Simulation conditions

We set the binding rate constant (kf) based on toehold length as follows ^[1,2].

• If toehold_length ? 6
     kf = 5.0×10^n-1 [M ^-1s^-1]
  else
     kf = 3.0×10⁶ [M^-1s^-1]
  Where
     n : toehold_length
  

Base sequence design and annealing protocol

Walker

DNA Walker (Figure 1) was composed of annealed DNA strands W1 and W2. Figure 2 shows the annealing conditions for DNA Walker. Table 1 shows the sequences of the DNA Walker.

Table 1: DNA sequences of Walker

Name	Base sequences (5'→3')	Length
W1	GGCAAAACTTAACAATACTAACTAATCCAATTCGCACGATTGCATAGCGAACGGACTCCAGGACATCCTACCGCTCAATCACCACCT	87
W2	CCCATAACATTACTTAACTAACATAACCTAGTCCGTTCGCTATGCAATCGTGCGAATCCAGCAGATCAACCGCTCAATCACCACCT	86

Ground A

Hairpins S1 and S2 (Figure 3) were mixed with single strands C1, G1, and G4 and subsequently annealed to produce Ground A, as shown in Figure 4. DNA sequences for Ground A are shown in Table 2.

Table 2: DNA sequences for Ground A

Name	Base sequences (5'→3')	Length
S1	GGTAGTTCTAGGGTGTCGAGGTGGTGATTGAGCGGTAGGATGTCACCACCTCTTCACCCATCCTACCGCTCAATCTCCTACCGCTCAATCACCACCT	75
S2	CACCTCGGATCTTGATGGAGGTGGTGATTGAGCGGTTGATCTCTCCACCTCAACTCCCATCAACCGCTCAATC	73
G1	CCATAGGGAGGGCTCAAGATCCGAGGTGCGTGCATAGATAGTCATAGCCTTGGACCACCCTAGAACTACC	70
G4	GTCCAAGGCTATGACTATCTATGCACG	27
C1	GCCCTCCCTATGGCATGGTACTCAGCT	27

Ground B

Hairpins S1 and S2 (Figure 5) were mixed with single strands C2, G2, and G4 and then annealed to produce Ground B under the conditions shown in Figure 6. DNA sequences for Ground B are shown in Table 3.

Table 3: DNA sequences for Ground B

Name	Base sequences (5'→3')	Length
G2	CGGATGAGTGGACCAAGATCCGAGGTGCGTGCATAGATAGTCATAGCCTTGGACCACCCTAGAACTACCAGCTGAGTACCATG	83
C2	GTCCACTCATCCGCAGTATCCGTGGCC	27

Ground C

Hairpin S1 and single strands S3 and S4 (Figure 7) were mixed with single strands G3 and S4, and then annealed to produce Ground C. Figure 8 shows an annealing conditions for Ground C. DNA sequences for Ground C are shown in Table 4.

Table 4: DNA sequences for Ground C

Name	Base sequences (5'→3')	Length
G2	CACCTCGGATCTTGCTGGAGGTGGTGATTGAGCGGTTGATCTCTCC	46
C2	GGAGAGATCAACCGCTCAATC	21
G3	GCAAGATCCGAGGTGCGTGCATAGATAGTCATAGCCTTGGACCACCCTAGAACTACCGGCCACGGATACTG	71

Ground

Grounds A, B, and C were incubated at room temperature for 3 h to produce Ground.

DNA Walker and Ground A

Ground A and the pre-assembled DNA Walker were incubated at room temperature for 3 h to produce DNA Walker and Ground A.

Fuel

We used two types of Fuel, F1 and F2. F1 was reacted with S1, and F2 was reacted with S2.

