www.sciencemag.org/content/
35
7
/
6
3
5
6
/
e
aan6558
/
suppl/DC1
Supp
lementary
Material
s
for
A cargo
-
sorting DNA robot
Anupama J. Thubagere,
Wei Li,
Robert F. Johnson,
Zibo Chen,
S
hayan Doroudi,
Yae Lim Lee,
Gregory Izatt,
Sarah Wittman,
Niranjan Srinivas,
Damien Woods,
Erik Winfree,
Lulu Qian
*
*
Corresponding author. E
mail:
luluqian@caltech.edu
Published
15
September
20
1
7
,
Science
35
7
,
e
aan6558
(201
7
)
DOI:
10.1126/
aan6558
This PDF file includes:
Materials and
M
ethods
Supplementary Text
Figs. S1 to S14
Tables S1 and S2
References
Supplementary Materials for
A cargo-sorting DNA robot
Anupama J. Thubagere, Wei Li, Robert F. Johnson,
Zibo Chen, Shayan Doroudi, Yae Lim Lee, Gregory Izatt, Sarah Wittman,
Niranjan Srinivas, Damien Woods, Erik Winfree & Lulu Qian
∗
∗
correspondence to: luluqian@caltech.edu
Contents
1 Materials and methods
2
1.1
DNA oligonucleotide synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
Annealing protocol and buffer condition . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Purification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4
DNA origami concentration measurement . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.5
Fluorescence spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.6
Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2 Supplementary data and analysis
4
2.1
The rigidity of DNA origami affects the undesired reactions . . . . . . . . . . . . . . . . .
4
2.2
The DNA sequence of the foot domains of the robot affects the rate of walking . . . . . . .
5
2.3
A biophysical model of the walking mechanism . . . . . . . . . . . . . . . . . . . . . . .
6
2.4
The purity of DNA origami affects the completion level of desired reactions . . . . . . . . 10
2.5
Numerical analysis of the random walk . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.6
Cargo pick-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7
Procedure for preparing cargo-sorting samples . . . . . . . . . . . . . . . . . . . . . . . . 13
2.8
Negative control for cargo sorting without a robot . . . . . . . . . . . . . . . . . . . . . . 14
2.9
Procedure for preparing cargo-sorting samples for AFM imaging . . . . . . . . . . . . . . 15
2.10 AFM images of the cargos at their initial locations and destinations . . . . . . . . . . . . . 16
2.11 Cargo sorting with mixed populations of DNA origami . . . . . . . . . . . . . . . . . . . 17
2.12 Analysis of the completion levels in the cargo-sorting experiments . . . . . . . . . . . . . 18
2.13 Multiple robots collectively performing a cargo-sorting task . . . . . . . . . . . . . . . . . 19
3 Cadnano diagram
20
3.1
Double-layer square DNA origami design . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4 DNA sequences
21
4.1
Staples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2
Robot, track, cargo and goal strands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References
26
1
1 Materials and methods
1.1 DNA oligonucleotide synthesis
DNA oligonucleotides were purchased from Integrated DNA Technologies (IDT). The regular staples,
track staples and trigger strands were purchased unpurified (standard desalting). The robot, cargo and
goal strands, the inhibitor strands, and the staples with extensions for localizing robot, cargos and goals
(referred to as robot start, cargo and goal staples, respectively) were purchased purified (HPLC). All
strands were purchased at 100
μ
M in TE buffer, pH 8.0, and stored at 4
◦
C.
1.2 Annealing protocol and buffer condition
DNA origami was annealed with 30 nM M13 scaffold (Bayou Biolabs), a 10-fold excess of the regular,
track, robot start, cargo and goal staples, 11-fold excess of the cargo attacher strands, and 12-fold excess
of the cargo strands in 1
×
TAE buffer with 12.5 mM Mg
2+
. The buffer was prepared from 50
×
TAE,
pH 8.0 (Fisher BioReagents) and magnesium acetate tetrahydrate (Fisher BioReagents). The inhibited
robot and goal complexes were annealed at 20
μ
M with a 20% excess of the inhibitor strands. Annealing
was performed in a thermal cycler (Eppendorf), first heating up to 90
◦
C for 5 minutes, and then slowly
cooling down to 20
◦
C at the rate of 6 sec per 0.1
◦
C.
