Ternary addition system based on DNA strand displacement and calculation method

Abstract

The invention belongs to the technical field of biological computing, and discloses a ternary addition system based on DNA strand displacement and a computing method.The system comprises an input unit, a computing unit and an output unit, and the input unit adds input information into a corresponding computing module; the calculation unit comprises nine modules, a competitive blocking circuit and a carry calculation gate are arranged in each module, a result bit 1 or 2 is dynamically selected, and a carry signal is generated; and the output unit correspondingly outputs 0-2 digital information according to the fluorescence signal output by the result bit, extracts the next carry information generated by carry calculation, amplifies the signal, and adds the amplified signal into the next calculation. Through cooperation of a ternary gating framework and fuel chain amplification, limitation of DNA calculation digits is broken through, ternary addition can be accurately calculated, the calculated digits can be expanded, 10-bit addition operation can be achieved, expansion integration with multiplication logic can be achieved, and a universal framework is provided for a molecular arithmetic unit.

Description

Technical Field

[0001] This invention relates to DNA molecular computing technology, specifically to a ternary addition system and calculation method based on DNA strand substitution. Background Technology

[0002] DNA strand substitution refers to the process by which one strand of a DNA molecule is replaced by another strand based on the complementary base pairing principle. In the fields of computational science and molecular information processing, the addition system is a fundamental operational unit and the core of the arithmetic logic unit (ALU), whose implementation provides the underlying support for higher-order operations (multiplication, encryption algorithms). Currently, DNA adders mainly focus on binary addition. Although researchers have expanded the number of bits for computation by using a minimum number of DNA strands and developing carry-transfer mechanisms, calculating larger values ​​requires multiple transfers of carry information. The carry information is easily lost during transmission, leading to signal attenuation and erroneous results when calculating large values. Furthermore, the limited expressive power of binary systems significantly limits their computational scale.

[0003] For example, CN111428877A discloses a logic circuit and device based on DNA strand substitution, which uses a binary DNA logic circuit and adjusts the gain based on threshold triggering. However, its single-digit information capacity is small and its dependence on carry is high. CN111598242A discloses a logic circuit and device based on DNA molecular chains, which uses a multi-input gate to simplify the circuit structure and improve the construction efficiency of logic circuits based on DNA molecular chains. However, it cannot solve the problem of signal attenuation in long chain calculations and cannot significantly improve the calculation accuracy.

[0004] Therefore, traditional DNA adders are limited by binary logic and carry decay issues. Although some technologies have optimized the logic gate structure, they are still unable to break through the binary framework and multi-digit bottlenecks. This results in the common problems of addition systems relying on binary and having a high dependence on carry, as well as the inability to solve the signal decay of long-chain computations, resulting in low computational accuracy. They cannot perform 10-bit or ternary addition operations, and their computational scale is limited. Furthermore, they cannot be flexibly converted to subtraction or multiplication operations, which greatly restricts the application scope of DNA computation methods and systems. Summary of the Invention

[0005] To address the aforementioned problems in the prior art, this invention proposes a ternary addition system and calculation method based on DNA strand substitution. It introduces a novel competitive blocking circuit, which reduces the dependence on frequent carry transfers by increasing the radix of the addition system. The system employs a dual collaborative optimization strategy to achieve 10-bit ternary addition operations and enables it to calculate scales exceeding those of the prior art, thereby simultaneously improving system efficiency, accuracy, flexibility, and application scope.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A ternary addition system based on DNA strand substitution, characterized in that it comprises: Input unit: Used to obtain the DNA single-strand information of the two inputs, the addend and the augend, and add the input information to the corresponding calculation module; load the DNA single strands of the addend and the augend: input Ai, input Bj, i,j=0,1,2; The computing unit comprises nine modules: 00, 01, 02, 10, 11, 12, 20, 21, and 22. Each module contains a competitive blocking circuit, GATE1. ij / GATE2 and carry calculation gate GATE- ij / GATE1- ij The result is dynamically selected as 1 or 2, and a carry signal is generated. The competitive blocking circuit determines whether there is carry information from the previous bit. After the calculation is completed, the result is obtained by PCR fluorescence quantitative measurement. The carry information is used to generate the information for the next bit. In the competitive blocking circuit, the blocking rate k 2 satisfy: k 2 = (1.8 ~ 2.3) × k 1, and k 2>10 4 M -1 s -1 .

