recently , 
 a new class of hybrid materials has been generated by 
 attaching dna to organic molecules , polymers , metal complexes , and nanoparticles .
some of the resulting 2d and 3d nanostructures have been used in dna detection and electronic 
 applications ; other applications such as drug delivery and therapeutics are emerging . 

a key factor that enables these applications is the degree of structural 
 control available when dna are linked to other molecules .
types of 
 linkers and linkage direction are crucial for providing the desired 
 control on product distributions of the assemblies and their stability . recent investigations into the self - assembly of small molecule - dna 
 hybrids in aqueous media have demonstrated that the structures of 
 these assemblies are dictated by several factors , including the number 
 of single - strand ( ss ) dnas attached to the organic cores , the specific 
 geometry and concentration of the dna strands , and the type ( na , k , ca , mg , etc . ) and 
 concentration of ions used in aqueous media .
we additionally showed 
 that the hydrophobic properties of organic cores is an important parameter 
 to be considered in the self - assembly of the small - molecule - dna hybrids 
 ( smdhs ) .
indeed , richert and co - workers 
 have utilized the hydrophobic properties of stilbenes and anthraquinones 
 linked to dna duplexes to stabilize small - duplex dna - detection probes . in a related study , bergstrom and co - workers end - capped small dna 
 hairpins with rigid , hydrophobic organic molecules to afford enhanced 
 stability .
moreover , perylenedimide ( pdi)-dna 
 hybrids have been found to form stable hairpin dimers and larger supramolecular oligomers due to the hydrophobicity 
 of the pdi cores , which leads to pdi 
pdi stacking via  
 interactions . despite emerging evidences 
 concerning the critical importance of 
 the hydrophobic interactions between organic cores and dna duplexes 
 in organic - dna hybrids ,
specifically , the effects of linking hydrophobic 
 organic cores to dna strands through either 3- or 5-ends 
 are still not known although it is clear that such different linkages 
 will lead to different types of hydrophobic interactions  such 
 as insertion into the minor groove , intercalation , and  
 stacking  in the self - assembly of the small molecule - dna building 
 blocks into dna - hybrid nanostructures .
probing these interactions 
 experimentally is a challenging task , so we decided to combine experimental 
 studies with molecular dynamics ( md ) simulations at the atomistic 
 level with the goal of unraveling the assembly of two complementary 
 smdhs into a cyclic dimer , the simplest dna - hybrid nanostructure possible . 
 with the continuous improvements in computer technology , utilization 
 of computational methods and tools to describe self - assembly is gaining 
 popularity .
while there are different methods available to describe 
 the properties of nucleic acid systems such as melting , mechanical 
 properties , and conformations using coarse - grain simulations , the atomistic details of these systems at long time scales can best 
 be described using atom - based force fields , such as amber and charmm .
previously , we reported 
 the remarkable effects of hydrophobic organic 
 cores in the assembly of small - molecule dna hybrids ( smdhs ) into caged 
 structures .
our experimental results 
 and computational simulations showed that the final nanostructures 
 assemble in aqueous environments in a manner that minimizes exposure 
 of the hydrophobic surfaces of the organic cores to solvent .
these 
 hydrophobic interactions are greatly influenced by the incorporation 
 of multiple noncomplementary deoxythymidine ( t ) spacers between the 
 core and the dna duplex , as the solvent - accessible surface area ( sasa ) 
 of the hydrophobic cores is greatly reduced when these spacers are 
 wrapped around the cores . soon after our report , sleiman and co - workers 
 published a broad study on the self - assembly of cyclic nanostructures 
 made from smdh2 building blocks .
they showed that while the small molecule - dna hybrid derived from 
 the flexible organic core 1 ( fsmdh2 ) assembled 
 exclusively into cyclic dimers , that derived from the rigid organic 
 core 2 ( smdh2 ) assembled into a mixture of 
 dimers and higher - order ( tetramer , hexamer , etc . )
they proposed that the presence 
 of rigid cores at either the 3- or 5-ends of dna duplexes 
 constrains the ways in which these duplexes can assemble and affects 
 the distributions of the final products ( dimer , tetramer , hexamer , 
 etc . ) .
schematic descriptions of the assembly of cyclic nanostructures 
 ( dimer , tetramer , hexamer ) from smdh2 building blocks containing 
 organic cores described by the sleiman group ( 1 , flexible ; 2 , rigid ) and us ( 3 , partially rigid ) . to explain why cyclic dimers are preferred in the case of 
 core 1 , sleiman and co - workers invoked a  strand - end 
 alignment  
 model that focuses only on the importance of duplex alignment ; once 
 the dna duplexes are ideally aligned by the first rigid core
, dimers 
 can form if the other ends of these duplexes are properly aligned 
 to accommodate the second rigid core .
the orientation 
 of the ends of the dna duplexes was defined as either convergent ( i.e. , 
 can accommodate the second rigid core ) or divergent ( i.e. , can not 
 accommodate the second rigid core ) .
while this assumption appears 
 to be a reasonable one , it was based on two cores that are quite different : 
 one ( 1 ) that is flexible and moderately hydrophilic and 
 the other ( 2 ) that is quite rigid and very hydrophobic . 

