
at later times , however , they transform 
 to a stable state where u2 and u21 are both 
 unstacked , while u1 and u20 are stacked on top 
 of the guanine of the terminal gc base pairs ( g3c38 and g22c19 ) ( figure 6c ) . in this form ,
both u1 and 
 u20 have flipped upside down sugars ( figure 6c ) , as seen previously in nmr and md analyses 
 of the single - stranded rna structure gacc .
although the crystal structure of 3syw has the dangling 
 uridine ends being inserted into the rna major grooves , this does 
 not mean that they will remain there when the system is equilibrated 
 at room temperature .
indeed , the md simulation of 3cug3syw shows the dangling uridine ends in very different conformations , 
 where stacking interactions play an important role in the final conformations 
 ( figure 6c ) . once the 
 dangling uridine ends transformed to this final stable conformation 
 ( figure 6c ) they stayed 
 there for the rest of the md simulation ( see supporting information ) .
however , we should note that this particular 
 result might be a force field artifact caused by the improper description 
 of the backbone , the nonbonded interactions , or solvent molecules . 

chen and garcia recently showed that the van der waals parameters 
 of adenine base atoms required revision , and a similar revision might be required for uridine .
conformational 
 transformation of the dangling uridine bases ( from 
 the md trajectory of 3cug3syw ) .
( a ) initial state 
 where dangling uridines are bent toward the rna major groove .
( c ) final 
 stable state where uridine ( u1 and u20 ) is flipped 
 upside down and stacked over the rna terminal base pair , while the 
 other uridine ( u2 and u19 ) is unstacked . for 
 residue numbering see figure 1b . in dm1 ,
hence , 
 the system in figure 1c was designed specifically to study the behavior of 11 uu 
 base pairs in an infinitely long linear rna system with continuous 
 cug repeats .
because a full turn of an a - form 
 rna duplex requires 11 basepairs , we designed the system shown 
 in figure 1c , such 
 that the rna duplex is along the z - axis , has 11 basepairs , 
 and stacks perfectly with the neighboring rna duplexes when periodic 
 boundary conditions are turned on .
no restraints ( either positional 
 or torsional ) were imposed on the rna duplex ; stacking interactions 
 between the neighboring gc base pairs keep the system in a linear 
 form automatically .
this trick , which we previously applied to rna 
 ccug repeats to investigate the dynamic properties 
 of cu / uc internal loops , allows us to 
 design an infinitely long linear rna duplex ( see movie s3 ) .
although r(3cuginf ) is not a perfect 
 rna cug repeat expansion , it is rather a linear 
 rna duplex having three continuous cug repeats 
 and then a ggcc / ccgg tetramer region ( see figure 1c ) .
if we leave off the  end - fraying  
 effects in the finite duplexes , this does give the same structural 
 properties of finite duplexes .
ultimately the periodic trick will 
 break down when the length of the structure is longer than the persistence 
 length .
force the rna duplex to stay in a linear form due to the stacking 
 of the neighboring rna duplexes and , hence , study the behavior of 
 11 uu base pairs in a linear rna geometry ( see supporting information ) .
two md simulations were run ; one 
 where the initial conformations of all the uu base pairs were anti 
anti ( 3cuginf / anti  anti ) and another 
 where the initial conformations of u3u20 and 
 u9u14 were anti  anti and u6u17 was syn 
we further completed two independent 
 md simulations on 3cuginf / syn  anti , which had low na concentration ( 0.24 mm ) . a 500 ns md simulation was run for this system . 