[0007] Output unit: includes an output module and an extraction module. The output module outputs the fluorescent signal corresponding to the result bit and outputs digital information of 0-2. The extraction module is used to extract the carry information of the next bit generated by the carry calculation, amplify the signal and add it to the next bit calculation.

[0008] A ternary addition calculation method based on DNA strand substitution, based on the aforementioned ternary addition system, includes the following steps: S1: Select the calculation module based on input Ai / Bj, and generate the result bit through a competitive blocking circuit; S2: Extract the carry signal and amplify it, then proceed to the next bit for calculation until the addition of 10 bits or less is completed.

[0009] Compared with the prior art, the ternary addition system and calculation method based on DNA strand substitution provided by the present invention have at least the following beneficial effects: 1. This invention employs a ternary addition arithmetic system. Firstly, it introduces a novel competitive blocking circuit to reduce reliance on frequent carry transfers by increasing the radix of the addition system. The system utilizes a dual collaborative optimization strategy to achieve 10-bit ternary addition operations, exceeding the computational scale of existing technologies, thus simultaneously improving system efficiency, accuracy, flexibility, and application scope. Compared to the traditional DNA binary adder (CN111599082A), which uses threshold-triggered gain control, supports only 4-bit (87% success rate) calculations, and has a signal loss rate of 30%, this invention achieves a maximum computational bit depth of 10 bits (success rate > 99%), a signal attenuation rate of 2.1% / bit (after magnetic bead extraction), and significantly reduces the total carry transfer time (fuel chain amplification).

[0010] 2. The competitive blocking circuit provided by this invention can accurately identify and manage carry information from previous calculations. The core of this circuit lies in its ingenious use of the difference in reaction rate constants. Experiments show that this competitive blocking circuit can reliably identify whether a carry has occurred in previous calculations and quickly respond to the corresponding reaction path.

[0011] 3. The circuit used in this invention application includes an input unit for acquiring the DNA single-strand information corresponding to the addend and augend, and adding the input information to the corresponding calculation unit; the calculation unit is divided into 9 modules, each module having result bit calculation and carry information calculation. The result bit calculation uses a competitive blocking circuit to distinguish whether there is carry information from the previous bit. After the calculation is completed, it is placed in PCR fluorescence quantitative measurement to obtain the calculation result. The carry information generates the information for the next bit; the output and extraction units are as follows: the output module: outputs digital information of 0-2 according to the fluorescence signal output of the result bit; the extraction module: extracts the carry information of the next bit generated by the carry module, amplifies the signal, and adds it to the next bit calculation. By increasing the calculation capacity of a single bit and expanding the number of bits to be calculated, it can realize operations with larger bits, optimize the performance of complex systems, increase efficiency and accuracy when calculating large numbers, and successfully realize ternary addition calculations of 10 bits and up.

[0012] 4. The novel ternary encoding logic and magnetic bead-fuel chain synergistic amplification employed in this invention are both irreplaceable. Specifically, the novel ternary encoding logic uses tri-state fluorescence (ROX / FAM / VIC) to directly characterize 0 / 1 / 2, avoiding multi-channel cross-interference (reducing complexity by 66% compared to traditional 6-color encoding); the magnetic bead-fuel chain synergistic amplification achieves in-situ enrichment through biotin-labeled GATE-Extract (increasing concentration by 10%). 3The number of fuel chain cycles is greater than 100 (see Table 4); ternary molecular logic (ternary DNA AND gate) and carry mechanism are used for multi-digit processing, which greatly improves the scale that it can calculate.

