Developmental self-assembly of a DNA ring
with stimulus-responsive size and growth direction
Allison T. Glynn
1
†
, Samuel R. Davidson
1
†
and Lulu Qian
1
,
2
?
1
Bioengineering and
2
Computer Science
California Institute of Technology, Pasadena, CA 91125, USA
†
Equal contribution,
?
e-mail: luluqian@caltech.edu
Supporting information
S1 Methods
S1.1 Sequence design
As shown in Figure S3, each hairpin consists of two exposed 7-nt toeholds, a conserved 6-nt branch migration domain
(x), a sequestered 7-nt toehold, and a 4-nt loop domain (s = TTTT). For implementation of a DNA ring with 4, 6, or
8 strands, nine unique toeholds (a through i) were needed in seven hairpins. Sequences of domains a, x, and b were
predetermined so as to utilize a previously designed reporter complex
1,2
for fluorescence readout. The remaining
seven toeholds (c through i) were designed using the multi-state concentration-based design tool in NUPACK.
3
A
three-letter code (A, T and C only)
4,5
was utilized for all asterisk domains (a
∗
, b
∗
, etc.), which reduces undesired
secondary structures in the single-stranded domains functioning as an input to open up a hairpin (e.g. c x b in
hairpin2 for reacting with hairpin1, c x d in hairpin3 for reacting with haripin2, etc.). However, this strategy does
not address spurious interactions between the two exposed toeholds in a hairpin, as they have opposite three-letter
codes (e.g. A, T, C for toehold c
∗
and A, T, G for toehold a in hairpin1). Thus, it was important that target hairpin
structures were specified in NUPACK. Moreover, to achieve roughly the same forward and backward reaction rates
of each reversible assembly step in the ring formation, we set the target concentrations of each hairpin at opened and
closed states both to be 50 nM. An example NUPACK script and preview for designing toehold c are shown below:
#
# design material, temperature (C), and trials
#
material = DNA
temperature = 25.0
trials = 5
#
# target structures
#
structure hairpin1 = U7 D13 U4 U7
structure input1 = U20
structure hairpin1input1 = U24 D20 +
#
# sequence domains
#
domain a = TGAGATG
domain x = TGATTG
domain b = TGTTATG
domain s = T4
domain c = D7
#
# strands
#
strand hairpin = a x b s b* x* c*
strand input = c x b
S1
#
# thread strands onto target structures
#
hairpin1.seq = hairpin
input1.seq = input
hairpin1input1.seq = hairpin input
#
# target test tubes
#
tube HItube = hairpin1 input1 hairpin1input1
#
# target concentrations for target structures in test tubes
#
HItube.hairpin1.conc[nM] = 50
HItube.input1.conc[nM] = 50
HItube.hairpin1input1.conc[nM] = 50
#
# design against all off-target ordered complexes of up to this
# number of strands (design against monomers, dimers, and trimers)
#
HItube.maxsize = 3
#
# stop conditions for normalized ensemble defect
#
HItube.stop[%] = 2.0
c
x
b
x
x*
b
b*
a
c*
s
b*
b
x*
x
c*
c
a
x
b
s
A
C
G
T
hairpin1
input1
hairpin1input1
Figure S1: NUPACK preview for designing the sequence of toehold c.
Toeholds c to i were designed sequentially, and every new toehold sequence was selected by comparing it to the
existing toeholds and ensuring that no pairs of toeholds share more than three continuous nucleotides. Once all
toehold sequences were obtained, hairpin structures at closed and opened states were analyzed with the NUPACK
analysis tool
6
(Figure S2). Linear structures involved in the designed self-assembly pathways were also analyzed to
verify that intermediate products are expected to assemble correctly and that no significant spurious interactions are
predicted among system components.