anti and stayed in this form during the 
 md simulation ( figure 7 ) .
similar to the results seen for 3cug3syw , three 
 11 uu base pair conformations are observed in the md trajectory 
 representing 2 , 1 , and 0 hydrogen - bond states ( figures 3 and 7 ) . even though 
 no anti  anti  syn  anti transformations are seen , 
 numerous anti  anti  anti  anti transformations are observed 
 ( figure 7 ) .
a hydrogen - bond 
 analysis indicates that the 11 uu base pairs in 3cuginf / anti  anti populate 
 states with 2 , 1 , and 0 hydrogen - bonds with probabilities 33% , 60% , 
 and 7% , respectively .
the reason for the increase in the 1 hydrogen - bond 
 state compared to 3cug3syw is due to the rigidity 
 of the 22 gc / cg regions flanked by 11 uu base - pairs in 
 3cuginf .
structurally , the 2 ( black ) and 1 ( red ) 
 hydrogen - bond states are alike , while the 0 ( cyan ) hydrogen - bond state 
 acts like an intermediate ( figure 3a  c ) .
thus , the black  red transformations 
 will be fast if no large distortions occur in the 22 gc / cg regions . 
 in 3cug3syw , because 22 gc / cg regions are flexible 
 the 11 uu base pairs have a higher probability of transforming 
 to the stable 2 hydrogen - bond states . on the other hand , analyses 
 showed that the conformations of the 22 gc / cg regions in 3cuginf / anti 
the results indicate that the 22 gc / cg regions in 3cuginf / anti  anti are 
 structurally more rigid than the ones in 3cug3syw . as a result
, it is harder for the 11 uu base - pairs to transform 
 to a stable 2 hydrogen - bond state without distorting the 22 
 gc / cg regions in 3cuginf / anti  anti .
rmsd analysis of 11 uu base pairs seen in the 3cuginf / anti  anti md simulation 
 ( see figure 1c for 
 residue numbering ) .
the color 
 scheme described in figure 3 was used to display the conformational transformations .
note 
 that black and red conformations ( figure 3 ) represent 2- and 1-hydrogen - bond states , 
 which can be described by two symmetric orientations ( figure 3a , b ) .
as described above , the initial conformation was designed 
 to have the middle uu base pair ( u6u17 ) in a syn 
anti conformation and the terminal 
 uu base pairs ( u3u20 and u9u14 ) in anti  anti . 

figure 8 shows the rmsd and na binding 
 analyses for this system . except for one case , which had low na concentration ,
anti  anti  anti transformations were seen for u3u20 and u9u14 , where 2 , 1 , and 0 hydrogen - bond 
 states were occupied with probabilities 47% , 48% , and 5% , respectively . 
 however , u6u17 , which stayed in the syn  anti conformation , exhibited 
 only 1 and 0 hydrogen - bond states with probabilities 93% and 7% , respectively . 

the green and blue conformations shown in figure 3 display 1 hydrogen - bond state when the 11 
 uu base pair has a syn  anti conformation .
even though no syn  anti  anti  anti transformation was observed for u6u17 in this 
 system we see that there are at least four times where u6 , which is in the syn conformation , unstacked from 
 the helical axis , colored orange in the rmsd plot ( figures 3 g and 8) . in this orange state
( figure 3 g ) , u6 is unstacked from the helical axis 
 via the minor groove but does not complete the syn  anti transformation ( movie s4 ) .
one reason for not observing the syn  anti transformation is the na binding pocket seen near u6 ( figure 9 ) .
the transformation of u6 from 
 a stacked state ( green , blue , and yellow colored states displayed 
 in figure 3 ) to an 
 unstacked state ( orange ) only happens when the na binding 
 pocket is not occupied by a na ion ( movie s4 ) .
however , this state was short - lived because na ions were found to rapidly occupy the binding pocket even 
 after u6 tried to unstack and then stabilize the syn  anti uu conformation by bringing 
 back u6 to the stacked conformation ( see md simulation 
 times 205 ,  360 ,  420 , and 545 ns 
 in figure 8) . as a 
 result , no syn  anti transformation 
 was observed .
rmsd of 11 uu base pairs and na binding 
 to the 
 pocket seen in 3cuginf / syn  anti md simulations ( see figure 1c for residue numbering ) .
the initial structures 
 of the terminal uu base pairs , u3u20 and u9u14 , were anti 
a na binding pocket was observed 
 near u6 when it was in the syn conformation 
 ( figure 9 ) . in the 
 na binding analysis
different colors represent different 
 na ions in the system where the distance between each 
 ion and the center - of - mass ( com ) of the three atoms shown in figure 9 ( o2p 
 and o2 of u6 , and n7 of g7 ) were calculated .
note that when the binding pocket was not occupied 
 by a na ion , u6 tried to unstack from the helical 
 axis and transformed to the orange state ( figure 3 g ) .
however , this state was short - lived , 
 and no syn  anti transformation 
 was observed ( movie s4 ) .
na binding pocket was observed near u6 when 
 it was in the syn orientation .
when occupied by a 
 na ion , there are three attractive electrostatic interactions . 