we suspect that a model built upon two such different cores may not 
 accurately reflect the assembly process of smdh2 , particularly 
 when the hydrophobic nature of the organic cores can force them to 
 interact very strongly with the bases of the dna component strands 
 as well as with stacked base - pairs of the assembled duplexes in aqueous 
 environments .
furthermore , the magnitude of this hydrophobic interaction 
 would be strongly modulated by the flexibility of the connection points 
 between the cores and the dna component strands .
indeed , we have observed 
 for the smdh3 system that 
 when there is not enough flexibility at the connection points , the 
 drive to minimize exposure of the hydrophobic organic cores to water 
 can sometime become so overwhelming that the system will destabilize 
 some of the dna base pairings in the assembled duplex arms .
these 
 observations prompted us to explore the assembly of smdh2 further using the core 3 , which is hydrophobic but 
 much more flexible than 2 .
herein , we present a 
 detailed computational study , supported by 
 experimental results , which suggests that both the hydrophobic nature 
 and the flexibility of the organic core play very important roles 
 in the self - assembly of smdh2s into cyclic dimers and higher - order 
 nanostructures . while duplex alignment may be important , the interactions 
 between the cores and the dna duplexes to minimize their sasa comprise 
 a dominant force that can not be ignored , especially when there is 
 restricted flexibility . indeed for cyclic dimers involving core 3 , when the cores are attached to the 3-ends of the 
 dna component strands , they prefer to insert into the minor groove 
 of the dna duplexes in the product dimers to minimize their sasa . 

in contrast when cores such as 3 are attached to the 
 5-ends of the dna component strands , they can only partially 
 insert themselves into the minor groove of the dna duplexes in the 
 product dimers , resulting in much less stable cyclic dimers .
consistent 
 with these insights , smdh2 building blocks containing cores 
 linked to 3-ends of the dna duplexes were found to yield higher 
 percentages of cyclic dimers compared to that obtained from 5-linked 
 smdh2s .
the important roles that such hydrophobic interactions 
 play in smdh2 assembly is further supported by the enhanced 
 thermodynamic stability of face - to - face ( ff ) dimers over analogous 
 cyclic dimers ; the former benefits from strong interactions between 
 two overlapping hydrophobic cores .
synthesis of unsymmetric smdh2s was achieved 
 by adding the phosphoramidite core ( scheme 
 s1 in the supporting 
 information ) to the initial dna arm grown from the surface 
 of a controlled porosity glass bead ( cpg ) from either the 3- 
 or 5-end of the dna strand , followed by synthesis of the second 
 arm via either 3-normal or 5-reverse phosphoramidite 
 chemistry ( scheme s2 in the supporting information ) .
the final dmt - protected products were 
 then cleaved from the solid support , purified by reverse - phase ( rp ) 
 high - performance liquid chromatography ( hplc ) , and subjected to dmt 
 deprotection to yield the desired smdh2s ( table 1 ) .
the purities of all smdh2s were ascertained 
 via analytical rp - hplc and their length and base compositions were 
 confirmed via maldi - tof mass spectrometry ( see figures s1s14 
 in the supporting information ) .
building 
 blocks ( smdh2s , table 1 ) containing 
 two different strands ( one of the strands is the reverse sequence 
 of the other to maintain similar thermal properties ) were designed 
 to control the formation of cyclic ( figure 1 ) versus ff smdh2 ( figure s15 in the supporting information ) nanostructures , depending on the orientation 
 of the linkage between the core and the dna strands .
the smdh2 assemblies and their controls ( table 2 ) were prepared by combining equimolar amounts of two complementary 
 components ( table 1 ) in tamg buffer ( 40 mm 
 tris base , 20 mm acetic acid , 7.5 mm mgcl26h2o ) and annealing the resulting mixtures using both normal 
 and slow - cooling methods ( see section s3 in the supporting information for more details ) .
amber force field parameters 
 for the organic core were calculated as previously described ( section 
 s4 in the supporting information ) .
the amber99 force field with revised  and / torsional parameter sets was used to define 
 the dna parameters .
all the model dna systems ( with sequences described 
 in table 1 ) were created in b - form using the 
 nucgen module of amber 9 . the smdh2 systems ( table 2 , entries 15 
 and 13 )
were then prepared , where the organic cores were attached 
 at either 3- or 5-ends of the dna sequences ( section 
 s5 in the supporting information ) .
most 
 md simulations were run in a generalized born implicit - solvent model 
 ( gb ) with 0.3 m salt concentrations . 