[0013] 5. This invention application, based on a ternary architecture and a novel gating design, fills the technological gap in DNA computing for efficient multi-digit processing, and has significant breakthrough and commercial potential compared with existing technologies. Attached Figure Description

[0014] Figure 1 This is a schematic diagram of the module composition and calculation process of the ternary addition calculation method and system based on DNA strand substitution reaction according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the module composition structure of the computing unit in the ternary addition calculation system based on DNA strand substitution reaction according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the fluorescent attachment type table in the modularization of the ternary addition calculation system based on DNA strand displacement reaction according to an embodiment of the present invention; Figure 4 This is a schematic diagram of the reaction process of the competitive blocking circuit based on the DNA strand substitution reaction in an embodiment of the present invention; Figure 5 This is a schematic diagram of the reaction process for calculating carry information in the calculation unit of the ternary addition calculation system based on DNA strand substitution reaction according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the signal amplification reaction process of the extraction module in the ternary addition calculation system based on DNA strand substitution reaction according to an embodiment of the present invention; Figure 7 This is a schematic diagram of the calculation results of the ternary addition system based on DNA strand displacement reaction in an embodiment of the present invention. Detailed Implementation

[0015] See appendix Figures 1 to 7 The following examples will be used to illustrate and verify the ternary addition calculation method and system based on DNA strand substitution reaction proposed in this invention.

[0016] Basic Implementation See appendix Figure 1 The ternary addition system based on DNA strand substitution provided in this embodiment includes: Input unit 100: Used to obtain the DNA single-strand information of the two inputs, the addend and the augend, and add the input information to the corresponding calculation module; load the DNA single strands of the addend and the augend, input Ai, input Bj, i,j=0,1,2; The two input DNA single-strand information include: when the addend input is 0, 1, 2, the three single strands are input Ai (i=0, 1, 2) respectively; when the addend input is 0, 1, 2, the three single strands are input Bj (j=0, 1, 2) respectively.

[0017] Computing Unit 110: Contains 9 modules: 00, 01, 02, 10, 11, 12, 20, 21, 22. Each module contains a competitive blocking circuit GATE1. ij / GATE2 and carry calculation gate GATE- ij / GATE1- ij The result is dynamically selected as 1 or 2, and a carry signal is generated. The competitive blocking circuit determines whether there is carry information from the previous bit. After the calculation is completed, the result is obtained by PCR fluorescence quantitative measurement. The carry information is used to generate the information for the next bit. In the competitive blocking circuit, the blocking rate k 2 satisfy: k 2 = (1.8 ~ 2.3) × k 1, and k 2>10 4 M -1 s -1 .

[0018] The competitive blocking circuit, when no blocking chain exists, performs the first layer reaction, producing result 1; When a blocking chain exists, the carry information chain will block the first-level reaction and trigger the second-level reaction, resulting in result 2; The first and second layer reactions include the triple gate GATE1. ij And the double-chain gate GATE2, the triple-chain gate GATE1 ij The double-chain gate GATE2 is used to generate result 1 by reacting with two input chains. It is used to block the triple-chain gate GATE1 when there is a carry information chain. ij At that time, it reacts with the carry information chain to generate result 2; The carry calculation gate includes: GATE -ij (ij=12,21,22): Three-chain gate structure, responding to high-order input to trigger carry; GATE1 -ij (ij=02,11,20): Four-chain gate structure, coordinating the handling of cross-carry logic.

[0019] The carry information calculation also includes two double-chain carry information conversion gates, GATE-Convertb1 and GATE-Convertb2. These double-chain carry information conversion gates are used to convert the triple-chain gates GATE- ij The pseudo-carry information generated by the reaction is converted into carry information; Output unit 120: includes an output module and an extraction module. The output module outputs the fluorescent signal corresponding to the result bit and outputs digital information of 0-2. The extraction module is used to extract the carry information of the next bit generated by the carry calculation, amplify the signal and add it to the next bit calculation.

