Yaakov Benenson, Rivka Adar, Tamar Paz-Elizur, Zvi Livneh and Ehud Shapiro- DNA molecule provides a computing machine with both data and fuel

8/3/2019 Yaakov Benenson, Rivka Adar, Tamar Paz-Elizur, Zvi Livneh and Ehud Shapiro- DNA molecule provides a computing machine with both data and fuel

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GGGCCT), babb2-as (5 -AGCCAGGCCCTGCGGCCCT-GCGGCAGCCAGGC), baaa2-s (5 -CAGGGCCTGGCTGC-CTGGCTGCCTGGCTGCCT), baaa2-as (5 -AGCCAG-GCAGCCAGGCAGCCAGGCAGCCAGGC), abbb3-s (5 -GGCTGCCGCAGGGCCGCAGGGCCGCAGGGCCG), andabbb3-as (5 -CCTGCGGCCCTGCGGCCCTGCGGCCCT-GCGGC).

The input building blocks were prepared by annealing of thesense and antisense strands of each block, i.e., abb (abb-s and

abb-as), etc. The inputs I3-I8 were prepared by stepwise ligationof the building blocks: I3 (babbabb), ligation of abb and babb2;I4 (babbabba), babb2 and abba; I5 (baaaabb), baaa2 and abb; I6(baaaabba), baaa2 and abba; I7 (abbbbabbabb), abbb3, babb2,and abb; and I8 (abbbbaaaabba), abbb3, baaa2, and abba.

When radioactive inputs were required, 20 pmol of the abb-asand abba-as oligonucleotides were 32 P-labeled and added to a varying amount of unlabeled oligonucleotides (2,000 6,000pmol each) before annealing. For radioactive labeling, 20 pmolof the substrate were mixed with 5 l of [ -32 P]ATP and 10 unitsof T4 PNK in 10 l of T4 PNK reaction buffer and incubated at37C for 60 min. Labeled oligonucleotides were purified with anucleotide removal kit (Qiagen, Valencia, CA), eluted into50100 l of EB buffer (10 mM Tris HCl, pH 8.5) (Qiagen), and

dried in a SpeedVac. Termini bound to ligate were phosphorylated before annealing. Typically, 6,000 pmol of a substrateoligonucleotide was phosphorylated by 160 units of T4 PNK in240 l of PNK buffer supplied with 1 mM ATP, for 60 min at37C, ethanol-precipitated, and resuspended in TE buffer(10 mM Tris HCl, 1 mM EDTA, pH 8.0). The annealing wasperformed by mixing equimolar (100 200 M) amounts of thesense and antisense oligonucleotides in 50 mM NaCl, heating to94C, and slow-cooling to room temperature. Double-strandedblocks (1,500 pmol of each) were ligated by T4 DNA ligase( 1,700 units) in 400 l of T4 DNA ligase buffer at 16 C for 1 h.The ligation products were ethanol-precipitated, resuspendedin TE buffer (pH 8.0), and purified from native PAGE (12%,16 cm 1.5 mm) (25). Purified duplexes were quantified byGeneQuant apparatus (Amersham Pharmacia). Single-nucleotide extrusions were introduced into all substrates to avoidblunt-end ligations in control experiments in the presence of ligase.

Computation Reaction. In a typical reaction the Fok I enzyme wasadded in a 1:1 ratio to the desired set of transition molecules, while each software molecule was maintained at least at 1 Mconcentration and at the same time in excess of or equal to theinput. The reactions were performed in 10 l of NEB4 buffer at8C and assayed by 20% denaturing PAGE with input moleculeslabeled in the 5 terminus of the antisense strands. In this assay,S0 and S1 outputs were represented by 15-nt and 16-nt bands,respectively.

Performance Optimization. Performance was optimized with software A2 and input I3. To calculate the total number of opera-tions, gel images were analyzed by using IMAGE GAUGE 3.41software (Fuji). The relative amounts of unreacted input, inter-mediates, and output were measured by assuming linear depen-dence between signal intensity and the amount of radioactivelabel. The total numberof steps S was calculatedaccording to theformula S N ( 1 2 2 . . . L L), where N is a total numberof molecules, L is a number of symbols in an input molecule, and i is a relative abundance of an ith intermediate.