unrestrained gb md simulations were carried for our three different 
 cyclic dimers ( table 2 , entries 13 ) 
 and the cyclic tetramer and hexamer for one smdh2 system 
 ( table 2 , entry 1 , see section s6 in the supporting information for details ) . restrained 
 gb md simulations ( both normal and annealed )
were carried out for 
 cyclic dimers ( table 2 , entries 13 ) 
 with varying dna duplex lengths ( 11 , 13 , 15 , 17 , 19 , 21 , and 23 base 
 pairs ) and a model system ( used for explicit solvent calculations 
 that were used to calibrate the gb model ) consisting of an 11 bp dna 
 duplex with a single organic core attached at either 3- or 
 5-end of the dna strands ( see section s7 in the supporting information ) .
sasa and root - mean - square 
 deviation ( rmsd ) analysis for all the md simulations were performed 
 according to our previously published work ( see sections s5 in the supporting information for details ) .
the implicit - solvent model used in this 
 study is preferred over explicit - solvent ones due to the large size 
 of our systems , whose computation would be quite long and expensive 
 if explicit - solvent models were used .
compared to explicit - solvent 
 md simulations , the viscosity in implicit - solvent md simulations is 
 low and this accelerates the sampling of md space .
yet , implicit - solvent 
 models are less realistic because they employ empirical parameters 
 to calculate the solvation free energies . to date ,
implicit - solvent 
 simulations of proteins are well developed while the corresponding simulations of nucleic acids still require 
 improvements .
while gb implicit - solvent simulations of regular dna 
 oligomers produce average structures that are in line with explicit - solvent 
 md simulations , the formers can distort 
 the dna backbone and promote fraying effects at terminal base pairs 
 that might not be physical .
this is one of the shortcomings of implicit - solvent 
 models and can cause dna to be more flexible than it actually is . 
 indeed , harris and co - workers showed that the use of implicit solvents 
 in dna minicircle topoisomers with varying lengths display structures 
 that are different from those seen in explicit - solvent simulation , 
 which can be attributed to dna flexibility .
one of the reasons for this outcome is the neglect of specific interactions 
 of water molecules with dna in implicit - solvent models ( such as the 
  spine of hydration  observed in the minor grooves of 
 a - tracks ) .
thus , the improper description of dna flexibility will 
 show its effects in exotic systems such as in dna minicircles and smdh molecules . as a result , to keep the 
 dna structures in their known native b - form
crick 
 and torsional restraints so that the md simulations have a physical 
 meaning .
additionally , explicit - solvent calculations were carried 
 out on our smallest model system ( see section s7 in the supporting information for more details ) to verify 
 the accuracy of the gb calculations with restraints .
combining equimolar amounts of [ 5-c-3 ] , [ 5-c-5 ] , 
 [ 3-c-3 ] , [ 5-t3ct3 - 3 ] , [ 5-t6 - 3 ] , [ 5-t6 - 5 ] , [ 5-t3 - 3 ] with their complements , 
 [ 5-c-3] , [ 5-c-5] , [ 3-c-3] , [ 5-t3ct3 - 3] , 
 [ 5-t6
- 3] , [ 5-t6 - 5] , 
 and [ 5-t3 - 3] , respectively , was expected to 
 result in cyclic structures ( figure 1 ; see 
 also table 2 , entries 17 ) as previously 
 reported .
our earlier 
 study showed that systems with core 3 with noncomplementary 
 t spacers ( table 2 , entry 4 ) exclusively formed 
 cyclic dimers at low concentrations of ss - dna ( up to 5 m total 
 ss - dna concentration in which each arm s concentration in the 
 smdh2 was calculated separately ) .
however , sleiman and co - workers recently reported that the rigidity 
 of the core and the linkage between the core and the dna strands ( 33 , 
 55 , and 35 orientations ; see figure 1 , inset b ) directly influence the product distributions : systems with flexible core 1 ( figure 1 , inset a ) attached to 3- or 5-end 
 of dna strands mostly formed cyclic dimers , while those with rigid 
 core 2 ( figure 1 , inset a ) afforded 
 a mixture of all cyclic products .
interestingly , page - gel analysis 
 of the [ 5-c-3]:[5-c-3] , [ 5-c-5]:[5-c-5] , and [ 3-c-3]:[3-c-3] 
 combinations in our present work revealed a mixture of cyclic structures 
 ( figure 2 ) instead of solely cyclic dimers 
 even though our core 3 can be classified as being overall 
 flexible with highly flexible ( ch2och2ch2o ) arms flanking a rigid 1,3-bis(ethynylphenyl)phenyl 
 component ( figure 1 , inset a ) .
nondenaturing page - gel 
 image ( 6% ) of dna assemblies with 5 m 
 total ss - dna concentration ( gel was prepared in 1 tamg buffer 
 ( 40 mm tris base , 20 mm acetic acid , 7.5 mm mgcl26h2o ) , and run at 4 c for 2 h at a 200 v potential ) . from 

left to right : lane 1 = hl5 dna ladder , lane 2 = cyclic-[5-c-3]:[5-c-3] ( normal annealing ) , lane 3 = cyclic-[5-c-3]:[5-c-3] ( slow annealing ) , lane 4 = control-[5-c-3 ] , lane 5 = cyclic-[5-c-5]:[5-c-5] ( normal annealing ) , lane 6 = cyclic-[5-c-5]:[5-c-5] ( slow annealing ) , lane 7 = control-[5-c-5 ] , lane 8 = cyclic-[3-c-3]:[3-c-3] ( normal annealing ) , lane 9 = cyclic-[3-c-3]:[3-c-3] ( slow annealing ) , and lane 10 = control-[3-c-3 ] . according to the strand - end alignment model
, the flexible arms of our core 3 should be long enough 
 to accommodate any strain put on the dna duplexes by the rigid 1,3-bis(ethynylphenyl)phenyl 
 component , favoring the formation of cyclic dimers . however , this 
 was not experimentally observed .
rather , exclusive formation of cyclic 
 dimers is observed when three noncomplementary deoxythymidine spacers 
 ( t3 ) were added to each side of our core 3 ( [ 5-t3ct3 - 3]:[5-t3ct3 - 3] ) , 
 according to the nondenaturing page - gel analysis ( see figure s17 in 
 the supporting information , lane 9 ) .
these 
 results , however , are in agreement with our previous report , which 
 concluded that dimer formation is favored when t3 spacers 
 are available to shield the hydrophobic surfaces of the cores from 
 the aqueous media .
the nondenaturing 
 page - gel analysis also revealed that there is 
 a higher percentage of dimer formed for [ 3-c-3]:[3-c-3] 
 compared to the [ 5-c-5]:[5-c-5] and [ 5-c-3]:[5-c-3] combination ( figure 2 , lanes 8 , 5 , and 2 , respectively ) . to further probe this 
 observation and eliminate the possibility that the formation of cyclic 
 dimers may be affected by the length of the annealing time , we annealed 
 our smdh2 systems ( table 2 , entries 
 13 ) with a cooling rate of 0.01 c / minute in a pcr instrument 
 in the range of 6025 c , which is 34 times slower than 
 our normal annealing protocol ( 0.34 c / minute in the 6040 
 c range ( figure s16 in the supporting information ) , where the complete melting of a mixture of cyclic structures occur ) . 