as shown in figure 8 , these interactions stabilize the syn  anti uu orientation .
when no na ion was present 
 in the pocket , u6 unstacked via the minor groove ( movie s4 ) .
a full syn  anti transformation , however , was not observed , due to the 
 rapid occupation of the pocket by na ions .
this can be 
 seen in the rmsd analyses of u6u17 ( figure 8) where the orange 
 colored state has a short lifetime . in order to investigate further the role of na ions
, 
 we designed another 3cuginf system , which had a low 
 na ion concentration .
in the first set , we observed a syn  anti transformation within 60 ns ( figure s3 ) .
this transformation happened right 
 after the loss of a na ion from the binding pocket ( figure s3 ) . in the second
set , however , we did 
 not observe any syn  anti transformation within 200 ns ( figure s4 ) . during the md simulation of the second set , the na binding pocket was occupied by different na ions
anti uu conformation 
 is intrinsically stable and is further stabilized by na ions through the na binding pocket .
the md results for 3cug3syw and 3cuginf have provided details of 
 the dynamics of each system . except for 
 one case ( 3cuginf with low na concentration )
anti  anti  anti transformation 
 for 11 uu base pairs . to further explore this result
, we utilized 
 umbrella sampling md simulations to build two 2d pmf surfaces , ( 1, ) and ( 1,2 ) ( variables 
 defined in figure 2 ) , to extract the transformation pathways for 11 uu base pairs 
 as well as other potentially stable uu conformations .
note , however , 
 that the calculated 2d pmf surfaces are approximations to the true 
 multidimensional energy landscapes .
for example , in the analysis we 
 assumed that the flanking gc basepairs will not be distorted during 
 base stacking  unstacking .
it is possible that the flanking 
 gc basepairs might stack on top of each other once the uridines are 
 fully unstacked from the helical axis .
the choice of pseudodihedral shown in figure 2b was made after 
 careful analysis , where we tried other reaction coordinates to mimic 
 base stacking  unstacking .
the use of pseudodihedrals to study 
 base flipping in nucleic acids was previously done by us and others .
figure 10 shows 
 the 2d ( 1, ) pmf surface predicted by umbrella 
 sampling calculations 
 for 11 uu base pairs .
there is excellent overlap of the ( 1, ) distributions calculated for each umbrella sampling 
 run ( figures s5 and s6 ) .
anti  anti  anti transformations : p1 , where 
 uridine unstacks via the minor groove in order to make the syn  anti transformation , p2 , where 
 uridine follows a direct transformation from syn  anti , while stacked within the rna helical axis , and p3 , 
 where uridine unstacks via the major groove to perform the syn  anti transformation .
these 
 pathways are similar to the ones predicted for rna cag repeats , but details of the free energy landscape ( figure s7 ) are different .
energy barriers in the 2d ( 1, ) 
 pmf surface predicted for 11 aa base pairs are roughly 2 to 
 4 kcal / mol lower than for the 11 uu base pairs considered in figure 10 ( see also figure s7 ) .
this result is expected because adenosine 
 mononucleoside is known to prefer 40% syn and 60% anti , while cytidine is known to 
 prefer over 90% anti , which results in different energy barriers ( figure s7 ) .
2d ( 1, ) pmf surface predicted 
 for 11 
 uu base pairs by umbrella sampling calculations .
the results include 
 11 minima , where ( g ) is the global minimum conformation ( anti  anti ) .
energy barriers , such 
 as the ones seen in b  e and j  g transformations , 
 might be the reason why we could not see any syn  anti  anti  anti transformation in regular md simulations at 300 k. see figure s7 for a comparison with the results previously 
 obtained for 11 aa base pairs .
figure 11 shows the 
 2d ( 1,2 ) pmf surface predicted 
 by umbrella sampling calculations for 11 uu base pairs ( for 
 details of the reaction coordinates see figure 2b ) .
the overlap of the ( 1,2 ) distributions calculated for each umbrella 
 sampling run is shown in figure s8 .
this 
 particular analysis was performed to investigate the correlation of 
 stacking  unstacking of each base in a 11 uu base pair . 