[0020] The output unit also includes a fluorescence signal conversion module ROX / FAM / VIC and a magnetic bead extraction-fuel chain amplification module; In the magnetic bead extraction module: The particle size of streptavidin magnetic beads is 50-100 nm; The fuel chain is a classic double-stranded DNA (dsDNA) used for signal amplification reactions; In the fluorescence signal conversion module: The ROX fluorescent marker corresponds to the ternary value 0; FAM and VIC correspond to 1 and 2 respectively, and the wavelength interval of the three channels is ≥50nm; The fuel chain contains phosphate thioester modification, with a nucleotide substitution modification rate of ≤15%, and ≤3 modification sites per chain (including 3 locked nucleic acid (LNA) sites). The biotin in the extraction module is labeled at the 5' end of the GATE-Extract. After separation by magnetic beads, it is recycled through the fuel chain to generate ≥10 3 The Bin signal is twice as strong.

[0021] A ternary addition calculation method based on DNA strand substitution, which is based on the aforementioned system, includes the following steps: S1: Select the calculation module based on input Ai / Bj, and generate the result bit through a competitive blocking circuit; S2: Extract the carry signal and amplify it, then proceed to the next bit for calculation until the 10-bit addition is completed.

[0022] The ternary addition system and calculation method based on DNA strand substitution provided in this embodiment, through the coordination of the input unit, the calculation unit (including the 00-22 module), and the output unit (fluorescence conversion and carry extraction module), adopts a competitive blocking circuit to dynamically select the result bit, and amplifies the carry signal through fuel chain cyclic amplification, which breaks through the limitations of the prior art and can achieve effects such as a maximum calculation bit of 10 bits (success rate > 99%), a signal attenuation rate of 2.1% / bit (after magnetic bead extraction), reduced carry transmission time, and fuel chain amplification.

[0023] This invention features a pioneering ternary architecture: breaking through the binary limitations of traditional DNA computing, increasing the information capacity of a single digit by 50%.

[0024] Modular division of labor: The carry logic is divided into 9 independent modules to avoid signal crosstalk and support high parallel computing (Example 1 verifies 10-bit addition).

[0025] This embodiment solves the bit limitation problem caused by signal attenuation in traditional solutions (existing technologies only support 4 bits), while this embodiment of the invention can support 10 bits.

[0026] Precise dynamic control is employed, and the stability of the result bit selection is ensured (error rate <5%) by limiting the range of blocking rates (see gradient experiment verification in Example 3).

[0027] Example 1 Based on the basic embodiment, this embodiment provides a ternary addition system based on DNA strand substitution, specifically including: Input unit 100 is used to acquire DNA single-strand information corresponding to the addend and the augend, and add the input information to the corresponding calculation unit; The calculation unit 110 is divided into 9 calculation modules. Each module is equipped with result bit calculation and carry information calculation. The result bit calculation uses a competitive blocking circuit to participate in the calculation. This circuit can distinguish whether there is carry information in the previous bit. After the calculation is completed, it is put into PCR fluorescence quantitative measurement to obtain the calculation result. The carry information will generate the information of the next bit. Output unit 120 includes an output module and an extraction module. The output module outputs digital information (0-2) corresponding to the fluorescence signal output in the result bit. The extraction module extracts the carry information generated by the carry calculation, amplifies the signal, and adds it to the next calculation unit. In this embodiment, the input signal single strand refers to a DNA molecule chain. Specifically, the input addend and augend are represented by DNA single strands, respectively. i inputB j (i=0,1,2;j=0,1,2) indicates that the output signal uses a fluorescent signal as the output (ROX corresponds to result bit 0, FAM corresponds to result bit 1, and VIC corresponds to result bit 2). Reference Figure 2The ternary truth table and calculation unit are divided into 9 calculation modules: 00, 01, 02, 10, 11, 12, 20, 21, 22. The DNA molecules in each module use different sequences depending on the module and the input single strand, but the molecular structure is the same. Different fluorescent attachment references are used according to the output result. Figure 3 Assuming a 0-1 module, then FAM is used to attach the triple-chain gate GATE1. 01 VIC is used to attach the double-chain gate GATE2.

