In the format provided by the authors and unedited.
ProgrammabledisorderinrandomDNAtilings
Supplementaryinformation(partIofII)
GrigoryTikhomirov
1
†
,PhilipPetersen
2
†
andLuluQian
1
,
3
�
Contents
S1Materialsandmethods..........................................3
S1.1Samplepreparation...............................................3
S1.2AFMimaging..................................................3
S1.3SyntaxoftheprogramminglanguageforrandomDNAtilings
.......................4
S2SquareDNAorigamitiles
........................................6
S2.1Scaffoldpathdesign..............................................6
S2.2Single-strandeddomainlengthcalculation..................................7
S2.3Stapledesign..................................................10
S2.4Twotypesofbridgestaples..........................................11
S2.5Threetypesofedgestaples..........................................12
S2.6HighresolutionAFMimages.........................................15
S2.7Yieldcalculation................................................16
S3UnboundedarraysofsquareDNAorigamitiles
...........................17
S3.1Usingstackingbondsonly...........................................17
S3.2Usingstackingbondsandstickyends.....................................19
S3.3Theformationoftubesvs.crystalarrays..................................20
S3.4Meltingtemperaturemeasurement......................................28
S3.5Crystalarraysizedependenceontheannealingtime............................29
S4RandomlooppatternsonunboundedDNAorigamiarrays
....................30
S4.1Patternstapledesign..............................................30
S4.2Fourtypesofsurfacemodifications......................................31
S4.3AFMimagecoloring..............................................32
S4.4Unboundedarraysofarctiles.........................................33
S4.5Analysisofarcpatternorientations......................................34
S4.6Unboundedarraysofarctileswithextendededges.............................35
S5Programmingthetile..........................................36
S5.1Designofrandommazepatterns.......................................36
S5.2UnboundedarraysofTtiles..........................................37
S5.3Analysisofarcloopsandmazesina10by10tilearea...........................40
S5.4AnalysisofTmazesina10by10tilearea.................................41
S5.5Exampleofmorecomplexpatterndesigns..................................42
S6Programmingthegrid..........................................43
S6.1Designofrandomtreepatterns........................................43
S6.2UnboundedarraysofT90tilesonafour-orientationgrid..........................44
S6.3UnboundedarraysofT180tilesonafour-orientationgrid.........................45
S6.4AnalysisofT90andT180treesina10by10tilearea...........................46
1
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S7Programmingtherandomchoice...................................47
S7.1Designofrandomloops,mazesandtreeswithtunablesizedistributions.................47
S7.2Designofrandomloopswithtunablenumberofcrossings.........................48
S7.3UnboundedarraysofT90tileswith
p
=0and1
/
3.............................49
S7.4AnalysisofT90treesina10by10tilearea.................................50
S7.5Unboundedarraysofarcandcrosstileswith
p
=0,1
/
3and1
/
2.....................51
S7.6Analysisofloopswithcrossingsina10by10tilearea...........................52
S8Programmingafinitegrid........................................53
S8.1Finitearraydesign...............................................53
S8.2Edgedesign...................................................56
S8.3Finitearraysofthefullyconnecteddesign..................................58
S8.4Finitearraysofthecombdesign.......................................61
S8.5Yieldcalculation................................................64
S8.6Randomloopsandmazesonafinitegrid..................................71
S8.7Examplefinitegridwithamorecomplexshape...............................73
S9Potentialapplications..........................................74
S9.1Operatingandtestingenvironmentformolecularrobots..........................74
S9.2Exampledesignofcombinatorialcircuits...................................75
S9.3Randommolecularelectronics,plasmonicsandphotonics..........................76
References....................................................77
2
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S1Materialsandmethods
S1.1Samplepreparation
Single-strandedM13mp18DNA(scaffoldstrand)waspurchasedfromBayouBiolabs(Catalog#P-107)at1g/Lin
1
×
TEbuffer(10mMTris-HCl,1mMEDTA,pH8.0).Theconcentrationofscaffoldstrandwascalculatedbased
onDNAUVabsorbancemeasurementat260nmusingNanoDrop2000(ThermoScientific).Staplestrandswere
purchasedunpurifiedfromIntegratedDNATechnologiesin1
×
TEbuffer(pH8.0)at100
μ
Meach.
