Supplementary Figures
2
-
.
6
1
2
f
10
1
-
1
.
5
6
ATTO590
-
1
.
5
23
ATTO488
2
-
1
.
2
1
2
f
53
5
2
-.6 1
2
f
39
22
2
-1.2 1
2
f
40
27
-.2 1
4
f
41
28
1
-.2 1
4
f
42
29
1
-.2 1
4
f
51
37
1
f
52
38
1
2
-1.2 1
2
f
26
13
2
-.6 1
2
f
20
8
3
-.6 1
4
f
34
18
1
3
-2.2 1
4
f
36
21
1
2
-1.2 1
2
f
44
31
-1.5
25
ATTO647
2
-.6 1
2
f
43
30
-1.5
24
ATTO550
-.2 1
6
f
49
33
1
1
-.2 1
6
f
50
35
1
1
-.2 1
4
a
b
L
1
L
0
C
0
C
1
R
1
R
0
R124
0
R124
1
R110
0
R110
1
L
0
L
1
C
0
C
1
R
0
R
1
R124
0
R124
1
R110
0
R110
1
Supplementary Figure 1:
Diagrams of the rule 110-124 circuit. a,
Dual-rail circuit diagram.
b,
Seesaw circuit
diagram.
1
a
b
푇ℎ
푗
,
푖
:
푖
푤
푗
,
푖
waste
waste
푤
푗
,
푖
퐺
푖
:
푖
,
푘
푤
푖
,
푘
푤
푖
,
푓
퐺
푗
,
푖
:
푖
퐺
푖
:
푖
,
푓
t
oehold binding
b
ranch migration
toehold disassociation
Supplementary Figure 2:
Basic DNA strand displacement reactions in a seesaw network
(adapted from
ref.
1
).
a,
Catalysis.
b,
Thresholding. Solid arrows indicate flows of the forward reactions and outlined arrows
indicate flows of the respective backward reactions. Catalysis is driven forward by a high concentration of the fuel
species
w
i,f
and downstream irreversible reactions (i.e. thresholding or reporting reactions) that consume the output
species
w
i,k
. Matching colors and stars in domain names suggest complementary DNA sequences. For example, the
blue domains
T
and
T
∗
are complementary to each other, the orange domains
Si
and
Si
∗
are complementary to
each other, etc.
sj
∗
is complementary to the first 5 nucleotides of the
Sj
domain. Thresholding is much faster than
catalysis because the
sj
∗
domain serves as an extended toehold, which significantly decreases the rate of toehold
disassociation and thus speeds up the overall rate of stand displacement.
2,3
푗
f
푖
2
Input
푤
푗
,
푖
-
.
5
1
y
푘
-
1.5
푇ℎ
44
,
31
:
31
푠푖푚
=
0
.
7
×
푇ℎ
44
,
31
:
31
푛표푚
=
0
.
5
×
푇ℎ
10
,
1
:
1
푠푖푚
=
0
.
7
×
푇ℎ
10
,
1
:
1
푛표푚
=
0
.
5
×
푇ℎ
43
,
30
:
30
푠푖푚
=
0
.
7
×
푇ℎ
43
,
30
:
30
푛표푚
=
0
.
5
×
푖
=
1
,
푗
=
10
,
푘
=
23
푖
=
30
,
푗
=
43
,
푘
=
24
푖
=
31
,
푗
=
44
,
푘
=
25
Supplementary Figure 3:
Estimating effective concentrations of distinct thresholds.
The small differences
between simulations and data for
Th
10
,
1:1
and
Th
44
,
31:31
are considered non-significant. We show that
β/α
= 1
.
4
works well enough for four distinct thresholds, including three shown here and one shown in Fig. 3c. 1
×
= 100 nM.
2
a
b
x
1
x
2
x
3
y
y
6
-
1.5
34
f
18
2
3
x
1
x
3
28
37
-
.
6
1
x
2
33
푇ℎ
34
,
18
:
18
푛표푚
=
0
.
4
×
y
23
-
1.5
36
f
21
2
3
x
1
x
3
29
38
-
2.
2
1
x
2
35
푇ℎ
36
,
21
:
21
푛표푚
=
1
.
6
×
x
1
x
2
x
3
y
ON
OFF
ON
OFF
Supplementary Figure 4:
Three-input logic gates with adjusted nominal thresholds. a,
OR gate. Not
all possible inputs were tested here (
x
1
x
2
x
3
= 000 and 111 were repeated twice), but we believe that the circuit
behavior for
x
1
x
2
x
3
= 010 and 101 should be similar to that for 100
/
001 and 110
/
011, respectively.
b,
AND gate.