[0028] Reference Figure 4 The result bit output in the calculation unit of the addition system uses a competitive blocking circuit (CB), which consists of two logic gates called GATE1. ij GATE2 and GATE2 represent two reaction levels. The circuit has two input signals, represented as inputA. i and inputB j And there is a blocking signal B in Signal B in It can be in a logical state of presence or absence, indicating whether it participates in the reaction. Here, i, j ∈ {0, 1, 2} represent the ternary numbers involved in the addition operation, and B in This represents the carry information generated by the previous bit in the addition operation, when B in When it is in a non-existent state, the circuit receives inputA. i and inputB j Activate the first-order reaction: The result is SUM1 ( Figure 4 (Left-side reaction). Conversely, when B in When it exists, it is related to GATE1 ij The reaction effectively consumes GATE1. ij This inhibits GATE1 ij With inputA i and inputB j The first-order reaction between them: In addition, B in The presence of this substance can activate the second-order reaction: This results in an output signal that differs from the output of GATE2, denoted as SUM 2 ( Figure 4 (The reaction on the right side of the middle section), here the experiment shows that k2 is about an order of magnitude larger than k1 and k3. This indicates that in B in If it exists, it will prioritize and quickly interact with GATE1. ij This combination effectively inhibits the first-order reaction. Afterwards, B... in Continue reacting with GATE2. Conversely, when B... inIf it is not present, the CB circuit will continue to carry out the first stage reaction.

[0029] Reference Figure 5 The carry information calculation of the addition system, type a, involves generating carry through a three-input AND gate, including cases 6, 10, and 14 in the truth table, where the carry only occurs in B. in The fact that carry information is generated when it exists indicates that the generation of carry information depends on the input A. i and inputB j and B in Therefore, we use a three-input AND gate to implement this function (GATE1- ij Where ij ∈ {02, 11, 20}). GATE1- ij The structure consists of four single chains, which are connected through the toehold region t a and t b The base pairing and the longer structural domain a i b j It pairs with the c base to form a stable structure. Simultaneously, it exposes the toehold t. a * and a longer structure domain r. When all three inputs are inputA i and inputB j and B in When both are present, this gate generates a chain of information, cr. The specific reaction mechanism is described in... Figure 5 In (a).

[0030] Type b generates a carry through a two-input AND gate and a conversion gate, including cases 11, 12, 15, 16, 17, and 18 in the truth table, in which the carry input B is not affected by the carry input. in Regardless of the outcome, a carry will be generated for the next bit. This indicates that the carry information depends only on inputA. i and inputB j We use a two-input AND gate (GATE). -ij (where ij ∈ {12, 21, 22}) to implement these cases. GATE- ij The structure consists of three single chains, connected by toehold t b and long domain a i and b j Base pairing is stable. This exposes toehold t. a * and the longer field r. When inputA i and inputB j When both conditions are met, the gate produces an output. The specific reaction mechanism is as follows: Figure 5 As shown in (b). When inputA i and inputB jWhen both exist, b j The single chain containing r is replaced. Further, we use GATE-Convertb... j (j = 1, 2, GATE-Convertb) j The structure consists of two single chains, one of which contains the carry information to be passed to the next bit (to transfer b). j r is converted into carry information cr single chain.

[0031] Furthermore, we use the carry information extractor GATE-Extract (see reference) in the extraction module. Figure 5 In the middle (c), the structure forms a hairpin shape through self-complementary base pairing between the structural domains c and c′, where the foothold t r Embedded within a hairpin, with biotin attached to its 5' end. When carry information is present in the test tube, the hairpin's structural domain r' undergoes a chain substitution reaction with the structural domain r of the information chain cr. This reaction opens the hairpin structure, exposing the toehold t. r The extended long domain c is called CC. The extractor, combined with carry information, places streptavidin magnetic beads to extract the CC. The streptavidin magnetic beads can bind tightly to biotin and can be attracted by a magnetic frame.

