阅读说明：本技术 基于dna链置换的四输入阶乘加法运算分子电路设计方法 (four-input factorial addition operation molecular circuit design method based on DNA strand displacement ) 是由 王延峰 *** 耿盛涛 袁国栋 孙军伟 姜素霞 王英聪 黄春 方洁 王妍 凌丹 于 2019-09-02 设计创作，主要内容包括：本发明提出了一种基于DNA链置换的四输入阶乘加法运算分子电路设计方法,其步骤为：列写出两位二进制数对应的阶乘,依照随机组合列出十种两个二进制数阶乘之和的真值表,构建阶乘加法运算电路；采用双轨思想将四输入阶乘加法运算电路转化为只包含逻辑与门及逻辑或门的双轨逻辑电路,利用DNA分子设计DNA分子逻辑门并构建四输入阶乘加法运算分子电路,通过Visual DSD仿真软件验证输出结果的正确性,分析四输入阶乘加法运算分子电路的复杂动力学行为,并验证其动力学行为。本发明对于以后构建更复杂的逻辑运算电路提供了基本的理论基础,促进了生物计算机的发展,从而提高生物计算机逻辑电路的可靠性。(The invention provides a four-input factorial addition operation molecular circuit design method based on DNA strand displacement, which comprises the following steps: factorial corresponding to two binary numbers are written in rows, a truth table of the sum of factorial of the ten binary numbers is listed according to random combination, and a factorial addition operation circuit is constructed; the four-input factorial addition operation circuit is converted into a double-track logic circuit only comprising a logic AND gate and a logic OR gate by adopting a double-track idea, a DNA molecule is utilized to design a DNA molecule logic gate and construct the four-input factorial addition operation molecular circuit, the correctness of an output result is verified by Visual DSD simulation software, the complex dynamic behavior of the four-input factorial addition operation molecular circuit is analyzed, and the dynamic behavior of the four-input factorial addition operation molecular circuit is verified. The invention provides a basic theoretical basis for constructing a more complex logic operation circuit later, and promotes the development of the biological computer, thereby improving the reliability of the logic circuit of the biological computer.)

1. A four-input factorial addition operation molecular circuit design method based on DNA strand displacement is characterized by comprising the following steps:

The method comprises the following steps: factoring corresponding to two binary numbers is written in rows and randomly combined to obtain a truth table of the factoring sum of the ten binary numbers, a Boolean logic expression is written according to the truth table, a factoring addition operation circuit is constructed, and the factoring addition operation circuit is converted into a four-input factoring addition double-track logic circuit by utilizing the double-track idea;

step two: researching a reaction mechanism based on DNA strand displacement, wherein a DNA single strand with a small branch point domain and a matched DNA double strand can generate a small branch point domain base complementary pairing reaction to displace a DNA output strand, and the small branch point domain base complementary pairing reaction is a spontaneous, dynamic and cascadable reversible reaction process;

Step three: designing a DNA molecule amplification gate, a DNA molecule AND gate, a DNA molecule OR gate, a DNA molecule integration gate, a DNA molecule threshold gate and a DNA molecule report gate by using DNA molecules, and converting the four-input multiplication-addition double-track logic circuit in the step two into a four-input multiplication-addition operation molecular circuit;

Step four: verifying the output results of ten different calculation modes of the four-input factorial addition operation molecular circuit constructed in the third step by Visual DSD simulation software, and verifying the correctness of the four-input factorial addition operation molecular circuit.

2. The design method of four-input factorial addition molecular circuit based on DNA strand displacement of claim 1, wherein the input of the factorial addition circuit is two-bit binary number comprising addend B2B1 and addend A2A1, the output is Y4Y3Y2Y1, the result of factoring two addends Y4Y3Y2Y1 is listed, and then the addend B2B1 and the addend A2A1 are randomly combined to obtain ten combination modes; and sequentially carrying out factorial addition operation on the inputs in the ten combination modes, listing operation results corresponding to the inputs to obtain a truth table, and obtaining a Boolean logic expression according to the truth table so as to build a four-input factorial addition operation circuit.

3. The design method of four-input factorial addition molecular circuit based on DNA strand displacement of claim 2, wherein when A2a 1-00 and B2B 1-00 are inputted to the four-input factorial addition molecular circuit, a factorial 0 and B factorial 0 sum to 0 and Y4Y3Y2Y 1-0000 is outputted; when the input A2a1 is 00 and B2B1 is 01, the sum of a factorial 0 and B factorial 1 is 1, and the output Y4Y3Y2Y1 is 0001; when the input A2a1 is 00 and B2B1 is 10, the sum of a factorial 0 and B factorial 2 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 00 and B2B1 is 11, the sum of a factorial 0 and B factorial 6 is 6, and the output Y4Y3Y2Y1 is 0110; when the input A2a1 is 01 and the input B2B1 is 01, the sum of the a factorial 1 and the B factorial 1 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 01 and the input B2B1 is 10, the sum of the a factorial 1 and the B factorial 2 is 3, and the output Y4Y3Y2Y1 is 0011; when the input A2a1 is 01 and the input B2B1 is 11, the sum of a factorial 1 and B factorial 6 is 7, and the output Y4Y3Y2Y1 is 0111; when the input A2a1 is 10 and B2B1 is 10, the sum of a factorial 2 and B factorial 2 is 4, and the output Y4Y3Y2Y1 is 0100; when the input A2a1 is 10 and B2B1 is 11, the sum of a factorial 2 and B factorial 6 is 8, and the output Y4Y3Y2Y1 is 1000; when the input A2a1 is 11 and B2B1 is 11, the sum of a factorial 6 and B factorial 6 is 12, and the output Y4Y3Y2Y1 is 1100; the logical operation expression of the output signal Y1 is: the logical operation expression of the output signal Y2 is: the logical operation expression of the output signal Y3 is that of the output signal Y4

4. The design method of four-input factorial addition molecular circuit based on DNA strand displacement as claimed in claim 2 or 3, wherein the idea of dual-rail is to represent the input signal and the output signal by a pair of opposite logic signals, to represent the input signal B2 by a pair of input signal B20 and input signal B21, respectively, to represent the input signal B1 by a pair of input signal B10 and input signal B11, to represent the input signal A2 by a pair of input signal A20 and input signal A21, respectively, and to represent the input signal A1 by a pair of input signal A10 and input signal A11, respectively; the output signal Y4 is represented by a pair of output signals Y40 and Y41, respectively, the output signal Y3 is represented by a pair of output signals Y30 and Y31, respectively, the output signal Y2 is represented by a pair of output signals Y20 and Y21, respectively, and the output signal Y1 is represented by a pair of output signals Y10 and Y11, respectively.