note , however , that the initial conformations of the 11 uu base 
 pairs are anti  anti .
thus , 
 the effect of syn  anti transformations 
 is omitted in this analysis .
first we note that the 2d pmf surface 
 is symmetric , which is expected for 11 uu base pairs in the 
 rna cug ( figure 11 ) .
second , we find that unstacking of each 
 uridine is negatively correlated . hence , when one of the uridines 
 starts to unstack the other uridine in the 11 uu base pair tends 
 to stay in the helical axis .
this result is illustrated in figure 11 with double - ended 
 arrows , here emphasizing the channels directing the stacking and unstacking 
 for each uridine .
third , the results indicate the lowest free energy 
 states describing the different stacked 11 uu base pair conformations . 

states a and b in figure 11 represent a mix of 2 and 1 hydrogen - bond conformations , while 
 state c represents a mix of 1 and 0 hydrogen - bond .
as described before , 
 the conformations of 2 and 1 hydrogen - bond uu base pairs are almost 
 identical and , therefore , overlap in figure 11 .
a detailed hydrogen - bond analysis is displayed 
 in figure s9 . in the 2d ( 1,2 ) pmf surface , regions around ( 1 = 40 , 2 = 70 ) and ( 1 = 70 , 2 = 40 ) represent 2 hydrogen - bond conformations , while the 
 other regions of states a and b shown in figure 11 represent 1 hydrogen - bond conformations 
 ( figure s9 ) .
the a  b , a  
 c , and b  c transformations displayed in figure 11 were also observed in the 
 md simulations of 3cug3syw and 3cuginf ( figures 4 and 7 ) .
2d ( 1,2 ) pmf surface 
 predicted 
 for 11 uu base pairs by umbrella sampling calculations .
double - ended 
 arrows indicate the channels directing the stacking and unstacking 
 of uridine in a 11 uu base pair .
a 
 and b represent a mix of 2 and 1 hydrogen - bond states , while c represents 
 a mix of 1 and 0 hydrogen - bond states ( see figure s9 for hydrogen - bond analyses ) . as described above , the syn and anti are two important rna conformations .
even though the 2d ( 1, ) pmf profile displayed high energy barriers , we also 
 investigated individual rna mononucleosides of a , g , u , and c , to 
 see if there are intrinsic differences between purines and pyrimidines . 

umbrella sampling calculations were utilized to create the 1d pmf 
 profiles for each rna residue along the  torsional axis ( figure s10 ) .
the results indicate that pyrimidines 
 mostly prefer anti , while purines can have significant 
 populations in syn ( figure s10 ) . in a and g , gsynanti ( ganti  gsyn )
differences are approximately 1.40 and 
 1.21 kcal / mol , respectively , while in u and c they are 0.39 
 and 0.21 kcal / mol , respectively ( figure s10 ) .
the percentage of anti conformations 
 extracted from gsynanti for a , g , u , and c at 300 k are 9% , 12% , 66% , and 58% , respectively , 
 in line with previous results .
furthermore , 
 the energy barriers seen in purines are lower than the ones seen in 
 pyrimidines ( figure s10 ) . in 1d pmf profiles , 