Energy Dissipation Calculation. A computation is a series of single-symbol cleavages, which occur sequentially for each input mol-ecule but concurrently for the entire set of input molecules:

a1 a2 a3 . . . an ^ a1 a2 a3 . . . an ^ a2 a3 . . . an

^ . . . ^ an 1 an .

Each elementary reaction is a hydrolysis of two phosphodiesterbonds with G o 44.31 kJ mol at 25C (26). A corrected value for 8C assuming the same equilibrium constant is G o

(281 K) 41.78 kJ mol. Actual G values depend on theconcentrations of the different species, thus energy dissipation

rate depends on the reaction coordinate. For a particularreaction, we directly measure the number of moles of eachintermediate a i. . . an at a time t and denote it as i(t). We denotethe number of moles of each cleaved symbol a i as i(t),

i t j i 1

n

j t .

To calculate average energy dissipation between time points t1and t2 , we measure the mole numbers of intermediates at thesetime points, then calculate the following for this time interval:(i) an average rate of each elementary reaction, which isequivalent to the transition rate of the molecular computer:

i it2

it1

t2 t1 ,

and ( ii) the average number of moles of each intermediate:

i

i t2 i t12 ,

i

i t2 i t12 .

The average value of G for each elementary reaction in thisinterval is

G i G0 281 K RT ln Q i, Q i

i i 1

iV 1 ,

where V is the reaction volume. The G i has the units of J mole.

To obtain energy dissipation rate, we multiply it by the averagetransition rate. For each elementary reaction, this dissipationrate is g 1 G 1 and the total dissipation is g 1 G 1 2 G 2

. . . n-1 G n-1 , which has units of J s or W. This includesboth enthalpy and entropy contribution, whereas strictly speak-ing, heat dissipation refers to enthalpy change only. There is noaccurate data on entropy change except that it is positive. Thecalculated value of g gives therefore an upper bound on heatdissipation.

ResultsState Machines and Finite Automata. Generally, a state machineconsists of ( i) a data tape divided into cells, each containing asymbol selected from the tape alphabet and ( ii) a computingdevice driven by transition rules. The device is positioned overone of the cells and is in one of a finite number of internal states.Depending on the symbol detected and the internal state, atransition rule instructs the device to write a new symbol, changestate, and move one cell to the left or to the right. The Turingmachine (27) is the most general type of state machine, capableof writing on the tape as well as moving in both directions.

A more restricted, yet important, class of state machines isfinite automata (28). A finite automaton is a unidirectionalread-only Turing machine. Its input is a finite string of symbols.It is initially positioned on the leftmost input symbol in a defaultinitial state, and in each transition moves one symbol to the right,possibly changing its internal state. Its software consists of transition rules, each specifying a next state based on the currentstate and current symbol. A computation terminates after the

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last input symbol is processed, the final state being its output. Alternatively, it may suspend without completion when notransition rule applies. Some states are deemed accepting. Anautomaton accepts an input if there is a computation with thisinput that ends in an accepting final state. A finite automaton with two states and an alphabet of two symbols is shown in Fig.1 A. It determines if an input over the alphabet { a, b} containsan even number of a symbols. Fig. 1 B shows the intermediateconfigurations obtained during a computation of this automa-ton. A two-state, two-symbol automaton can have eight possibletransition rules. Programming such an automaton amounts toselecting transition rules anddeciding which states are accepting. A selection of such programs is shown in Fig. 1 C.