5. The design method of the four-input factorial addition molecular circuit based on DNA strand displacement of claim 4, wherein the input signals A20, B20 and B10 of the four-input factorial addition double-rail logic circuit are all connected with a three-input OR gate I, and the output of the three-input AND gate I is an output signal Y41; the input signals A21, B21 and B11 are all connected with a three-input AND gate I, and the output of the three-input AND gate I is an output signal Y40; input signals A21, B21 and B21 are all connected with a four-input OR gate I, input signals A21, B21 and B21 are all connected with a four-input AND gate I, input signals A21, B21 and B21 are all connected with a four-input OR gate II, input signals A21, B21 and B21 are all connected with a four-input AND gate II, input signals A21, B21 and B21 are all connected with a four-input OR gate III, input signals A21, B21 and B21 are all connected with a four-input AND gate IV, four-input signals A21, B21 and B21 are all connected with a four-input AND gate I, four-input gate II, four-input gate III and four-gate IV, four-input gate V or gate IV, four-input signals V and four-input gate IV, four-input or gate V are all connected with a four-input or gate II, four-input gate III, four-input gate V-input or gate III, four-input gate III, four-, The four-input OR gate III and the four-input OR gate IV are both connected with a four-input AND gate V, and the output of the four-input AND gate V is an output signal Y30; the input signals A21, A11 and B20 are all connected with a three-input OR gate II, the input signals A20, A10 and B21 are all connected with a three-input AND gate II, the input signals A21, A10, B21 and B10 are all connected with a four-input OR gate VI, the input signals A20, A11, B20 and B11 are all connected with a four-input AND gate VI, the input signals A21, A10 and B20 are all connected with a three-input OR gate III, the input signals A20, A11 and B21 are all connected with a three-input AND gate III, the three-input AND gate II, the four-input AND gate VI and the three-input AND gate III are all connected with a three-input OR gate IV, the output of the three-input OR gate IV is an output signal Y21, the three-input OR gate II, the four-input OR gate VI and the three-input AND gate III are all connected with a three-input AND gate IV, and gate IV output signal Y20; the input signals A21, A11, B21 and B10 are all connected with a four-input OR gate VII, the input signals A20, A10, B20 and B11 are all connected with a four-input AND gate VII, the input signals A21, A10 and B20 are all connected with a three-input OR gate V, the input signals A20, A11 and B21 are all connected with a three-input AND gate V, the four-input OR gate VII and the three-input OR gate V are all connected with a two-input AND gate, the output of the two-input AND gate is an output signal Y10, the four-input AND gate VII and the three-input AND gate V are all connected with a two-input OR gate, and the output of the two-input OR gate is an output signal Y11.

6. The method of claim 1, wherein the reaction kinetics of the DNA strand displacement are derived from molecular forces between base-complementary pairings, and the DNA single strand < mt n > is bound by complementary pairing with a small complementary pivot t on the DNA double strand { t } [ n t ] < p > to form a molecular complex; that is, a domain n on a single-stranded DNA < m t n > is complementarily paired with a complementary small branch domain n on a double-stranded DNA < m > [ t ] < n > [ n t ] < p >, and instead of the domain n which was previously complementarily paired with n, the strand < n t p > is detached from the molecular complex < m > [ t n ] < n > [ t ] < p >, and finally, is released in the solution as a single-stranded DNA, wherein t is a small branch domain and t is a Watson Crick base complementary pairing domain of t.

7. The design method of four-input multiplication-addition molecular circuit based on DNA strand displacement according to claim 1 or 6, wherein the DNA molecule amplifying gate is a DNA molecule gate circuit with one input and multiple outputs, the DNA molecule amplifying gates include four one-input ten-output DNA molecule amplifying gates, two one-input nine-output DNA molecule amplifying gates and two one-input seven-output DNA molecule amplifying gates, the four one-input ten-output DNA molecule amplifying gates are respectively connected with input signals A20, A21, B20 and B21, the two one-input nine-output DNA molecule amplifying gates are respectively connected with input signals A10 and A11, and the two one-input seven-output DNA molecule amplifying gates are respectively connected with input signals B10 and B11; the DNA molecule AND gate comprises an integrated gate and a threshold gate with a threshold value of 1.2, which are connected in series, and comprises a two-output one-output DNA molecule AND gate, five three-input one-output DNA molecule AND gates and seven four-input one-output DNA molecule AND gates; the DNA molecule OR gate comprises an integrated gate and a threshold gate with a threshold value of 0.6 which are connected in series, and the DNA molecule OR gate comprises a two-output one-output DNA molecule OR gate, five three-input one-output DNA molecule OR gates and seven four-input one-output DNA molecule OR gates.

8. The method according to claim 7, wherein the input signal B is represented by a single DNA strand < S4 ^ T ^ S5^ S, the input signal B is represented by a single DNA strand < S6 ^ T ^ S7 ^ S, the input signal B is represented by a single DNA strand < S8 ^ T ^ S9^ S11 ^ S, the input signal A is represented by a single DNA strand < S12 ^ S13 ^ S, the input signal A is represented by a single DNA strand < S14 ^ T ^ S15 ^ S, the input signal A is represented by a single DNA strand < S17^ S, the input signal A is represented by a single DNA strand < S18 ^ S16 ^ S19 ^ S S19 ^ S11 ^ S; the output signal Y11 is expressed by a single DNA strand < S128L ^ S128S 128R ^ Fluor128>, the output signal Y10 is expressed by a single DNA strand < S130L ^ S130S 130R ^ Fluor130>, the output signal Y21 is expressed by a single DNA strand < S132L ^ S132S 132R ^ Fluor132>, the output signal Y20 is expressed by a single DNA strand < S134L ^ S134S R ^ Fluor134>, the output signal Y31 is expressed by a single DNA strand < S136L ^ S136S 136R ^ Fluor136>, the output signal Y30 is expressed by a single DNA strand < S138 ^ S138S 138R ^ Fluor138>, the output signal Y41 is expressed by a single DNA strand < S140^ S L ^ S140S 140^ S2 ^ S695142 > and the output signal Y86142 is expressed by a single DNA strand < S84142 > S84142S 86142; each output signal corresponds to a DNA molecular report gate, and the DNA chains of the DNA molecular report gate participating in the reaction of generating the output signal chains are respectively as follows: { T ^ S128L ^ S128S 128R ^ Fluor128>, { T ^ S130L ^ S130S 130R ^ Fluor130>, { T ^ S132L ^ S132S 132R ^ Fluor132>, { T ^ S134S R ^ Fluor134>, { T ^ S134L ^ S134S R ^ Fluor134>, { T ^ S140^ S L S136S 136 ^ Fluor136>, { T138L ^ S138S R ^ Fluor138 ^ S138 ^ Fluor142>, { T138 ^ S140^ S138 ^ S89140 >, { T138 ^ S138/142 ^ Fluor142 }; wherein T is a small branch point structural domain, and T is a complementary small branch point structural domain of the small branch point structural domain T; si represents a DNA domain, i ═ 1,2, …,246, Fluori represents a fluorescent domain, L represents a left domain, R represents a right domain, and ^ represents a small branch point domain in the DNA molecule; logic 1 indicates that the concentration of DNA molecules is high, and logic 0 indicates that the concentration of DNA molecules is low.

