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Molecular Computing Machine Uses its Input as Fuel Kobi Benenson Joint work with Rivka Molecular Computing Machine Uses its Input as Fuel Kobi Benenson Joint work with Rivka Adar, Tamar Paz-Elizur, Zvi Livneh and Ehud Shapiro Department of Computer Science and Applied Math & Department of Biological Chemistry Weizmann Institute of Science, Rehovot, Israel

Free energy Information destruction in electronic computers: bit reset to zero (Landauer, Bennett) 0 Free energy Information destruction in electronic computers: bit reset to zero (Landauer, Bennett) 0 yz W = Tkln 2 xyz Entropy decreasing and hence free energy-consuming operation, which is avoided in reversible computing

Information destruction in biology: physical degradation of the bit sequence (string to multiset) Free Information destruction in biology: physical degradation of the bit sequence (string to multiset) Free energy xyz > 40 k. T {x, yz} Entropy increasing and energy-releasing operation, which can be exploited to avoid the demand for external energy source

 • Input destruction can be used as a source of energy • If • Input destruction can be used as a source of energy • If output is smaller than input (e. g. yes/no questions), computation can be accomplished without external energy • We realized this theoretical possibility

Finite automaton: an example An even number of a’s a S 0, a S Finite automaton: an example An even number of a’s a S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 b S 0 S 1 a Two-states, two-symbols automaton b

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 S 0 a b a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 S 0, a S 1 S 0 a b a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 b a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 S 1 b a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1, a S 0 S 1 a

Automaton A 1 An even number of a’s S 0, a S 1 S Automaton A 1 An even number of a’s S 0, a S 1 S 0, b S 0 S 1, a S 0 S 1, b S 1 S 0 The output

Previous molecular finite automaton Benenson, Paz-Elizur, Adar, Keinan, Livneh & Shapiro, Nature 414, 430 Previous molecular finite automaton Benenson, Paz-Elizur, Adar, Keinan, Livneh & Shapiro, Nature 414, 430 (2001)

Ligase and ATP use Software is consumed Ligase and ATP use Software is consumed

A new molecular automaton • Key differences: • No Ligase, hence no ATP • A new molecular automaton • Key differences: • No Ligase, hence no ATP • Software reuse – molecule not consumed during transition • Hence a fixed amount of hardware and software molecules may process input of any length without external source of energy

A new molecular automaton • Significant improvement of yields and performance A new molecular automaton • Significant improvement of yields and performance

Modifications in the molecular design No Ligase – no ATP Software is recycled Modifications in the molecular design No Ligase – no ATP Software is recycled

Problems of the previous design • Evidence of Ligase-free computation, but inefficient • Often Problems of the previous design • Evidence of Ligase-free computation, but inefficient • Often Fok. I cuts only one input DNA strand • Computation stalled after a few steps

Modifications in the molecular design 3 -bp spacers between symbols Symbols 5 -bp long Modifications in the molecular design 3 -bp spacers between symbols Symbols 5 -bp long

Modifications in the molecular design The software molecules Shortest possible spacers between the Fok. Modifications in the molecular design The software molecules Shortest possible spacers between the Fok. I site and the recognition sticky ends: 0 -, 1 - and 2 -bp

Experimental implementation Experimental implementation

The automata A 1: even number of a’s A 2: even number of symbols The automata A 1: even number of a’s A 2: even number of symbols A 3: ends with b The inputs I 1: abb I 5: baaaabb I 2: abba I 6: baaaabba I 3: babbabb I 7: abbbbabbabb I 4: babbabba I 8: abbbbaaaabba GGCTGCCGCAGGGCCGCAGGGCCTGGCTGCCTGGCTGCCGCAGGGCCTGGCTGCCGTCGGTACCGATTAAGTTGGA CGGCGTCCCGGCGTCCCGGACCGACGGACCGACGGCGTCCCGGCGTGGCGGACCGACGGCAGCCATGGCTAATTCAACC

Single step proof Ia P-O-GGCT 22 CA 32 G- P Ib H-O-GGCT 22 CA Single step proof Ia P-O-GGCT 22 CA 32 G- P Ib H-O-GGCT 22 CA 32 G- P Phosphorylated and nonphosphorylated single-symbol input

Single step proof Phosphorylated and nonphosphorylated transition molecule (T 1) Ta 32 P-A 12 Single step proof Phosphorylated and nonphosphorylated transition molecule (T 1) Ta 32 P-A 12 GGATGC CCTACGCCGA-O-P Tb 32 P-A 12 GGATGC CCTACGCCGA-O-H

Single step proof Ia Ia Ib Ib Ta Tb • All possible combinations are Single step proof Ia Ia Ib Ib Ta Tb • All possible combinations are mixed with Fok. I (No Ligase and No ATP in all the reactions) • We prove that there is no Ligase and ATP contamination in the Fok. I batch Fok. I

Single step proof Ia Ia Ib Ib Ia P-O-GGCT 22 CA 32 G- P Single step proof Ia Ia Ib Ib Ia P-O-GGCT 22 CA 32 G- P Ib Ta Tb H-O-GGCT 22 CA 32 G- P Ta 32 P-A 12 GGATGC CCTACGCCGA-O-P Tb 32 P-A 12 GGATGC CCTACGCCGA-O-H Fok. I

Computation capabilities A set of 8 inputs was tested with 3 software programs, at Computation capabilities A set of 8 inputs was tested with 3 software programs, at standard conditions: 4 m. M Fok. I 4 m. M software 1 m. M input 8 o. C 20 min

Computation capabilities Direct output detection by denaturing PAGE Automaton A 1 A 2 A Computation capabilities Direct output detection by denaturing PAGE Automaton A 1 A 2 A 3 Expected output S… 10010110 10101010 12345678 S 1 S 0 Input I…

Computation capabilities • All the runs allowed correct major results with minor byproducts • Computation capabilities • All the runs allowed correct major results with minor byproducts • Only small ratio of the byproducts represent computation error Automaton A 1 A 2 A 3 Expected output S… 10010110 10101010 12345678 S 1 S 0 Input I…

T 2 T 8 T 8 T 5 T 2 Software recycling • Automaton: T 2 T 8 T 8 T 5 T 2 Software recycling • Automaton: A 1 • Input: I 8 • Each software molecule: 0. 075 molar ratio to the input T 5 T 2, T 5 and T 8 performed on the average 29, 21 and 54 transitions each. T 8 T 2 T 8 T 5 S 0 time

Optimization: the fastest computation • 4 m. M software, 4 m. M hardware and Optimization: the fastest computation • 4 m. M software, 4 m. M hardware and 10 n. M input • Rate: 20 sec/operation/molecule • 50 -fold improvement over the previous system

Optimization: the best parallel performance • 10 m. M software, 10 m. M hardware Optimization: the best parallel performance • 10 m. M software, 10 m. M hardware and 5 m. M input • Combined rate: 6. 646 x 1010 operations/sec/ml • ~8000 -fold improvement over the previous system

Conclusions Our experiments demonstrate: • 3 x 1012 automata/ml (240 -fold improvement) • Performing Conclusions Our experiments demonstrate: • 3 x 1012 automata/ml (240 -fold improvement) • Performing 6. 6 x 1010 transitions/sec/ml (8000 -fold improvement) • With transition fidelity of 99. 9% (2 -fold improvement) • Dissipating 1. 02 x 10 -8 W/ml as heat at ambient temperature

Conclusions We developed a molecular finite automaton that realizes theoretical possibility using the input Conclusions We developed a molecular finite automaton that realizes theoretical possibility using the input as the sole source of energy

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