there are two barriers for the syn  anti transformation : one around   120 
 ( pb ) and the other around   360 ( pa ) ( figure s10 ) .
while the energy 
 barrier around   120 is only slightly larger 
 in pyrimidines , the barrier around   360 is over 
 2 kcal / mol higher than for purines ( figure s10 ) .
the results indicate that purines in free mononucleoside forms 
 would prefer the syn orientation over anti and will readily sample the syn  anti transformation via pa and pb due 
 to the low energy barriers , while pyrimidines would prefer anti over syn in free mononucleoside forms 
 and will follow pb to perform the syn  anti transformation ( figure s10 ) . even though 
 the umbrella sampling calculations predicted three transformation 
 pathways for syn 
anti  anti  anti , we did not observe any 
 such transformation in the 600 ns md simulation of 3cuginf / syn  anti ( except 
 when na concentration was low ) . an intermediate state 
 represented in orange ( figure 3 g ) , corresponding to the potential minimum state b shown in figure 10 , was observed 
 in the md trajectory of 3cuginf / syn  anti ( figure 8) where u6 ( in syn conformation ) 
 unstacked from the helical axis .
however , the b  e transformation 
 through p1 was not observed ( figure 10 ) even though this pathway was followed 
 by 11 aa base pairs in the syn  anti  anti  anti transformation .
one reason for not 
 seeing the full transformation is due to the high energy barriers 
 observed in the free energy profile of the 11 uu base pair ( figure 10 ) , which were increased 
 by the na binding pocket near uu stabilizing the syn  anti uu conformation ( figures 8 and 9 ) .
we therefore utilized 1cug ( figure 1a ) and increased the temperature of the system 
 slowly from 300 to 400 k to study the syn 
ten independent md simulations 
 starting with syn  anti and anti  anti 11 uu base pair 
 conformations were run .
anti systems ended up with anti  anti uu conformations , while no anti  anti  syn  anti was observed .
anti  anti  anti transformations 
 observed in the temperature jump md simulations occurred via p1 and p3 , which were followed 1 and 5 times , respectively 
 ( for definitions of pathways see figure 10 ) .
conformational states observed in the 
 temperature jump md simulations and the pathways followed during the syn 
pathways p1 and p3 include unstacking via minor and major grooves , respectively . 
 in the temperature jump md simulations , even though numerous i  
 b transformations were observed , only one of them overcame the energy 
 barrier and followed the b  e transformation ( figure 10 ) .
these results are different 
 from the corresponding rna cag results , where 
 the favorable syn 
anti  anti  anti pathway is via p1 in 11 aa base pairs ( figure s7 ) .
indeed , the relative energy barriers of b  
 e and j  g transformations are 2.4 and 6.0 kcal / mol in the 
 2d ( 1, ) pmf surface for 11 aa base 
 pairs , while the same barriers for 11 uu base pairs are 4.4 
 and 3.8 kcal / mol , respectively ( figure s7 ) . as a result ,
anti  anti  anti transformation pathways for 11 
 aa and uu base pairs , respectively , due to the associated energy barriers .
the potential and free energy disconnectivity graphs 
 for the rna system containing one cug repeat 
 are shown in figures 12 and s12 , respectively .
the free energy 
 disconnectivity graph was computed at 300 k using a regrouping threshold 
 of 2 kcal / mol .
the red and blue branches 
 lead to minima with the uu base 
 pair in syn  anti and anti  anti conformations , respectively . 

the green and pink branches lead to minima , in which the uridine is 
 unstacked via minor and major grooves , respectively .
some representative 
 structures corresponding to different conformational states are also 
 shown . to make a direct comparison with 
 the 2d pmf obtained from umbrella 
 sampling calculations ,
the disconnectivity graph in figure 12 clearly illustrates 
 the double - funnel character of the underlying potential energy landscape . 
 the anti  anti and the syn 
anti states of the uu base pair 
 corresponding to the two major funnels are colored blue and red , respectively . 

this observation is in agreement with the 2d pmf obtained from umbrella 
 sampling calculations , where the two major free energy basins correspond 
 to the anti  anti and syn  anti conformational states . 

