DNA Logic Multiplexing Using Toehold-Mediated Strand Displacement

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I. INTRODUCTION
DNA as a natural material is an excellent tool for many applications. It was used as a novel material for nanostructures, as its length and diameter are in nanometer [1]- [4]. The natural affinity of DNA made it a perfect medium for drug delivery and bio-detection [5]- [7]. Most importantly, the Watson-Crick base-pairing provides the foundation for biocomputing [8]- [9], information storage [10]- [11], synthetic biology [12], etc. One crucial technology for DNA based computing is the DNA combinatorial strand displacement (DSD) [13].
The toehold mediates DNA strand replacement was proposed by Turberfield et al. [13]. The DSD principle involves the short single strand domain (toehold) and the replacement of paired double strands. The diagram of DSD mechanism is illustrated in Fig 1. Various DSD based computing systems were verified [14]- [16], the traditional logic gate such as AND, OR, NOR, and INHIBIT gate [17]- [19]. Complex Chemical Reaction Network (CRN) such as polynomial and The associate editor coordinating the review of this manuscript and approving it for publication was Shubhajit Roy Chowdhury .
In prior works, researchers involved in assembling simple logic gates to complex cascaded circuits or improving the traditional logic gates. To assemble large scale circuits, Qian et al. proposed the seesaw gate and verified its abilities, cascade and parallel-connected them into large scale logic circuits [25]. Salehi and coworkers designed four basic formations and computed some advanced mathematic formulas based on the DSD system [20]. While some researchers involved in improving the traditional logic gate to implement novel applications. Song et al. designed autocatalytic amplifiers to compute logarithmic and exponential formulas [26]. DelRosso et al. designed a DNA molecular Regenerator and used it for regeneration and multiple cycles of computing [27]. Song et al. introduced an architecture method to program DSD reaction networks on cell membranes [28]. Additionally, they presented another architecture for fast and compact DNA circuits on Bst2.0 DNA polymerase [29].
In the DNA-based circuits, most gate motifs are useonce only, which are strands consuming. There are some works about constructing renewable circuits [30]- [33], [37]. Song et al. used azobenzene isomerization for designing the renewable DNA seesaw logic circuits [30]. Eshra and El-Sayed utilized the DNA-zyme machine as an odd parity checker, and the enzyme-based machine is reusable [31]. Additionally, Eshra and her coworkers built renewable DNA circuits by reversing the hairpin-gate motif [32]. Garg et al. used the dual-rail logic method to realize renewable DNA circuits [33].
Notably, the introduction of the INHIBIT gate that competes with the input strands helps giving an instant stop, avoided the priming of output and secondary productions. Researchers [37]. However, the traditional INHIBIT gate completely quenched the input signals. Therefore, we intend to improve the traditional INHIBIT gate and use it for further applications.
In this paper, we architected a multiplexer DNA logic circuit based on DNA strand displacement. Besides, we improved the INHIBIT gate and used it as a demultiplexer so that different input signals were selected and different output signals can be identified. Lastly, we adjusted the multiplexer and fulfilled a cyclic circuit, which can be extended for more potential applications.

A. BASIC LOGIC GATES
The primary logic gate, such as AND, OR, INHIBIT can be integrated into more complex circuits. Here, we designed these three basic gates by DNA strand displacement, and structured a 3-layer 3-to-2 circuit. The structure of those gates is shown in Table. 1.
As shown in the AND gate, the output strand has two domains that connected with the substrate. Only if Input1 and Input2 coexist and react with this substrate together, the output strand can be completely replaced and released the output signal ''1''. While in the OR gate, the substrate is a complex, consist of two segments with toehold t * 1 and t * 2 . Usually, the OR gate has two input strands and one output strand. But in this work, the existence of the output strand or not represents the result of ''1''/''0''. If one of the input strands Input1/Input2 exists, it will react with the substrate  then release the output signal ''1''. In the INHIBIT gate, the control strand (INHIBIT Substrate), complement Input1 and Input2. If there still exist the INHIBIT strands, the input strands will be quenched. The control strand servers as an INHIBIT gate, no matter what the input is, it gives the output signal ''0''. Further, the control strand can be used as a threshold, and we can set threshold gate for the input and output signal.