analysis of the nondenaturing page - gel image ( figure 2 ) showed a clear increase in dimer formation for all cases 
 during slow annealing .
moreover , the cyclic dimer formed in high yield 
 ( 79% ) for [ 3-c-3]:[3-c-3] in slow annealing , much 
 higher than the [ 5-c-3]:[5-c-3] and [ 5-c-5]:[5-c-5] combinations ( 43 and 34% , respectively ) . 

the latter afforded the highest percentage of large cyclic structures 
 ( 31% , figure 2 , lane 6 ) in the slow annealing 
 method compared to the former two ( 11 and 5% , respectively ) .
similar 
 observations were also reported by sleiman and co - workers for systems 
 derived from core 2 .
cyclic 
 dimers were formed exclusively in the nondenaturing page - gel analysis 
 when deoxythymidine linkers ( t3 and t6 , table 2 , entries 57 ) were used in place of organic 
 core 3 ( see figure s18 in the supporting 
 information , lanes 35 ) .
our previous computational 
 work showed that hydrophobic interactions between the organic cores 
 and noncomplementary t spacers in smdh3 building blocks 
 play a crucial role in the self - assembly process and the final properties 
 of smdh3-based nanostructures .
in such structures , the cores  strive  to minimize 
 their sasa values through interaction with both the t spacer and the 
 base pairs of the duplexes . when the sasa values were too high for 
 dimers , other structures with lower sasa become dominant . nevertheless , 
 we were surprised to observe that the directionality of the linkage 
 ( 3- or 5- ) between the core and the duplex dramatically 
 affected the product distributions in the assembly of smdh2-based nanostructures in the absence of noncomplementary t spacers 
 ( see the discussion of experimental results ) .
as such , we utilized 
 md simulations to elucidate the details of the self - assembly process . 

computationally , we began by examining the simpler dna - hybrid components 
 that constitute the larger cyclic nanostructures ( dimers , tetramers , 
 hexamers , etc . ) : ( 1 ) organic core 3 attached to either 
 3- or 5-ends of a dna duplex ( figure 3a ) ; ( 2 ) single organic core attached at 3- and 5-ends 
 of two dna duplexes , control-[5-c-3 ] 
 ( figure 3b ) ; ( 3 ) cyclic-[5-c-3]:[5-c-3] structures ( dimer structure is shown 
 in figure 3c ; tetramer and hexamer structures 
 are shown in figure 1 ) .
initial 
 modeling of ( a ) organic core 3 attached to 
 a dna duplex , ( b ) control-[5-c-3 ] , and ( c ) cyclic-[5-c-3]:[5-c-3] 
 dimer .
the simplest component system , 
 consisting of the organic core 3 attached to an 11 bp 
 dna duplex , allows us to investigate how the organic cores attached 
 to either 3- or 5-ends of dna duplexes ( see section 
 s7 in the supporting information ) interact 
 with these duplexes in an aqueous environment .
crick base pairing and torsional restraints were 
 applied to dna duplexes to keep them in their native b - form since 
 gb implicit solvent md simulations can distort the dna backbone and 
 cause fraying at terminal base pairs ( see the discussions below concerning 
 unrestrained and restrained md simulations and section s7 in the supporting information ) . after 10 ns of md simulations ,
the 3-linked organic core 
 is already inserted fully into the dna minor groove ( figure 4b ) while the 5-linked core is only partially 
 inserted ( figure 4c ) .
average sasa values for 
 the 3- and 5-linked organic cores are 153.7  
 19.6 and 250.8  18.4  , respectively , and remain 
 constant over the course of the simulation time ( 55 ns , figure 4a ) . because the 3-ends of dna duplexes are 
 spatially closer to the minor grooves compared to 5-ends , 
 it is easier for a 3-linked organic core to be fully inserted 
 into the dna minor groove . on the other hand ,
the 5-linked 
 organic core needs to stretch over the terminal base pairs before 
 it can reach dna minor grooves ; so it is only partially inserted , 
 has a much larger sasa value , and is less stable in aqueous solution . 

these results suggest that the differences in the distribution of 
 cyclic nanostructures , as observed in the page - gel experiments ( figure 2 , lanes 6 versus 9 ) , can be rationalized by how 
 well organic cores are inserted in dna minor grooves to minimize exposure 
 to the aqueous outside environment .
to calibrate the stabilities 
 of these restrained gb - based structures , we also performed explicit - solvent 
 calculations for the same model . in these calculations , each final 
 conformation from the gb calculations was solvated with na / cl ions and water molecules and the imposed restraints 
 were removed on the dna duplexes ( see section s7 in the supporting information for more details ) .
the 
 simulations show that the 3-linked organic core stays in the 
 dna minor groove while the global dna conformation remains in b - form 
 ( figure s22 in the supporting information ) .
it is also found that the organic core in the 5-linked 
 core - dna system is dynamic and does not stay in the dna minor groove 
 for a long time .
the terminal base pair is broken , and the organic 
 core stacks within the bases of the distorted terminal side ( figure 
 s22 in the supporting information ) .
this 
 clearly shows that dna minor groove insertion is a viable option for 
 3-linked organic cores to lower their sasa without distorting 
 the dna .
this is not the case in 5-linked core - dna systems , 
 where the only option for organic cores to lower their sasa is through 
 stacking within terminal bases after disrupting the canonical base 
 pairing .
these results indicate that the restrained implicit - solvent 
 md simulations exhibit similar behavior for the hydrophobic organic 
 cores to the explicit - solvent md simulations without restraints .
( a ) sasa values of hydrophobic cores attached at 3- 
 ( black ) and 5-ends ( red ) of dna duplexes over the course of 
 the simulation .
final structures of 3- and 5-linked 3-dna hybrids are shown in ( b , c ) , respectively .
the 3-linked 
 core is fully inserted into dna minor groove compared to the 5-linked 
 core ( see figure s22 in the supporting information ) .
we next examined the control-[5-c-3 ] system ( figure 3b ) to evaluate potential interactions between organic core 3 and the two dna duplex arms that are linked to it .
after 
 96 ns , restrained implicit - solvent md simulations showed that the 
 organic core already minimized its sasa by inserting itself within 
 the minor groove of one dna duplex and  stacking  with 
 the terminal dna base pairs of the other duplex ( figure 5 ; see also movie s1 
 in the supporting information ) . as a result , 
 the control-[5-c-3 ] 
 system forms an almost continuous 30 bp dna duplex with a single core 
 stacked in the middle .
molecular surface representations of initial ( top ) and 
 final ( below , 
 after 96 ns ) structures of the control-[5-c-3 ] system obtained from md simulations .
the two 15 bp dna duplexes 
 are brought together by the hydrophobic nature of 3 . 