1.3 Purification
After annealing, the DNA origami sample was loaded on a 2% agarose gel, run on ice for 2 hours at 80 V in
1
×
TAE/Mg
2+
buffer. The appropriate bands were then cut out from the gel and purified using the Freeze
’N Squeeze DNA gel extraction spin columns (Biorad). The inhibited robot and goal complexes were
purified using 15% polyacrylamide gel electrophoresis (PAGE). After incubating the DNA origami with
an approximately 2-fold excess of the inhibited robot and goal complexes for 5 hours at room temperature,
the sample was purified three times using 0.5 mL and 100 KDa spin filters (Amicon, #UFC510096), each
time for 12 minutes at 2,500 Relative Centrifugal Force (RCF).
1.4 DNA origami concentration measurement
The concentration of DNA origami with the robot, tracks, cargos and goals was measured in a spectroflu-
orimeter (Fluorolog-3, Horiba), using the fluorescence signal of an embedded staple labeled with a ROX
fluorophore, and comparing the signal with a calibration curve (i.e. a linear fit of the measurements of raw
fluorescence levels at varying concentrations) of the fluorophore-labeled strand by itself.
1.5 Fluorescence spectroscopy
Fluorescence kinetics data were collected every 2 minutes in a spectrofluorimeter (Fluorolog-3, Horiba).
Experiments were performed with 50
μ
L reaction mixture per cuvette, in fluorescence cuvettes (Hellma
#105.251-QS) at 25
◦
C. The excitation/emission wavelengths were set to 534/554 nm for ATTO 532 and
602/624 nm for ATTO 590. Both excitation and emission bandwidths were set to 5 nm, and the integration
time was 10 seconds for all experiments. Samples for fluorescence spectroscopy were diluted to 3 nM of
the origami concentration. Baseline measurements of the samples were taken for 30 minutes. A 20-fold
2
excess of the trigger strands was then added. To measure the maximum possible completion level at the
end of each experiment, a 20-fold excess of free-floating robot strands with and without quenchers was
added in random walk and cargo pick-up experiments, respectively; a 20-fold excess of free-floating goal
strands with quenchers was added in cargo sorting experiments.
1.6 Atomic force microscopy
Samples for AFM imaging were prepared by diluting the origami to 1 nM in
1
×
TAE/Mg
2+
buffer. After
dilution, 40
μ
L of the sample was deposited onto freshly cleaved mica (SPI Supplies, 9.5 mm diameter,
#01873-CA). After 3 minutes the solution was removed and 40
μ
L of 1
×
TE/Mg
2+
buffer was added onto
the mica, then the sample was imaged. Samples of cargo-sorting experiments were first incubated with a
20-fold excess of goal remover strands for one hour at room temperature, and then incubated with 10 units
per
μ
L of exonuclease I (New England Biolabs #M0293S) for 18 hours at 25
◦
C before imaging. AFM
images were taken in tapping mode in fluid on a Dimension FastScan Bio (Bruker) using FastScan-D
probes (Bruker). All images were scanned at a resolution of 1024 lines with 1024 pixels per line.
3
2 Supplementary data and analysis
2.1 The rigidity of DNA origami affects the undesired reactions
50 nm
A
B
high
low
Fluorescence
D
95 nm
48
24
12
Surface
distance
(nm)
72
48
24
Surface
distance
(nm)
high
low
Fluorescence
E
58 nm
less
rigid
more
rigid
100 nm
C
F
Fig. S1. The rigidity of DNA origami affects the undesired reactions.