IndividualDNAorigamitilesforcreatingunboundedarrayswerepreparedwith50nMscaffoldstrandand75nM
staplestrandsin1
×
TE/Mg
2+
(1
×
TEbuffercontaining12.5mMmagnesiumacetate).IndividualDNAorigami
tilesforcreatingfinitearrayswithdesignedsizewerepreparedwith10nMscaffoldstrandand75nMstaplesin
1
×
TE/Mg
2+
buffer.Inbothprotocolsthescaffoldandstaplemixtureswerekeptat90
◦
Cfor2minutesand
annealedfrom90to20
◦
Cat6sec/0
.
1
◦
C.
Unboundedarrayswereconstructedusing1)anovernightannealfrom40to30
◦
Cat5min/0
.
1
◦
Candthenfrom
30to20
◦
Cat10sec/0
.
1
◦
C(examplesincludethearraysshowninFigs.2to5),2)atwo-dayannealfrom40to
30
◦
Cat25min/0
.
1
◦
Candthenfrom30to20
◦
Cat10sec/0
.
1
◦
C(examplesincludethearrayshowninFig.S19),
or3)aone-weekannealfrom40to30
◦
Cat60min/0
.
1
◦
Candthenfrom30to20
◦
Cat30min/0
.
1
◦
C(examples
includethearraysshowninFigs.S20andS21).
Priortomixingdifferenttypesoftilesforcreatingfinitearrayswithdesignedsize,a10-foldexcess(relativeto
theconcentrationofstaplestrands)ofafullsetof44negationstrands(sequenceslistedinTableS6)wereaddedto
eachtypeofDNAorigamitilesandquicklycooleddownfrom50to20
◦
Cat2sec/0
.
1
◦
C.Differenttypesoftiles
werethenmixedtogetherandannealedfrom50to20
◦
Cat2min/0
.
1
◦
C.
S1.2AFMimaging
SamplesforAFMimagingofunboundedarrayswerepreparedbydilutingorigamito5nM(monomerconcentration)
in1
×
TE/Mg
2+
buffer.Afterdilution,40
μ
Lofsamplewasdepositedontofreshly-cleavedmica(SPISupplies,
9.5mmdiameter,LOT#1170203).After30secondsthesolutionwasremovedbysuckingupalltheliquidthat
comesoffinasinglethumb-upmovementwhilekeepingthepipetteattachedtoandalmostperpendiculartothe
micasurface.Afterthat,80
μ
Lof1
×
TE/Mg
2+
bufferwasaddedontothemicaandthesamplewasimaged.
SamplesforAFMimagingofindividualDNAorigamitilesandfinitearrayswithdesignedsizewerepreparedby
dilutingorigamito1nM(singletileortargetfiniteshapeconcentration)in1
×
TE/Mg
2+
buffer.Thefollowingsteps
werethesameasforunboundedarrays,exceptafterremovingthesolution,themicasurfacewaswashedthreetimes
with40
μ
LTEbuffercontaining10mMMgCl
2
and10mMNaCl,byperforming10down-and-upthumbmovements
foreachwash.Comparedtounboundedarrays,thefinitearrayshadamuchlargerexcessofshortstrands(including
a5timeshigherratioofstaplestoscaffoldandanadditionofnegationsstrandsat10timestheconcentrationof
staples),andthusthewashingstepwasusedtoremovetheshortstrandsandprovideacleanerbackgroundfor
imaging.
AFMimagesweretakenintappingmodeinfluidonaDimensionFastScanBio(Bruker)usingFastScan-Dtips
(Bruker).Typicalscanningparameterswere:scanrate=5Hz,lines=512,amplitudesetpoint=30-50mV,drive
amplitude=180-240mV,drivefrequency=110Hz,integralgain=1,proportionalgain=2.
3
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S1.3SyntaxoftheprogramminglanguageforrandomDNAtilings
•
Definingpatternsonatile:
tile
=
Connect
[((
x
1
,y
1
)
,
(
x
2
,y
2
))@(
cx
1
,cy
1
)
,...
]
(
x
i
,y
i
)definesthestartandendpointsofaline.
(
cx
i
,cy
i
)definesthecenterofanarc.
When@ismissing,thepointsareconnectedbyastraightline.
•
Definingagrid:
grid
[(
i,j
)
,tile
]=[
If
cond
1
(
i,j
)
,tile
@
orient
1
;
...