Design and Mechanism of Operation of the Molecular Finite Autom-

aton. Double-stranded DNA molecules with sticky ends realizeboth the software (Fig. 2 C) and the input (Fig. 2 D) and the classIIS restriction enzyme Fok I functions as the hardware (Fig. 2 B).Unlike previous work (22), the core computational step (Fig.2 E) does not use energy-consuming ligase to bond the input andsoftware molecules. Rather, it uses a hitherto unknown capa-bility of Fok I to cleave DNA in the presence of a noncovalenthybridization complex between its recognition and cleavagesites. As a beneficial side effect, the software molecule used inthis step is not consumed, unlike previous work, because itdissociates spontaneously from the cleaved input symbol (Fig.2 E), rendering it reusable for subsequent transitions. The software molecules (Fig. 2C) effectively operate as a family of cofactors of variable specificity (29) to Fok I, each determininga specific Fok I cleavage site on the input molecule, and a fixedamount of software and hardware molecules can, in principle,process any input molecule of any length.

Each computational step cleaves and scatters one input sym-bol, a short molecule with an even shorter double-strandedregion (3 5 bp), which probably dissociates in solution to single-stranded DNAs (Fig. 2 E). For very long inputs the accumulationof input fragments may slow the computation down by reversiblybinding to the sticky ends of the input and the software. It isconceivable that the residual energy of these fragments may besufficient to dispose of them, for example, through selectivehydrolytic digestion.

The computation proceeds until no software moleculematches the state-symbol pair encoded by the exposed sticky endor until the special terminator symbol is cleaved. This final state

encoded by the output molecule can be identified according toeither its length (Fig. 3) or its sticky end (22).

Although a hint of ligase-free operation has been observed(22), its direct realization via removal of ligase and ATP provedimpossible, requiring important design changes. We found thatthe ability of Fok I to cleave DNA with its recognition andcleavage sites attached by sticky-end hybridization was limited tospecific hybridization complexes. To identify them we varied thecomposition of the spacer between the Fok I recognition site and

the sticky end of the software molecule, the length of the spacerand the composition of the sticky end, with correspondingmodifications to the input molecules. We observed that longspacers and low GC content often resulted in cleaving only oneof the input strands, producing a computationally illegal con-figuration. Correct performance was achieved with short spacersand high GC content of the sticky ends. Our final design uses theshortest possible spacers of 0, 1, and 2 bp (Fig. 2 C), whichdictates a particular symbol encoding (Fig. 2 A) and the intro-duction of spacers between the symbols (Fig. 2 D).

To optimize reaction conditions, we calculated the relativeabundance of the hardware software input complex for differ-ent initial concentrations of these molecules, assuming dissoci-ation constants of 2 nM (30) for the hardware software complexand 50 M for software input hybrid. The highest proportion of the complex was found at equimolar ratio of hardware andsoftware molecules, the absolute concentrations of both being inthe micromolar range and in excess of the input. This findingsuggests that the reactive species is a tight (30) hardwaresoftware complex (Fig. 2 E), possessing both recognition andcleavage capabilities. Indeed, experiments showed that preincu-bation of hardware and software molecules before input addi-tion resulted in almost a 2-fold rate increase, supporting thissuggestion.

Proof of the Proposed Mechanism. Conclusive evidence for theability of Fok I to perform a transition based on hybridization without ligation is shown in Fig. 3 A. We incubated a one-symbolinput, complementary software and Fok I and compared phos-

phorylated and nonphosphorylated 5 termini of the input andsoftware molecules. The reaction proceeded independently of the 5 phosphate availability and therefore it was ligase inde-pendent (1). In addition, the software molecule did not undergoany change as judged from the gel image and, as expected, servedas a double-stranded DNA cofactor for the enzyme.

System Performance. This ATP-free system retains the compu-tational capabilities of the previous automaton and even out-performs it. Three programs (Fig. 1 A and C) were applied to aselection of eight inputs up to 12 symbols long (Fig. 1 D). In eachcase the major output molecule was formed in agreement withthe prediction (Fig. 3 B). The byproducts visible at the locationsof the incorrect outputs cannot be unambiguously assigned atthis stage. The correctness of the computation, based on the worst-case assumption that the byproducts represent incorrectoutputs, depends on the software. We obtained single-stepfidelity of 99.9% with input I8 and software A3 whereas theaverage value for 12-symbol inputs was 99.5%. We alsoobserved that the abundance of the putative erroneous bands was almost independent of input length, resulting in lowersingle-step fidelity values for shorter inputs. For example, pro-gram A1 applied to input I2 (four symbols long) renderedsingle-step correctness of only 95%. However, it is clear that thereal fidelity is higher, otherwise the computations would ran-domize completely after 12 steps. Indeed, analysis of the cor-rectness with detection molecules able to hybridize selectively todifferent outputs (22) indicates that at least some of the by-products do not represent realerrors, and theaverage single-step