two md simulations were carried out ; see movie s1 in the supporting information for further details . as we have shown in previous md 
 simulations , the hydrophobic nature of 
 core 3 forces it to minimize 
 its exposed surfaces in an aqueous environment through interactions 
 with the dna duplexes . to simulate the cyclic nanostructures that 
 may form in an experiment
, we carried out implicit - solvent md simulations 
 ( this is a more feasible option compared to expensive explicit - solvent 
 md simulations for these large systems ; see detailed discussion in 
 section s7 in the supporting information ) for all possible combinations of cyclic dimers ( figure 6 ) as well as tetramer and hexamer structures ( figures 7a - b ) for the [ 5-c-3]:[5-c-3] 
 system without any restraints on dna duplexes ( see section s6 in the supporting information for more details ) .
a sasa 
 analysis of the cyclic-[5-c-3]:[5-c-3] dimer , tetramer , and hexamer 
 systems shows that the organic cores 3 in these structures 
 can lower their sasa better in higher - order structures ( table 3 , entries 13 ) . while the average sasa value 
 of the cyclic-[5-c-3]:[5-c-3] dimer is 200  , it is reduced to 134  in the tetramer 
 and 122  in the hexamer ( table 3 ) . in the cyclic dimer
, the organic cores can not lower their 
 sasa as much due to strain . as shown above for the 3-linked 
 core model system
, the organic cores in cyclic dimers can minimize 
 their sasas through interactions with the dna minor grooves , which 
 severely distort the two dna arms ( figure 6 ) .
on the other hand , the organic cores in the tetramer and hexamer 
 have additional means to minimize their sasas ( figures 7c  f ) , such as  stacking  with the terminal 
 base pairs of the adjacent dna duplex , as shown for the control-[5-c-3 ] system ( figure 5 ) .
schematic representations of initial ( top ) and lowest sasa ( below ) 
 cyclic - dimer structures after 91 ns md simulations .
that due to the flexible 
 t linkers , dna deformations in ( d , e ) are not severe compared to ( a  c ) 
 ( see table s2 in the supporting information ) .
molecular surface representations of the initial 
 ( left ) and final 
 ( middle ) structures of the cyclic tetramer ( a ) and hexamer ( b ) formed 
 from the [ 5-c-3]:[5-c-3] system ( see figures s20 
 and s21 in the supporting information ) . 

the organic cores 3 are represented in green color and 
 are shown interacting with neighboring dna duplexes in different manners : 
 ( c ) being sandwiched between neighboring dna duplexes via -stacking , 
 ( d ) fully inserting into the minor groove , ( e ) inserting into the 
 minor groove in a distorted manner , and ( f ) -stacking with 
 distorted terminal base pairs of neighboring dna duplexes ( the dna 
 distortions are not as severe in comparison to that observed in the 
 cyclic - dimer structures shown in figure 6 ) .
interestingly , md simulations 
 of the cyclic-[5-t3ct3 - 3]:[5-t3ct3 - 3] dimer 
 structure show average sasa values around 119  ( table 3 ) .
the rmsd s of the dna duplexes 
 are lower than those for the other cyclic - dimer systems that have 
 only organic cores 3 , implying that introducing t3 spacers provides additional flexibility that helps to minimize 
 the sasas of the cores without distorting the dna duplexes ( table 3 and figure 6d ) .
consistently , 
 the percentage of hydrogen bond loss in the cyclic-[5-t3ct3 - 3]:[5-t3ct3 - 3] dimer 
 is only 5% while those for the cyclic-[5-c-3]:[5-c-3] , 
 cyclic-[3-c-3]:[3-c-3] , and cyclic-[5-c-5]:[5-c-5] dimers are over 20% ( table 3 ) .
these results are in line with our previous work and page - gel experiments , which show exclusive 
 formation of dimer structures in cyclic-[5-t3ct3 - 3]:[5-t3ct3 - 3] ( see figure s17 in the supporting information , lane 9 ) . in the absence of the organic 
 cores
3 , exclusive cyclic dimer formation was observed 
 for [ 5-t6 - 3]:[5-t6 - 3] , [ 5-t6 - 5]:[5-t6 - 5] , and [ 5-t3 - 3]:[5-t3 - 3] ( see figure s17 
 in the supporting information , lanes 35 ) . 