S2
1 uM
100 nM
hairpin1
+ input1
0.84
uM
58 nM
hairpin2
+ input2
0.81
uM
52 nM
hairpin3
+ input3
0.80
uM
51 nM
hairpin4
+ input4
0.81
uM
51 nM
hairpin5
+ input5
0.80
uM
50 nM
hairpin6
+ input6
0.76
uM
43 nM
hairpin7
+ input7
0.79
uM
49 nM
Average equilibrium constant (
푲푲
풄풄
)
4
1
a
b
c
hairpin1
hairpin2
hairpin3
hairpin4
hairpin5
hairpin6
hairpin7
hairpin1+input1
hairpin2+input2
hairpin3+input3
hairpin4+input4
hairpin5+input5
hairpin6+input6
hairpin7+input7
Figure S2: NUPACK analysis of hairpin structures and equilibrium conditions. (a) Equilibrium concentration of
each hairpin:input complex with 1
μ
M or 100 nM of each strand. (b) Minimum free energy (MFE) structure of each
hairpin at 25
◦
C. (c) Minimum free energy (MFE) structure of each hairpin:input complex at 25
◦
C.
S3
Sequences of the key complexes were simply obtained by composing the domain sequences together. For under-
standing the kinetics of ring formation, an additional 7-nt toehold (t) was designed and used in hairpin1 and keys
(Figure S3).
For realizing the reporting mechanism shown in Figure 5b, the fluorophore and quencher-labeled strands were di-
rectly taken from a previously developed reporter.
1,2
A cover strand partially complementary to the quencher-labeled
strand was designed to facilitate the reporting reaction, which is initiated by a 5-nt effective toehold consisting of a
2-nt single-stranded domain in the partially exposed b
∗
domain together with the fluorophore-quencher interaction
which was experimentally measured to be equivalent to approximately 3 nucleotides. All DNA sequences of strands
for creating a ring and detecting the ring formation are listed in Table S1.
Eleven non-hairpin strands used in formation gel controls were designed with random domain sequences satisfying
the three-letter code (Table S2). Each strand consists of four unique 7-nt domains, two unique 6-nt domains, and a
4-nt TTTT domain equivalent to the toeholds, branch migration domains, and loop domain in the hairpins. Strands 1
through 3, together with strand4-linear and key4-F were designed to form a 5-stranded linear structure similar to
that shown in Figure 3, but the single-stranded part of the structure does not have the same sequence as key4-F and
thus cannot displace it. Strands 1 through 3, together with strand4-ring were designed to form a 4-stranded ring
structure similar to that shown in Figure 3, but all double-stranded domains have unique sequences so that the only
product that should form after annealing is a ring. Similarly, strands 5 through 8 were designed as controls for the
6 and 8-stranded ring formation.
Three trigger strands used in control experiments for fluorescence data normalization (Figure S8a) were designed
by taking the existing domain sequences and shortening them to create an 8-nt toehold for releasing the key-F strand
in each of the three key complexes (Table S3).
S1.2 Sample preparation
DNA oligonucleotide synthesis.
Custom single-stranded DNA oligos were manufactured by Integrated DNA
Technologies (IDT). Strands modified with a fluorescent dye or dark quencher were delivered HPLC-purified while
unmodified strands were delivered with standard desalting only. With formulation service LabReady, all strands were
provided at approximately 100
μ
M in IDTE, i.e., IDT-brand Tris-EDTA (TE) buffer (10 mM Tris, 0.1 mM EDTA,
pH 8.0). Before use, concentration of each strand was confirmed on a NanoDrop (Thermo Fisher) by averaging three
measurements of absorbance at 260 nm for a 1
μ
L droplet. All strands were stored at 4
◦
C.
Annealing protocol and buffer condition.
TE buffer with 10
×
MgCl
2
was added to mixtures of strands intended
to form double-stranded complexes or individual strands intended to form hairpins to produce samples that are ready
for annealing in a final buffer of TE with 12.5 mM MgCl
2
. The two strands in the keys and the reporter were mixed
at an equimolar ratio and annealed at 10
μ
M. The linear and circular control strands were mixed at equimolar ratios
and annealed at 3.5
μ
M. Each hairpin strand was annealed at 90
μ
M. Reaction mixtures were all held at 90
◦
C for
2 minutes, then ramped down to 20
◦
C by 0.1
◦
C per 6 seconds on a thermal cycler (Eppendorf).