B. LOGIC CASCADED CIRCUITS
We used those three basic logic gates, constructed a threelayer logic circuit. The initial Inputs and Joints are in Table. 2, and the structure of this circuit is shown in Fig. 2.
As shown in Table. 2, the initial input strands are Input1 with toehold t 1 and domain a, Input2 with toehold t 2 and domain b, separately. The initial joint substrates are Joint1, Joint2, and Joint3. When Input1 and Input2 transmit to Joint1, they will react with joint substrate (Joint1), and produce the output strands: Output1 and Output2. The two output strands will transfer to the next joint substrate (Joint3), and react with Joint3, product the final output signals: Signal1 and Signal2. Signal 1&2 are tethered with the same signal (labeled as a-tether(n), b-tether(n)), either exist of Input1 or Input2, this reaction pathway produces the Final output signal ''1''. That is the first pathway.  In the second reaction pathway, Input1 and Input2 transmit to the joint substrate (Joint2). They will work together to replace the original domain and release the output strand, Output3 (the AND gate reaction). Then Output3 transmits to the joint substrate (Joint3), and produce the final signals: Signal1 and Signal2. If either loss of the Input strands, this pathway will be obscured, with no final signal, giving logic signal ''0''.
The two pathways are integrated into the multiplexer. The truth table is shown in table3, and the reaction network is illustrated in Fig. 3.
Simulation results (Fig. 4) and the truth table (Table. 3) show the output signal according to different input situations. We set the concentrations of Input1 and Input2 are all 70nM, the Control strand is 75nM. If Input1 and Input2 both exist in the system, then the Control strand will be 150nM. The Control strand is just a little more than input strands. Hence, while existing INHIBIT gate, the Final output will be ''0''.
We also found that the trajectory of Final output Sig-nal1&2 has a difference. The output signal trajectory in ''(1,0,0;1)'' and ''(0,1,0;1)'' are the same. While in  ''(1,1,0;1)'', trajectories of those two Signals have a small gap. We think it is because the AND gate reaction rate is slower than the OR gate, as Input1 and Input2 must work 88110 VOLUME 8, 2020  together to replace the original strand. However, the final concentrations of the two Signals 1&2 are the same. Additionally, in real experiments, the signal in the final output strand can be fluorescent dyes, nanoparticles, etc.

C. DEMULTIPLXER
In this logic circuit, the INHIBIT gate completely quenched the input signals. Those input strands are wasted and cannot be reused. Hence, we improved the INHIBIT gate that input strands can be integrated and co-worked in further reactions. We redesigned the INHIBIT gate, both input strands can be inhibited but have the change for further branch immigration. The improved INHIBIT gate is shown in Fig. 5.
After reacting, Input1 and Input2 DNA strands are integrated into this INHIBIT substrate. The improved INHIBIT gate can restrain the input signals, but toehold domain t 1 and t 2 aren't annihilated. That is, the unpaired toehold t x , t y , and t m are the remained domains where input strands can be replaced. In this improved inhibit gate, Input1 can be immigrated by Tx strand (toehold t x with domain a, from 5' to 3' direction); Input2 can be immigrated by Ty strand (toehold t y with domain b, from 5' to 3' direction); Input 1&2 can be immigrated by Tm strand from this substrate, simultaneously. The reactions are shown in Fig. 6, reaction network of Demultiplexer is shown in supplementary Fig. S1.
With the extra strands Tx, Ty, and Tm, the improved INHIBIT gate can be functioned as a demultiplexer. Tx strand selects the final Signal1, Ty selects the final Signal2, and Tm produces the final Signal1&2, gives output signal ''1''. In this way, the different Final output signals are identified. The simulation results are in Fig. 7. Fig. 7 shows the simulation results of adding Tx, Ty, Tm, separately. If no extra strand is added into this system, there won't be a Final output signal. The improved INHIBIT gate will consume all the input strands (we set the Inhibit strands 75nM, which is more than the input strands). If we added the  Tx strands (70nM), then the Input1 strand will be produced form the inhibit substrate, and Signal1 will be the output. The same situation, we added Ty, Signal2 is the Final output.
In this method, Input1 and Input2 are selected, and different Output Signal1 and Signal2 are identified. Additionally, if we add the Tm strands, it will produce the Input1 and Input2, simultaneously.
In the demultiplex simulation results, Input1 and Input2 become the in-process produces, hence they are labeled as sp1 and sp2 by the DSD software, separately. The yellow curve (Input1) and purple curve (Input2) rise rapidly when adding the extra strands Tx (or Ty), then they are consumed by the downstream reactions (multiplexer circuits). Therefore, the trajectory is risen at the beginning and then slowly falls to zero.