Table 5: DNA sequences of Fuel

Name	Base sequences (5'→3')	Length
F1	GTAGGAAGGGTGAAGAGGTGGTGACATCCTACCGCTCAATCACCACCTGCTCGCA	55
F2	GTTGAAGGGAGTTGAGGTGGAGAGATCAACCGCTCAATCACCACCTCAACTCGCA	55

Experiment A

Sample preparation

Step1 Dilution

We diluted each strand in Tris-ethylenediaminetetraacetic acid (EDTA) buffer supplemented with 12.5 mM MgCl2 as shown in below. The experiment was performed at 20°C. We conducted four types of experiments:

A double-stranded DNA (S1-W1) and a single-stranded DNA (F1)

Table 6: Concentrations for Pattern A

DNA	Concentration[nM]
S1-W1	20
F1	80

A double-stranded DNA (S1-W1) and a single-stranded DNA (F2)

Table 7: Concentrations for Pattern B

DNA	Concentration[nM]
S1-W1	20
F2	40

A double-stranded DNA (S2-W2) and a single-stranded DNA (F2)

Table 8: Concentrations for Pattern C

DNA	Concentration[nM]
S1-W2	20
F2	40

A double-stranded DNA (S2-W2) and a single-stranded DNA (F1)

Table 9: Concentration for Pattern D

Name	Concentration[nM]
S2-W2	20
F1	80

Step2 Annealing

We annealed DNA samples under the conditions as described in the Types and strands section. We determined the annealing conditions through the simulation in NUPACK ^[3]. We heated the mixture at 95°C for 5 min and slowly cooled it with a thermal cycler.

The annealing conditions of Pattern A and B are shown in Figure 12, and the conditions of annealing of Patterns C and D are shown in Figure 13.

Signal intensity measurements

We measured the signal intensity using a spectrofluoremeter (FP-8300; JASCO) for 3 h with 5-min intervals.

Output confirmation

We applied fluorescence resonance energy transfer (FRET) to confirm whether the output was released. The base sequences of Reporter1 are shown in Table 10. Before the output reacted with Reporter1, FAM did not show fluorescence since Reporter1 of FAM was absorbed by BHQ1. When the output reacted with Reporter1, Reporter1 of FAM became detectable because the distance between the FAM and BHQ1 molecules increased (Figure 15).

Table 10: DNA sequences of Reporter1

Name	Base sequences (5'→3')
RP1	[FAM-] CACACGCTCAATCAC
RP2	AGGTGGTGATTGAGCGTGTG[-BHQ1]

Electrophoresis

1. The gel was set on an electrophoresis chamber.
2. Samples (10 μL) and loading dye (2 μL) were mixed.
3. Samples (10 μL) were added to wells, and 80 V was applied for approximately 200 min.
4. Gels were taken out of wells and stained using a DNA staining solution for 30 min.
5. Fluorescence was observed using a gel imager.

Experiment B

Sample preparation

Step1 Dilution

We diluted each strand to 10 μM in Tris-EDTA buffer supplemented with 12.5 mM MgCl2. The experiment was performed at 20°C.

Step2 Annealing

We annealed DNA samples under the conditions as described in the Types and strands section. We determined the annealing conditions through the simulation in NUPACK ^[3]. We heated the mixture at 95°C for 5 min and slowly cooled it with a thermal cycler. The annealing conditions of S1 and W1 are shown in Figure 18, and the annealing conditions of S2 and W2 are shown in Figure 19.

Electrophoresis

1. The gel was set on an electrophoresis chamber.
2. Samples (10 μL) and loading dye (2 μL) were mixed.
3. Samples (10 μL) were added to wells, and 80 V was applied for approximately 200 min.
4. Gels were taken out of wells and stained using a DNA staining solution for 30 min.
5. Fluorescence was observed using a gel imager.

Experiment C

Sample preparation

Step1 Dilution

We diluted each strand to 10 μM in Tris-EDTA buffer supplemented with 12.5 mM MgCl2. The experiment was performed at 20°C.

Step2 Annealing

We annealed DNA samples under the conditions as described in the Types and strands section. We determined the annealing conditions through the simulation in NUPACK ^[3]. We heated the mixture at 95°C for 5 min and slowly cooled it with a thermal cycler. The annealing condition of DNA walker is shown Figure 20.

