Enzyme-Free Nucleic Acid Logic Circuits

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Science  08 Dec 2006:
Vol. 314, Issue 5805, pp. 1585-1588
DOI: 10.1126/science.1132493


Biological organisms perform complex information processing and control tasks using sophisticated biochemical circuits, yet the engineering of such circuits remains ineffective compared with that of electronic circuits. To systematically create complex yet reliable circuits, electrical engineers use digital logic, wherein gates and subcircuits are composed modularly and signal restoration prevents signal degradation. We report the design and experimental implementation of DNA-based digital logic circuits. We demonstrate AND, OR, and NOT gates, signal restoration, amplification, feedback, and cascading. Gate design and circuit construction is modular. The gates use single-stranded nucleic acids as inputs and outputs, and the mechanism relies exclusively on sequence recognition and strand displacement. Biological nucleic acids such as microRNAs can serve as inputs, suggesting applications in biotechnology and bioengineering.

To date, no man-made chemical circuits even remotely approach the complexity and reliability of silicon-based electronics. Once reliable principles for their design are established, synthetic chemical circuits could be used routinely to control nanoscale devices in vitro, to analyze complex chemical samples in situ, or to interface with existing biological circuits in vivo (1). Construction of synthetic biological circuits de novo is a powerful test of design principles (2).

Rational design of nucleic acid devices is simplified by the predictability of Watson-Crick base pairing; thus, nucleic acids are a promising alternative to proteins for synthetic chemical circuits. Allosteric ribozymes that take small molecules as input have been shown to perform logical functions (3). However, their output (a cleaved or ligated oligonucleotide) is of a different form than the input; hence, cascading is difficult. Automata performing multiple logical operations in parallel (4), single-step signaling cascades (5), and a feedback cycle that acts as an exponential chain reaction (6) were built using deoxyribozymes controlled by input oligonucleotides (7). Another approach uses sequence recognition to control enzyme catalysis of covalent bond formation and breakage (810). Alternatively, nucleic acid reactions can be driven without enzyme or (deoxy)ribozyme catalysis (11, 12); this principle has been exploited to construct DNA-based logic gates and signaling cascades (13, 14). Such molecular automata may give rise to “smart” therapeutics for medical applications (7, 9, 10). Recently, engineered nucleic acid logic switches based on hybridization and conformational changes have been successfully demonstrated in vivo (15, 16). The remaining challenge is to design chemical logic gates that can be combined to construct large, reliable circuits. The analogous challenge for engineering electronic circuits was met by the development of digital design principles (17); these may also prove essential for designing complex yet robust chemical circuits.

We report the construction of in vitro DNA-based logic gates and circuits that embody digital design principles: logic, cascading, restoration, fan-out, and modularity. These circuits implement a complete set of Boolean logic functions (AND, OR, and NOT) using short oligonucleotides as input and output. Because the input and output are of the same form, the gates can be cascaded to create multilayer circuits. Logical values “0” and “1” are represented by low and high concentrations, respectively. Signal restoration is performed by threshold and amplifier gates that protect against noise, signal loss, and leaky reactions. Amplifier gates can also be used to ensure that a logic gate generates sufficient signal to drive multiple downstream targets. Watson-Crick interactions between modular recognition domains determine the connectivity of gates. Sequences can be chosen with few constraints, allowing the construction of arbitrary circuits with negligible cross-activation. Furthermore, modular construction allows for interfacing with existing molecular components—be they predesigned subcircuits or naturally occurring nucleic acids.

Gate function is entirely determined by base pairing and breaking. Every gate consists of one or more gate strands and one output strand (Fig. 1A and fig. S1). The output strand either serves as an input to a downstream gate or is modified with a dye label to provide a readout in a fluorescence experiment. Both ends of the output strand (Fig. 1A), or only one end (translator gates in Fig. 2), can be attached to the gate complex. Figure 1A shows an AND-gate assembled from an output strand and two gate strands. The addition of single-stranded inputs to a solution containing the gate initiates a computation. Each gate strand contains a recognition region that is complementary to its input. Initially, the recognition regions of all gate strands are double-stranded and therefore inert, except for the toehold farthest from the output strand (strand G in Fig. 1A). When the first input binds this toehold, it displaces the first gate strand by three-way branch migration (18, 19), exposing the toehold for the subsequent input and releasing an inert double-stranded waste product. A similar process can now occur for the second input. The output strand is released if and only if both inputs are present. To implement this design, DNA sequences (tables S1 to S3) were selected to ensure correct complementarity while minimizing spurious interactions (20).

Fig. 1.