1
×
= 100 nM.
푖
=
18
,
푗
=
34
,
푘
=
24
푖
=
1
,
푗
=
10
,
푘
=
23
푖
=
5
,
푗
=
53
,
푘
=
6
푗
푖
1
y
푘
-
1.5
푤
푗
,
푖
푤
푖
,
푘
퐺
1
:
1
,
2
3
푡푟푖
=
0
.
8
×
퐺
5
:
5
,
6
푡푟푖
=
0
.
8
×
퐺
18
:
18
,
24
푡푟푖
=
0
.
8
×
Supplementary Figure 5:
Estimating effective concentrations of distinct gates.
Data show steady state
fluorescence level, as signal strands and gate molecules were mixed together and incubated before the measurements.
We show that
γ/α
= 0
.
8 works well for four distinct gates, including three shown here and one shown in Fig. 4b.
1
×
= 100 nM.
3
Supplementary Figure 6:
The rule 124 sub-circuit. a,
Logic circuit diagram.
b,
Dual-rail circuit diagram.
c,
Experimental data. 1
×
= 100 nM.
4
Supplementary
Table
1
Supplementary Table 1: DNA sequences.
Name
Domain
Sequence
L^0: w41.28
S28 T S41
CATCTACAATTCACA TCT CAACAAACCATTACA
L^1: w42.29
S29 T S42
CACCAATACTCCTCA TCT CACTTTTCACTATCA
C^0: w49.33
S33 T S49
CAACTCAAACATACA TCT CATCCTTAACTCCCA
C^1: w50.35
S35 T S50
CACTCTCCATCACCA TCT CATTACCAACCACCA
R^0: w51.37
S37 T S51
CACCTCTTCCCTTCA TCT CACAAACTACATCCA
R^1: w52.38
S38 T S52
CATACCCTTTTCTCA TCT CACTTCACAACTACA
Th41.28:28-t
S28
CATCTACAATTCACA
Th41.28:28-b
s41* T* S28*
TTTGTTG AGA TGTGAATTGTAGATG
w28.34
S34 T S28
CACATAACAAAACCA TCT CATCTACAATTCACA
w28.40
S40 T S28
CAATACAAATCCACA TCT CATCTACAATTCACA
G28-b
T* S28* T*
TG AGA TGTGAATTGTAGATG AGA TG
w28.f
Sf T S28
CATTTTTTTTTTTCA TCT CATCTACAATTCACA
Th42.29:29-t
S29
CACCAATACTCCTCA
Th42.29:29-b
s42* T* S29*
AAAAGTG AGA TGAGGAGTATTGGTG
w29.36
S36 T S29
CAAACTAAACAACCA TCT CACCAATACTCCTCA
w29.39
S39 T S29
CACTATACACACCCA TCT CACCAATACTCCTCA
G29-b
T* S29* T*
TG AGA TGAGGAGTATTGGTG AGA TG
w29.f
Sf T S29
CATTTTTTTTTTTCA TCT CACCAATACTCCTCA
Th49.33:33-t
S33
CAACTCAAACATACA
Th49.33:33-b
s49* T* S33*
AAGGATG AGA TGTATGTTTGAGTTG
w33.34
S34 T S33
CACATAACAAAACCA TCT CAACTCAAACATACA
w33.40
S40 T S33
CAATACAAATCCACA TCT CAACTCAAACATACA
w33.26
S26 T S33
CATTCATTACCTCCA TCT CAACTCAAACATACA
G33-b
T* S33* T*
TG AGA TGTATGTTTGAGTTG AGA TG
w33.f
Sf T S33
CATTTTTTTTTTTCA TCT CAACTCAAACATACA
Th50.35:35-t
S35
CACTCTCCATCACCA
Th50.35:35-b
s50* T* S35*
GGTAATG AGA TGGTGATGGAGAGTG
w35.36
S36 T S35
CAAACTAAACAACCA TCT CACTCTCCATCACCA
w35.39
S39 T S35
CACTATACACACCCA TCT CACTCTCCATCACCA
w35.20
S20 T S35
CAATCTAACACTCCA TCT CACTCTCCATCACCA