]
(
i,j
)indicatesalocationonthegrid.
cond
i
definesasetofspecificlocationsonthegrid,asafunctionof(
i,j
).
orient
i
definestheorientationofatileat
cond
i
onthegrid.
Thedefaultgridis
grid
[(
i,j
)
,tile
]=[
tile
@0degree],whichhasthesameorientationoftilesatalllocations.
tile
canbereplacedbyasetoftiles
tile
[1
,
2
,...,n
]
,inwhichcaseeach
cond
i
willbeassociatedwitha
subsetoftiles
tile
[
t
1
,t
2
,...
]
,
t
i
∈{
1
,
2
,...,n
}
.
•
Definingarandomchoiceoftileorientations:
tile
@
RandomChoice
[(
p
1
,p
2
,...
)
→
(
orient
1
,orient
2
,...
)]
(
∑
p
i
=1)
orient
i
definesanorientationofthetile.
p
i
istheprobabilityof
orient
i
.
Thedefaultprobabilityis1
/n
,where
n
isthetotalnumberofchoices.
•
Definingarandomchoiceoftiletypes:
RandomChoice
[(
p
1
,p
2
,...
)
→
(
tile
1
@
orient
1
,tile
2
@
orient
2
,...
)]
(
∑
p
i
=1)
orient
i
definesanorientationof
tile
i
.
p
i
istheprobabilityof
tile
i
@
orient
i
.
Thedefaultprobabilityis1
/n
,where
n
isthetotalnumberofchoices.
Thedefaultorientationis0degree.
•
Definingarandomarray:
array
=
tile
@
RandomChoice
@
grid
4
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DNA sequences
T_tile= Connect[((0, 1/2), (1, 1/2)), ((1/2, 1/2), (1/2, 0))];
FourOrientGrid[(i,j),tile]=[
If Odd(i) and Odd(j), tile @ 0 degree;
If Odd(i) and Even(j), tile @ 90 degree;
If Even(i) and Even(j), tile @ 180 degree;
If Even(i) and Odd(j), tile @ 270 degree];
T90_trees = T_tile@ RandomChoice[(0, 90) degree] @ FourOrientGrid
High-level description
Abstract array and numerical simulation
Number of random arrays
Largest tree size
DNA origami tile design
AFM images
Bri
-T1R02C5
GATACATTTCGCTTTTTTGACCCTGTAAT
Bri
-T1R04C4
AATATAATGCTGTATTTTTTTGTGAGAAAGGCCGG
Bri
-T1R07C2
TGGATAGCAAGCCCGA
TTTTTAATCGTAAAC
GCCAT
Bri
-T1R08C2
AGTTTT
GCCAGAGGGGGTTTTGCCTTCCTGTAGCCAGCT
Bri
-T1R12C1
AGGACAGATGATTTTTTCACCAGTAGC
Bri
-T1R14C2
TGCCACTAC
TTTTTTT
GCCACCCTC
Bri
-T1R15C3
GCTGAGGAATGACAACAACCATTTTTTCATACAT
GGCTTTTAAGCGCA
ڮ
ڮ
FigureS1:
AutomateddesignstepsforrandomDNAorigamiarrays.
5
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S2SquareDNAorigamitiles
S2.1Scaffoldpathdesign
WeproposedseveraldesignprinciplesforaDNAorigamishapethatcouldbeusedtoimplementTruchettiles:First,
theorigamitilesshouldbesymmetriconallfoursideswhenrotatedinthetwo-dimensionalplaneofthetile,such
thatitcanadoptanunbiasedchoiceofanyofthefourorientationswhenself-assembledintoanarray.Second,the
continuoussurfaceareaoftheorigamitileshouldbemaximized,suchthatawiderangeofTruchetpatternscanbe
createdwithoutleavingoutmanypixels(apixelreferstothe5’or3’endofeachstaple,becauseitiscommonlyused
asanattachmentsiteforothermolecules).Third,thestaplesneartheedgesofthesquareshapecanbemodifiedto
obtainweaktile-tileinteractionsusingstackingbonds
1,2
orshortstickyends,suchthatwhenthetilesarebinding
toeachother,sufficientreversibilitycanbeprovidedandkinetictrapsfromspuriousinteractionscanbeavoided.