Two-input AND gate. (A) The gate consists of three DNA strands, Eout [57 nucleotides (nt)], F (60 nt), and G (36 nt). The 3′ ends are marked by arrows. Toeholds and toehold binding regions (all six nucleotides) are indicated in color. Input strands Fin and Gin (36 nt) are complementary to recognition regions within the corresponding gate strands F and G. (B) Truth table for the two-input AND gate. The released output strand is highlighted. (C) In fluorescence experiments, strands Ff [carboxytetramethylrhodamine (TAMRA) fluorophore at the 3′ end] and Eq (Iowa Black RQ quencher at the 5′ end, without bulge loop) were used instead of F and Eout (see inset). Release of output strand results in increased fluorescence. Experiments were conducted at 25°C with gate concentrations of 250 nM and input concentrations of 300 nM in a Tris-acetate-EDTA buffer containing 12.5 mM Mg++. (D) Nondenaturing gel electrophoresis directly confirms reaction intermediates and waste products for each possible input combination. Lanes 1 to 4: The samples are as described in entries 1 to 4 of the truth table. The gate used in this experiment is as shown in (A). Lane 5: 10–base pair (bp) ladder.

Fig. 2.

Translator gates, NOT operation, and signal restoration. Dashed arrows indicate where input or output strands can serve as inputs to downstream gates. (A) Circuit operation at 37°C with RNA inputs and DNA gates in a total RNA background. All gates are at 25 nM, synthetic RNA inputs are at 30 nM, and total RNA (mouse brain) is at a concentration of 200 μg/ml. Proper function is observed. For comparison, experiments with no total RNA were performed, using either both RNA inputs or both DNA inputs. (B) The NOT gate consists of a translator gate and an inverter strand complementary to let-7c. Gate, inverter strand, and input concentrations are 250 nM, 300 nM, and 300 nM, respectively. Here and in all subsequent experiments, the temperature was 25°C and DNA equivalents of the biological microRNAs were used. If let-7c was present, inverter strand K preferentially hybridized to let-7c. Otherwise, inverter strand K triggered the translator. (C) The thresholding gate, using a dye/quencher-labeled readout gate to monitor the output. Strand Th2in is part of the thresholding unit and was added before the start of the experiment. The final fluorescence is plotted against the input concentration for two different concentrations of the threshold gate.

The two-input AND gate has four entries in its truth table (Fig. 1B) and was shown to function correctly when tested by fluorescence kinetics experiments and gel electrophoresis (Fig. 1, C and D). We also designed multi-input AND gates using the same principles and showed that they work reliably (fig. S2). The gates in all of our experiments were purified by gel electrophoresis after triggering “leaky” complexes (20) (fig. S3).

The output strand of one gate may be an input strand to a downstream gate. It is essential that the output strand not interact with downstream gates before release. Protecting the toehold binding region of output strands in upstream gates prevents such interactions. We built a circuit composed of one AND gate and two translator gates that demonstrates this principle (Fig. 2A and fig. S4). A translator gate converts the signal encoded in the input strand to the signal encoded in the output strand and is implemented as a single-input AND gate. The translator gates JK and LM translate two biological microRNA sequences (mouse let-7c and miR-124a) into outputs with recognition regions identical to strands Gin and Fin. The input to a translator gate and the recognition region of its output strand need only share sequence in the toehold region. If two translators are cascaded, then there is no sequence restriction between the initial input strand and the final output strand. This is called a full translator; the cascading of NO and HI is an example (Fig. 3 and fig. S1). Translators can connect subcircuits that do not a priori use the same sequences for the toehold and recognition regions. This is particularly useful for adapting an existing circuit to compute on arbitrary biological inputs.

Fig. 3.

Signal propagation through a complex chemical circuit combining AND, OR, sequence translation, input amplification, and signal restoration. The five-layer circuit consists of a total of 11 gates and accepts six inputs. With the exception of the threshold gate, which was at 100 nM with its Th2in strand at 150 nM, all gates were at 200 nM (1×) per gate. Unless otherwise specified, inputs were added at 250 nM (1.25×). miR-143 was added at 50 nM (0.25×) and subsequently amplified by the input amplifier. (Inset) Fluorescence traces of circuit operation without and with the signal restoration module (threshold plus amplifier). The traces for input conditions corresponding to a logical TRUE output (ON) are clearly distinguishable from the logical FALSE output (OFF). Cases tested include when all inputs are present, all cases in which exactly one input is missing, and combinations of inputs that turn off an OR clause. Assuming monotonicity, withholding additional inputs will never lead to a logical TRUE output. To determine the response of the circuit to a leaky OFF signal, input miR-124a was added at 50 nM (0.25×) while all other inputs were added normally.

The circuit of Fig. 2A was also tested under conditions relevant to potential biological applications. The circuit works comparably with RNA inputs as with DNA inputs because gate function depends solely on Watson-Crick complementarity (Fig. 2A and fig. S4). Increasing the temperature to 37°C does not degrade circuit performance. Finally, the circuit functions well in the presence of potentially interfering biological RNA (mouse brain total RNA) at a concentration in excess of gate complexes and input strands.