G35-b
T* S35* T*
TG AGA TGGTGATGGAGAGTG AGA TG
w35.f
Sf T S35
CATTTTTTTTTTTCA TCT CACTCTCCATCACCA
Th51.37:37-t
S37
CACCTCTTCCCTTCA
Th51.37:37-b
s51* T* S37*
GTTTGTG AGA TGAAGGGAAGAGGTG
w37.34
S34 T S37
CACATAACAAAACCA TCT CACCTCTTCCCTTCA
w37.26
S26 T S37
CATTCATTACCTCCA TCT CACCTCTTCCCTTCA
G37-b
T* S37* T*
TG AGA TGAAGGGAAGAGGTG AGA TG
w37.f
Sf T S37
CATTTTTTTTTTTCA TCT CACCTCTTCCCTTCA
Th52.38:38-t
S38
CATACCCTTTTCTCA
Th52.38:38-b
s52* T* S38*
TGAAGTG AGA TGAGAAAAGGGTATG
w38.36
S36 T S38
CAAACTAAACAACCA TCT CATACCCTTTTCTCA
w38.20
S20 T S38
CAATCTAACACTCCA TCT CATACCCTTTTCTCA
G38-b
T* S38* T*
TG AGA TGAGAAAAGGGTATG AGA TG
w38.f
Sf T S38
CATTTTTTTTTTTCA TCT CATACCCTTTTCTCA
w34.18
S18 T S34
CATCTTCTAACATCA TCT CACATAACAAAACCA
G34-b
T* S34* T*
TG AGA TGGTTTTGTTATGTG AGA TG
Th34.18:18-t
S18
CATCTTCTAACATCA
Th34.18:18-b
s34* T* S18*
TTATGTG AGA TGATGTTAGAAGATG
w18.53
S53 T S18
CATATCTAATCTCCA TCT CATCTTCTAACATCA
w18.44
S44 T S18
CAAAACTCTCTCTCA TCT CATCTTCTAACATCA
5
Name
Domain
Sequence
G18-b
T* S18* T*
TG AGA TGATGTTAGAAGATG AGA TG
w18.f
Sf T S18
CATTTTTTTTTTTCA TCT CATCTTCTAACATCA
w36.21
S21 T S36
CAACCATACTAAACA TCT CAAACTAAACAACCA
G36-b
T* S36* T*
TG AGA TGGTTGTTTAGTTTG AGA TG
Th36.21:21-t
S21
CAACCATACTAAACA
Th36.21:21-b
s36* T* S21*
TAGTTTG AGA TGTTTAGTATGGTTG
w21.10
S10 T S21
CATACAACATCTACA TCT CAACCATACTAAACA
w21.43
S43 T S21
CATCATACCTACTCA TCT CAACCATACTAAACA
G21-b
T* S21* T*
TG AGA TGTTTAGTATGGTTG AGA TG
w21.f
Sf T S21
CATTTTTTTTTTTCA TCT CAACCATACTAAACA
w26.13
S13 T S26
CACAACTCATTACCA TCT CATTCATTACCTCCA
G26-b
T* S26* T*
TG AGA TGGAGGTAATGAATG AGA TG
Th26.13:13-t
S13
CACAACTCATTACCA
Th26.13:13-b
s26* T* S13*
ATGAATG AGA TGGTAATGAGTTGTG
w13.43
S43 T S13
CATCATACCTACTCA TCT CACAACTCATTACCA
G13-b
T* S13* T*
TG AGA TGGTAATGAGTTGTG AGA TG
w13.f
Sf T S13
CATTTTTTTTTTTCA TCT CACAACTCATTACCA
w20.8
S8 T S20
CACTAACATACAACA TCT CAATCTAACACTCCA
G20-b
T* S20* T*
TG AGA TGGAGTGTTAGATTG AGA TG
Th20.8:8-t
S8
CACTAACATACAACA
Th20.8:8-b
s20* T* S8*
TAGATTG AGA TGTTGTATGTTAGTG
w8.44
S44 T S8
CAAAACTCTCTCTCA TCT CACTAACATACAACA
G8-b
T* S8* T*
TG AGA TGTTGTATGTTAGTG AGA TG
w8.f
Sf T S8
CATTTTTTTTTTTCA TCT CACTAACATACAACA
w43.30
S30 T S43
CACCATTACAATCCA TCT CATCATACCTACTCA
G43-b
T* S43* T*
TG AGA TGAGTAGGTATGATG AGA TG
Th43.30:30-t
S30
CACCATTACAATCCA