(
A
) Scaffold path, schematic diagram, and Atomic
Force Microscope (AFM) image of a single-layer rectangular DNA origami (
6
) with a linear track. (
B
) Schematic diagram
and fluorescence kinetics data of a negative control experiment for the robot reaching the goal without any track on the single-
layer origami. Three distinct surface distances between the robot and the goal were tested. (
C
) CanDo (
32
) diagram showing
the predicted deformations of the single-layer origami structure. Substantial thermal fluctuations can be observed in a CanDo
movie. (
D
) Scaffold path, schematic diagram, and AFM image of a double-layer square DNA origami with a linear track. (
E
)
Schematic diagram and fluorescence kinetics data of a negative control experiment for the robot reaching the goal without any
track on the double-layer origami. Three distinct surface distances between the robot and the goal were tested. (
F
) CanDo
diagram showing the degree of thermal fluctuations of the double-layer origami structure. Limited thermal fluctuations can be
observed in a CanDo movie.
4
2.2 The DNA sequence of the foot domains of the robot affects the rate of walking
C
Foot domains
on robot
B
robot
(inhibited)
A
robot
(activated)
robot
trigger
robot
(inhibited)
robot
at
goal
waste
+
+
Fig. S2. The DNA sequence of the foot domains of the robot affects the rate of walking.
(
A
) Sequence-level diagram of the
mechanism of the robot making a single step to reach the goal after being triggered. Two distinct sequences are used for the
two feet. (
B
) Sequence-level diagram of the same setup as shown in A, but with identical sequences used for the two feet. (
C
)
Schematic diagram and fluorescence kinetics data of the robot taking a single step. Two sequence choices shown in A and B
were both tested. The sequence of foot1 has a stronger standard free energy and that of foot2 has a weaker standard free energy.
NUPACK (
52
) predicts -8.76 kcal/mol for foot1 and -8.55 kcal/mol for foot2 at 25
◦
C, without considering the stacking energy
on the 5’ and 3’ ends.
5
2.3 A biophysical model of the walking mechanism
To better understand the mechanism of walking, we developed a biophysical model. We do not have
enough experimental data to accurately fit parameters or verify mechanisms involved in the model, but it
is already conceptually insightful for understanding why the robot walks at a fairly slow rate and how the
rate could potentially be much faster.
We start with an irreversible reaction from track type 1 to the goal, as shown in Fig. S3A. In this model,
RTr1[27] is the robot at the track1 location. 27 corresponds to the total number of nucleotides in the robot
strand that are involved in walking: two foot domains that each have 6 nucleotides and one leg domain that
has 15 nucleotides. RG[
i
] is the robot with
i
nucleotides bound to the goal location.
k
h
is the rate constant
of localized hybridization. In position
i
,
k
i
5
d
and
k
i
3
d
are the rate constants of disassociation from the 5’ end
and 3’ end of the robot strand, respectively.
k
i
5
b
and
k
i
3
b
are the rate constants of a single-base-pair branch
migration step from the
i
-th nucleotide toward the 5’ end and 3’ end of the robot strand, respectively.
k
h
can be estimated using two methods. First, similar to the estimates in localized DNA circuits
(
50, 53
),
k
h
=
the rate constant of hybridization in solution
×
the local concentration. The rate of DNA
hybridization is approximately
10
6
/M/s at 25
◦
C (
54
). The local concentration can be estimated as (1 /
N
A
)
/ (
4
π/
3
×
(6
nm
)
3
), where
N
A
is the Avogadro’s constant, and 6 nm is the distance between the robot start
and goal locations. Therefore,
k
h
≈
1835
/s. Second,
k
h
can be estimated as the rate constant of closing a
hairpin. From a previous study on the kinetics of hairpin opening and closing (
55
),
k
n
close
≈
k
0
(
n
+ 5)
−
2
.
5
at 25
◦
C, where
n
is the loop size, and
k
30
close
≈
5
×
10
3
/s. In our system, the loop size can be estimated
as
((15 + 6 + 15)
bp
×
0
.
34
nm/bp
+ 6
nm
+ (15 + 6)
nt
×
0
.
43
nm/nt
)
/
(0
.
43
nm/nt
) = 63
nt. Therefore,
k
h
≈
950
/s. We use
k
h
= 10
3
/s, which roughly agrees with both estimates.