Lastly,theorigamitileshouldbeasflatandrigidaspossible,suchthatwhenthetilesinteractwitheachother,they
donothaveapreferredthree-dimensionalconfigurationandtheformationoflargetwo-dimensionalarrayswillbe
encouraged.
Weconsideredthreeoptionsforascaffoldpaththatisrotationallysymmetric(Fig.S2),andchosetheonewith
themostcontinuoussurfacearea(Fig.S2c).
a
b
c
FigureS2:
ThreedesignsofscaffoldfoldingpathsforasquareDNAorigamitilethatissymmetricand
allowsstackingbondsonallfoursides.a,
Ascaffoldpaththatfillsinfourisoscelesrighttrianglessequentially,
withscaffoldcrossoversattheendofeachhelixrowbothneartheinterioredgesandexterioredgesofthetriangles.
Thelengthofeachhelixrowisanintegernumberofturnsplushalfaturn.Thedisadvantageofthisdesignisthe
smallholesnearthediagonals,whichresultindiscontinuoussurfaceareaandmayleadtoinsufficientrigidityof
theorigamitile.
b,
Ascaffoldpaththatfillsinfoursquare-shapedquadrantsequentially.Thedisadvantageofthis
designisthelongscaffoldloopsconnectingtheadjacentcornersofthesquare,whichmayinterferewithinteractions
betweentiles.
c,
Ascaffoldpaththatfillsinfourisoscelesrighttrianglessequentially,withscaffoldcrossoversat
theendofeachhelixrowneartheexterioredgesofthetriangles,andshortsingle-strandedscaffoldloopsnearthe
interioredges.Thisdesignallowsanarbitrarynumberofbasepairsineachhelixrowandthuscontinuoussurface
areaoftheorigamitile.
6
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S2.2Single-strandeddomainlengthcalculation
ClassicDNAorigamidesignsrequireeachrowofhelixtoconsistofanintegernumberofblocks,andeachblockisa
helixturnwith10to11basepairs.
3
Incontrast,ourscaffoldpathallowsanarbitrarynumberofbasepairsineach
helixrowbyintroducingshortsingle-strandedscaffoldloopsatthelocationswherethescaffoldmakesaturnfrom
onehelixtoanother.Thisapproachmakesitpossibleforthefourisoscelestrianglestobecloselycomposedtogether
inthesquareshape.
Theuseofsingle-strandeddomainsinscaffoldloopsandalsoinstaplesbridgingbetweenthetrianglesrequires
carefuldesignoftheDNAorigami:thesamedistanceinthetwo-dimensionalplaneofthesquareorigamitilecould
correspondtosingle-strandedlengthsthatdifferbyseveralbases.Iftheselengthsarenotproperlychosen,itwould
straintheDNAatsomelocationsandresultinundesiredtwistoftheorigami.Toresolvethischallenge,wedeveloped
athree-dimensionalmodel,atthelevelofeachbasepair,forcalculatingthelengthsofsingle-strandeddomainsin
staplebridgesandscaffoldloops.Coordinatelocationsofwhereeachbasejoinsthebackbonewerecalculatedand
theEuclideandistancesbetweenallpairsofcoordinatelocationsinstaplebridgesandscaffoldloopswereusedto
determinethelengthsofsingle-strandeddomains,assuming0.4nmforeachnucleotideinarelaxedsinglestrand.
Whencalculatingthelengthsofsingle-strandeddomainsinstaplebridges,weadjustedthedistancebetweenthe
centerofthesquaretothecentralvertexofeachisoscelestriangletomakesurethatthefourtriangleswereclosely
composedtogether,butnottooclosetoallowoverlapofanybasepairsintheadjacenttriangles.Takingasideview
fromacornerofthesquaretoitsoppositecorner,lookingatthesingle-strandedbridgesalongthediagonal,the
three-dimensionalmodelalsohelpedustoidentifythatthestaplebridgeshadroughlybalancedorientationswithin
the2nmheightofthedoublehelicesandtheadjacenttrianglesshouldbewellalignedwithinthetwo-dimensional
planeofthesquare.
