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**Challenging Traditional Approaches to Computation**

Challenging Traditional Approaches to Computation A Biomolecular Transducer Employing Ternary Language and Rendering a Biological Output Mark Chaskes and Paul Lazarescu Mentor: Tamar Ratner The Schulich Faculty of Chemistry Technion, Haifa, Israel, 32000

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Objective Design a theoretical biomolecular transducer to solve consecutive mathematical equations in ternary. -First divide an input by three and then divide the yeild of that by two

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**What is biomolecular computing?**

A biomolecular computer is a group of molecules that ‘read’ dsDNA and can ‘print’ an output.

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**What is a DNA based transducer?**

A transducer is not a PC; it has unique capabilities that an ordinary computer does not. Advantages include: Direct interface with a biological system Can release a biological output Able to compute in parallel Store large amounts of data in a small volume

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Schematic Diagram S0 S1 Key S0 and S1 are states “a” and “b” are symbols Begins in S0 and changes states depending on read symbols

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**Design on the Molecular Level**

Symbols are dsDNA strands Restriction enzymes cleave the sequence at recognition sites States are determined by the location of cleavage within the symbol

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**Reading 2 from S0 prints 0 and goes to S2**

Process Divide by three transducer reading the input 2-0-0 Reading 2 from S0 prints 0 and goes to S2 State 0 2

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**Reading 0 from S2 prints 2 and goes to S0**

Process Divide by three transducer reading the input 2-0-0 Reading 0 from S2 prints 2 and goes to S0 State 2

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**Reading 0 from S0 prints 0 and encodes the output 0-2-0**

Process Divide by three transducer reading the input 2-0-0 Reading 0 from S0 prints 0 and encodes the output 0-2-0 2 State 0

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**Reading 0 from S0 prints 0 and goes to S0**

Process Divide by two transducer reading the input 0-2-0 S1 Reading 0 from S0 prints 0 and goes to S0 State 0 2

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**Reading 2 from S0 prints 1 and goes to S0**

Process Divide by two transducer reading the input 0-2-0 S1 Reading 2 from S0 prints 1 and goes to S0 State 0 2

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**Reading 0 from S0 prints 0 and goes to S0**

Process Divide by two transducer reading the input 0-2-0 S1 Reading 0 from S0 prints 0 and goes to S0 1 State 0

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**Molecular Design of the Input**

Encoding in Ternary (18 in base ten) Terminator EagI Recognition Site BbvI Recognition Site Spacers AATTCGGCCGTT..8 base..CTCCTCGCAGC..8 base..CTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAA..pairs ..GAGGAGCGTCG..pairs ..GAGCAATCAGAATCAGAAACGACTTTAA Plasmid BseRI Recognition Site

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**Divide-by-three Computation**

First Restriction AATTCGGCCGTT..8 base..CTCCTCGCAGC..8 base..CTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAA..pairs ..GAGGAGCGTCG..pairs ..GAGCAATCAGAATCAGAAACGACTTTAA GGTATT...8 base...CTCCTCGCAGC...3 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CAGA S1 to S0, read 0, print 1 CTCGTT...8 base...CTCCTCGCAGC...4 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...AGAA S2 to S0, read 0, print 2 AGTCTT...8 base...CTCCTCGCAGC...2 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...TCAG S0 to S0, read 0, print 0 AGTCTT...8 base...CTCCTCGCAGC...1 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...CCAT S0 to S1, read 1, print 0 GGTATT...8 base...CTCCTCGCAGC...2 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CATA S1 to S1, read 1, print 1 CTCGTT...8 base...CTCCTCGCAGC...3 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...ATAA S2 to S1, read 1, print 2 GGTATT...8 base...CTCCTCGCAGC...1 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...AGCA S1 to S2, read 2, print 1 AGTCTT...8 base...CTCCTCGCAGC AATCAGAA...pairs ...GAGGAGCGTCGGAGC S0 to S2, read 2, print 0 CTCGTT...8 base...CTCCTCGCAGC...2 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...GCAA S2 to S2, read 2, print 2

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**Divide-by-three Computation**