For a generic sequence, the disassociation rate constant can be modeled as
k
d
= 10
(6
−
L
)
/s for a
hybridization domain of length
L
with a reference standard free energy
∆
G
for each base pair, which is
close to the average standard free energy at 25
◦
C (
54
). Therefore, in our system,
k
i
5
d
= 10
6
−
i
/s and
k
i
3
d
= 10
6
−
(27
−
i
)
/s. Because we are interested in how the standard free energy of the foot domain near
the 3’ end of the robot strand affects the rate of walking (Fig. S2), for the irreversible reaction shown in
Fig. S3A, we re-define
k
i
3
d
= 10
6
−
∆
G/
∆
G
(27
−
i
)
/s, where
∆
G
is the standard free energy for each base pair
with a specific sequence that could be stronger (
∆
G/
∆
G >
1
) or weaker (
∆
G/
∆
G <
1
) than average.
From a previous biophysics study of strand displacement reactions (
56
), the initiation of branch migra-
tion is about 5 /s and each of the following steps is about
10
4
/s. We use these two rate constants to define
k
i
5
b
, for branch migration away from the DNA origami surface (except there will be no initiation step for an
irreversible reaction that ends at the 5’ end). However, taking the elasticity of double- and single-stranded
DNA into consideration (
34
), branch migration toward the DNA origami surface should lead to a tighter
stretch of the DNA strands and thus a slowdown of the rate constant. Since we designed appropriate linker
lengths for the robot to reach an adjacent track location (Fig. S4A), the strands should not be overstretched
and thus should remain within the “entropic elasticity” regime where the force increases linearly with the
distance stretched, coresponding to a quadratic energy cost for stretching the “entropic spring”. Thus we
define
k
i
3
b
= 5
/s when
i
= 6
,
k
i
3
b
= 10
4
/s when
6
< i
≤
th
, and
k
i
3
b
= 10
4
−
w
(
i
−
th
)
/s when
i > th
, where
th
is nucleotide location for which the force starts to increase when branch migration moves close enough
to the origami surface, and
w
is the energy change per step. This model is qualitatively consistent with a
molecular dynamics study of a similar system (
33
).
By comparing simulation with the experimental data shown in Fig. S2C, we were able to determine
that
th
= 19
and
w
= 2
are reasonable parameters for our system. The model suggest that (1) the entropic
cost of stretching the DNA strands significantly slows down branch migration toward the DNA origami
6
surface, when the junction of branch migration is close enough to the surface. (2) Branch migration
becomes slower than disassociation near the end of the reaction, resulting in disassociation prior to branch
migration through the foot domain. Thus, a weaker sequence of the foot domain near the 3’ end of the
robot leads to a faster overall reaction rate because of faster disassociation. (3) A small difference in the
standard free energy of the DNA sequence (
∆
G/
∆
G
= 1
.
1
vs.
0
.
8
for each base pair) can result in a large
difference in the rate of the robot taking a single step (half completion time
≈
15
hours vs. 10 minutes).
Similarly, a reversible strand displacement reaction of the robot walking from one track location to
another (RTr1[27]
RTr2[27]) can be modeled with analogous hybridization, branch migration and disas-
sociation steps (Fig. S3B). The disassociation rate constants are the same as discussed above:
k
i
5
d
= 10
6
−
i
/s
k
i
3
d
= 10
6
−
(2
T
+15
−
i
)
/s
Branch migration toward and away from the origami surface now both include an initiation step. To
explore how the rate of initiation and the strength of the foot domains affect the overall speed of walking,
we set the initiation rate constant to be a variable
k
0
, and the length of the foot domains in the robot strand
to be a variable
T
, while keeping the track strands unchanged:
k
i
5
b
=
{
10
4
/s
i < T
+ 15
k
0
i
=
T
+ 15
k
i
3
b
=
k
0
i
=
T
10
4
/s
T < i
≤
th
−
6 +
T
10
4
−
w
(
i
−
(
th
−
6+
T
))
/s
i > th
−
6 +
T
The energies of the beginning and end states shown in Fig. S3B should be approximately the same, as in
both cases the robot is bound to its track by the same total number of base pairs and has similar geometric
constraints. To satisfy detailed balance, the ratio between the product of all forward rate constants and
that of all reverse rate constants for all pathways between any two given states should also be the same.