Wefirstcalculatedthetotalnumberofrowsineachofthefourisoscelesrighttrianglescomposingthesquare,
andthenumberofbasepairsineachrowofthedoublehelix.Thenwecalculatedthecoordinatelocationsofwhere
eachbasejoinsthebackbone,withthecenterofthesquarebeing(0
,
0
,
0).Weassumedthatthelengthofeachbase
pairinadoublehelixis0.34nmandtheheightis2nm.Weused1.5turnsstandardspacingofstaplecrossovers,
whichresultedina1nmgapbetweentwoadjacenthelices.Wedeleted1basepairineverythreecolumnsofstaples
toapplytwistcorrectiontotheorigami,whichresultedin10.44bpperhelixturnthus360
◦
/
10
.
44anglebetween
adjacentbasesonthesamestrand.Ineachtwo-dimensionalplaneofabasepair,weassumed150degreefrom
thecenterofthehelixaxistothetwolocationswherethescaffoldandstaplebasesjointhebackbone.Lastly,we
calculatedtheEuclideandistancesbetweenallpairsofcoordinatelocationsofwhereeachbasejoinsthebackbone
instaplesconnectingtwosidesoftheseamsandinscaffoldconnectingtwoadjacenthelixrows(Fig.S3).
Step1:Calculatethenumberofbasepairsineachrowofdoublehelix
•
Thelengthoftheshortestrowofdoublehelix:
I
1
=11
.
3nm
•
Thetotalnumberofrowswithincreasinglengthineachofthefourisoscelesrighttrianglescomposingthe
square:
R
=11
•
Thenumberofbasepairsinthe
i
throwofdoublehelix:
A
i
=
I
1
+(1+2)nm
×
(
i
−
1)
0
.
34nm/bp
,
1
≤
i
≤
R
A
i
=
A
2
R
+1
−
i
,R
+1
≤
i
≤
2
R
Step2:Calculatethelocationsofwhereeachbasejoinsthebackbone
•
Thedistancebetweenthecenterofthesquaretothecentralvertexofeachofthefourtriangles:
G
=1
.
42nm.
(Thisadjustableparametermakesthefourtrianglesfittighterorlooser.)
•
Thelengthofthesideofthesquare:
W
=2
×
(
I
1
+
G
)+(1+2)nm
×
(2
R
−
1)
•
Thecoordinatelocationofthe
center
ofthesquareis(0
,
0
,
0).
7
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staple bridge
scaffold loop
ܫ
ଵ
ܴʹ
helices
ܩ
ܹ
ݔ
ݖ
ݕ
FigureS3:
Athree-dimensionalmodelforcalculatingthelengthsofsingle-strandeddomainsinstaple
bridgesandscaffoldloops.
•
Thecoordinatelocationofthe
helixaxis
inthetwo-dimensionalplaneofthe
j
thbasepairinthe
i
throwin
thefirsttriangle:
C
1
,i,j
=(
cx,cy,cz
)
cx
=
−
W
2
+(
I
1
+
G
)+(1+2)nm
×
(
i
−
1)
cy
=0
cz
=
−
W
2
+0
.
34nm/bp
×
j
•
Thecoordinatelocationofwherethe
scaffoldbase
joinsthebackboneinthetwo-dimensionalplaneofthe
j
thbasepairinthe
i
throwinthefirsttriangle:
SC
1
,i,j
=(1
,θ
1
,i,j
,
0)transformfromCylindricaltoCartesiancoordinate+
C
1
,i,j
θ
1
,i,j
=0
◦
+(
j
−
1)
×
360
◦
10
.
44bp/turn
,
if
i
isodd
θ
1
,i,j
=180
◦
+(
j
−
1)
×
360
◦
10
.
44bp/turn
,
if
i
iseven
8
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•
Thecoordinatelocationofwherethe
staplebase
joinsthebackboneinthetwo-dimensionalplaneofthe
j
th
basepairinthe
i
throwinthefirsttriangle:
ST
1
,i,j
=(1
,θ
1
,i,j
,
0)transformfromCylindricaltoCartesiancoordinate+
C
1
,i,j
θ
1
,i,j
=(0
−
150)
◦
+(
j
−
1)
×
360
◦
10
.
44bp/turn
,
if
i
isodd
θ
1
,i,j
=(180+150)
◦
+(
j
−
1)
×
360
◦
10
.