[0032] The specific working steps of the extraction module are as follows: The completed reaction system is placed on a magnetic rack. The GATE-Extract, bound to streptavidin magnetic beads, will be magnetically adsorbed to the bottom of the test tube. After discarding the supernatant, refer to... Figure 6 A dual-chain signal amplification gate (GATE-amplifier) ​​and a fuel chain are added for signal amplification. The carry information (Bin) is extracted from the gate via a chain substitution reaction between the CC and GATE-amplifier, simultaneously exposing the toehold t within the gate. x The generated products then react with toehold t in the fuel chain. x By combining, the opened GATE-Extract is re-displaced through a chain substitution reaction, allowing it to continue reacting with the GATE-amplifier to generate more B. in This amplifies the signal, and after another magnetic separation, the supernatant is added to the next calculation module.

[0033] This embodiment provides high stability for long-chain computation, achieved through modular carry separation (… Figure 6The signal strength retention rate remains at 78.5% even at the 10th bit (compared to 31% at the 6th bit in traditional schemes); energy consumption is significantly reduced, with a computational energy consumption of 0.3nJ per bit, which is only 0.02% of that of the optical quantum computing chip (IBM Q System One); and it has technical advantages, as shown in the graph comparing the number of computation bits and the signal attenuation rate (data:image / png;base64 and simulated line graph). In this embodiment, the attenuation rate is only 21% when performing 10-bit computation, while the attenuation rate of the prior art exceeds 30% when performing 4-bit computation.

[0034] Example 2 Based on the basic embodiment and embodiment 1, this embodiment further verifies the performance of 10-bit ternary addition.

[0035] To evaluate the feasibility of a ternary addition system based on DNA strand substitution, a 10-bit ternary addition calculation (1012212101+2211220122) was implemented. First, input A1 and input B2 were added to designated test tubes in the 12-module. Then, the result bit in the test tube was calculated using a competitive blocking circuit. The fluorescence signal of the result was measured by PCR, and subsequently extracted using an extractor in the extraction module. The carry information was calculated and amplified. After a round of magnetic separation, the supernatant, along with the input for the next bit, was transferred to the next bit calculation module (input A0 and input B2). The output from the fluorescence reporter gate was then recorded. This process continued until all bits were calculated, and the result was recorded. Figure 7 The figure shows that the gray, red, and blue curves correspond to the fluorescence signals of ROX, FAM, and VIC, representing values ​​of 0, 1, and 2, respectively. The total result shown in the figure is 11001210000, thus confirming the feasibility and accuracy of the design.

[0036] Test case: 1012212101 + 2211220122 = 11001210000 Quantification results are shown Figure 5 : Inter-bit error rate: 7th bit FAM signal drift <5% (meets the standard after error correction).

[0037] Example 3 This embodiment, based on the basic embodiment and embodiments 1-2, further optimizes the dynamic parameters. The experimental parameters for the fuel chain concentration gradient are shown in Table 4.

[0038] Table 4

[0039] Conclusion: Optimal balance is achieved at 100 nM (magnification factor is positively correlated with stability).

[0040] Example 4 Based on the basic embodiment and embodiments 1-3, this embodiment further integrates mixed logic operations.

[0041] The aforementioned ternary addition system based on DNA strand substitution integrates a competitive blocking circuit with an AND gate to form a ternary multiplication unit. The input strand contains multi-target localization sequences. This system adjusts GATE1 within a range of 1:(0.2~5). ij The concentration ratio supports ternary subtraction operations.

[0042] Ternary multiplication verification: 2 × 2 = 11 (ternary). Experimental data shows: The success rate of NAND gate cooperative operation is 91%, which is 40% higher than that of single addition.

[0043] It supports up to 6-bit ternary multiplication.

[0044] In summary, the DNA strand substitution-based logic circuit employed in this application can accurately calculate ternary addition through its input, calculation, and output units, and can also expand the number of bits calculated by adjusting the concentration ratio. The invention overcomes the limitation on the number of bits in DNA computation through a ternary gating architecture in conjunction with fuel chain amplification. The above embodiments verify the optimization of signal stability by dynamic parameter adjustment and achieve extended integration with multiplication logic, providing a generalized framework for molecular arithmetic units.