Fig.1. Finite automataand inputs forwhichwe showmolecularrealizations.( A ) Automaton A1. Incoming unlabeled arrow marks the initial state, andlabeled arrows represent transition rules. A double circle represents an ac-ceptingstate. ( B ) A computationof A1 scanningand digestingthe inputabba.Eachrow represents an intermediatecon gurationshowing currentstate andremaininginput. Thetransition rule applied is shown in brackets.( C ) The twoother automatafor which we demonstratemolecular operation.( D )Thesetofinputs used as fuel.

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fidelity for long inputs determined by this method is 99.9%(data not shown). We have yet to explain this discrepancy.

The reusability of software molecules was demonstrated byusing a small amount of software to process a large amount of input (Fig. 3 C). During this computation one type of softwaremolecule (T8) performed on the average 54 transitions permolecule, with some molecules necessarily performing manymore transitions than the average.

Optimization of the Computation Reactions. We optimized systemperformance in two respects. First, the duration of a singlecomputational step was minimized. The fastest computation wasachieved when 4 M of program A2 (1 M of each softwaremolecule) and 4 M of hardware were mixed with 10 nM of theI3 input at 8 C. This computation proceeded with an initial rateof 20 s per step per input molecule, about 50-fold improvementcompared with the previous system (22) (1,000 s per step per

Fig. 2. A molecular nite automaton that uses input as fuel. ( A ) Encoding of a, b, and terminator (sense strands) and the state, symbol interpretation ofexposed 4-ntsticky ends, the leftmost representingthe current symbol andthe state S1,similarlythe rightmost for S0.( B ) Hardware: The Fok I restriction enzyme,which recognizes the sequence GGATG and cleaves 9 and 13 nt apart on the 5 3 3 and 3 3 5 strands, respectively. ( C ) Software: Each DNA molecule realizesa different transition rule by detecting a current state and symbol and determining a next state. It consists of a state, symbol detector (yellow), a Fok Irecognition site (blue), anda spacer(gray) of variable lengththat determines the Fok I cleavage site insidethe next symbol, which in turn de nesthe next state.

Empty spacers effect S1 to S0 transition, 1-bp spacers maintain the current state, and 2-bp spacers transfer S0 to S1. (D

) Input: The exposed sticky end at the 5terminus of the DNA molecule encodes the initial state and rst symbol. Each symbol is encoded with 5 bp separated by 3-bp spacers. ( E ) Suggested mechanismof operation of the automaton. The computation proceeds via a cascade of transition cycles, each cleaving and scattering one input symbol, exempli ed withthe input molecule bab in the initial state S0 and the transition S0 b3 S1. Both hardware and software molecules are recycled.



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molecule. Even when the ligation is avoided, tile moleculescannot be reused during the same run and the amount consumedis linear in the length of the computation for simple automataand quadratic for universal automata.

Structural decomposition of DNA and other biopolymers isthermodynamically downhill because turning a spatially con-strained sequence of bits into an unordered collection increasesentropy and, furthermore, biopolymer cleavage dissipates heat.Hence input destruction can drive biomolecular computations.

This principle is not readily realized by electronic computers, which destroy information via erasure. Erasure is thermodynam-ically uphill because resetting an unknown bit to zero decreasesentropy (31 33), and past research on energy-efficient comput-ing focused on reversible computers that avoid informationdestruction (31 40).

One hypothetical way to obtain energy from informationproposed by Bennett (31) was based on scanning the input tapeand replacing each input symbol by a random symbol. Informa-tion destruction by randomization can only extract energy froma nonrandom input, as randomizing an already random inputdoes not increase entropy (31, 32). Furthermore, it is not clearhow this method can be realized in practice. Another possibilityis to destroy the input structure while preserving the inputsymbols, effectively turning the sequence of symbols (string) intoan unordered collection (multiset). Indeed this increase inentropy is responsible in part for driving our computing machine.