Using these two requirements, all hybridization rate constants can be calculated based on
k
T
5
h
and the
disassociation and branch migration rate constants:
k
i
5
h
=
10
3
/s
i
=
T
k
T
5
h
∏
i
−
1
n
=
T
k
n
3
b
k
T
5
d
∏
i
n
=
T
+1
k
n
5
b
×
k
i
5
d
/s
i > T
k
i
3
h
=
k
T
+15
3
h
∏
T
+15
n
=
i
+1
k
n
5
b
k
T
+15
3
d
∏
T
+14
n
=
i
k
n
3
b
×
k
i
3
d
/s
i < T
+ 15
10
3
−
∑
20
−
th
n
=1
n
×
w
/s
i
=
T
+ 15
Before the initiation of branch migration (
k
0
) becomes the rate limiting step, the overall reaction rate
will still largely depend on the disassociation near the end of the reaction, and therefore the robot walks
7
at a fairly slow rate of roughly 5 min per step. Since the critical difference between the first and second
step of branch migration is the presence of one versus two single-stranded tails at the branch point (
56
),
k
0
could potentially be increased from 5 /s to at least
10
3
/s by adding a few Ts at the 3’ end of the track
strands. Simulations suggest that, with an increased
k
0
, weaker foot domains (e.g. 2 to 4 nucleotides)
could speed up walking by at least tens to hundreds of times (Fig. S3B).
The biophysics of the DNA robot performing random walking merits further theoretical and experi-
mental study.
8
simulation
RTr1[27
]
RG[6]
푘
ℎ
푘
5푑
6
RG[7]
푘
3푏
6
푘
5푏
7
RG[26]
푘
3푏
25
푘
5푏
26
RG[27]
푘
3푏
26
⋯
푘
3푏
7
푘
5푏
8
푘
3푑
6
푘
3푑
7
푘
3푑
26
푘
ℎ
=
10
3
/s
푘
3푑
푖
=
10
6
−
∆
퐺
/
∆
퐺
(
27
−
푖
)
/s
푘
5푏
푖
=
10
4
/s
푘
3푏
푖
=
ቐ
5
/s
if
푖
=
6
10
4
/s
if
6
<
푖
≤
푡ℎ
10
4
−
푤
(
푖
−
푡ℎ
)
/s
if
푖
>
푡ℎ
푘
5푑
푖
=
10
6
−
푖
/s
RS[27]
RG[6]
RG[14]
RG[27]
⋯
⋯
⋯
⋯
B
A
simulations
RTr1[2T+15]
RTr2[T]
푘
5ℎ
푇
푘
5푑
푇
RTr2[T+1]
푘
0
푘
5푏
푇
+
1
RTr2[T+14]
푘
3푏
푇
+
13
푘
5푏
푇
+
14
⋯
푘
3푏
푇
+
1
푘
5푏
푇
+
2
RTr2[2T+15]
푘
3푑
푇
+
15
푘
3
ℎ
푇
+
15
RTr2[T+15]
푘
3푏
푇
+
14
푘
0
푘
5푑
푇
+
1
/
푘
5ℎ
푇
+
1
푘
3
ℎ
푇
+
1
/
푘
3푑
푇
+
1
푘
3
ℎ
푇
+
14
/
푘
3푑
푇
+
14
푘
5푑
푇
+
15
/
푘
5ℎ
푇
+
15
푘
5푑
푇
+
14
/
푘
5ℎ
푇
+
14
푘
3ℎ
푇
/
푘
3푑
푇
RTr1[2T+15]
RTr2[2T+15]
RTr2[T]
RTr2[T+15]
RTr2[T+1]
RTr2[T+14]
⋯
∆
∆
퐸
=
log
10
Τ
푘
푓
표푟푤푎푟푑
푘
푟
푒푣푒푟푠푒
Fig. S3. A biophysical model of the walking mechanism.