First Restriction AATTCGGCCGTT CTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGC AATCAGAATCAGAAACGACTTTAA GGTATT...8 base...CTCCTCGCAGC...3 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CAGA S1 to S0, read 0, print 1 CTCGTT...8 base...CTCCTCGCAGC...4 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...AGAA S2 to S0, read 0, print 2 AGTCTT...8 base...CTCCTCGCAGC...2 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...TCAG S0 to S0, read 0, print 0 AGTCTT...8 base...CTCCTCGCAGC...1 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...CCAT S0 to S1, read 1, print 0 GGTATT...8 base...CTCCTCGCAGC...2 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CATA S1 to S1, read 1, print 1 CTCGTT...8 base...CTCCTCGCAGC...3 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...ATAA S2 to S1, read 1, print 2 GGTATT...8 base...CTCCTCGCAGC...1 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...AGCA S1 to S2, read 2, print 1 AGTCTT...8 base...CTCCTCGCAGC AATCAGAA...pairs ...GAGGAGCGTCGGAGC S0 to S2, read 2, print 0 CTCGTT...8 base...CTCCTCGCAGC...2 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...GCAA S2 to S2, read 2, print 2

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**Divide-by-three Computation**

First Ligation AGTCTT...8 base...CTCCTCGCAGC AATCAGAA...pairs ...GAGGAGCGTCGGAGC Transition Molecule S0 to S2, reading 2, printing 0 AATTCGGCCGTT CTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGC AATCAGAATCAGAAACGACTTTAA DNA Ligase CTCGTT...8 base...CTCCTCGCAGC...4 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...AGAA S2 to S0, read 0, print 2 AGTCTT...8 base...CTCCTCGCAGC...2 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...TCAG S0 to S0, read 0, print 0 GGTATT...8 base...CTCCTCGCAGC...3 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CAGA S1 to S0, read 0, print 1 AGTCTT...8 base...CTCCTCGCAGC...1 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...CCAT S0 to S1, read 1, print 0 GGTATT...8 base...CTCCTCGCAGC...2 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CATA S1 to S1, read 1, print 1 CTCGTT...8 base...CTCCTCGCAGC...3 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...ATAA S2 to S1, read 1, print 2 GGTATT...8 base...CTCCTCGCAGC...1 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...AGCA S1 to S2, read 2, print 1 S0 to S2, read 2, print 0 CTCGTT...8 base...CTCCTCGCAGC...2 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...GCAA S2 to S2, read 2, print 2 AGTCTT...8 base...CTCCTCGCAGC AATCAGAA...pairs ...GAGGAGCGTCGGAGC

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**Divide-by-three Computation**

First Ligation AATTCGGCCGTTAGTCTT...8 base...CTCCTCGCAGCCTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAATCAGAA...pairs ...GAGGAGCGTCGGAGCAATCAGAATCAGAAACGACTTTAA AATTCGGCCGTTAGTCTT...8 base...CTCCTCGCAGCCTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAATCAGAA...pairs ...GAGGAGCGTCGGAGCAATCAGAATCAGAAACGACTTTAA CTCGTT...8 base...CTCCTCGCAGC...4 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...AGAA S2 to S0, read 0, print 2 AGTCTT...8 base...CTCCTCGCAGC...2 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...TCAG S0 to S0, read 0, print 0 GGTATT...8 base...CTCCTCGCAGC...3 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CAGA S1 to S0, read 0, print 1 AGTCTT...8 base...CTCCTCGCAGC...1 base AATCAGAA...pairs ...GAGGAGCGTCG...pairs...CCAT S0 to S1, read 1, print 0 GGTATT...8 base...CTCCTCGCAGC...2 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...CATA S1 to S1, read 1, print 1 CTCGTT...8 base...CTCCTCGCAGC...3 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...ATAA S2 to S1, read 1, print 2 GGTATT...8 base...CTCCTCGCAGC...1 base AACCATAA...pairs ...GAGGAGCGTCG...pairs...AGCA S1 to S2, read 2, print 1 S0 to S2, read 2, print 0 CTCGTT...8 base...CTCCTCGCAGC...2 base AAGAGCAA...pairs ...GAGGAGCGTCG...pairs...GCAA S2 to S2, read 2, print 2 AGTCTT...8 base...CTCCTCGCAGC AATCAGAA...pairs ...GAGGAGCGTCGGAGC

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**Continue cycle of restriction, hybridization, and ligation until terminator is cleaved**