9. The method of claim 8, wherein the molecular circuit of the branch circuit of the output signal Y41 is a molecular circuit with a reaction sequence of: the chains of the three-input-one-output DNA molecule OR gate X10 input-side integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > react with the single-chain sp311[ S17L ^ S17^ S17R ^ T ^ S124L ^ S124^ S R ] of the input signal A20 replaced by the amplification gate to replace the chains sp313< S140 2 ^ S140^ T ^ S125L S125^ S R > with the chains sp312{ T } [ S124^ S140^ S124^ T ] < S125^ S L ^ S17^ S R >; the chains of the three-input-one-output DNA molecule OR gate X10 input-side integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > react with the single-chain sp493[ S5L ^ S5^ S5R ^ T ^ S124L ^ S124^ S R ] replaced by the amplified gate of the input signal B10 to replace the chain sp494{ T } [ S124^ S2 ^ S124^ T ] < S5L ^ S5^ S5 > 7378 > and the chain sp313< S140^ S R ^ T ^ S L ^ S125S 36125 > S R >; the chain of the three-input-one-output DNA molecule or gate X10 input integrated gate, gatel-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > reacts with the single chain sp455< S9L ^ S9^ S9R ^ T ^ S124L ^ S124^ S R > substituted by the amplification gate of the input signal B20 to substitute the chain sp456{ T ^ S124^ S5963 ^ S R ^ T ] < S L ^ S9^ S9 > and the chain sp313< S140^ S R ^ T ^ S125S L ^ S686125S 36125 > R; three input-one output DNA molecule or chain gate X10 output threshold gate, chain gate-49 { T ^ S125^ S125R ^ T ] < S140L ^ S140^ S140R > reacts with chain sp313< S140L ^ S140^ T63S 125L ^ S125^ S125R > to replace chain sp314{ T ^ S140^ S125^ S63R ^ T ] < S124^ S R > with chain sp316< S125L ^ S125^ S140^ S140 > R ^ S T S58140 ^ S140^ S140R >; the chain of the DNA molecular reporter, { T } [ S140^ S140R ] < fluor140> and the chain sp316< S125^ S125R ^ T ^ S140L ^ S140^ S140R > react and replace the chain sp315{ T } [ S140L ^ S140^ S483140R ] < S125L ^ S125^ S125R > and the chain sp210< S140L ^ S140^ S23 ^ fluor140>, and obtain an output signal Y41.

Technical Field

The invention relates to the technical field of molecular circuits, in particular to a four-input factorial addition operation molecular circuit design method based on DNA strand displacement.

Background

The rapid development and continuous update of electronic computers make the computers face the problem of miniaturization. With the development of silicon-based materials into large-scale integrated circuits, microelectronic devices have become more and more demanding with respect to integration. Consequently, very large scale and very large scale integrated circuits must face both physical principles and conventional process technology. This problem may be solved by developing new fabrication processes or introducing new alternative fabrication materials, but this requires higher costs and also increases the possibility of various uncertain errors. Thus, the advantages of the powerful parallel computing power and high precision of the DNA molecular computation model are beginning to make more people try and solve problems with DNA computation. DNA calculation is a branch of biological calculation, and the basic idea is to encode information by using the special double helix structure of DNA molecules and the Watson-Crick complementation principle. Since it is a calculation method, i.e. it is a mathematical problem, the solution is a solving process, and in DNA calculation, data is mapped highly in parallel to generate DNA molecular chains. The first step is to map the data object in the original question to generate a DNA molecular chain; the second step is to code the generated DNA molecular chain, and the coding is completed by adopting different DNA sequences; thirdly, forming a data pool by the DNA molecular chains under the catalysis of biological enzyme; the fourth step is to carry out controllable biochemical operation which can be completed instantly on the mapped DNA molecular chain, and new DNA fragments are generated after the biochemical operation is completed, which is all possible solution spaces of a mathematical problem; finally, by extracting the desired DNA fragments, which is the solution to the original problem, the extraction process requires the use of biological detection techniques. In the process of calculating the DNA, the DNA self-assembly technology solves the problem of high error rate of manual operation, reduces the manual operation and improves the precision of the algorithm. The calculation mode has large information storage capacity, high information processing speed and simple synthesis of molecular devices, and various logic gates are constructed based on the self-assembly principle. The method for constructing the logic gate has the advantages of simplicity and the disadvantage of no universality, namely, when a new problem is met, a DNA chain needs to be redesigned, so that the speed of the multilayer logic circuit in operation is greatly reduced. Thus, a novel computational method, DNA strand displacement technology, has emerged.

The DNA strand displacement technology is simple to operate, and the reaction is a spontaneous reaction without adding any biochemical enzyme; because of the dynamic characteristic, a dynamic cascade system can be constructed. Most DNA devices based on DNA strand displacement reaction networks can be dynamically operated, and are applied to machines, biosensing, circuits and the like. Because the DNA strand displacement technology is a nano technology based on biological molecules, the DNA strand displacement technology has the advantages of high parallel computation speed of the biological molecules, large amount of stored information and programmable simulation. The DNA strand displacement technology is well applied to the aspects of nano computers, sensors, molecular detection, DNA nano robots, DNA nano structures, intelligent medicine carrying, disease diagnosis, treatment and the like.

Disclosure of Invention

Aiming at the technical problem of poor universality of the existing DNA self-assembly technology, the invention provides a four-input factorial addition operation molecular circuit design method based on DNA strand displacement, which is characterized in that a DNA molecule amplification gate, a DNA molecule AND gate, a DNA molecule OR gate, a DNA molecule integration gate, a DNA molecule threshold gate, a DNA molecule report gate and a four-input factorial addition operation molecular double-track logic circuit are constructed based on a reaction mechanism of the strand displacement, and Visual DSD simulation software is used for analyzing the complex dynamics behaviors of the operation molecular double-track logic circuit, thereby playing a good role in promoting the development of a biological computer.

In order to achieve the purpose, the technical scheme of the invention is realized as follows: a four-input factorial addition operation molecular circuit design method based on DNA strand displacement comprises the following steps:

the method comprises the following steps: factoring corresponding to two binary numbers is written in rows and randomly combined to obtain a truth table of the factoring sum of the ten binary numbers, a Boolean logic expression is written according to the truth table, a factoring addition operation circuit is constructed, and the factoring addition operation circuit is converted into a four-input factoring addition double-track logic circuit by utilizing the double-track idea;

Step two: researching a reaction mechanism based on DNA strand displacement, wherein a DNA single strand with a small branch point domain and a matched DNA double strand can generate a small branch point domain base complementary pairing reaction to displace a DNA output strand, and the small branch point domain base complementary pairing reaction is a spontaneous, dynamic and cascadable reversible reaction process;

Step three: designing a DNA molecule amplification gate, a DNA molecule AND gate, a DNA molecule OR gate, a DNA molecule integration gate, a DNA molecule threshold gate and a DNA molecule report gate by using DNA molecules, and converting the four-input multiplication-addition double-track logic circuit in the step two into a four-input multiplication-addition operation molecular circuit;

Step four: verifying the output results of ten different calculation modes of the four-input factorial addition operation molecular circuit constructed in the third step by Visual DSD simulation software, and verifying the correctness of the four-input factorial addition operation molecular circuit.

The input of the factorial addition operation circuit is a two-digit binary number comprising an addend B2B1 and an addend A2A1, the output is Y4Y3Y2Y1, a result Y4Y3Y2Y1 obtained after factorial operation is performed on the two addends is listed, and then random combination is performed on the addend B2B1 and the addend A2A1 to obtain ten combination modes; and sequentially carrying out factorial addition operation on the inputs in the ten combination modes, listing operation results corresponding to the inputs to obtain a truth table, and obtaining a Boolean logic expression according to the truth table so as to build a four-input factorial addition operation circuit.

