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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

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Information destruction in electronic computers: bit reset to zero (Landauer, Bennett) xyz 0yz Free energy W = Tkln2 Entropy decreasing and hence free energy-consuming operation, which is avoided in reversible computing

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

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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

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Finite automaton: an example An even number of a’s S0, a S1 S0, b S0 S1, a S0 S1, b S1 S1 S0 a b a b Two-states, two-symbols automaton

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Automaton A1 aba S0 S0, a S1 S0, b S0 S1, a S0 S1, b S1 An even number of a’s

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S0 S0, a S1 S0, b S0 S1, a S0 S1, b S1 aba An even number of a’s Automaton A1

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S1 S0, a S1 S0, b S0 S1, a S0 S1, b S1 ba An even number of a’s Automaton A1

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S1 S1, b S1 S0, a S1 S0, b S0 S1, a S0 S1, b S1 ba An even number of a’s Automaton A1

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S1 S0, a S1 S0, b S0 S1, a S0 S1, b S1 a An even number of a’s Automaton A1

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S1 S1, a S0 S0, a S1 S0, b S0 S1, a S0 S1, b S1 a An even number of a’s Automaton A1

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S0 The output S0, a S1 S0, b S0 S1, a S0 S1, b S1 An even number of a’s Automaton A1

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

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

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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

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A new molecular automaton Significant improvement of yields and performance

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

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

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

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

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Experimental implementation

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The automata A1: even number of a’sA2: even number of symbolsA3: ends with b The inputs I1: abb I2: abba I3: babbabb I4: babbabba I5: baaaabb I6: baaaabba I7: abbbbabbabb I8: abbbbaaaabba GGCTGCCGCAGGGCCGCAGGGCCGCAGGGCCGCAGGGCCTGGCTGCCTGGCTGCCTGGCTGCCTGGCTGCCGCAGGGCCGCAGGGCCTGGCTGCCGTCGGTACCGATTAAGTTGGA CGGCGTCCCGGCGTCCCGGCGTCCCGGCGTCCCGGACCGACGGACCGACGGACCGACGGACCGACGGCGTCCCGGCGTGGCGGACCGACGGCAGCCATGGCTAATTCAACC

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Single step proof P-O-GGCT CA G- 32 P 22 H-O-GGCT CA G- 32 P 22 IaIa IbIb Phosphorylated and non- phosphorylated single- symbol input

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Single step proof 32 P-A GGATGC CCTACGCCGA-O-P P-A GGATGC CCTACGCCGA-O-H 12 TaTa TbTb Phosphorylated and non- phosphorylated transition molecule (T1)

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Single step proof IaIa TaTa IaIa TbTb IbIb TaTa IbIb TbTb FokI All possible combinations are mixed with FokI (No Ligase and No ATP in all the reactions) We prove that there is no Ligase and ATP contamination in the FokI batch All possible combinations are mixed with FokI (No Ligase and No ATP in all the reactions) We prove that there is no Ligase and ATP contamination in the FokI batch

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Single step proof 32 P-A GGATGC CCTACGCCGA-O-P 12 P-O-GGCT CA G- 32 P 22 H-O-GGCT CA G- 32 P P-A GGATGC CCTACGCCGA-O-H 12 IaIa IbIb TaTa TbTb IaIa TaTa IaIa TbTb IbIb TaTa IbIb TbTb FokI

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

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Computation capabilities A1Automaton Input I … Expected output S … A2A3 S1 S0 Direct output detection by denaturing PAGE

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Computation capabilities A1Automaton Input I … Expected output S … A2A3 S1 S0 All the runs allowed correct major results with minor byproducts Only small ratio of the byproducts represent computation error All the runs allowed correct major results with minor byproducts Only small ratio of the byproducts represent computation error

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Automaton: A1 Input: I8 Each software molecule: molar ratio to the input T2, T5 and T8 performed on the average 29, 21 and 54 transitions each. Automaton: A1 Input: I8 Each software molecule: molar ratio to the input T2, T5 and T8 performed on the average 29, 21 and 54 transitions each. T2 T8 T5 T2 T5 T2 T8 T5 S0 time Software recycling

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

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Optimization: the best parallel performance 10 M software, 10 M hardware and 5 M input Combined rate: 6.646x10 10 operations/sec/ l ~8000-fold improvement over the previous system

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Conclusions Our experiments demonstrate: 3x10 12 automata/ l (240-fold improvement) Performing 6.6x10 10 transitions/sec/ l (8000-fold improvement) With transition fidelity of 99.9% (2-fold improvement) Dissipating 1.02x10 -8 W/ l as heat at ambient temperature

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

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