The theoretical possibility of performing any computation with arbitrarily little energy was suggested three decades ago(31). Our automaton is very similar in its overall logical structureto a hypothetical biomolecular computing device envisioned by

Bennett (ref. 35, p. 531) in 1973, as a possible design for such alow-energy computing device. The important difference is thatunlike the reversible hypothetical device of Bennett, the use of input destruction by our automaton entails entropy increase andnontrivial heat dissipation, and therefore is irreversible. Ourcomputing machine dissipates about 34 kT per transition, whichis 50 times higher than kT ln 2, the theoretical energy gain of randomizing a known bit (32). One can envision other comput-ing machines that dissipate smaller amounts of heat at the

expense of reduced speed and or reduced precision (31, 32, 35,37). Yet DNA cleavage together with its inverse operations of elongation and ligation seem to strike a very practical balancebetween energy, speed, and precision. Furthermore, we believethat the design choice made by living systems to packageinformation in metastable polymers, namely DNA, RNA, andproteins, the decomposition of which dissipates heat and in-creases entropy, is of fundamental importance. This designinhibits the formation of unwanted random information andfacilitates discarding dated, erroneous, or hostile information inthe cell and recycling its constituent bits, rendering the cell anefficient information-processing device. These two observationsregarding the packaging of information and fuel in DNA mayhelp explain its selection as the basis of nature s informationsystem.

We thank A. Regev and A. Horovitz for critical review of this manuscriptand E. Moses, D. Tawfik, N. Tishby, and B. Yurke for helpfuldiscussions.Z.L. is the Incumbent of The Maxwell Ellis Professorial Chair inBiomedical Research. This work was supported by a research grant fromthe Dolphi and Lola Ebner Center for Biomedical Research, the SamuelR. Dweck Foundation, and the Minerva Foundation.

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DNA Input as Fuel | Biological Nanocomputer | Turing Machine-Like Mode

F

Molecular computer fueled by its DNA input

The field of experimental molecular computing, almost a decade old by now, continues to throw new light ontomany aspects of computation. Our recent research mainly deals with the aspect of energy consumption by acomputer. We were able to construct a molecular computer whose sole energy source is its input, acombination unthinkable of in the realm of electronic computers. This energy is extracted as the input datamolecule is destroyed during computation. As a side-effect we were able to modify our previous molecular computer so that it does not consume software molecules during computation: the only component thatchanges is the input, while the hardware and the software molecules remain unchanged.

The computation capabilities of the computer are similar to that of the previous one. The computer is a specialcase of a Turing machine, a two-state, two-symbol finite automaton and as such it is able to answer simplequestions about binary strings, such as Does a binary string of as and bs contain an even number of as? or Is the length of the string even or odd? A sample computation on an input string abba, which gives an answeto the question about the even as is presented below:

The combination of the initial automaton state and input string (S0-abba) as well as the combinations of theintermediate state and the remaining input symbols are all configurations of an automaton. A particular set of the transition rules defines a question that the automaton can answer, and therefore comprises its program.The computation is a succession of configurations, which are generated by applying in turn a suitabletransition rule from the program set to a configuration. In our automaton, each configuration, as well as eachtransition rule, are encoded by a single molecule.

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we follow their formation by a denaturing gel electrophoresis.

The new computer has greatly improved performance characteristics compared to our previous one. Thefastest computation optimized for a single input molecule required only 20 seconds per step per molecule,about 50-fold improvement. Under optimized parallel performance, the cumulative number of operations was6.646x10 operations per second per ml, an ~8000-fold improvement over the previous system. Heatdissipation due to input destruction is about 5.3x10 W/ l.

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Yaakov Benenson, Rivka Adar, Tamar Paz-Elizur, Zvi Livneh and Ehud Shapiro- DNA molecule provides a computing machine with both data and fuel