similarly , the md simulations show no major dna distortions in [ 5-t6 - 3]:[5-t6 - 3] , with 9% 
 hydrogen bond loss ( table 3 and figure 6e ) .
one md simulation was carried 
 out for each of the hexamer and tetramer ; four independent md simulations 
 were carried out for cyclic - dimer systems but only the lowest rmsd 
 results are shown ( see section s6 in the supporting 
 information for more details ) . in the unrestrained md simulations of the 
 cyclic dimers discussed 
 above , the dna duplexes can be easily distorted due to the conformational 
 stress put on by the organic cores while trying to minimize their 
 sasas ( figures 6a  c ) .
one consequence 
 of this is excessive fraying of the terminal base pairs in the dna 
 duplex arms of the dimers ( figures 6a  c ) , 
 making it difficult to evaluate their relative stabilities .
thus , 
 restrained md simulations ( see detailed discussion in section s7 of 
 the supporting information ) were carried 
 out where the dna duplex arms of the dimers were constrained in b - form 
 while their lengths were varied over one helix turn ( 11 , 13 , 15 , 17 , 
 19 , 21 , and 23 bp , see section s7 in the supporting 
 information for more details ) . on average , the total sasa values 
 of the organic cores in the [ 3-c-3]:[3-c-3] 
 systems are lower than those for the [ 5-c-3]:[5-c-3] 
 and [ 5-c-5]:[5-c-5] systems ( see figure s23 
 and table s3 in the supporting information ) , suggesting that the manner in which the cores are attached to 
 the dna duplexes does matter .
while constraining the dna duplex 
 arms gave us a starting point to 
 compare the three different dimer systems via md simulations , these 
 structures may be trapped in local minima and do not accurately reflect 
 the energy landscape of the system .
thus , we performed simulated annealing 
 on all of the 21 smdh2 dimers shown in table s4 in the supporting information ( see also section s8 in 
 the supporting information ) . while the 
 dna structures were kept in b - form conformations with watson  crick , 
 torsional , and chirality restraints , the temperature of each system 

was increased to 3000 k and gradually cooled down to 100 k. for each 
 system , 301 simulated annealing md simulations were run sequentially 
 where the starting structure for each run was taken from the final 
 structure of the previous run . this way , each system was allowed to 
 move away from any potential minimum state and sample other regions 
 in phase space . for each dimer ,
sasa values of the organic cores were 
 calculated from the simulated annealing md simulations for structures 
 having final restraint energies and duplex rmsd values less than 10 
 kcal / mol and 10  , respectively . within these structures ,
sasa 
 values that are uniformly lower than those obtained for the restrained 
 md simulations shown earlier can be obtained for each cyclic dimer 
 ( see data in table s3 in supporting information and figure 8 ; see also figures s23 and s24 
 in the supporting information ) , suggesting 
 that simulated annealing offers a more self - consistent basis for comparing 
 the dimers . as discussed above
, implicit - solvent simulations 
 of smdh2 can yield unphysical structures if no restraints 
 are imposed on dna to keep them in their native b - form conformation . 
 to see the effects of removal of restraints imposed on dna duplexes 
 in these cyclic dimers ,
the lowest sasa structures were simulated 
 for over 125 ns without restraints . as expected and similar to the 
 results shown in figure 6 , the dna duplexes 
 are distorted from the b - form conformation ( table s5 in the supporting information ) . in some cases , one of 
 the dna duplexes in these cyclic dimers
is fully unfolded ( see table 
 s5 in the supporting information , bp_17 
 [ 5-c-5]:[5-c-5] ) . furthermore , the % of 
 hydrogen bonds lost increased with the size of the duplex while the 
 sasa of the organic cores decreased suggesting that dna duplexes are 
 more flexible than they actually are ( table s5 in the supporting information ) . therefore , to study 
 these types of large dna - hybrid systems with the current implicit - solvent 
 models one is required to impose restraints on dna structures to keep 
 them in b - form conformation so that results have physical meaning .
sasa values 
 of the organic cores in smdh2 cyclic dimers 
 as a function of dna length .
the black , red , and green trends represent 
 the results for [ 3-c-3]:[3-c-3] , [ 5-c-3]:[5-c-3] , and [ 5-c-5]:[5-c-5] , 
 respectively , where the lowest sasa values for the organic cores were 
 extracted from simulated annealing md simulations with final restraint 
 energies and duplex rmsd values less than 10 kcal / mol and 10  , 
 respectively . as shown in figure 8 , there is a clear overall 
 trend , which shows that the dimers with organic cores linked at the 
 3-ends of the dna strands ( cyclic-[3-c-3]:[3-c-3] ) are much better at minimizing the sasas of their 
 organic cores than the other two dimer systems .
there is a higher 
 chance for the organic cores 3 to be inserted into the 
 minor grooves of the flanking dna duplex in cyclic-[3-c-3]:[3-c-3]. as a result , organic cores can lower 
 their sasas more significantly in these systems than would be possible 
 for the cores in the cyclic-[5-c-5]:[5-c-5] 
 systems , which prevent full minor groove insertion of organic cores . 
 for the [ 5-c-3]:[5-c-3] cyclic dimer , where the 
 organic cores are linked at both 5- and 3-ends of 
 the dna strands , the cores can be inserted into the minor groove only 
 if the dna orientations are favorable .
not surprisingly , the sasa 
 values for this system lie in the middle of the other two .
( for a 
 more detailed discussion of this system , please see section s8 in 
 the supporting information ) one interesting 
 result shown in figure 8 is the nonmonotonic 
 behavior observed around base pair lengths 11 
 and 21 .
this phenomenon could be due to the dna helical turn , which 
 is approximately 10 base pairs , suggesting a real connection to the 
 physical system .
the sasa of organic cores in the 11 base paired cyclic-[5-c-3]:[5-c-3] 
 system is lower than the cyclic-[3-c-3]:[3-c-3] 
 system . after adding 10 base pairs to the dna sequences , which results 
 in dna duplexes with 21 base pairs ,
a similar result was observed 
 ( figure s8 and table s24 in the supporting information ) . in cyclic-[5-c-3]:[5-c-3] 
 systems with 11 and 21 dna base pairs the organic cores almost fully 
 insert themselves into the dna minor grooves , which provides an explanation 
 for the nonmonotonic behavior observed in these dna sequences ( figure 
 s23 in the supporting information ) .
note 
 that no such behavior has been observed in cyclic-[5-c-5]:[5-c-5] 
 systems ( green curve in figure 8) .
the idea that the 
 hydrophobic organic cores 3 in smdh2 cyclic 
 dimers can be stabilized in aqueous solutions by inserting into the 
 minor groove can be used to explain the results that we reported above 
 for the slow - cooling experiments of 15 bp smdh2 systems 
 ( figure 2 ) . in that experiment ,
the percentage 
 of cyclic dimers formed in [ 3-c-3]:[3-c-3] 
 is 79% , much higher than those observed for [ 5-c-3]:[5-c-3] and [ 5-c-5]:[5-c-5] 
 ( 43 and 34% , respectively ; see figure 2 , lanes 
 3 , 6 , and 9 ) .
this trend closely follows the simulated 
 annealing md simulation results described in figure 8 : a higher proportion of dimers can form when the cores are 
 linked to both 3-ends of the dnas because the cores can be 
 better stabilized by inserting into the minor grooves of the two dna 
 arms . in other smdh2 systems where the cores are linked 
 to 5-ends of dnas , other higher - order structures are formed 
 because there is no predominant stabilization mechanism for the core 
 in the dimer structures . to further test the insights
obtained from our md calculations , 
 we designed an smdh system where one side of the cyclic dimer had 
 the organic core 3 and the other side had flexible linkers 
 such as t3-c - t3 and t6 ( table 2 , entries 810 ) . 