AATTCGGCCGTTAGTCTT...8 base...CTCCTCGCAGCCTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAATCAGAA...pairs ...GAGGAGCGTCGGAGCAATCAGAATCAGAAACGACTTTAA AATTCGGCCGTTAGTCTT...8 base...CTCCTCGCAGCCTCGTTAGTCTTAGTCTTTGCTGAAATT TTAAGCCGGCAATCAGAA...pairs ...GAGGAGCGTCGGAGCAATCAGAATCAGAAACGACTTTAA

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**Divide-by-three Computation**

Final Restriction AATTCGGCCGTTAGTCTTCTCGTTAGTCTT TGCTGAAATT TTAAGCCGGCAATCAGAAGAGCAATCAG CTTTAA

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**Divide-by-three Computation**

Final Ligation TGCTGA...Reporter... AAACGACT....Gene 0....ACGA Detection Molecule AATTCGGCCGTTAGTCTTCTCGTTAGTCTT TGCTGAAATT TTAAGCCGGCAATCAGAAGAGCAATCAG CTTTAA

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**Divide-by-three Computation**

Final Ligation AATTCGGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGGCAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA This transducer has printed 020, which is 6 in base ten (610). Check: 18/3 = 6? Yes.

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Biological Function 0 AATTCGGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGGCAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA Biological Function 0 could be releasing a drug, changing the bacteria phenotype, etc.

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**Divide-by-two Computation**

Transition Stage AATTCGGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGGCAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA A third restriction enzyme that cleaves within its recognition site is necessary only when consecutive computation (using two separate transducers) occurs.

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**Divide-by-two Computation**

Transition Stage GGCCTTTCTCCTCGCAGCT AAAGAGGAGCGTCGACCGG Reinsertion Molecule AATTC GGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGG CAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA Reinsertion of the recognition sites is also required for consecutive computation.

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**Divide-by-two Computation**

Transition Stage AATTCGGCCTTTCTCCTCGCAGCTGGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGGAAAGAGGAGCGTCGACCGGCAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA

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**Divide-by-two Computation**

Entire cycle repeats again until terminator is cleaved once more AATTCGGCCTTTCTCCTCGCAGCTGGCCGTTAGTCTTCTCGTTAGTCTTTGCTGA...Reporter...TGCTGAAATT TTAAGCCGGAAAGAGGAGCGTCGACCGGCAATCAGAAGAGCAATCAGAAACGACT....Gene 0....ACGACTTTAA

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**Divide-by-two Computation**

Final Restriction AATTAGTCTTGGTATTAGTCTT TGCTGA...Reporter...TGCTGAAATT TTAATCAGAACCATAATCAG CT....Gene 0....ACGACTTTAA

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**Divide-by-two Computation**

Final Ligation TGCTGA...Reporter... AAACGACT....Gene 0....ACGA Detection Molecule AATTAGTCTTGGTATTAGTCTT TGCTGA...Reporter...TGCTGAAATT TTAATCAGAACCATAATCAG CT....Gene 0....ACGACTTTAA

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**Divide-by-two Computation**

Final Ligation AATTAGTCTTGGTATTAGTCTTTGCTGA...Reporter...TGCTGA...Reporter...TGCTGAAATT TTAATCAGAACCATAATCAGAAACGACT....Gene 0....ACGACT....Gene 0....ACGACTTTAA (310) This transducer has printed 010, which is 3 in base ten. Check: (18/3)/2 = 3? Yes.

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Biological Function 0 AATTAGTCTTGGTATTAGTCTTTGCTGA...Reporter...TGCTGA...Reporter...TGCTGAAATT TTAATCAGAACCATAATCAGAAACGACT....Gene 0....ACGACT....Gene 0....ACGACTTTAA

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**Discussion & Conclusions**

This project worked as expected. 18 ÷ 3= 6 ; 6 ÷ 2= 3 No molecule encoded the recognition site of an enzyme Proof of concept worked however not done in practicality. Transducers engineered functioned as coded

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Acknowledgements We would like to sincerely thank Mr. Russell N. Stern for his generosity and donation. Thank you to the Louis Herman Israel Experience Fund for their contribution. We would also like to thank our mentor Tamar Ratner, for her continued dedication and help. Finally, we would like to thank Professor Ehud Keinan for allowing us to use his laboratory and his student.

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