of 12
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
,
:
,
waste
waste
,
:
,
,
,
,
:
:
,
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
f
2
Input
,
-
.
5
1
y
-
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
×
=
1
,
=
10
,
=
23
=
30
,
=
43
,
=
24
=
31
,
=
44
,
=
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.
=
18
,
=
34
,
=
24
=
1
,
=
10
,
=
23
=
5
,
=
53
,
=
6
1
y
-
1.5
,
,
1
:
1
,
2
3
푡푟푖
=
0
.
8
×
5
:
5
,
6
푡푟푖
=
0
.
8
×
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