these systems would also allow us to assess the relative importance 
 of minimizing hydrophobicity versus strand - end alignment .
if strand - end 
 alignment is of primary importance , cyclic dimers would form predominantly 
 if one of the linkage sites is flexible ( i.e. , with t3-c - t3 or t6 linkers ) enough 
 to alleviate the strain resulting from the rigid core on the other 
 side . however , as shown in figure 9 , the nondenaturing 
 page - gel analyses for [ 5-c-3]:[5-t6 - 3] , [ 5-c-5]:[5-t6 - 5] , and [ 5-c-3]:[5-t3ct3 - 3] systems , 
 both normal and slow - annealing , all afforded a mixture of dimers , 
 tetramers , and hexamers . that all six experiments shown in figure 9 formed a mixture of products instead of only cyclic 
 dimers points to the importance of the organic core not having the 
 freedom to isolate its hydrophobic surface . moreover
, imagej analysis 
 of the gel image showed that [ 5-c-3]:[5-t6 - 3] gave higher percentages 
 of cyclic dimer ( 82% dimer , 14% tetramer , slow cooling , figure 9 , lanes 2 and 3 ) compared to [ 5-c-5]:[5-t6 - 5] 
 ( 62% dimer , 29% tetramer , slow cooling , figure 9 , lanes 4 and 5 ) , which is consistent with the 3-linkage 
 providing better shielding for the hydrophobic organic cores via minor - groove 
 insertion . in effect , the better that the organic cores insert into 
 the minor groove , the larger is the fraction of cyclic dimers formed . 

this argument is further supported by the results for [ 5-c-3]:[5-t3ct3 - 3] 
 ( figure 9 , lanes 6 and 7 ) , both of which show 
 higher cyclic dimer formation than [ 5-c-5]:[5-t6 - 5]. nondenaturing 
 page - gel image ( 6% ) of dna assemblies from an smdh 
 component possessing the organic core 3 and the complementary 
 smdh component possessing a flexible linker ( either t3-c - t3 or t6 ) with 5 m 
 total ss - dna concentration .
( gel was prepared in 1 tamg buffer 
 ( 40 mm tris base , 20 mm acetic acid , 7.5 mm mgcl26h2o ) , and run at 4 c for 2 h under a 200 v field ) . from 
 left to right : lane 1 = hl5 dna ladder , lane 2 = cyclic-[5-c-3]:[5-t6 - 3] 
 ( normal annealing ) , lane 3 = cyclic-[5-c-3]:[5-t6 - 3] ( slow annealing ) , 
 lane 4 = cyclic-[5-c-5]:[5-t6 - 5] ( normal annealing ) , lane 5 = cyclic-[5-c-5]:[5-t6 - 5] 
 ( slow annealing ) , lane 6 = cyclic-[5-c-3]:[5-t3ct3 - 3] ( normal 
 annealing ) , lane 7 = cyclic-[5-c-3]:[5-t3ct3 - 3] ( slow annealing ) .
the strong hydrophobic interactions 
 between cores can also be invoked 
 to explain the exclusive formation of ff dimers in the [ 3-c-3]:[5-c-5] and [ 3-c-3]:[5-t6 - 5] systems 
 ( table 2 , entries 11 and 12 ; see also figure 
 s18 in the supporting information , lanes 
 9 and 10 ) .
we attribute this behavior 
 to the combination of reduced configurational entropy and increased 
 ion - cloud sharing that occurs when the organic linkages bring the 
 dna duplexes into close proximity .
notably , the [ 3-c-3]:[5-c-5] 
 ff dimer has a much higher thermal stability , as illustrated by its 
 higher tm , compared to the cyclic-[5-t3 - 3]:[5-t3 - 3] dimer , whose t3 linker is comparable in size to the core c ( figure 10 ) .
indeed , the [ 3-c-3]:[5-c-5] 
 ff dimer is consistently more stable than all the cyclic dimers that 
 we examined ( tm = 52.453 c , 
 table 4 , cf entry 10 and entries 79 ) . 