Th43.30:30-b
s43* T* S30*
TATGATG AGA TGGATTGTAATGGTG
w30.24
S24 T S30
CACTCATCCTTTACA TCT CACCATTACAATCCA
G30-b
T* S30* T*
TG AGA TGGATTGTAATGGTG AGA TG
w30.f
Sf T S30
CATTTTTTTTTTTCA TCT CACCATTACAATCCA
w44.31
S31 T S44
CAATCCACACTTCCA TCT CAAAACTCTCTCTCA
G44-b
T* S44* T*
TG AGA TGAGAGAGAGTTTTG AGA TG
Th44.31:31-t
S31
CAATCCACACTTCCA
Th44.31:31-b
s44* T* S31*
AGTTTTG AGA TGGAAGTGTGGATTG
w31.25
S25 T S31
CAATTCACTCAATCA TCT CAATCCACACTTCCA
G31-b
T* S31* T*
TG AGA TGGAAGTGTGGATTG AGA TG
w31.f
Sf T S31
CATTTTTTTTTTTCA TCT CAATCCACACTTCCA
w40.27
S27 T S40
CAAACACTCTATTCA TCT CAATACAAATCCACA
G40-b
T* S40* T*
TG AGA TGTGGATTTGTATTG AGA TG
Th40.27:27-t
S27
CAAACACTCTATTCA
Th40.27:27-b
s40* T* S27*
TGTATTG AGA TGAATAGAGTGTTTG
w27.10
S10 T S27
CATACAACATCTACA TCT CAAACACTCTATTCA
G27-b
T* S27* T*
TG AGA TGAATAGAGTGTTTG AGA TG
w27.f
Sf T S27
CATTTTTTTTTTTCA TCT CAAACACTCTATTCA
w39.22
S22 T S39
CATTCCTACATTTCA TCT CACTATACACACCCA
G39-b
T* S39* T*
TG AGA TGGGTGTGTATAGTG AGA TG
Th39.22:22-t
S22
CATTCCTACATTTCA
Th39.22:22-b
s39* T* S22*
TATAGTG AGA TGAAATGTAGGAATG
w22.53
S53 T S22
CATATCTAATCTCCA TCT CATTCCTACATTTCA
G22-b
T* S22* T*
TG AGA TGAAATGTAGGAATG AGA TG
w22.f
Sf T S22
CATTTTTTTTTTTCA TCT CATTCCTACATTTCA
w10.1
S1 T S10
CATCCATTCCACTCA TCT CATACAACATCTACA
6
Name
Domain
Sequence
G10-b
T* S10* T*
TG AGA TGTAGATGTTGTATG AGA TG
Th10.1:1-t
S1
CATCCATTCCACTCA
Th10.1:1-b
s10* T* S1*
TTGTATG AGA TGAGTGGAATGGATG
w1.23
S23 T S1
CAAATCTTCATCCCA TCT CATCCATTCCACTCA
G1-b
T* S1* T*
TG AGA TGAGTGGAATGGATG AGA TG
w1.f
Sf T S1
CATTTTTTTTTTTCA TCT CATCCATTCCACTCA
w53.5
S5 T S53
CACCACCAAACTTCA TCT CATATCTAATCTCCA
G53-b
T* S53* T*
TG AGA TGGAGATTAGATATG AGA TG
Th53.5:5-t
S5
CACCACCAAACTTCA
Th53.5:5-b
s53* T* S5*
AGATATG AGA TGAAGTTTGGTGGTG
w5.6
S6 T S5
CATAACACAATCACA TCT CACCACCAAACTTCA
G5-b
T* S5* T*
TG AGA TGAAGTTTGGTGGTG AGA TG
w5.f
Sf T S5
CATTTTTTTTTTTCA TCT CACCACCAAACTTCA
Rep6-t
RQ S6
/5IAbRQ/ CATAACACAATCACA
Rep6-b
T* S6* ATTO590
TG AGA TGTGATTGTGTTATG /3ATTO590N/
Rep23-t
FQ S23
/5IABkFQ/ CAAATCTTCATCCCA
Rep23-b
T* S23* ATTO488
TG AGA TGGGATGAAGATTTG /3ATTO488N/
Rep24-t
RQ S24
/5IAbRQ/ CACTCATCCTTTACA
Rep24-b
T* S24* ATTO550
TG AGA TGTAAAGGATGAGTG /3ATTO550N/
Rep25-t
RQ S25
/5IAbRQ/ CAATTCACTCAATCA
Rep25-b
T* S25* ATTO647
TG AGA TGATTGAGTGAATTG /3ATTO647NN/
7