When the input A2a1 is 00 and the input B2B1 is 00, the sum of a factorial 0 and B factorial 0 is 0, and the output Y4Y3Y2Y1 is 0000 in the four-input factorial addition circuit; when the input A2a1 is 00 and B2B1 is 01, the sum of a factorial 0 and B factorial 1 is 1, and the output Y4Y3Y2Y1 is 0001; when the input A2a1 is 00 and B2B1 is 10, the sum of a factorial 0 and B factorial 2 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 00 and B2B1 is 11, the sum of a factorial 0 and B factorial 6 is 6, and the output Y4Y3Y2Y1 is 0110; when the input A2a1 is 01 and the input B2B1 is 01, the sum of the a factorial 1 and the B factorial 1 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 01 and the input B2B1 is 10, the sum of the a factorial 1 and the B factorial 2 is 3, and the output Y4Y3Y2Y1 is 0011; when the input A2a1 is 01 and the input B2B1 is 11, the sum of a factorial 1 and B factorial 6 is 7, and the output Y4Y3Y2Y1 is 0111; when the input A2a1 is 10 and B2B1 is 10, the sum of a factorial 2 and B factorial 2 is 4, and the output Y4Y3Y2Y1 is 0100; when the input A2a1 is 10 and B2B1 is 11, the sum of a factorial 2 and B factorial 6 is 8, and the output Y4Y3Y2Y1 is 1000; when the input A2a1 is 11 and B2B1 is 11, the sum of a factorial 6 and B factorial 6 is 12, and the output Y4Y3Y2Y1 is 1100; the logical operation expression of the output signal Y1 is: the logical operation expression of the output signal Y2 is: the logical operation expression of the output signal Y3 is that of the output signal Y4

the dual-rail concept represents the input signal and the output signal as a pair of opposite logic signals, the input signal B2 as a pair of input signal B20 and input signal B21, the input signal B1 as a pair of input signal B10 and input signal B11, the input signal a2 as a pair of input signal a20 and input signal a21, and the input signal a1 as a pair of input signal a10 and input signal a 11; the output signal Y4 is represented by a pair of output signals Y40 and Y41, respectively, the output signal Y3 is represented by a pair of output signals Y30 and Y31, respectively, the output signal Y2 is represented by a pair of output signals Y20 and Y21, respectively, and the output signal Y1 is represented by a pair of output signals Y10 and Y11, respectively.

Input signals A20, B20 and B10 of the four-input factorial addition operation double-rail logic circuit are all connected with a three-input OR gate I, and the output of the three-input AND gate I is an output signal Y41; the input signals A21, B21 and B11 are all connected with a three-input AND gate I, and the output of the three-input AND gate I is an output signal Y40; input signals A21, B21 and B21 are all connected with a four-input OR gate I, input signals A21, B21 and B21 are all connected with a four-input AND gate I, input signals A21, B21 and B21 are all connected with a four-input OR gate II, input signals A21, B21 and B21 are all connected with a four-input AND gate II, input signals A21, B21 and B21 are all connected with a four-input OR gate III, input signals A21, B21 and B21 are all connected with a four-input AND gate IV, four-input signals A21, B21 and B21 are all connected with a four-input AND gate I, four-input gate II, four-input gate III and four-gate IV, four-input gate V or gate IV, four-input signals V and four-input gate IV, four-input or gate V are all connected with a four-input or gate II, four-input gate III, four-input gate V-input or gate III, four-input gate III, four-, The four-input OR gate III and the four-input OR gate IV are both connected with a four-input AND gate V, and the output of the four-input AND gate V is an output signal Y30; the input signals A21, A11 and B20 are all connected with a three-input OR gate II, the input signals A20, A10 and B21 are all connected with a three-input AND gate II, the input signals A21, A10, B21 and B10 are all connected with a four-input OR gate VI, the input signals A20, A11, B20 and B11 are all connected with a four-input AND gate VI, the input signals A21, A10 and B20 are all connected with a three-input OR gate III, the input signals A20, A11 and B21 are all connected with a three-input AND gate III, the three-input AND gate II, the four-input AND gate VI and the three-input AND gate III are all connected with a three-input OR gate IV, the output of the three-input OR gate IV is an output signal Y21, the three-input OR gate II, the four-input OR gate VI and the three-input AND gate III are all connected with a three-input AND gate IV, and gate IV output signal Y20; the input signals A21, A11, B21 and B10 are all connected with a four-input OR gate VII, the input signals A20, A10, B20 and B11 are all connected with a four-input AND gate VII, the input signals A21, A10 and B20 are all connected with a three-input OR gate V, the input signals A20, A11 and B21 are all connected with a three-input AND gate V, the four-input OR gate VII and the three-input OR gate V are all connected with a two-input AND gate, the output of the two-input AND gate is an output signal Y10, the four-input AND gate VII and the three-input AND gate V are all connected with a two-input OR gate, and the output of the two-input OR gate is an output signal Y11.

The reaction power of the DNA strand displacement is derived from molecular acting force between base complementary pairing, and the DNA single strand < m t n > is combined through complementary pairing with a complementary small fulcrum t on the DNA double strand { t x } [ n t ] < p > to form a molecular complex; that is, a domain n on a single-stranded DNA < m t n > is complementarily paired with a complementary small branch domain n on a double-stranded DNA < m > [ t ] < n > [ n t ] < p >, and instead of the domain n which was previously complementarily paired with n, the strand < n t p > is detached from the molecular complex < m > [ t n ] < n > [ t ] < p >, and finally, is released in the solution as a single-stranded DNA, wherein t is a small branch domain and t is a Watson Crick base complementary pairing domain of t.

The DNA molecule amplification gate is a DNA molecule gate circuit with multiple inputs and outputs, and comprises four one-input ten-output DNA molecule amplification gates, two one-input nine-output DNA molecule amplification gates and two one-input seven-output DNA molecule amplification gates, wherein the four one-input ten-output DNA molecule amplification gates are respectively connected with input signals A20, A21, B20 and B21, the two one-input nine-output DNA molecule amplification gates are respectively connected with the input signals A10 and A11, and the two one-input seven-output DNA molecule amplification gates are respectively connected with input signals B10 and B11; the DNA molecule AND gate comprises an integrated gate and a threshold gate with a threshold value of 1.2, which are connected in series, and comprises a two-output one-output DNA molecule AND gate, five three-input one-output DNA molecule AND gates and seven four-input one-output DNA molecule AND gates; the DNA molecule OR gate comprises an integrated gate and a threshold gate with a threshold value of 0.6 which are connected in series, and the DNA molecule OR gate comprises a two-output one-output DNA molecule OR gate, five three-input one-output DNA molecule OR gates and seven four-input one-output DNA molecule OR gates.

