The main mechanism by which our system functions is through toehold exchange. A toehold is a short sequence of DNA bases, five in our system that acts as a “toehold” to allow an invading strand of DNA to displace the original top strand. In the diagram shown below, we show the simplest example of a toehold exchange. The original duplex has two identical toeholds on either side of the “domain region.” The domain region is simply a 20 nt. strand of DNA that is given a name. The invading strand binds to the free toehold on the left side and displaces the original top strand. This leaves the right toehold exposed allowing the reverse reaction to occur. Overall, the toehold on the left side is replaced by the toehold on the right side, thus this system is called a toehold “exchange.”
Our System (basic components)
Our system uses five components:
- Signal - a single strand of DNA. Characterized by a toehold region surrounded by two domain regions.
- Gate - contains the reverse complement of the signal. Branch migration between the signal and gate leads to an output signal. Characterized by a compliment domain region surrounded by two compliment toehold regions
- Fuel - a single strand of DNA which returns the Signal to solution after it is absorbed by a gate. Characterized by a domain region with a toehold region on the 3’ end.
- Threshold – a duplex that has an extended toehold allowing it to irreversibly bind to a signal.
- Killer – a duplex similar to a gate, but specifically binds to the input strand and releases no output.
Our System (how it works)
Our counter can be broken down into several sections:
- The Transducer: The transducer simply converts the input into another signal by using a single gate with fuel, this step is necessary to prevent the system from being affected by the decay of the fuel over time.
- The Time-Delay: The time delay is composed of two gates, with fuel, and two thresholds (one for each output of the gates.) The thresholds serve two functions, to prevent leakage by taking up unwanted signal strands and to make the system take time to reach the next section. This phase is necessary to give the killer time to remove the input from the system completely.
- The AND gate: The AND gate is the final step of our system. The output from the last gate in the time delay exposes a toehold in the AND gate which can react with input to produce the next signal. It is crucial that the killer remove all of the previous input before this step or else one pulse of input will count two counts instead of one.
- The Killer: The killer is simply the duplex that removes input from the system, it is necessary to remove the input so the counter can function properly.
The molecules we have designed are most easily visualized in line notation, in which only the backbones of nucleic acid strands are drawn. Furthermore, dna duplexes will be represented by parallel straight lines, though they realistically will form twisted, helical structures.
For example, a simple DNA duplex is converted to a pair of connected, parallel lines.
We chose a naming system that describes each component of the counter using a letter-dash system. Letters represent 20 nt. long sequences of DNA called domains, “dashes” represent the toehold, _ is used to signify a duplex, G is a gate, T is a threshold, K is the killer.
X-A is a toehold with the X domain on the left and the A domain on the right.
T_A1 is a threshold with the domain region A1
G_X is a gate that has the X domain
The AND does not follow this naming system. To signify the AND gate we use the domain of the signal it reacts with first followed by AND, and finally an X.
Finally, all duplexes can have different top strands depending on the progress of the system. To show which top strand is present on a particular bottom strand, we assume the original state of the duplex does not require explicit naming, but if another strand is present we use a colon and the name of the topstrand.
G_X is the X domain gate with the top strand X-A
G_X:-X is the X domain gate with the top strand –X
A2ANDX is the initial state of the AND gate
A2ANDX:A1-A2 is the intermediate state of the AND gate
A2ANDX:-X in the final state of the AND gate when it has released its output X-B
One further representation of our system uses the system of the Winfree DNA group at Caltech. The nodes in the diagram correspond to one of the following types: Input, Fuel, Gate, and Threshold.