A signal pulse counter can be constructed using delays and amplifying AND gates, as shown below. Hence, a counting device can be implemented using only delay units and amplifying AND gates made from DNA strands. We have designed a delay unit with two intermediate signals in addition to its final output using 8 molecules: 3 transducers, two thresholds, and three fuels. The structures of these molecules are given in Rationale. A good design for an amplifying and gate can be found in (1); we use this design (see also Rationale).
It is reasonable to assume that this system may function only when the delay units and and gates are present in certain concentration ranges. Hence, we applied simulation techniques to determine a safe range of system concentrations where the system will behave as designed. Unfortunately, no existant simulation software was applicable to our situation. Hence, we developed TripleSim, a general purpose nucleic acid system simulation application. We applied TripleSim to this DNA system to answer the question: What should the concentration of the threshold components be to give a certain signal delay at each delay unit?
This article proceeds first by showing the results of this investigation via TripleSim.
Section 2: TripleSim was used to simulate the behavior of the system containing a single delay unit. In the DNA System specification format accepted by CircDesigNA (http://cssb.utexas.edu/circdesigna),
INPUT [T X x}
G_X [X(x(T(A a}[T*)x*)X*)T*}
G_A [A(a(T(A1 a1}[T*)a*)A*)T*}
G_A1 [A1(a1(T(A2 a2}[T*)a1*)A1*)T*}
X- [X x T}
A- [A a T}
A1- [A1 a1 T}
T_A1 [A1(a1(}[a1*)A1*)T* a*}
T_A2 [A2(a2(}[a2*)A2*)T* a1*}
The 10 molecules in this system (including input) are rendered in line notation below:
We can investigate this system by varying the concentration of any of these 10 molecules, keeping the rest of the system constant. However, we assume that gates should be present at excess concentrations. Furthermore, the fuel strands X-, A-, and A1- should be present at concentrations even higher than the gate strands - hence, at excess. The Killer should also be present at high concentrations, to ensure that it can "kill" even large pulses of the input strand, INPUT. Using TripleSim, we investigate the kinetics of this system based on the concentration of Input strand and based on the concentration of the thresholds.
In the following investigations, the kinetics of the production of two intermediate signals (XTA and ATA1) and the delayed output signal (A1TA2) are recorded.
Section 2.1: Increasing the concentration of the input strand has the effect of reducing the delay of time before the signal strand is produced at noticable concentration. However, for low concentrations of input, the system reliably delays the production of the signal strand A1TA2 for 30 minutes.
Section 2.2 Only when the thresholds are at high concentration does the system behave as a delay unit. However, above a certain concentration, the system becomes so damped by the thresholds that production of the output signal is severely inhibited.
Section 2.3: Investigation of second exposure behavior. It is shown that, unless the second pulse occurs sufficiently later than the first pulse, no output is produced.
1: DY Zhang, AJ Turberfield, B Yurke, et.al. "Engineering entropy-driven reactions and networks catalyzed by DNA." Science, 2007.