The input signal B is represented by a DNA single strand < S4 ^ S5^ S, the input signal B is represented by a DNA single strand < S6 ^ T ^ S7 ^ S, the input signal B is represented by a DNA single strand < S8 ^ T ^ S9^ S, the input signal B is represented by a DNA single strand < S10 ^ T ^ S11 ^ S, the input signal A is represented by a DNA single strand < S12 ^ S13 ^ S, the input signal A is represented by a DNA strand < S14 ^ S15 ^ S, the input signal A is represented by a DNA single strand < S17^ S S; the output signal Y11 is expressed by a single DNA strand < S128L ^ S128S 128R ^ Fluor128>, the output signal Y10 is expressed by a single DNA strand < S130L ^ S130S 130R ^ Fluor130>, the output signal Y21 is expressed by a single DNA strand < S132L ^ S132S 132R ^ Fluor132>, the output signal Y20 is expressed by a single DNA strand < S134L ^ S134S R ^ Fluor134>, the output signal Y31 is expressed by a single DNA strand < S136L ^ S136S 136R ^ Fluor136>, the output signal Y30 is expressed by a single DNA strand < S138 ^ S138S 138R ^ Fluor138>, the output signal Y41 is expressed by a single DNA strand < S140^ S L ^ S140S 140^ S2 ^ S695142 > and the output signal Y86142 is expressed by a single DNA strand < S84142 > S84142S 86142; each output signal corresponds to a DNA molecular report gate, and the DNA chains of the DNA molecular report gate participating in the reaction of generating the output signal chains are respectively as follows: { T ^ S128L ^ S128S 128R ^ Fluor128>, { T ^ S130L ^ S130S 130R ^ Fluor130>, { T ^ S132L ^ S132S 132R ^ Fluor132>, { T ^ S134S R ^ Fluor134>, { T ^ S134L ^ S134S R ^ Fluor134>, { T ^ S140^ S136S 136 ^ S136 >, { T138 ^ S138S 138R ^ S138 ^ Fluor138>, { T ^ S140^ S45 ^ S138 ^ S89140 ^ S138 ^ S142 ^ S138/142 ^ Fluor138>, { T138 ^ S89142 ^ S140 ^. Wherein T is the small branch point structural domain, and T is the complementary small branch point structural domain of the small branch point structural domain T. Si represents a DNA domain, i ═ 1,2, …,246, Fluori represents a fluorescent domain, L represents a left domain, R represents a right domain, and ^ represents a small branch point domain in the DNA molecule. Logic 1 indicates that the concentration of DNA molecules is high, and logic 0 indicates that the concentration of DNA molecules is low.

The reaction process of the molecular circuit of the branch circuit of the output signal Y41 is as follows: the chains of the three-input-one-output DNA molecule OR gate X10 input-side integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > react with the single-chain sp311[ S17L ^ S17^ S17R ^ T ^ S124L ^ S124^ S R ] of the input signal A20 replaced by the amplification gate to replace the chains sp313< S140 2 ^ S140^ T ^ S125L S125^ S R > with the chains sp312{ T } [ S124^ S140^ S124^ T ] < S125^ S L ^ S17^ S R >; the chains of the three-input-one-output DNA molecule OR gate X10 input-side integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > react with the single-chain sp493[ S5L ^ S5^ S5R ^ T ^ S124L ^ S124^ S R ] replaced by the amplified gate of the input signal B10 to replace the chain sp494{ T } [ S124^ S2 ^ S124^ T ] < S5L ^ S5^ S5 > 7378 > and the chain sp313< S140^ S R ^ T ^ S L ^ S125S 36125 > S R >; the chain of the three-input-one-output DNA molecule or gate X10 input integrated gate, gatel-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > reacts with the single chain sp455< S9L ^ S9^ S9R ^ T ^ S124L ^ S124^ S R > substituted by the amplification gate of the input signal B20 to substitute the chain sp456{ T ^ S124^ S5963 ^ S R ^ T ] < S L ^ S9^ S9 > and the chain sp313< S140^ S R ^ T ^ S125S L ^ S686125S 36125 > R; three input-one output DNA molecule or chain gate X10 output threshold gate, chain gate-49 { T ^ S125^ S125R ^ T ] < S140L ^ S140^ S140R > reacts with chain sp313< S140L ^ S140^ T63S 125L ^ S125^ S125R > to replace chain sp314{ T ^ S140^ S125^ S63R ^ T ] < S124^ S R > with chain sp316< S125L ^ S125^ S140^ S140 > R ^ S T S58140 ^ S140^ S140R >; the chain of the DNA molecular reporter, { T } [ S140^ S140R ] < fluor140> and the chain sp316< S125^ S125R ^ T ^ S140L ^ S140^ S140R > react and replace the chain sp315{ T } [ S140L ^ S140^ S483140R ] < S125L ^ S125^ S125R > and the chain sp210< S140L ^ S140^ S23 ^ fluor140>, and obtain an output signal Y41.

the invention has the beneficial effects that: constructing a DNA molecular logic gate based on a reaction mechanism of DNA strand displacement to form two binary number multiplication addition operation molecular circuits; factorial corresponding to two binary numbers are written in columns, a truth table of the sum of factorial of the ten binary numbers is listed according to random combination, a factorial addition operation circuit is constructed according to the truth table, and a Boolean logic expression is written; because the expression has NOT gate and the NOT gate is difficult to be realized in the DNA molecular circuit, the idea of double track is adopted to convert the four-input multiplication addition operation circuit into a double track logic circuit only comprising a logic AND gate and a logic OR gate, DNA molecules are used to design a DNA molecule amplification gate, a DNA molecule integration gate, a DNA molecule threshold gate, a DNA molecule AND gate, a DNA molecule OR gate and a DNA molecule report gate, and the designed DNA molecule gate is used to construct the four-input multiplication addition operation molecular circuit, the DNA molecular circuit has ten different calculation modes, the correctness of the output result is verified through Visual DSD simulation software, the complex dynamic behavior of the four-input factorial addition operation molecular circuit is analyzed, the four-input factorial addition operation molecular circuit based on DNA strand displacement is constructed, the dynamic behavior is verified, and the simulation result proves the reasonability and the effectiveness of the circuit. The invention provides a basic theoretical basis for constructing a more complex logic operation circuit later, and promotes the development of the biological computer, thereby improving the reliability of the logic circuit of the biological computer.

drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a diagram of a four-bit factorial addition dual-rail circuit according to the present invention.

FIG. 2 is a schematic diagram showing the mechanism of the displacement reaction of DNA strand displacement.

FIG. 3 is a Seesaw diagram of basic logic gates, wherein (a) is a DNA molecule amplification gate, (b) is a DNA molecule OR gate, (c) is a DNA molecule AND gate, (d) is a DNA molecule integration gate, (e) is a DNA molecule threshold gate, and (f) is a DNA molecule reporter gate.

FIG. 4 is a diagram of a four-digit factorial addition biochemical circuit of the present invention.

FIG. 5 shows the process of the strand displacement reaction of the molecular circuit outputting signal Y41.

Fig. 6 is a simulation diagram of a four-digit factorial addition molecular circuit of the present invention, where (a) is Y4Y3Y2Y1 ═ 0000, (b) is Y4Y3Y2Y1 ═ 0001, (c) is Y4Y3Y2Y1 ═ 0010, (d) is Y4Y3Y2Y1 ═ 0011, (e) is Y4Y3Y2Y1 ═ 0101, (f) is Y4Y3Y2Y1 ═ 0110, (g) is Y4Y3Y2Y1 ═ 0111, (h) is Y4Y3Y2Y1 ═ 1010, (i) is Y4Y3Y2Y1 ═ 1011, and (j) is Y4Y3Y2Y1 ═ 1111.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without inventive effort based on the embodiments of the present invention, are within the scope of the present invention.

A four-input factorial addition operation molecular circuit design method based on DNA strand displacement comprises the following steps:

The method comprises the following steps: factorial multiplication corresponding to two binary numbers is written in a row and randomly combined to obtain a truth table of the factorial sum of the ten binary numbers, a Boolean logic expression is written according to the truth table, a factorial addition operation circuit is constructed, and the factorial addition operation circuit is converted into a four-input factorial addition double-track logic circuit by utilizing the double-track idea.

binary numbers are used for representing input signals and output signals of a factorial addition operation numerator circuit, the input of the factorial addition operation numerator circuit is a two-bit binary number comprising an addend B2B1 and an addend A2A1, the output is Y4Y3Y2Y1, and Y4Y3Y2Y1 represents the outputs obtained by adding after respective factorial operations of the addend B2B1 and the addend A2A 1. Listing results Y4Y3Y2Y1 after two addends are subjected to factorial operation, and then randomly combining the addend B2B1 and the addend A2A1 to obtain ten combination modes; the inputs of the ten combinations are sequentially subjected to factorial addition operation, and operation results corresponding to the inputs are listed to obtain a truth table, as shown in table 1. And obtaining a Boolean logic expression according to the truth table, obtaining a Boolean logic expression of the four-digit factorial addition operation circuit as shown in the formula (1), and thus constructing the four-input factorial addition operation circuit as shown in the figure 1.