however , when the linker for one side of the ff dimer was changed 
 to a flexible t6 ( [ 3-c-3]:[5-t6 - 5] ) , the tm was decreased by 4.7 c ( table 4 , cf entries 10 and 11 ) . melting profiles for 
 control ,
cyclic- , and ff - dimer smdh2 assemblies ( 5 m ) 
 in tamg buffer ( 40 mm tris base , 20 mm acetic 
 acid , 7.5 mm mgcl26h2o ) . for accurate 
 comparison to ff 
 dimers , only systems that afford cyclic dimers exclusively are listed . for details , see tables 1 and 2 .
the aforementioned results are consistent 
 with our previous work , indicating that 
 hydrophobic interactions between 
 the two organic cores ( and that between cores and the dna duplexes ) 
 can play a major role in determining the thermal properties of the 
 final hybridized systems .
thus , such hydrophobic interactions must 
 be taken into account in the consideration of product distributions 
 in the assembly of organic - linked dna materials .
we note that sleiman 
 and co - workers have also observed similar thermal stability enhancements 
 for ff dimers that are analogous to the one reported herein .
however , these tm increases were only attributed to allosteric and chelate cooperativities 
 of the dnas ; contributions by hydrophobic interactions were not discussed . 
 comparing to the cyclic dimers
, the increases in thermal stabilities 
 for our ff-[3-c-3]:[5-c-5] and ff-[3-c-3]:[5-t6 - 5] dimer systems can be attributed to two factors : 
 ( 1 ) hydrophobic interactions between the cores , and ( 2 ) effective 
 extension of the dna helix through the organic core / linkers , which was referred by sleiman and co - workers 
 as chelate cooperativity . the first effect 
 is strongly supported by fluorescent studies in similar ff diphenyl 
 acetylene- and 1,3,5-tris(p - ethynylphenyl)benzene - linked dimer systems .
the second factor has been ascribed by leumann and co - workers as 
 due to close structural communications between the two linked helical 
 domains . while chelate cooperativity 
 may be important , our thermal data clearly point to hydrophobic interactions 
 between the cores as a major effect .
in 
 summary , we have elucidated the effect of linking hydrophobic 
 organic cores to the 3- and 5- ends of the dna components 
 used in the assembly of smdh2 materials .
md simulations show that the organic cores of these building 
 blocks minimize their hydrophobic surfaces by choosing the best stacking 
 pattern possible when they self - assemble in aqueous media .
computational 
 results indicate a high correlation between the linkage type ( 3 
 or 5 ) and the final sasa of organic cores that can be attributed 
 to the extent that the cores can insert into the dna minor grooves 
 in the duplex arms of the resulting smdh2 . while 3-linked 
 organic cores can insert almost perfectly into the minor groove , 5-linked 
 cores can only insert partially , resulting in less - stable dimers ( i.e. , 
 with higher sasa ) .
these results can be used to explain why higher 
 percentages of cyclic dimers form in smdh2 materials with 
 3-linked organic cores in comparison to those with 5-linked 
 cores , as observed experimentally for a broad range of structures : 
 smdh2 materials with 5-linked cores are simply 
 less stable in aqueous media due to the inability of the hydrophobic 
 cores to insert completely into the minor groove .
inadequate shielding 
 of the hydrophobic cores then forces these systems to choose other 
 assembly patterns such as higher - order structures ( tetramer , hexamer , 
 etc . ) , as shown by nondenaturing page gel analysis .
notably , 
 the important role that hydrophobic organic cores play 
 in the assembly of smdh2 hybrids is strongly supported 
 by comparing the thermodynamic stability of several ff and cyclic 
 dimers : ff - dimer systems consistently have tm s that are several degrees higher than analogous cyclic 
 dimers , suggesting that hydrophobic interactions between the cores 
 as a major factor contributing to stability . together with the strong 
 interactions observed between 3-linked cores and the minor 
 groove in smdh2 , this result opens up the possibility of 
 controlling the product distribution in smdh assembly using the hydrophobic 
 nature of the organic cores in conjunction with the different linking 
 modes ( 3 and 5 ) to dna strands .
incorporating these 
 design parameters to the synthesis of small molecule - dna hybrids should 
 expand the range of future applications for dna - based hybrid materials .
 detailed 
 computational and experimental studies reveal the crucial 
 role that hydrophobic interactions play in the self - assembly of small 
 molecule - dna hybrids ( smdhs ) into cyclic nanostructures . in aqueous 
 environments , 
 the distribution of the cyclic structures ( dimers or 
 higher - order structures ) greatly depends on how well the hydrophobic 
 surfaces of the organic cores in these nanostructures are minimized . 
 specifically , 
 when the cores are attached to the 3-ends of 
 the dna component strands , they can insert into the minor groove of 
 the duplex that forms upon self - assembly , favoring the formation of 
 cyclic dimers . 
 however , when the cores are attached to the 5-ends 
 of the dna component strands , such insertion is hindered , leading 
 to the formation of higher - order cyclic structures . 
 these computational 
 insights are supported by experimental results that show clear differences 
 in product distributions and stabilities for a broad range of organic 
 core - linked dna hybrids with different linkage directions and flexibilities . 