Information-based autonomous reconfiguration
in systems of interacting DNA nanostructures
Petersen et al.
1
Supplementary Figures
a
500
nm
b
c
f
e
200 nm
2 nM
4 nM
d
200 nm
2 nM
4 nM
cover
tile
base
tile
invader
tile
Q
F
=
=
simulations
simulations
Supplementary Figure 1
|
Discovery of DNA tile displacement.
(
a
) A 2 by 2 array design that uses one tile with 11 edge staples
along two edges. Each staple has a stacking bond and a 1-nt sticky end. (
b
) AFM image of the 2 by 2 array, with 50 nM of the tile
annealed from 90 to 20
◦
C at 6 sec per 0.1
◦
C. (
c
) Possible self-assembly pathways without (solid arrows) and with (dotted arrows) tile
displacement. Fainter tiles are duplicate and rotated representations of the same monomer, dimer or trimer. Simulations were performed
with all possible reactions at the same effective rate
k
= 2
.
5
×
10
4
M
−
1
s
−
1
, which is the binding rate (and maximum effective tile
displacement rate) for tiles with 1-nt sticky ends in the model shown in Fig. 1e. Simulations suggest that, if all bindings are irreversible,
then without tile displacement, monomer depletion will prevent trimers from further converting to 2 by 2 arrays and lead to a significant
fraction of kinetically trapped trimers at the end point. With tile displacement, a trimer could interact with a dimer to form a 2 by 2
array while releasing a monomer, and two copies of trimers could interact with each other to form a 2 by 2 array while releasing a dimer,
resulting in nearly 100% of 2 by 2 arrays at the end point. (
d
) Design diagram and AFM image of a square dimer mixed together with an
triangular invader
1
without a toehold and (
e
) with a toehold. Experiments were performed at 25
◦
C with 2 nM square dimer and 4 nM
triangular invader. AFM images were collected after 48 hours. Dotted and solid boxes highlight reactants and products, respectively.
(
f
) Edge staples composing the toehold and branch migration domains of a tile displacement reaction shown in Fig. 1c.
2
Inv
CT
BT
b
a
C T: BT
푥푥
+ Inv
푥푥푦푦
푘푘
on
푘푘
off
C T: BT
푥푥
:Inv
푥푥푦푦
푘푘
d
CT + Inv
푥푥푦푦
:BT
푥푥
simulations
experiments
푘푘
on
= 2.5 × 10
4
M
-1
s
-1
❶
③④
푘푘
off
= 4.0 × 10
−4
s
-1
①③④
푘푘
d
= 0.02 5
s
-1
①②③④⑤
①
②
④
⑤
③
푘푘
on
= 2.5 × 10
4
M
-1
s
-1
①
③④
푘푘
off
= 10
1−1
.
1푦푦
s
-1
①③
❹
푘푘
d
= 0.025
s
-1
①②③④⑤
푘푘
on
= 4.5 × 10
5
M
-1
s
-1
❷
⑤
푘푘
off
= 10
−5
s
-1
②⑤
푘푘
d
= 0.025
s
-1
①②③④⑤
푘푘
on
= 4.5 × 10
5
M
-1
s
-1
②
⑤
푘푘
off
= 10
3−2푦푦
s
-1
②
❺
푘푘
d
= 0.025
s
-1
①②③④⑤
푘푘
on
= 2.5 × 10
4
M
-1
s
-1
①③④
푘푘
off
= 10
1−1
.
1푦푦
s
-1
①③④
푘푘
d
= 0.025
s
-1
①②③④⑤
Cover Tile (CT): six 2-
nt
staples in the branch migration domain
Base Tile (BT
푥푥
): four
푥푥
-nt
staples in the toehold (
푥푥
=
1 or 2)
Invader (Inv
푥푥푦푦
):
푦푦푥푥
-nt
staples in the toehold (
푦푦
=
0 through 4)
CT
Inv
BT
binding
(
푘푘
on
)
dissociation
(
푘푘
off
)
displacement (
푘푘
d
)
Supplementary Figure 2
|
Kinetics of DNA tile displacement.
(
a
) The pathway of a tile displacement reaction. Dotted box
highlights an intermediate state of the displacement step. (
b
) Fluorescence kinetics experiments and simulations. Experiments were
performed at 25
◦
C with 2 nM (1
×
) cover:base dimer and 4 nM (2
×
) invader (or otherwise specified invader concentrations in the plot
legend).
k
on
,
k
off
, and
k
d
are the rates of binding, dissociation, and displacement, respectively. Numbers next to the rates indicate the
plots for which each rate is associated with, and the highlighted numbers indicate the plot for which the rate was largely derived from.
3
b
a
CT:BT1 (reactant)
CT:BT2 (reactant)
Inv:BT1 (product)
Inv:BT2 (product)
C T: BT1
9
1
.
3
±
2
.
7
%
Inv:BT1
8
.
7
±
0
.
8
%
C T: BT2
43
.
0
±
3
.
1
%
Inv:BT2
57
.
0
±
3
.
6
%
CT:BT (reactant)
Inv:BT
(product)
CT:BT (reactant)
Inv:BT
(product)
C T: BT
3
.
8
±
0
.
7
%
Inv:BT
96
.
2
±
3
.
7
%
C T: BT
9
6
.
2
±
2
.
6
%
Inv:BT
3
.
8
±
0
.
5
%
C T: BT1
2
.
3
±
0
.
3
%
Inv:BT1
97
.
7
±
2
.
3
%
C T: BT2
0
%
Inv:BT2
100
%
Supplementary Figure 3
|
Yield estimation of basic and competitive tile displacement.
(
a
) Cover:base tile complex mixed
together with an invader without (top) and with (bottom) a toehold. (
b
) Two types of cover:based tile complexes mixed together with
0
.
6
×
(top) and 3
×
(bottom) invader. All AFM images are 5 by 5
μ
m. Each two-tile complex is highlighted as either a reactant (dotted
boxes) or a product (solid boxes). The yield of each tile displacement reaction was estimated as
p
=
m/n
, where
m
is the total number
of products and
n
is the total number of reactants and products counted in each image. Ambiguous and spurious structures were not
counted. The standard error was calculated as
p
√
1
−
p/
√
n
, treating the yield as a Bernoulli probability.
2
4