the two funnels are separated by high energy barriers , leading to 
 two competing morphologies . to quantify the barriers separating the 
 two conformational states at 300 k
anti  anti  anti transformations using 
 the graph transformation employing a 
 regrouping threshold of 2 kcal / mol .
this 
 choice is appropriate , as similar values were obtained in terms of 
 rate constants and disconnectivity graphs for a range of values around 
 this selection . the rate constant for the conformational transition 
 from syn  anti to anti 
anti is estimated as 17240 
 s. the reverse transformation 
 ( i.e. , anti 
anti  syn  anti ) is at least 2 orders of 
 magnitude slower , with an estimated rate constant of 174 s. these rate constants approximately correspond 
 to time scales of 58 s and 6 ms , respectively .
the presence 
 of such competing morphologies separated by high barriers is normally 
 associated with multiple relaxation time scales and features in the 
 heat capacity profile .
the minima 
 corresponding to the flipped - out conformations of the 
 uu base pair are colored green and purple for unstacking through the 
 minor and major grooves , respectively .
these conformations do not 
 constitute any major funnel on the energy landscape and are distributed 
 over a wide energy range in the disconnectivity graph .
the free energy 
 disconnectivity graph at 300 k ( figure s12 ) displays essentially the same features as the potential energy 
 landscape , with two major funnels corresponding to the syn  anti and anti  anti states . in general
, we find that the selected 
 order parameters distinguish 
 the two major funnels quite well .
nonetheless , the intermixing of 
 colors in certain regions of the graph suggests that structural order 
 parameters alone are not sufficient to correctly represent the complexities 
 of the underlying landscape .
hence , we use the recursive 
 regrouping scheme instead , which is based 
 on kinetic criteria , to estimate the rate constants . the kinetically relevant pathways 
 between the syn  anti and anti  anti conformational states 
 of the uridine base pairs were extracted from the stationary point 
 databases using the recursive enumeration algorithm , which is based on kinetic criteria to estimate the rate 
 constants
. the diverse range of pathways 
 that exist between the two conformational states can be classified 
 in terms of three distinct mechanisms : ( i ) pathway p1 ( figure 10 ) , in which the uridine flips 
 out via minor groove ( figure s13a ) prior 
 to the rotation of the uracil base around its glycosidic bond ; ( ii ) 
 pathway p2 ( figure 10 ) , in which the uridine transforms from syn to anti without unstacking significantly from the helical axis 
 ( figure s13b ) ; and ( iii ) pathway p3 ( figure 10 ) , in which the 
 uridine flips out via the major groove ( figure s13c ) followed by rotation of the uracil base around its glycosidic 
 bond resulting a transformation from syn to anti . for pathways
p1 and p3 , unstacking of uridine 
 outside the helical axis ( via minor and major grooves , respectively ) 
 precedes the rotation of the uracil base around its glycosidic bond 
 that causes the syn  anti transformation .
these transitions are effectively the rate - determining 
 steps in the two mechanisms . for pathway p2 ,
the rotation around the 
 glycosidic bond resulting in the flip of the  torsion from syn to anti is associated with the surmounting 
 of a transition state and corresponds to the rate - determining step . 