Because a small set of logic gates (AND, OR, and NOT) is sufficient for effective computation of any Boolean function, we developed DNA gates to perform these operations. Logical OR functionality is obtained by using two gates that produce the same output. We constructed a three-gate chemical circuit in which a logical OR feeds into a logical AND (fig. S4B). Acting as a logical OR, translator gates ST and UV take different inputs (miR-15a and miR-10b) but release outputs with identical recognition regions. If Boolean values are represented by the presence of either one strand (“0”) or another strand (“1”)—the so-called “dual-rail” representation (21)—then AND and OR are themselves sufficient to compute any Boolean function.

If a Boolean value is represented by the presence or absence of a single input strand, a NOT gate may be necessary. We modified the circuit shown in Fig. 2A to invert the let-7c input (Fig. 2B). The NOT gate makes use of an additional “inverter” strand that triggers the gate unless the input strand is present to act as a competitive inhibitor. Because the inverter strand must be added simultaneously with the input, NOT gates are restricted to the first layer of the circuit. This is sufficient to create a dual-rail representation from which arbitrary subsequent computation can be performed with just AND and OR.

A gate may fail in two ways: It may fail to produce enough output when triggered, or it may “leak” by spontaneously releasing the output strand. Both types of error require signal restoration; the former requires increasing a moderate output amount to the full activation level, and the latter requires decreasing a small output amount to a negligible level. To implement signal restoration, we developed gates for amplification and thresholding. The threshold gate (Fig. 2C) is a three-input AND gate with identical first and third inputs. The second input is only necessary for structural purposes; it is always present and can be considered part of the thresholding unit. A substoichiometric amount of input (with respect to threshold gates) will cause most gates to lose only their first and second gate strands, thus releasing no output. Input concentrations two times as high as the concentration of threshold gates will cause most gates to produce output. The threshold gate's concentration sets the threshold for a sigmoidal nonlinearity (Fig. 2C and fig. S5) (20).

Because the threshold gate's output cannot exceed half the input signal, subsequent amplification is necessary. A hybridization-based system for catalytic amplification was demonstrated previously (22). With minor modifications, the system serves as both an input amplifier and full translator (fig. S6 and Fig. 3, left, miR-143 translator), or as a fluorescence readout (fig. S7A and Fig. 3, right). Alternatively, amplifiers based on feedback logic can be designed (fig. S6B). A threshold gate together with an amplifier gate constitutes a signal restoration module whose incorporation into large circuits at multiple intermediate points ensures the stability of digital representation (23).

Finally, to demonstrate modularity and scalability, we composed eleven gates into a larger circuit. The circuit combines previously introduced modules for input translation and amplification, calculation of AND and OR, and signal restoration (Fig. 3). The inputs to the circuit are DNA analogs of six mouse microRNAs. To determine the effectiveness of signal restoration, we constructed an equivalent circuit without signal restoration and tested both circuits with an input at one-quarter the strength of a signal that is fully on (0.25×) to simulate a large upstream leak. The complete circuit maintained a low output signal, whereas the circuit without signal restoration exhibited a ≈25% output leak (Fig. 3, inset). To verify other circuit components, several subcircuits were constructed and tested independently (figs. S8 and S9). The feedback fluorescence amplifier was tested as a replacement for the catalytic amplifier at the output, resulting in a circuit containing 12 gates (fig. S10).

As increasingly larger circuits are constructed, speed becomes a limiting factor. The circuit without signal restoration takes 2 hours to reach half-activation (Fig. 3, left inset). The circuit with signal restoration has two additional layers and takes 10 hours to achieve half-activation (Fig. 3, right inset). Despite the slow operation, in both cases a clear difference between off and on states can be distinguished much earlier. Speeding up the responses of individual gates (e.g., by shortening recognition domains) or changing other reaction conditions may improve overall circuit performance.

Our success in creating large circuits can be attributed to adherence to the tenets of digital logic, toehold sequestering combined with branch migration and strand displacement, reduction of leak reactions by purification, and modularity of design. The logic gates developed here and the principles on which they are based can also be used to construct analog or hybrid circuits (24) and are likely to prove compatible with other approaches to building molecular automata in vitro and in vivo (5, 79, 13, 15, 16). Because evidence suggests that our logic gates can use natural RNA as input and that they behave correctly in the presence of mouse total RNA, our hybridization-based circuits might be adapted for in situ detection of complex expression patterns or even in vivo logic processing.

Supporting Online Material

Materials and Methods

Figs. S1 to S10

Tables S1 to S3

References and Notes

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