D. CYCLIC MOLECULAR CIRCUIT
In this multiplexer circuits, the concentrations of Input1 and Input2 are 70nM, and the concentration of the Improved INHIBIT substrate is 150nM. The INHIBIT gate just annihilates all the inputs strands. And we set the concentrations of Tx, Ty, Tm are all 70nM. Hence, the concentration of Final output stands is decided by Tx, Ty, Tm. (Downstream Joints VOLUME 8, 2020  are all oversupplied) We wondered whether this system could be adjusted when adding the extra input strand (Tx, Ty, Tm). The system can continuously produce Input1 and Input2 so that the circuits cyclically reacted.
To fulfill this assumption, we adjusted the Final output signal strand1&2, added extra toehold domain t m on them, as shown in Fig. 8. Therefore, the Output Signal 1&2 can participate in the cyclic reactions to produce the input strands. We added 70nM of Tx (Ty/Tm) in this cyclic reaction system. Fig. 9 is the simulation results, and the Reaction cycle is illustrated in Fig. 10.
Comparing the simulation results in Fig. 9 and Fig.7, several differences illustrate the cyclic reaction. First, the final concentration of Signal 1&2 is 10nM, while in Fig.7, the final concentration of them is 35nM. Therefore, the signal degradation is about 28.6% (10/35). Second, the reaction time is different. In Fig. 7, Signal1&2 were produced in 300s. In Fig. 10, the Signal 1&2 took 1500s to fall to 10nM. Therefore, three cyclic reactions occurred in the system. Lastly, the concentrations of Joints are all constant variables in this simulation (we set constant order for Joints when simulation), therefore the cyclic reaction won't stop because of exhausting of the Joints. Judging by those facts, we think the cyclic reaction circuit works.

III. DISCUSSION
The mechanism of DSD is the toehold mediates strands immigration. The toehold domain is short sequences that can fast bound to its base-pair domain and displace the other part by its migration domain. To make sure all the reactions are toehold-mediated. We only design the necessary domains in the whole system. This is the reason why all the Inputs, Outputs, and Joints are so short. There are only two migration domains in this system (a&b); the key exchanges are in the toehold domains. As we added extra toehold domain in the final output strands, and formed a cyclic reaction network. Researchers can add extra migration domains on our system to fulfill some functions, such as feedback circuits, mathematic formulas, DNA-based computing, etc.
In this paper, we architected a 3-layer logic cascaded circuit based on the DNA combinatorial strand displacement, and verified its logic truth through DSD simulation. Besides, we improved the INHIBIT gate so that it can be used as a demultiplexer. In many multilayer DNA circuits [20], [34], [35], the outputs are mixed, and the individual strand can't be selected. The proposed demultiplexer has significant usages in signal selection. Lastly, we modified the toehold domain on the output strands, and formed a cyclic reaction network. The cyclic system is different from the above-mentioned works [30]- [32]. We do not add extra strands to pull back motifs [32] or use extra mechanisms for reverse [30], [31], the key point in our cyclic circuits is the cyclic replacement of the toehold domains. (Adding additional strand to restore the circuits is also viable in the proposed system as shown in supplementary Fig. S2) The system demonstrated that the proposed circuit has powerful potentials for large scale computing and other functions.
In the future, we intend to use this logic circuit to form more complex structures and fulfill more functions. The system can be ejected into the living cell, and implement the incell computing. We can also apply our circuits onto surface substrates and complete the surface aid computing, such as on membrane, on DNA origami, etc. The proposed circuits can be adapted and utilized on DNA computing, nanocircuits, and other fields.
XIAOLONG SHI received the Ph.D. degree in systems engineering from the Huazhong University of Science and Technology. He was a Tenured Professor with the Huazhong University of Science and Technology, and he is currently the Dean/Professor of the Institute of Computer Science and Technology, Guangzhou University.
JIN XU received the first Ph.D. degree from Xi'an Jiaotong University in 1993, and received the second Ph.D. degree from the Beijing Institute of Technology in 1994. He is currently a Tenured Professor at Peking University.
He has published more than 200 SCI papers as the first or corresponding author. He has leaded 10 national projects, including NSFC project, ''973'' Project, ''863'' Project, etc. His main research areas include graph theory, biological computing, and information security.