Electrophoresis

1. The gel was set on an electrophoresis chamber.
2. Samples (10 μL) and loading dye (2 μL) were mixed.
3. Samples (10 μL) were added to wells, and 80 V was applied for approximately 200 min.
4. Gels were taken out of wells and stained using a DNA staining solution for 30 min.
5. Fluorescence was observed using a gel imager.

Experiment D

Sample preparation

Step1 Dilution

We diluted each strand to 10 μM in Tris-EDTA buffer supplemented with 12.5 mM MgCl2. The experiment was performed at 20°C.

Step2 Annealing

We annealed DNA samples under the conditions as described in the Types and strands section. We determined the annealing conditions through the simulation in NUPACK ^[3]. We heated the mixture at 95°C for 5 min and slowly cooled it with a thermal cycler. The annealing condition of Ground is shown Figure 21.

Electrophoresis

1. The gel was set on an electrophoresis chamber.
2. Samples (10 μL) and loading dye (2 μL) were mixed.
3. Samples (10 μL) were added to wells, and 80 V was applied for approximately 200 min.
4. Gels were taken out of wells and stained using a DNA staining solution for 30 min.
5. Fluorescence was observed using a gel imager.

Incubation

We incubated Grounds A, B, and C at room temperature for 5 h with a thermal cycler to produce Ground A+B, Ground B+C, and Ground (Ground A+B+C).

Experiment E

Sample preparation

Step1 Dilution

We diluted each strand to 10 μM in Tris-EDTA buffer supplemented with 12.5 mM MgCl2 as shown below. The experiment was performed at 20°C.

Table 11: Concentrations for experiment E

Name	Concentration A[nM]	Concentration B[nM]
Walker	20	20
Ground	20	20
F1	80	5
F2	40	2.5
Reporter2	20	20

Signal intensity measurements

We measured the signal intensity using a spectrofluoremeter (FP-8300; JASCO) for 5 h with 10-min intervals.

Output confirmation

We applied fluorescence resonance energy transfer (FRET) to confirm whether the output was released. The base sequences of Reporter2 are shown in Table 12. Before the output reacted with Reporter2, FAM did not show fluorescence since Reporter2 of FAM was absorbed by BHQ1. When the output reacted with Reporter2, Reporter2 of FAM became detectable because the distance between the FAM and BHQ1 molecules increased (Figure 22).

Table 12: DNA sequences of Reporter2

Name	Base sequences (5'→3')	Length
RP3	AGATCAACCGCTCAATC [-BHQ1]	17
RP4	[FAM-] GATTGAGCGGTTGATCTCTCC	21

Electrophoresis

1. The gel was set on an electrophoresis chamber.
2. Samples (10 μL) and loading dye (2 μL) were mixed.
3. Each sample (10 μL) was added to wells and 80 V was applied for approximately 200 minutes.
4. Gels were taken out of wells and stained using a DNA staining solution for 30 minutes.
5. Fluorescence was observed using a gel imager.

Materials and equipment

Materials and equipment were purchased from the companies indicated below.

Table 13: Materials

Material	Name	Company
Poly-Acrylamide Gel	e-PAGEL	ATTO, JAPAN
TBE Buffer	WSE-7051EzRunTBE	ATTO, JAPAN
Loading dye	Gel Loading Dye Purple (6×) B7024S	BioLabs, JAPAN
DNA stain	GelGreen Nucleic Acid Stain 10,000× DMSO (0.5 mL)	Biotium, USA
DNA ladder	Low Molecular Weight DNA	BioLabs, JAPAN

Table 14: Equipment

Equipment	Name	Company
spectrofluoremeter	FP-8300	JASCO, JAPAN
Electrophoresis chamber	AE-y530MW	ATTO, JAPAN
Thermal cycler	GeneAtlas(ASTEC325)	ASTEC, JAPAN
Gel imager	GELSCAN-2	iMeasure, JAPAN