Purification.
Polyacrylamide gel electrophoresis (PAGE) was used to purify annealed hairpins on a 12% gel made
with, and run in, TAE buffer with 12.5 mM magnesium acetate tetrahydrate at 150 volts for 9 hours. A single desired
band for each complex was excised, minced, and left idle for at least 24 hours at room temperature (approximately
24
◦
C) in TE buffer with 12.5 mM MgCl
2
, during which period DNA transferred from the gel to the buffer by
diffusion. After buffer recovery, concentrations of purified hairpins were measured on a NanoDrop (Thermo Fisher).
S1.3 Formation gel experiments
Native PAGE was used to separate DNA on a 6% gel made with, and run in, TBE buffer with 12.5 mM magnesium
acetate tetrahydrate at 100 volts for 112 minutes. Gels were imaged using the Bio-Rad ChemiDoc MP Imaging
System and Image Lab software. For imaging gels stained with SYBR Gold, the default Image Lab settings for
SYBR Gold were used – Standard Filter (Filter 1) and UV trans illumination. For imaging strands with fluorophore
ATTO590, the 695/55 filter and red epi LED light source were used.
S1.4 Fluorescence kinetics experiments
A 96-well plate (Corning) was used to organize 110
μ
L of each sample, mixed at a standard concentration 1
×
=100 nM.
Fluorescence levels were taken in 2-minute intervals on a microplate reader (Synergy H1, Biotek) at room temperature
S4
(approximately 22
◦
C). 598 nm excitation and 629 nm emission wavelengths were used for fluorophore ATTO590.
2
μ
M of a 20-nt poly-T strand (referred to as 20T) was added to each master mix to coat the walls of pipette tips
and tubes prior to adding any other strands.
4
20T, along with ubiquitous use of LoRetention tips and DNA LoBind
tubes (Eppendorf), mitigated the loss of DNA strands to surfaces.
In each set of fluorescence kinetics experiments, a master mix was made with 20
×
20T, 1
×
key, and 1.5
×
reporter.
The master mix was transferred to one well per sample on a microplate, and various combinations of trigger strands
or hairpins at 1
.
5
×
were added to each of the wells. For negative controls, TE was added to maintain the same
target concentration. Employing a master mix rather than preparing each sample individually is known to result in
data with better reproducibility.
S1.5 Data normalization
As shown in Figure S8, each set of fluorescence kinetics experiments included a negative control with just a key and
reporter as well as a positive control with an excess trigger strand added to directly release the fluorophore-labeled
strand from the key complex without the need for any hairpins. The maximum raw fluorescence was calculated by
averaging the initial five measurements of the negative control, and the minimum raw fluorescence was calculated by
averaging the final five measurements of the positive control. These values were respectively taken as 0
×
and 1
×
to
convert fluorescence data to concentration data. In this data normalization method, 0 nM (0
×
) is interpreted as the
highest fluorescence of the reaction mixture when no key-F strand has been released, and 100 nM (1
×
) is interpreted
as the lowest fluorescence of the reaction mixture after key-F has been fully released from the key complex and
become quenched by the reporter.
S5
S2 Modeling and simulation
All simulations were performed with mass-action kinetics using CRNSimulator.
7
The following reactions were used to model the assembly steps:
key
i
+
hairpin
i
−
1
kf
−
⇀
↽
−
kr
KH
i
−
1
i
= 4
,
6
,
8
KH
i
+
H
i
−
1
kf
−
⇀
↽
−
kr
KH
i
−
1
i
= 2
,
3
,...,
7
(1)
where
kf
= 2
×
10
6
/M/s and
kr
= 0
.
2 /s. Each species
KH
i
indicates a linear polymer that starts with a key and
ends with hairpin
i
.
kf
was estimated based on the effective strand displacement rate with a 7-nt toehold.