44bp/turn
,
if
i
iseven
•
Intheotherthreetriangles,eachcoordinatelocation
C
k,i,j
,SC
k,i,j
and
ST
k,i,j
,where
k
=2,3and4,isin
format(
x,y,z
)withthefollowingcalculations:
(
x
k,i,j
,z
k,i,j
)=(
x
k
−
1
,i,j
,z
k
−
1
,i,j
)rotate90
◦
y
k,i,j
=
y
k
−
1
,i,j
Step3:Calculatethelengthsofsingle-strandeddomainsinstaplebridgesandinscaffoldloops
•
Thelengthofthe
i
thstaplebridge,innucleotides,is
Euclideandistancebetween
ST
2
,i,A
i
and
ST
1
,
2
R
+1
−
i,A
i
0
.
4nm/nt
−
1
Staplebridges=
{
7,5,4,7,6,4,7,3,5,8
}
nt
•
Thelengthofthescaffoldloopbetweenthe
i
thand(
i
+1)throwofhelix,innucleotides,is
Euclideandistancebetween
SC
1
,i,A
i
and
SC
1
,i
+1
,A
i
+1
0
.
4nm/nt
−
1
,i
iseven
Scaffoldloops=
{
12,8,11,13,8,8,13,11,8,12
}
nt
Note:anearlierversionofthe3Dmodeldidnottaketwistcorrectionintoconsideration,andgaveusslightly
differentnumbersforthescaffoldloops:
Scaffoldloops=
{
11,8,13,10,8,8,10,13,8,11
}
nt
Aftercomparingthetwosetsofnumbers,wedecidedthatthedifferencewassmallenoughthatwewere
comfortableusingthenon-optimalnumberstoavoidthecostforre-orderingallstaplestrands.
•
Thelengthofthescaffoldbridgebetweenthetwoadjacenttriangles,innucleotides,is
Euclideandistancebetween
SC
2
,
1
,A
1
and
SC
1
,
2
R,A
2
R
0
.
4nm/nt
−
1
Scaffoldbridge=8nt
Thescaffoldbridgeswereadjustedto
{
10,10,10,11
}
ntsuchthatthefulllengthofM13scaffold(7,249nt)
wasused.
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S2.3Stapledesign
Itisknownthatthechoiceofdouble-strandeddomainlengthsinstaplesorothershortstrandbuildingblockscould
affecttheyieldandstabilityofDNAnanostructures.
4,5
Weexploredtwodesignsofbridgestaples(coloredingreen
intheCadnano
6
diagramsshowninFig.S4).Onedesignthatwereferredtoasthe“strong-weak”bridgedesign
usedlongerdomainsononesideoftheseamsandshorterdomainsontheother.Themotivationforthisdesignwas
toreducethepossibilitythatscaffoldloopsandstaplebridgesgettangledandgeometricallytrappedinanundesired
conformationduringtheprocessofself-assembly.Butthecostofthisdesignwasthattheconnectionbetweenthe
adjacenttrianglescouldbeweak,andweobservedthatsomelocationsalongtheseamswererippedopenduring
imaging(Fig.S5).Theotherdesignthatwereferredtoasthe“strong-strong”bridgedesignusedsufficientlylong
domainsonbothsidesoftheseams,suchthatthefourtriangleswerebroughttogetherwithastrongerconnection.
Ourresultswiththeseconddesignsuggestedthatscaffoldloopsandstaplebridgeswereabletoformwithout
interferingwitheachother,evenwhenthebindingofbridgestaplesonbothsidesoftheseamsoccurredatsimilar
temperatureduringanneal(Fig.S6).The“strong-strong”bridgestapledesignwasthenusedinallDNAorigami
tiles.
Edgestaples(coloredinbrowninFig.S4)weredesignedwithnostaplecrossoversattheendofeachhelixrow,
allowingrelaxededgesinwhichbluntendsarefreetoadoptnormalgrooveanglesandstackinginteractionsbetween
tilesareencouraged.
1
Incontrast,iftheedgestaplesaredesignedwithstaplecrossovers,thescaffoldandstaple
crossoverswillpullthephosphates180
◦
awayfromeachotherinthebluntendsandresultinweakenedstacking
interactions.
Interiorstaples(coloredinpurpleinFig.S4)weredesignedwiththelocationsof3’and5’endsfollowinga
hexagonalgridnearthesamesurfaceofthesquaretile,allowingtheselocationstobeusedasattachmentsitesfor
othermolecules,orasextensionsitesforcreatingsurfacemodificationssuchasdouble-strandedstapleextensions.