although pathways p1 and p3 have similar path lengths , p3 is associated 
 with relatively lower barriers and emerges as the  fastest 
 pathway  in our kinetic transition network .
pathway p2 is longer 
 than paths p1 and p3 and makes a smaller contribution .
thus , the properties 
 of our kinetic transition network , in particular the existence of 
 three different pathways from syn to anti conformational states as well as the mechanistic details of the 
 transformation , are consistent with the predictions of the 2d ( 1, ) pmf profile obtained from umbrella sampling . in dm1 ,
inhibition of rna - mbnl1 binding through 
 small molecules , which will target 11 uu base pairs , could ameliorate 
 the disease .
therefore , understanding the structural and thermodynamic 
 properties of rna 11 uu internal loops could help us discover 
 the binding mechanism of small molecules to rna internal loops and 
 thus the design rules for drugs , which will effectively target these 
 rna structures .
previously , we studied the binding mechanism of a 
 substituted naphthyridine ( c-2 ) that targets rna cug repeats .
the results indicated complex 
 structural transformations of the rna internal loop in the small molecule 
 binding process .
the lowest two binding modes displayed 11 
 uu base pair in conformations near ( 1 = 55 , 
  = 200 ) and ( 1 = 55 , 2 = 55 ) .
indeed , ( 1 = 55 , 
  = 200 ) represents one of the local minima , 
furthermore , ( 1 = 55 , 2 = 55 ) is one of 
 the local minima in figure 11 . in other words , upon c-2 binding to rna cug , 11 uu base pair was transformed from global minimum g ( anti  anti ) to local minimum e ( anti  anti ) ( figure 10 ) .
our previous results combined with the 
 current work suggest that small molecules can exploit the stable local 
 minima states of 11 uu base pairs if the final bound state is 
 thermodynamically favorable .
it is known that mbnl1 
 binds to rna cug repeats , but the details are 
 uncertain .
patel and co - workers solved the crystal 
 structure of the mbnl1 tandem zinc finger 3 and 4 domains ( zn3/4 ) 
 interacting with a single - stranded rna , r(cgcugu ) , which shows guanosine 
 residues interacting with zn3/4 .
studies 
 have suggested that the binding to cug hairpins 
 occurs upon a conformational change in the structure that melts the 
 hairpin .
based on 
 the results of 3cug3syw , we discovered that tandem 
 gc / cg base pairs flanked by 11 uu internal loops are less stable 
 than when they are located in rna stem regions .
this result might 
 give insight into how mbnl1 binds to rna cug repeat expansions .
the distortions seen in tandem gc / cg regions 
 flanked by 11 uu base pairs might enhance the binding of mbnl1 
 to rna cug repeat expansions .
these studies 
 also suggest that small molecules that stabilize rna repeats could 
 be effective modulators of cellular function . using the cossmos database developed 
 by znosko and co - workers we found 73 rna structures that have cug motifs with 11 uu loops ( table s2 ) .
the biological systems that have the rna cug motifs include rna , ribosomes , zinc finger / rna , transcription / rna , 
 and ribosome / antibiotic complexes ( table s2 ) .
importantly , there are many rnas that have single copies of the 
 cug motif , which might be targeted through 
 binding to multiple motifs in a cug hairpin 
 simultaneously or using small molecules that 
 cooperatively bind to repeats .
the rna 
 cug motifs in these structures either interact 
 with mg ions or have tertiary interactions .
note that 
 all the 11 uu base pairs in these cug 
 motifs have anti  anti conformations . using an in - house code , we extracted all the rna cug motifs from the structures and calculated the ( 1, ) and ( 1,2 ) values for 
 each 11 uu base pair .
the results were then plotted on top of 
 the md results , which showed that the regions sampled by md simulations 
 were in line with the conformations seen in the literature ( figure s14 ) .
basically , the 11 uu base 
 pairs in these structures have 2 , 1 , or 0 hydrogen - bonds and prefer anti  anti .
this observation suggests 
 that the interaction of ions or tertiary interactions does not disturb 
 the base orientations of uridines with respect to sugar , so the 11 
 uu base pairs prefer to stay in anti  anti .
furthermore , our binding studies of compound c-2 to 
 rna cug repeats included over 25 s md 
 simulations where 11 uu base pair stayed in anti 
these results are in line with the umbrella sampling calculations , 
 where the free energy difference of syn  anti to anti  anti ( gsyn  anti  ganti  anti ) is over 5 kcal / mol 
 for 11 uu base pairs ( figure 10 ) , while no significant difference was seen in the 
 umbrella sampling calculations of rna cag repeats 
 ( figure s7 ) .
trinucleotide and tetranucleotide 
 repeat expansions caused by mutations 
 in certain genes lead to neuromuscular disorders .
these 
 rna transcripts are known to form stable hairpin structures with 11 
 or 22 internal loops regularly placed in the stem regions . however , 
 a thorough understanding of the atomistic details of rna hairpins 
 formed by expanded repeats is a must for designing rules and , therefore , 
 better compounds , which will target rna repeat expansions at nanomolar 
 levels . in the present contribution we utilized regular and 
 umbrella sampling 
 md simulations of model rna cug systems and 
 explained the structural and thermodynamic properties of 11 
 uu internal loops .
the results indicate that rna 11 uu internal 
 loops are dynamic and can form more than one stable conformation where 
 the global minimum conformation of the 11 uu base pair is anti  anti .
our md results indicate 
 that the 11 uu base pairs have 2 , 1 , and 0 hydrogen - bond states , 
 which are in line with the 73 nmr / x - ray structures we analyzed , as 
 well as with previous studies . moreover , 
 the global picture of the 2d ( 1, ) pmf surface 
 for 11 uu base pairs has the same topology as one we previously 
 determined for 11 aa base pairs , but with different energy barriers 
 and free energy differences . while the syn  anti aa conformation is a possible 
 state for rna cag repeats upon small molecule 
 binding it is not as stable as anti 
this conclusion 
 follows from umbrella sampling studies where the anti  anti uu conformation is over 5 kcal / mol 
 more favorable than syn  anti . the result is also supported by experimental studies where no syn 
anti uu conformations were seen 
 in the reported structures with rna cug motifs . 