8,9
kr
was
calculated as follows:
kr
=
kf
×
c
K
c
(2)
where standard concentration
c
= 100 nM, and
K
c
= 1 was obtained from NUPACK analysis (Figure S2a).
The following reaction was used to model the disassembly step:
KH
1
4
k/i
−−−→
ring
+
keyt
(3)
where
k
= 0
.
0001 /s, 0.04 /s, and 0.5 /s for 0, 4, and 7-nt toeholds, respectively, were estimated based on experiments
shown in Figure S9c. Here we assume that the unimolecular strand displacement rate scales inversely proportional
to the ring size (
i
= 4
,
6
,
8).
The following reaction was used to model the reporting step for creating a ring with responsive size:
keyt
+
reporter
krep
−−−→
wasteFQ
+
waste
(4)
where
krep
= 10
5
/M/s was estimated based on control experiments shown in Figure S8c.
The following reactions were used to model the reporting step for creating a ring with responsive growth direction:
key
4
At
+
translatorA
kt
−
⇀
↽
−
kt
signalA
+
wasteA
key
4
Bt
+
translatorB
kt
−
⇀
↽
−
kt
signalB
+
wasteB
signalA
+
reporterA
krep
1
−−−−
⇀
↽
−−−−
kF Q
1
wasteF
1 +
wasteQ
1
signalB
+
reporterB
krep
2
−−−−
⇀
↽
−−−−
kF Q
2
wasteF
2 +
wasteQ
2
(5)
where
kt
= 2
×
10
6
/M/s was estimated based on the effective strand displacement rate with a 7-nt toehold on
the translators,
krep
1 =
krep
2 = 10
5
/M/s were estimated based on the effective strand displacement rate with a
5-nt toehold on the reporters, and
kFQ
1 = 1
.
5
×
10
3
/M/s and
kFQ
2 = 2
×
10
3
/M/s were estimated based on
experiments shown in Figure 6c. The reverse rates of the reporters (
kFQ
1 and
kFQ
2) are due to the interaction
between a fluorophore and a quencher, and the estimates here are consistent with previous estimates using the same
reporters.
S6
The following reactions were used to model leak:
key
i
+
reporter
klrep
−−−→
wasteFQ
+
waste i
= 4
,
6
,
8
key
i
+
hairpin
1
kl
−→
keyt i
= 4
,
6
,
8
(6)
where
klrep
= 4 /M/s, and
kl
= 0 /M/s, 0 /M/s, and 3 /M/s for 0, 4, and 7-nt toeholds, respectively, were estimated
based on experiments shown in Figures S9a and b.
The following reactions were used to model the assembly steps in growing a linear polymer longer than the target
ring size:
KH
1
+
key
i
kp
−→
KKH
i
+
keyt i
= 4
,
6
,
8
KH
1
+
KH
i
kp
−→
KKH
i
+
keyt i
= 1
,
2
,...,
7
KKH
i
+
H
i
−
1
kf
−
⇀
↽
−
kr
KKH
i
−
1
i
= 2
,
3
,...,
8
(7)
where
kf
and
kr
are the same as above and
kp
= 10
6
/M/s was estimated based on gel electrophoresis data shown
in Figures S4 and S5.
The following reaction was used to model the disassembly step in a linear polymer closing up to form a double-sized
ring:
KKH
1
4
k/i
−−−→
ring
2 +
keyt
(8)
where
k
is the same as above and
i
= 8
,
12
,
16 were used for the doubled ring sizes.
S7
S3 Supplementary design diagrams, simulations, and experiments
key4
hairpin1
hairpin2
hairpin3
hairpin4
hairpin5
hairpin6
hairpin7
key6
key8
Figure S3: Sequence-level design diagrams of the DNA ring with responsive size. A 7-nt toehold t in hairpin1 and
its complementary toehold t
∗
in the keys are shown here. For experiments on the kinetics of ring closure with 0 and
4-nt toeholds (Figure 5), the t domain was TTTT in hairpin1 (same as the s domain in other hairpins) and the t
∗
domain was nonexistent or AAAA in key4.
S8