Table 1 truth table for operation of factorial addition operations

As can be seen from table 1, when the input A2a1 is 00 and the input B2B1 is 00 in the four-input factorial addition circuit, the sum of a factorial 0 and B factorial 0 is 0, and the output Y4Y3Y2Y1 is 0000; when the input A2a1 is 00 and B2B1 is 01, the sum of a factorial 0 and B factorial 1 is 1, and the output Y4Y3Y2Y1 is 0001; when the input A2a1 is 00 and B2B1 is 10, the sum of a factorial 0 and B factorial 2 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 00 and B2B1 is 11, the sum of a factorial 0 and B factorial 6 is 6, and the output Y4Y3Y2Y1 is 0110; when the input A2a1 is 01 and the input B2B1 is 01, the sum of the a factorial 1 and the B factorial 1 is 2, and the output Y4Y3Y2Y1 is 0010; when the input A2a1 is 01 and the input B2B1 is 10, the sum of the a factorial 1 and the B factorial 2 is 3, and the output Y4Y3Y2Y1 is 0011; when the input A2a1 is 01 and the input B2B1 is 11, the sum of a factorial 1 and B factorial 6 is 7, and the output Y4Y3Y2Y1 is 0111; when the input A2a1 is 10 and B2B1 is 10, the sum of a factorial 2 and B factorial 2 is 4, and the output Y4Y3Y2Y1 is 0100; when the input A2a1 is 10 and B2B1 is 11, the sum of a factorial 2 and B factorial 6 is 8, and the output Y4Y3Y2Y1 is 1000; when the input A2a1 and B2B1 are 11, the sum of a factorial 6 and B factorial 6 is 12, and the output Y4Y3Y2Y1 is 1100. Establishing a truth table, and as can be seen from table 1, when the output signal Y1 has an output, the input signals are 0001, 0110 and 0111, and the logical operation expression of the output signal Y1 obtained by performing or operation on the three signals is: when the output signal Y2 has output, the input signals are 0010, 0011, 0101, 0110 and 0111, and the logical operation expression of the five signals subjected to the or operation to obtain the output signal Y2 is: when the output signal Y3 has output, the input signals are 0011, 0111, 1010 and 1111, the logical operation expression of the four signals which are subjected to the OR operation to obtain the output signal Y3 is 1011 and 1111 when the output signal Y4 has output, and the logical operation expression of the two signals which are subjected to the OR operation to obtain the output signal Y4 is

As can be seen from equation (1), since the four-bit multiplication-addition operation circuit includes the not gate in the boolean logic expression, and since the not gate is difficult to distinguish between the low-concentration input signal from the upstream and the low-concentration input signal that has not been completely calculated, an uncertainty error of the output signal is caused, that is, the not gate is difficult to implement in the DNA molecular circuit, the occurrence of such problems is avoided using the double-rail concept, and the four-bit multiplication-addition operation circuit is constructed as a double-rail molecular logic circuit including only the logic and gate and the logic or gate using the double-rail concept. There is no not a not gate in its dual-rail molecular circuit, so the idea of dual-rail is adopted to make its input signal and output signal respectively represented by a pair of input signals and a pair of output signals, each signal being replaced by a pair of opposite logic signals, respectively logic "1" and logic "0". A pair of input signals are represented as corresponding input signals having opposite logical values, respectively, and a pair of output signals are represented as corresponding output signals having opposite logical values, respectively.

The dual-rail concept is to represent the input signal B2 by a pair of input signal B20 and input signal B21, respectively, and when the value of the input signal B2 is 1, the logic value of the input signal B20 is 0, and the logic value of the input signal B21 is 1, and similarly, when the value of the input signal B2 is 0, the logic value of the input signal B20 is 1, and the logic value of the input signal B21 is 0. The input signal B1 is represented by a pair of input signals B10 and B11, respectively, the input signal a2 is represented by a pair of input signals a20 and a21, respectively, and the input signal a1 is represented by a pair of input signals a10 and a11, respectively; the output signal Y4 is represented by a pair of output signals Y40 and Y41, respectively, the output signal Y3 is represented by a pair of output signals Y30 and Y31, respectively, the output signal Y2 is represented by a pair of output signals Y20 and Y21, respectively, and the output signal Y1 is represented by a pair of output signals Y10 and Y11, respectively. A four-input factorial addition operation double-rail logic circuit is constructed by utilizing the double-rail idea.

The logic circuit can be converted into a circuit only comprising a logic AND gate and a logic OR gate by utilizing a double-rail idea, and the four-input factorial addition operation circuit is converted into a four-input factorial addition double-rail logic circuit according to the double-rail idea, as shown in FIG. 1.

Input signals A20, B20 and B10 of the four-input factorial addition operation double-rail logic circuit are all connected with a three-input OR gate I, and the output of the three-input AND gate I is an output signal Y41; the input signals A21, B21 and B11 are all connected with a three-input AND gate I, and the output of the three-input AND gate I is an output signal Y40; input signals A21, B21 and B21 are all connected with a four-input OR gate I, input signals A21, B21 and B21 are all connected with a four-input AND gate I, input signals A21, B21 and B21 are all connected with a four-input OR gate II, input signals A21, B21 and B21 are all connected with a four-input AND gate II, input signals A21, B21 and B21 are all connected with a four-input OR gate III, input signals A21, B21 and B21 are all connected with a four-input AND gate IV, four-input signals A21, B21 and B21 are all connected with a four-input AND gate I, four-input gate II, four-input gate III and four-gate IV, four-input gate V or gate IV, four-input signals V and four-input gate IV, four-input or gate V are all connected with a four-input or gate II, four-input gate III, four-input gate V-input or gate III, four-input gate III, four-, The four-input OR gate III and the four-input OR gate IV are both connected with a four-input AND gate V, and the output of the four-input AND gate V is an output signal Y30; the input signals A21, A11 and B20 are all connected with a three-input OR gate II, the input signals A20, A10 and B21 are all connected with a three-input AND gate II, the input signals A21, A10, B21 and B10 are all connected with a four-input OR gate VI, the input signals A20, A11, B20 and B11 are all connected with a four-input AND gate VI, the input signals A21, A10 and B20 are all connected with a three-input OR gate III, the input signals A20, A11 and B21 are all connected with a three-input AND gate III, the three-input AND gate II, the four-input AND gate VI and the three-input AND gate III are all connected with a three-input OR gate IV, the output of the three-input OR gate IV is an output signal Y21, the three-input OR gate II, the four-input OR gate VI and the three-input AND gate III are all connected with a three-input AND gate IV, and gate IV output signal Y20; the input signals A21, A11, B21 and B10 are all connected with a four-input OR gate VII, the input signals A20, A10, B20 and B11 are all connected with a four-input AND gate VII, the input signals A21, A10 and B20 are all connected with a three-input OR gate V, the input signals A20, A11 and B21 are all connected with a three-input AND gate V, the four-input OR gate VII and the three-input OR gate V are all connected with a two-input AND gate, the output of the two-input AND gate is an output signal Y10, the four-input AND gate VII and the three-input AND gate V are all connected with a two-input OR gate, and the output of the two-input OR gate is an output signal Y11.

