DNA approach to Turing machines

One of the most exciting moments in DNA computing was the physical real-ization of an abstract Turing machine using DNA molecules [Benenson et al., 2001]. The paradigm is to use DNA as software, and enzymes as hardware.

The way in which these molecules undergo chemical reactions with each other allows simple operations to be performed as a byproduct of the reactions. The devices can be controlled by the composition of the DNA software molecules.

Of course this is a completely different approach as compared to pushing elec-trons around a dry circuit in a conventional computer.

Turing machines. In the 1930’s several mathematicians began to think about what it means to be able to compute a function. Alan Turing and Alonzo Church independently arrived at equivalent conclusions. As we might phrase their common definition now, a function is computable if it can be computed by a Turing machine.

In fact, a Turing machine (TM) is a very simple machine. Yet, a TM has the power of any digital computing machinery. A Turing machine processes an infinite tape. This tape is divided into squares (cells), any square of which may contain a symbol from a finite alphabet, with the restriction that there can be only finitely many non-blank squares on the tape. The TM has a read/write head positioned at some square on the tape. Furthermore, at any time, the Turing machine is in any one of a finite number of internal states. The Turing machine is further specified by a set of instructions of the following form:

(currentState, currentSymbol,nextState, newSymbol,left/right).

This instruction means: if the TM is now in currentState, and the sym-bol under the readwrite head is currentSymbol, change its internal state to nextState, replace the symbol on the tape at its current position bynewSymbol, and move the readwrite head one square in the given direction (left or right). If a Turing machine is in a condition for which it has no instruction, it halts.

DNA implementation of Turing machines. In 2001 Shapiro and colleagues introduced the first version of a Turing machine (biomolecular computer) cre-Nevenka Dimitrova

29 ated in a test tube capable of performing simple mathematical calculations [Be-nenson et al., 2001; Regev et al., 2002]. In this implementation they used ATP molecules for energy. An improved design that uses its input DNA molecule as its sole source of energy, was introduced in 2003 [Benenson et al., 2003].

In this approach, symbols are encoded with 5 base pairs: the symbol ais encoded by ‘tggct’, the symbolbis encoded by ‘gcagg’ and the terminal sym-boltis encoded by ‘gtcgg’. The sticky ends for state-symbol pairs are encoded as follows: S1,ais encoded by ‘tggc’,S1,bis encoded by ‘gcag’,S1,tis encoded by ‘gtcg’,S₀,ais encoded by ‘ggct’,S₀,b is encoded by ‘cagg’, S0,tis encoded by ‘tcgg’. The ‘hardware’ is implemented using the property of the FokI enzyme and recognition site: FokI always recognizes the sequence

‘ggatg’ and then ‘cuts’ 9 and 13 nucleotides on the 5→3and 3→5strands, respectively, leaving ‘sticky’ (not even) ends (see Figure 2.4). DNA stores en-ergy, available upon hybridization of complementary strands or hydrolysis of its phosphodiester backbone.

n g g a t g n n n n n n n n n n n n n n c c t a c n n n n n n n n n n n n n

5′ 3′

FokI recognition

sequence 9 nucleotides

13 nucleotides

Figure 2.4. FokI enzyme recognition sequence and cutting action.

Figure 2.5 shows an example of the DNA molecules that embody the soft-ware (i.e. transition rules): each molecule realizes a different transition rule by detecting a current state and symbol and determining a next state. Each transi-tion consists of a FokI recognitransi-tion site,state,symboldetector molecule (four nucleotides, single stranded). A so called spacer double stranded DNA of variable length that determines the FokI cutting site inside the next symbol is introduced. The spacers define the next state. There are empty spacers that re-alizeS₁toS₀transition, 1-base-pair long spacers that maintain the current state, and 2-base-pair spacers that transferS0toS1. For transitionT1, the molecule contains the FokI recognition site, then one base pair spacer, followed by the ccga which is the complement ofS₀,a(represented by ‘ggct’, as introduced above). The software molecules (shown in Figure 2.5) effectively operate as a family of cofactors of variable specificity to FokI enzyme, each determining a specific FokI cleavage site on the input molecule. A fixed amount of software and hardware molecules can process any input molecule of any length.

An example of an input molecule is shown in Figure 2.6 where the exposed uneven (or ‘sticky’) end at the 5 terminus of the DNA molecule encodes the

– The Many Strands of DNA Computing

30

Figure 2.5. DNA sequences representing transitions starting with stateS₀.

initial state and first symbol. Each symbol is encoded with 5 base pairs sepa-rated by 3-base-pair spacers.

Figure 2.6 illustrates one computational cycle of the automaton. The com-putation proceeds via a series of transition cycles. During each transition, the hardware-software complex cuts and scatters one input symbol. This is exem-plified with the input molecule that starts withab...in the initial stateS0and the transitionS0 a

→S1. At the top of the figure there is a software molecule and an input molecule. In the middle of the figure a ligated software-input mole-cule is shown with the recognition site for the FokI enzyme. FokI cuts the input molecule inside the next symbol as shown in the third row of the figure. We should note here that the hardware-software molecules are recycled. Each sub-sequent computational step of the automaton consists of a reversible hybridiza-tion between a software molecule – and an input molecule, followed by an irreversible software-directed cleavage (cutting) of the input molecule, which drives the computation forward by increasing entropy and releasing heat. The cleavage uses the capability of the restriction enzyme FokI, which serves as the hardware, to operate on a noncovalent software-input hybrid. In Shapiro’s initial implementation, the software-input ligation step consumed one software molecule and two ATP molecules per step. In this implementation there is no need for ligation, which means that a fixed amount of software and hardware molecules can, in principle, process any input molecule of any length without external energy.

Medical computer using DNA Turing machines. A novel application of the DNA turing machine is to assess concentrations of specific RNA molecules [Benenson et al., 2004] (in vitro), which may be overproduced or underpro-duced, in specific types of cancer. Using pre-programmed medical knowledge, the computer then makes its diagnosis based on the detected RNA levels. In response to a cancer diagnosis, the output unit of the computer can initiate the controlled release of a single-stranded DNA molecule that is known to inter-fere with the cancer cell’s activities, causing it to self-destruct (apoptosis). In case everything looks normal the drug does not get released.

Nevenka Dimitrova

31 FokI recognition site 9 nt

13 nt

Figure 2.6. Software computation of the input sequenceab...

Critics question what is special about this method. In truth, the novelty of their study does not lie in the method of recognizing cancer; they do rely on existing diagnostic methodology. What is different about their approach is its potential for performing diagnostics and therapy within tissue itself. Tradi-tional diagnostic methods require tissue extraction, isolation of the molecular marker in question, and its comparison to the normal tissue. The end goal for the medical computer in the future is to be administered as a drug, and distrib-uted throughout the body by the blood stream to detect specific disease markers autonomously and independently in every cell. In this manner, a single cancer cell could be detected and destroyed before the tumor develops.

The most interesting achievement to date in DNA computing is the

pro-four base codon framework by employing the protein synthesis mechanism of E. coli. The best student paper award went to this paper. This is the first in vivo implementation of a Turing machine paving the way to doctor-in-a-cell/programmable DNA computer.