additionally , the lowest free energy binding state of a compound to 
 a model rna cug system exhibited a conformation 
 in line with the present results described .
thus , the local minima conformations discovered for 11 uu 
 base pairs by the umbrella sampling calculations could be important 
 targets for small molecule binding .
our studies also showed that a 
 na binding pocket similar to the one detected in rna cag repeats exists for rna cug 
 repeats , and it stabilizes the syn  anti uu conformation .
this pocket includes three attractive 
 electrostatic interactions between na ions and rna backbone / bases , 
 so it could be used in drug design where electropositive groups such 
 as nh2 and nh are incorporated in small 
 molecules to utilize this binding pocket for a higher binding affinity . 
 hence
, our results should help explain the mechanism behind small 
 molecule driven structural change in rna cug repeat expansions .
our results also indicate that there is 
 an intrinsic difference 
 between rna cag and cug repeats , where purines prefer both syn and anti , while pyrimidines predominantly prefer anti . furthermore
, the differences we see in the 
 2d pmf surfaces and md calculations for rna cag and cug repeats can be traced to intrinsic 
 properties in the torsion dependence of the force field .
these results 
 are , therefore , dependent on improvements implemented recently in 
 the rna force field .
it was shown that the  torsional parameters 
 for the amber force field needed revision to make physically meaningful 
 computational predictions including structural and thermodynamic properties 
 of rna mononucleosides , single - stranded rna , rna structures with modified 
 residues , and rna hairpins . using these revised rna force 
 fields , other rna repeat expansions such as ccug , ccg , and cgg
these studies should produce insight that 
 can be used in understanding the mechanisms of different rna repeat 
 expansions and designing drugs that will target them .
 myotonic dystrophy 1 ( dm1 ) is a genetic 
 disease caused by expansion 
 of ctg repeats in dna . once transcribed , these repeats form rna hairpins 
 with repeating 11 nucleotide uu internal loop motifs , r(cug)n , which attract muscleblind - like 1 ( mbnl1 ) 
 protein leading to the disease . in dm1 cug 
 
 can be repeated thousands of times , so these structures are intractable 
 to characterization using structural biology 
 . however , inhibition 
 of mbnl1-r(cug)n binding requires 
 a detailed analysis of the 11 uu internal loops . in this contribution 
 
 we employ regular and umbrella sampling molecular dynamics ( md ) simulations 
 to describe the structural and thermodynamic properties of 11 
 uu internal loops . 
 calculations were run on a reported crystal structure 
 and a designed system , which mimics an infinitely long rna molecule 
 with continuous cug repeats . 
 two - dimensional 
 ( 2d ) potential of mean force ( pmf ) surfaces were created by umbrella 
 sampling , and the discrete path sampling ( dps ) method was utilized 
 to investigate the energy landscape of 11 uu rna internal loops , 
 revealing that 11 uu base pairs are dynamic and strongly prefer 
 the anti  anti conformation . 
 
 two 2d pmf surfaces were calculated for the 11 uu base pairs , 
 revealing several local minima and three syn  
 anti  anti  anti transformation pathways . 
 although at room temperature the syn  anti  anti  anti transformation is not observed on the 
 md time scale , one of these pathways dominates the dynamics of the 
 11 uu base pairs in temperature jump md simulations . 
 this mechanism 
 has now been treated successfully using the dps approach . 
 our results 
 suggest that local minima predicted by umbrella sampling calculations 
 could be stabilized by small molecules , which is of great interest 
 for future drug design . 
 furthermore , distorted gc / cg conformations 
 may be important in understanding how mbnl1 binds to rna cug repeats . hence we provide new insight into the dynamic 
 roles of rna loops and their contributions to presently incurable 
 diseases . 
Introduction
Methods
Results and Discussion
Summary and Conclusions