The input signal B is represented by a DNA single strand < S4 ^ S5^ S, the input signal B is represented by a DNA single strand < S6 ^ T ^ S7 ^ S, the input signal B is represented by a DNA single strand < S8 ^ T ^ S9^ S, the input signal B is represented by a DNA single strand < S10 ^ T ^ S11 ^ S, the input signal A is represented by a DNA single strand < S12 ^ S13 ^ S, the input signal A is represented by a DNA strand < S14 ^ S15 ^ S, the input signal A is represented by a DNA single strand < S17^ S S; the output signal Y11 is expressed by a single-stranded DNA < S128L ^ S128S 128R ^ Fluor128>, the output signal Y10 is expressed by a single-stranded DNA < S130L ^ S130S 130R ^ Fluor130>, the output signal Y21 is expressed by a single-stranded DNA < S132 29 ^ S132S 132R ^ Fluor132>, the output signal Y20 is expressed by a single-stranded DNA < S134S R ^ Fluor134>, the output signal Y31 is expressed by a single-stranded DNA < S136L ^ S136S 136R ^ Fluor136>, the output signal Y30 is expressed by a single-stranded DNA < S138 ^ S138S 138R ^ Fluor138>, the output signal Y41 is expressed by a single-stranded DNA < S140^ S L ^ S140S 140^ S140 > S2 ^ Fluor 86142, and the output signal Y86142 is expressed by a single-stranded DNA < S84140 ^ S84142. Each output signal corresponds to a DNA molecular report gate, and the DNA chains of the report gates participating in the reaction of generating the output signal chains are respectively: { T ^ S128L ^ S128S 128R ^ Fluor128>, { T ^ S130L ^ S130S 130R ^ Fluor130>, { T ^ S132L ^ S132S 132R ^ Fluor132>, { T ^ S134S R ^ Fluor134>, { T ^ S134L ^ S134S R ^ Fluor134>, { T ^ S140^ S136S 136 ^ S136 >, { T138 ^ S138S 138R ^ S138 ^ Fluor138>, { T ^ S140^ S45 ^ S138 ^ S89140 ^ S138 ^ S142 ^ S138/142 ^ Fluor138>, { T138 ^ S89142 ^ S140 ^. Wherein T is the small branch point structural domain, and T is the complementary small branch point structural domain of the small branch point structural domain T. Si represents a DNA domain, i ═ 1,2, …,246, Fluori represents a fluorescent domain, L represents a left domain, R represents a right domain, and ^ represents a small branch point domain in the DNA molecule. Logic 1 indicates that the concentration of DNA molecules is high, and logic 0 indicates that the concentration of DNA molecules is low.

step two: the research is based on the reaction mechanism of DNA strand displacement, the DNA single strand with the small branch point domain and the matched DNA double strand can generate the small branch point domain base complementary pairing reaction to displace the DNA output strand, and the small branch point domain base complementary pairing reaction is a spontaneous, dynamic and cascadable reversible reaction process.

The key point of constructing the four-input factorial addition operation double-track molecular circuit lies in the technical principle of DNA strand displacement reaction, the reaction power of DNA strand displacement is derived from molecular acting force between base complementary pairing, and the DNA strand displacement reaction can be realized spontaneously and in cascade at normal temperature without enzyme or transcription mechanism. As shown in FIG. 2, t is a small branch domain, and t is a Watson Crick base complementary pairing domain of t. The first single strand of DNA < mt n > binds by complementary pairing with a small complementary pivot t on the DNA duplex { t x } [ n t ] < p >, forming a molecular complex; then the domain n on the DNA single strand < mtn > is combined with the complementary domain n on the DNA double strand < m > [ t ] < n > [ n t ] < p >, and replaces the domain n which is complementary and paired with n; thus, the strand < n t p > is detached from the molecular complex < m > [ t n ] < n > [ t ] < p >, and finally, is released in the form of a single-stranded DNA in the solution thereof. That is, the process of replacing the single-stranded DNA < ntp > by the single-stranded DNA < mtn > through the reaction with the double-stranded DNA { t } [ n t ] < p > is the global DNA strand displacement reaction. From this, it is known that the DNA strand displacement reaction is a spontaneous, dynamic, cascadable, reversible reaction process.

Step three: and designing a DNA molecule amplification gate, a DNA molecule AND gate, a DNA molecule OR gate, a DNA molecule integration gate, a DNA molecule threshold gate and a DNA molecule report gate by using DNA molecules, and converting the four-input multiplication-addition operation double-track logic circuit in the step two into a four-input multiplication-addition operation molecular circuit.

The DNA strand displacement biochemical circuit technology is utilized to realize six DNA molecular gates, namely a DNA molecular amplification gate, a DNA molecular OR gate, a DNA molecular integration gate, a DNA molecular threshold gate and a DNA molecular report gate. Designing DNA molecule amplification gates with three structure types, designing DNA molecule AND gates with three structure types, designing DNA molecule OR gates with three structure types, and combining the DNA molecule integration gate with different threshold gates to respectively obtain the DNA molecule AND gate and the DNA molecule OR gate. The input signals A20, A21, A10, A11, B20 and B21, B10 and B11 are respectively cascaded with a DNA molecule AND gate and a DNA molecule OR gate through a DNA molecule amplification gate, and the output of the DNA molecule AND gate or the DNA molecule OR gate obtains an output signal.

The Seesaw pattern of the basic logic gate is shown in FIG. 3, and the construction of a DNA molecule biochemical circuit based on this principle is shown in FIG. 4. The DNA molecule amplification gate is a DNA molecule gate circuit with multiple inputs and outputs, the input signals A20, A21, B20 and B10 are four one-input ten-output DNA molecule amplification gates, the input signals A10 and A11 are two one-input nine-output DNA molecule amplification gates, the input signals B10 and B11 are two one-input seven-output DNA molecule amplification gates, the four one-input ten-output DNA molecule amplification gates are respectively connected with the input signals A20, A21, B20 and B21, the two one-input nine-output DNA molecule amplification gates are respectively connected with the input signals A10 and A11, and the two one-input seven-output DNA molecule amplification gates are respectively connected with the input signals B10 and B20. The DNA molecule and gate comprises an integrated gate and a threshold gate with a threshold value of 1.2 which are connected in series, and the DNA molecule and gate comprises a two-output one-output DNA molecule and gate Y10 which are formed by signals X90 and X100. The five three-input one-output DNA molecular AND gates are X11, X61, X81, X101 and Y21 respectively, the AND gate X11 is connected with input signals A21, B11 and B21, the AND gate X61 is connected with input signals A20, A10 and B21, the AND gate X81 is connected with input signals A20, A11 and B21, the AND gate X101 is connected with input signals A20, A11 and B21, and the AND gate Y21 is connected with signals X70, X60 and X81. The seven four-input one-output DNA molecular AND gates are respectively X21, X31, X41, X51, X91, X71 and Y30. The and gate X21 is connected by input signals a20, a10, B21 and B11, the and gate X31 by input signals a20, a11, B20 and B11, the and gate X41 by input signals a21, a10, B21 and B10, the and gate X51 by input signals a21, a11, B21 and B11, the and gate X71 by input signals a20, a11, B20 and B11, the and gate X91 by input signals a20, a10, B20 and B11, and the and gate Y30 by signals X20, X30, X40 and X50, the DNA molecule or gate comprises an integration gate and a threshold gate with a threshold value of 0.6 connected in series, the DNA molecule or gate comprises a two-output DNA molecule or gate Y11 by signals X91, X101. Five three-input one-output DNA molecules or gates are respectively X10, X60, X80, X100 and Y20, wherein an OR gate X10 is connected by input signals A20, B10 and B20, an OR gate X60 is connected by input signals A21, A11 and B20, an OR gate X80 is connected by input signals A21, A10 and B20, an OR gate X100 is connected by input signals A21, A10 and B20, or a gate Y20 is connected by signals X71, X61 and X80. The seven four-input one-output DNA molecular OR gates are respectively X20, X30, X40, X50, X90, X70 and Y31. Or gate X20 is connected by input signals a21, a11, B20 and B10, or gate X30 is connected by input signals a21, a10, B21 and B10, or gate X40 is connected by input signals a20, a11, B20 and B11, or gate X50 is connected by input signals a20, a10, B20 and B10, or gate X70 is connected by input signals a21, a10, B21 and B10, or gate X90 is connected by input signals a21, a11, B21 and B10, or gate Y31 is connected by signals X21, X31, X41 and X51.

