Review: "Three-Input Majority Logic Gate and Multiple Input Logic Circuit Based on DNA Strand Displacement"

Review

Nano Letters

Li, Wei; Yang, Yang; Yan, Hao; Liu, Yan. 

"Three-Input Majority Logic Gate and Multiple Input Logic Circuit

Based on DNA Strand Displacement"

Three-input majority logic gates are useful tools in computation; they work on the principle that if at least 2/3 of the inputs are true, then the result is true. The result is false if only 1/3 of the inputs is true. At first glance, this seems like a convenient system for tuning the on-state of a system for non-binary inputs; theoretically, any odd-number of inputs can be turned into a majority logic gate. 

The true versatility of this system lies in the fact that it is easy to convert 3-input logic gates into the more standard OR or AND gates, simply by setting of the inputs as true or false. If one input is set as true , then either one of the other two (or both) could be true in order to get a true result. If one input is set as false, then both the other two must be true to get a true result. 

OR and AND gates, and calculations:

In simple terms, OR gates represent additions. In order for the equation to be true (have a value of at least 1), the sum of the inputs has to be at least one. Thus, if you have 2 inputs, an OR gate states that input A OR input B can be zero because 1+0 and 0+1 both end up having true outputs.

AND gates, on the other hand, represent multiplications. Since any number multiplied by 0 = 0, in order for the net output to be TRUE, all of the inputs must be TRUE (in other words, none of the inputs can be false (0). 

The Paper

Wei Li,Yang Yang, Hao Yan, and Yan Liu at Arizona State University have been able to make these logic gates based on DNA hybridization properties. The concept of DNA-based logic gates has been around for many years, and the field is fertile with new developments.

Li et al use a circular piece of single stranded DNA with 3 different hybridization sequences, corresponding to the 3 inputs of the logic gate. These sequences are flanked by repeating "joint" sequences that are complementary to a detector sequence. Finally, this single stranded circular DNA is hybridized to complementary sequences each bearing a toehold - that is, a segment of DNA that will allow the strands to be displaced upon binding to input strands that have regions complementary to the toeholds. The principle of displacement here is 1) the greater stability of the longer piece of DNA with more base pairing as opposed to shorter base paired strands (thermodynamic) and 2) the initial binding efficiency of the input strands is higher with a toehold than without (kinetic).

When two of the inputs are complementary to the toehold strands, it opens up a joint region that exists between the two toehold strands. A detector sequence consisting of a double stranded DNA sequence containing a fluorophore quencher pair (see Molecular Beacon) is then able to bind the quencher sequence, allowing the fluorophore to fluoresce and form a turn-on signal. However, when only one input is present, the joint region is not fully exposed, and fluorophore quenching is maintained.

The researchers expand upon this model to build more complex logic cascades based on the principle of turning three-input majority gates into AND and OR gates. A variety of calculations can be accomplished using just two steps in sequence. To accomplish the presets, one of the three calculation sequences is present or absent in the reaction mixture when the input sequence(s) are introduced. The output of the first DNA calculation takes the form of a double stranded piece of DNA, with one strand binding to the exposed joint region of the first calculator, and the second strand binding acting as an input for the second DNA calculator.

In practice, the design of these DNA calculators is trickier. One design flaw is that the flanking regions to the recognition parts of the calculator and inputs are the same, causing non-specific inputs to sometimes bind the calculator strands. This, however, should not be a problem in the detection, as the fully complementary sequences are pre-hybridized with the single stranded calculator to form the calculator DNA.

The calculators work as predicted for the single gate problem. When the calculator is challenged with 0 or 1 input, no fluorescence increase is detected, with 2 or 3 inputs, fluorescence is detected. With a higher ratio of detector strand to calculator DNA, the authors are able to distinguish well between a 2 and 3 input challenge. This agrees with the relative molar ratios of exposed joint domains.

For the multi-gate problems some signal leakage is seen - as fluorescence occurs even for cases where the output should be false, but in general the system works quite well. The main weakness in using DNA as a computational tool is time. It takes at least half an hour for a signal to process, and sometimes hours for it to be processed unambiguously. The kinetics of the signal formation are also offset by the signal leakage - the faster a true positive result is able to distinguish itself from a false positive, the better. The authors attribute slow kinetics to the fact that strand displacement is likely to occur concomitantly between calculators, causing steric crowding to limit the rates of the reaction. Signal leakage, on the other hand, is due to cross talk between the two logical gates. Signal leakage can be optimized  by careful design of the sequences used for the calculators, and by tuning the concentrations. Rates, on the other hand, are more tricky- a certain amount of crowding is inevitable, and as calculations get more involved, the lengths of the DNA used to compute them will get longer in order to decrease crosstalk. Longer DNA will inevitably lead to slower kinetics. Thus, signal leakage and speed are at odds with one another, but both need to be optimized in order to make a feasible DNA computer.

How one might optimize for speed.

In nature, the kinetics of a reaction are governed by temperature and catalysts. In short, the higher the reaction temperature, the faster the kinetics. The problem with this strategy is that it also favors non-specific interactions. In the case of these calculators, higher temperatures will lead to easier strand displacement and possible false positives. (For other examples, higher temperatures will increase specificity in that only the correct sequence will bind).

Another strategy may be to use catalysts. DNA catalysts take the form of proteins - enzymes in particular, which nature exploits in order to make the process of gene replication and expression occur in seconds rather than hours. A helicase that is specific for certain DNA structures - toehold-strand-breaks for example - may expedite the sensing processes.