(
A
) Model and simulation of an irreversible pathway for the robot
taking one step to reach the goal location. (
B
) Model of an reversible pathway for the robot taking one step from a track location
to another, and simulations of two steps of walking to a goal, with
th
= 19
,
w
= 2
, and toehold lengths (
T
) from 1 to 6.
9
2.4 The purity of DNA origami affects the completion level of desired reactions
C
D
E
B
F
Unpurified
1
2
3
excess
staples
1
2
3
Spin
-
filter purified
200 nm
unpurified
spin
-
filter purified
gel purified
A
=
6 nm
2 nm
linker:
11
nt
×
0.43 nm/
nt
linker:
5
nt
×
0.43 nm/
nt
f
oot:
6
bp
×
0.34 nm/
bp
Fig. S4. The purity of DNA origami affects the completion level of desired reactions.
(
A
) The checkerboard layout of two
distinct types of track strands in all random-walking systems. The lengths (11 and 5 nt) of the linkers in the two types of track
strands are designed to allow the robot to reach an adjacent track location:
4
.
73 + 2 + 2
.
04 + 2
.
15 = 10
.
92
nm
>
6
nm.
(
B
) Schematic diagrams of the robot walking on linear tracks of three distinct lengths and a negative control with no track.
Fluorescence kinetics data of the setup shown in A, using (
C
) unpurified, (
D
) spin-filter purified, and (
E
) gel purified double-
layer DNA origami. (
F
) Spin-filter purified and unpurified origami on an agarose gel and AFM images of the three labeled
bands extracted from the unpurified lanes on the gel. Band 3 was subsequently used for all gel-purified samples. To obtain
enough DNA structures after gel purification, we used five lanes of the same unpurified sample. We assumed that the three
bands in the spin-filtered lane had the same types of DNA structures shown in the AFM images, because the locations of the
bands were identical compared to the unpurified lanes. The scale bar applies to all three images.
10
2.5 Numerical analysis of the random walk
A
B
Fig. S5. Numerical analysis of the random walk.
Average hitting time and two-thirds completion time of random walks on
linear tracks of lengths 1 to
n
, with (
A
)
n
= 100
and 1,000 trials for each track length, and (
B
)
n
= 8
and 10,000 trials for
each track length. The linear track consists of sites 0, 1, 2,
...,n
. The random walk starts at site 0. For any site
0
< i < n
,
the random walk moves to
i
−
1
or
i
+ 1
with equal probability. If the random walk returns to 0, it continues to 1. The hitting
time is defined as the number of steps for the random walk to hit site
n
for the first time. The average hitting time is the mean
of the hitting time for all trials. The two-thirds completion time is the smallest number of steps that is greater than or equal to
the hitting time for two-thirds of all trials.
The average hitting time (also referred to as the first-passage time) of a random walk on a linear track
has been well studied (
31, 57
). However, the average hitting time cannot be directly read off from exper-
imental data, unlike the related notions of the fractional completion times, such as the half-completion
time (i.e. the median hitting time) and the two-thirds completion time. For random walks in general, these
quantities can behave quite differently and we are not aware of direct mathematical relationships that al-
low calculating one from the other. Therefore, we performed numerical simulations of one-dimensional
random walks to establish that, in the case relevant to our experimental investigations, the two-thirds
completion time scales quadratically with the track length, just like the average hitting time.
For track lengths
n
= 1
to 100, numerical simulations of 1,000 trials per track length confirmed that
the average hitting time
T
is quadratically related to
n
(Fig. S5A, left). The two-thirds completion time
is fairly similar to the average hitting time (Fig. S5A, middle), but can be better estimated as
T
= 1
.
1
n
2
(Fig. S5A, right). Taking a closer look at track lengths
n
= 1
to 8 (which are the lengths used in our random
walk experiments) with numerical simulations of 10,000 trials per track length,
T
=
n
2
is practically an
exact function for the average hitting time while
T
= 1
.
1
n
2
remains a very good estimate for the two-
thirds completion time (Fig. S5B). Thus, we concluded that it is reasonable to apply a quadratic fit to
the two-thirds completion time extracted from the experimental data, and use that to determine the rate
constants in the mass action simulation of the reactions involved in our random walk system.
11