The reaction process of the molecular circuit is described in detail by taking the branch circuit with the output signal of Y41 as an example, and the complete molecular reaction process of the branch circuit of Y41 is shown in fig. 5. The reaction process of the molecular circuit of the branch circuit of the output signal Y41 is as follows: the chain of the three-input-one-output OR gate X10 input integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > reacts with the single-chain sp311[ S17L ^ S17^ S17R ^ T ^ S124L ^ S124^ S R ] replaced by the amplified gate of the input signal A20 with the replacement chain sp313< S140 2 ^ S140^ T ^ S125L ^ S125^ S R > reacts with the chain sp312{ T } [ S124^ S8 ^ S124^ S6 ^ T ] < S L ^ S17^ S R >; the chain of the three-input-one-output OR gate X10 input integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > reacts with the single chain sp493[ S5L ^ S5^ S5R ^ T ^ S124L ^ S124^ S R ] replaced by the amplified gate of the input signal B10 with the replacement chain sp494{ T } [ S124^ S R ^ T ] < S5L ^ S5^ S5 > and the chain sp313< S140^ S124^ S125^ S L ^ S36125; the chain of the three-input-one-output OR gate X10 input integrated gate GATEL-48{ T } [ S124L ^ S124^ S124R ^ T ] < S125L ^ S125^ S R > reacts with the single chain sp455< S9L ^ S9^ S9R ^ T ^ S124L ^ S124^ S R > replaced by the input signal B20 through the amplification gate to replace the chain sp456{ T } [ S124L ^ S124^ S R ^ T ] < S L ^ S9 > S9^ S140^ S R ^ T125 ^ S L ^ S36125 > with the chain sp313< S L ^ S140^ S R ^ S124^ S R ^ S125; the chain of gates of the three-input-one-output OR gate X10 output threshold gate, GATEL-49{ T } [ S125^ S125R ^ T ] < S140L ^ S140^ S140R > reacts with the chain sp313< S140L ^ S140^ S R ^ T125L ^ S125^ S125R > to replace the chain sp314{ T ^ T } [ S125L ^ S125^ S R ^ T ] < S L ^ S124^ S124R > and the chain sp316< S125^ S140^ S140 > 58140T S L ^ S140 >; the chain { T } [ S140^ S140R ] < fluor140> and the chain sp316< S125L ^ S125^ S125R ^ T ^ S140L ^ S140^ S140R > in the DNA molecular report gate react and replace the chain sp315{ T } [ S140L ^ S140^ S140R ] < S125L ^ S125^ S R > and the chain sp210< S L ^ S140^ S140^ fluor140>, and obtain an output signal Y41.

step four: verifying the output results of ten different calculation modes of the four-input factorial addition operation molecular circuit constructed in the third step by Visual DSD simulation software, and verifying the correctness of the four-input factorial addition operation molecular circuit.

The four-input factorial addition molecular circuit constructed by utilizing six DNA molecular gates has ten output signals in total, and can complete ten different addition operations. And (3) performing simulation analysis and analysis verification on the four-input factorial addition operation molecular circuit by using Visual DSD simulation software, and obtaining a simulation result diagram that the molecular circuit design realizes the expected function.

The simulation results of the simulation analysis of the four-input factorial addition molecular circuit using Visual DSD software are shown in fig. 6(a) - (i), where the horizontal axis represents time axis in units of seconds "s" and the vertical axis represents concentration axis in units of nanomole per liter "nM". The input signals B20, B21, B10, B11, a20, a21, a10, a11 share 10 different combinations. When B2B1 is 00 and A2A1 is 00, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON, OFF" and "OFF, ON", respectively, and Y4Y3Y2Y1 is 0000, as shown in fig. 6 (a); when B2B1 is 00 and A2A1 is 01, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON, OFF" and "ON, OFF, ON", respectively, and Y4Y3Y2Y1 is 0001, as shown in fig. 6 (B); when B2B1 is 00 and A2A1 is 10, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON, OFF" and "OFF, ON, OFF", respectively, and Y4Y3Y2Y1 is 0010, as shown in fig. 6 (c); when B2B1 is 00 and A2A1 is 11, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON, OFF" and "OFF, ON, OFF, ON", respectively, and Y4Y3Y2Y1 is 0110, as shown in fig. 6 (d); when B2B1 is 01 and A2A1 is 01, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON" and "ON, OFF, ON", respectively, and Y4Y3Y2Y1 is 0010, as shown in fig. 6 (e); when B2B1 is 01 and A2A1 is 10, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON" and "OFF, ON, OFF", respectively, and Y4Y3Y2Y1 is 0011, as shown in fig. 6 (f); when B2B1 is 01 and A2A1 is 11, its input signals B20B21B10B11 and a20a21a10a11 are "ON, OFF, ON" and "OFF, ON, OFF, ON", respectively, and Y4Y3Y2Y1 is 0111, as shown in fig. 6 (g); when B2B1 is 10 and A2A1 is 10, its input signals B20B21B10B11 and a20a21a10a11 are "OFF, ON, OFF" and "OFF, ON, OFF", respectively, and Y4Y3Y2Y1 is 0100, as shown in fig. 6 (h); when B2B1 is 10 and A2A1 is 10, its input signals B20B21B10B11 and a20a21a10a11 are "OFF, ON, OFF" and "OFF, ON, OFF", respectively, and when B2B1 is 10 and A2A1 is 11, its input signals B20B21B10B11 and a20a21a10a11 are "OFF, ON, OFF", respectively, and "OFF, ON, OFF, ON", Y4Y3Y2Y1 is 1000, as shown in fig. 6 (i); when B2B1 is 11 and A2A1 is 11, its input signals B20B21B10B11 and a20a21a10a11 are "OFF, ON, OFF, ON" and "OFF, ON, OFF, ON", respectively, and Y4Y3Y2Y1 is 1100, as shown in fig. 6 (j). The invention realizes the function of multiplication-addition operation by using the DNA strand displacement technology, and the molecular circuit of the DNA strand displacement chip is subjected to simulation analysis by Visual DSD software, so that the design of the DNA strand displacement chip realizes the expected function, and the specific analysis is as described above.

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.