Notethattheinteriorstaplesadjacenttothebridgestaplesmaynotsatisfythiscriterion.Twistcorrectionwas
appliedbydeleting1basepair(indicatedasredcrossesinFig.S4)ineverythreecolumnsofstaples.
1,7
ab
FigureS4:
TwodesignsofbridgestaplesforasquareDNAorigamitile.a,
A“strong-weak”bridgedesign
thatuseslongerdomainsononesideoftheseamsbetweenadjacenttrianglesandshorterdomainsontheother.In
eachofthebridgestaples,thestrongersidehastwodomainsconnectedbyastaplecrossover.Eitheroneofthemis
longerthan12nucleotides,orbothofthemare7nucleotidesorlonger.Theweakersidehasasingledomainof6
to8nucleotides.
b,
A“strong-strong”bridgedesignthatusessufficientlylongdomainsonbothsidesoftheseams
betweenadjacenttriangles.
10
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S2.4Twotypesofbridgestaples
ab
500 nm
500 nm
FigureS5:
SquareDNAorigamitileswith“strong-weak”bridgestaples.a,
Tileswithnoedgestaples.
TheseamswereeasilyrippedopenduringAFMimaging.
b,
Tileswithafullsetofedgestapleseachcappedwith
twohairpins.Thetilesweremoreintactcomparedtothosewithoutedgestaples.
500 nm
500 nm
ab
FigureS6:
SquareDNAorigamitileswith“strong-strong”bridgestaples.a,
Tileswithnoedgestaples.
TheseamsmostlyremainedclosedduringAFMimaging.
b,
Tileswithafullsetofedgestapleseachcappedwith
twohairpins.Thetileswerefullyintact.
11
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S2.5Threetypesofedgestaples
Toverifytheformationofsquareorigamitilesasmonomers,wemodifiedtheedgestaplestominimizetheinteractions
betweentiles.Weexploredfouroptions:removingalledgestaples(Fig.S6a),usingtruncatededgestaples(Fig.S7),
creatingcodededges(Fig.S8),andcappingtheedgestapleswithhairpins(Fig.S9).Thelastdesignworkedthe
bestintermsofpreservingtheintegrityofthesquareshapeandeffectivelyreducingthetile-tileinteractions.The
cappingmechanismwasalsousedforcreatinginertedgesneartheexterioroffinitearrayswithdesignedsize,sothat
thefinitearrayswereprotectedfromaggregatingintolargerstructures.
abc
-2 nt
-4 nt
-6 nt
1 μm
100 nm
1 μm
100 nm
1 μm
100 nm
ڮ
ڮ
ڮ
FigureS7:
SquareDNAorigamitileswithtruncatededgestaples.
Abstracttilediagrams,edgedesigns,and
AFMimagesoftileswith
a,
2-nucleotide,
b,
4-nucleotide,and
c,
6-nucleotidetruncationsatboth3’and5’ends
ofeachedgestaple.Tileswithedgestaplestruncatedinallthreelengthswerestillabletobindtoeachotherand
aggregateintolargerstructures,presumablybecausetheshortsingle-strandedscaffoldloopscanmoveoutofthe
wayandtheremainingbluntendsofdoubleheliceswerestillabletoformstackingbonds.
12
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a
-4 nt
code 1
code 2
500 nm
100 nm
b
500 nm
100 nm
FigureS8:
SquareDNAorigamitileswithcodededges.
Abstracttilediagrams,edgedesigns,andAFM
imagesoftileswith
a,
code1(42462626424)and
b,
code2(
4
2
6
2
4
).Numbersindicatethelengthsofnucleotide
truncationsintheedgestaples.Underscoresindicateedgestaplesthatwereremoved.Tilesmostlyremainedas
monomerswithbothcodes.Tileswithcode1hadsignificantdeformationofthesquareshape,presumablybecause
theshortsingle-strandedscaffoldloopsnearaparticularedgehadsignificantspuriousinteractionswitheachother
andpulledthatedgetighterthanothers.Tileswithcode2hadlessdeformation,butsomemonomerswerestillable
tobindtoeachotherandformsmallgroupsof2to5tiles.
13
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DOI: 10.1038/NNANO.2016.256