[0045] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A ternary addition system based on DNA strand substitution, characterized in that, It includes: Input unit: Used to obtain the DNA single-strand information of the addend and augend, and add the input information to the corresponding calculation module; load the DNA single strands of the addend and augend: input Ai, input Bj, i,j=0,1,2; The computing unit comprises nine modules: 00, 01, 02, 10, 11, 12, 20, 21, and 22. Each module contains a competitive blocking circuit, GATE1. ij / GATE2 and carry calculation gate GATE- ij / GATE1- ij The result is dynamically selected as 1 or 2, and a carry signal is generated. The competitive blocking circuit determines whether there is carry information from the previous bit. After the calculation is completed, the result is obtained by PCR fluorescence quantitative measurement. The carry information is used to generate the information for the next bit. Output unit: includes an output module and an extraction module. The output module outputs the fluorescent signal corresponding to the result bit and outputs digital information from 0 to 2. The extraction module is used to extract the carry information of the next bit generated by the carry calculation, amplify the signal and add it to the next bit calculation.

2. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, In the competitive blocking circuit, the blocking rate k 2 satisfy: k 2 = (1.8 ~ 2.3) × k 1, and k 2>10 4 M -1 s -1 .

3. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, The output unit also includes a fluorescence signal conversion module ROX / FAM / VIC and a magnetic bead extraction-fuel chain amplification module; In the magnetic bead extraction module: The particle size of streptavidin magnetic beads is 50-100 nm; The fuel chain is a double-stranded DNA, used for signal amplification reactions; In the fluorescence signal conversion module: The ROX fluorescent marker corresponds to the ternary value 0; FAM and VIC correspond to 1 and 2 respectively, and the wavelength interval of the three channels is ≥50nm; The fuel chain contains thiophosphate modification, and each chain has ≤3 modification sites; The biotin in the extraction module is labeled at the 5' end of the GATE-Extract. After separation by magnetic beads, it is recycled through the fuel chain to generate ≥10 3 The Bin signal is twice as strong.

4. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, The carry calculation gate includes: GATE-ij (ij=12,21,22): A three-chain gate structure that responds to a high-order input to trigger a carry; GATE1-ij (ij=02,11,20): A four-chain gate structure that collaboratively handles cross-carry logic.

5. The ternary addition system based on DNA strand substitution according to claim 4, characterized in that, The carry information calculation also includes two double-chain carry information conversion gates, GATE-Convertb1 and GATE-Convertb2. These double-chain carry information conversion gates are used to convert the carry information of the triple-chain gate GATE-Convertb1 into a single carry information. ij The pseudo-carry information generated by the reaction is converted into carry information.

6. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, The two input DNA single-strand information include: when the addend input is 0, 1, or 2, the corresponding three single-strand inputs are respectively inputA. i (i=0, 1, 2), when the addend is 0, 1, 2, the three single-chain inputs B are respectively... j (j=0, 1, 2).

7. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, The competitive blocking circuit of the computing unit performs the first-level reaction when there is no blocking chain, producing result 1; When a blocking chain exists, the carry information chain will block the first-level reaction and trigger the second-level reaction, resulting in result 2; The first and second layer reactions include a triple-gate GATE1 ij And the double-chain gate GATE2, the triple-chain gate GATE1 ij The double-chain gate GATE2 is used to generate result 1 by reacting with two input chains. It is used to block the triple-chain gate GATE1 when there is a carry information chain. ij At that time, the result 2 is generated in response to the carry information chain.

8. The ternary addition system based on DNA strand substitution according to claim 1, characterized in that, The competitive blocking circuit is integrated with the AND gate to form a ternary multiplication unit, and the input chain contains a multi-target positioning sequence.

9. The ternary addition system based on DNA strand substitution according to any one of claims 1-8, characterized in that, By adjusting GATE1 within the range of 1: (0.2~5) ij The concentration ratio supports ternary subtraction operations.

10. A ternary addition calculation method based on DNA strand substitution, characterized in that, The ternary addition system according to any one of claims 1-9 includes the following steps: S1: Select the calculation module based on input Ai / Bj, and generate the result bit through a competitive blocking circuit; S2: Extract the carry signal and amplify it, then proceed to the next bit for calculation until the addition of 10 bits or less is completed.

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