Implementing digital computing with DNA-based switching circuits

DNA strand displacement reactions (SDRs) provide a set of intelligent toolboxes for developing molecular computation. Whereas SDR-based logic gate circuits have achieved a high level of complexity, the scale-up for practical achievable computational tasks remains a hurdle. Switching circuits that were originally proposed by Shannon in 1938 and nowadays widely used in telecommunication represent an alternative and efficient means to realize fast-speed and high-bandwidth communication. Here we develop SDR-based DNA switching circuits (DSCs) for implementing digital computing. Using a routing strategy on a programmable DNA switch canvas, we show that arbitrary Boolean functions can be represented by DSCs and implemented with molecular switches with high computing speed. We further demonstrate the implementation of full-adder and square-rooting functions using DSCs, which only uses down to 1/4 DNA strands as compared with a dual-rail logic expression-based design. We expect that DSCs provide a design paradigm for digital computation with biomolecules.


Supplementary Methods Materials
The DNA oligonucleotides used in this study were purchased from Sangon Biotech (Shanghai). Unlabeled DNA oligonucleotides were purified by Sangon using ULPAGE, and labeled DNA oligonucleotides were purified by Sangon using HPLC. Individual unlabeled DNA oligonucleotides were dissolved in 1×TE buffer (nuclease free, pH 8.0, Sigma-Aldrich), quantified by A260 using UV/Vis spectrometry and stored at -20℃. Oligos labelled with dyes or quenchers were dissolved in deionized water (Milli-Q), quantified by A260 and stored in deionized water at -20℃.

Preparation of a computing circuit.
To prepare a downstream switch molecule, s1, s2 and s3 were mixed in Tris-EDTA buffer (1× Tris-EDTA: 40 mM Tris base, 20 mM acetic acid, 2 mM EDTA adjusted to pH 8.0) with 12.5 mM MgCl2 to final concentrations of 11 μM ,10 μM and 15 μM respectively ( Supplementary  Fig. 1). To prepare a starting switch molecule, s1 and s2 were mixed in Tris-EDTA buffer to final concentration of 11 μM and 10 μM respectively. Quencher strand and fluorescence strand were mix at molar ratio of 1.5:1 in Tris-EDTA buffer with 12.5 mM MgCl2 to 10 μM. The reaction mix was then annealed by heating to 95 ℃ for 2 min and slowly cooling to room temperature at 0.1 ℃ every 6 s, then held at 4 ℃. The hybridized molecules were stored at 4 ℃ for further use.

Numerical simulation of reaction kinetics
Models of switching circuit ( Supplementary Fig. 2a) and logic gate circuit ( Supplementary Fig.  2b) were built using SimBiology Tool in Matlab. Desired reaction rate and unwanted leakage rate were considered for each reaction. MassAction was used as KineticLaw for all reactions. To theoretically understand the difference of logic gate circuit and switching circuit architectures, we used universal reaction rate and leakage rate. And we used the same reactions rate for logic gate circuit and switch circuit (Supplementary Table 5). The output kinetics were simulated with all possible input combinations.

Supplementary Figures
Supplementary Figure 1. Optimization of ratio between strands within a switch. a, Switching performance with different concentration ratios between S1 and S2 in a starting switch. A higher concentration of S1 ensures complete hybridization of S2, decreasing signal leakage. As 1.1× is sufficient for suppressing leakage, we used S1:S2=1.1:1 for experimental tests. b, Switching performance with different S3 concentrations in a downstream switch. Excessive S3 helps suppress leakage caused by unwanted switch flipping by switching signal at the absence of current signal (red line). So we used the ratio S1:S2:S3=1.1:1:1.5 for experimental tests. Source data are provided as a Source Data file.

Supplementary Figure 2. Output and leakage with different ratios of upstream switch and downstream switch.
To ensure that the upstream switch could produce sufficient output for the downstream switch, we used a ratio of 1.5:1. Source data are provided as a Source Data file. A downstream switch contains a C domain for current signal and a S domain for switching signal, which is formed by hybridization of three strands. The required features are quick replacement of S3 by current signal and low leakage from replacement of S2 by switching signal at the absence of current signal. We found a 0 nt gap led to slow reaction and a 2 nt gap led to higher leakage. We chose 1 nt as the gap length which has low leakage similar to the 0 nt gap and high reaction rate identical to the 2nt gap. Source data are provided as a Source Data file.

Supplementary Figure 7. The influence of reaction temperature on the operation of DSCs.
Increasing temperature from 20 °C to 35 °C did not have significant influence on the leakage and output of the signal-switch and two-switch circuits. Despite the leakage for a fan-out circuit slightly increased with the temperature, it remained at low level. Source data are provided as a Source Data file. Figure 8. Modular sequence design for possible adjacent connection patterns within a DSC. a, For the pattern that an upstream switch (u) followed by one downstream switch (d), the sequence design constraint is determined by C(d)=cs(u), where C(d) means C domain of d and cs(u) means current signal from u. b, For a fan-in pattern that n upstream switches are followed by one downstream switch, the constraints are determined by C(d)=cs(u1) =cs(u2)=…=cs(un). c, For a fan-out pattern that one upstream switch is followed by n downstream switches, the constraints are determined by C(d1)= C(d2)=…= C(dn)=cs(u). d, For a pattern that n upstream switches are followed by m downstream switches, the constraints are determined by C(d1)= C(d2)=…= C(dm)= cs(u1) =cs(u2)=…=cs(un).