CN114386574A - Nonlinear neural network based on DNA fulcrum-mediated strand displacement reaction technology - Google Patents

Nonlinear neural network based on DNA fulcrum-mediated strand displacement reaction technology Download PDF

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CN114386574A
CN114386574A CN202210012614.6A CN202210012614A CN114386574A CN 114386574 A CN114386574 A CN 114386574A CN 202210012614 A CN202210012614 A CN 202210012614A CN 114386574 A CN114386574 A CN 114386574A
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邹成业
张强
王鹏飞
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Dalian University of Technology
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Abstract

The invention provides a novel neural network based on an engineering DNA strand displacement analog circuit, which is composed of a catalytic reaction module, a degradation reaction module and an adjustment reaction module, has a frame structure similar to an error back propagation type neural network, namely a BP type neural network, and can be divided into an input layer, a hidden layer and an output layer. Different from BP type neural network, the learning ability of the neural network does not depend on a certain algorithm, but combines the reaction characteristic of DNA strand displacement, and the weight is updated when the DNA strand displacement reaction reaches dynamic balance by depending on the dynamics adaptivity of the reaction network, so that the neural network has the ability of supervised learning and can fit the standard quadratic function.

Description

Nonlinear neural network based on DNA fulcrum-mediated strand displacement reaction technology
Technical Field
The invention relates to the field of biological computation and artificial intelligence, and relates to a nonlinear neural network based on a DNA fulcrum-mediated strand displacement reaction technology.
Background
In recent years, the size of semiconductor devices has reached the order of a few nanometers, but integrated circuits will not continue to evolve in the near future according to moore's law due to physical limitations. It is against this background that computers with smaller microscopic dimensions are the main subject of computational demand. At present, the main platform for realizing artificial intelligence is an electronic computer, and therefore, the development of artificial intelligence is inevitably limited by the development of the performance of the electronic computer. The electronic computer adopts a linear data placement mode and a serial information processing mode, the information storage and processing mode can limit the operation speed of the computer, and the biological computer can realize the parallel processing and operation of information due to the advantages of biochemical reaction, thereby having great advantage for solving the problem of large-scale NP.
Semi-synthetic biology as a new semiconductor technology may lead to a completely new storage and computation model due to the excellent information storage and processing capabilities of DNA or RNA. DNA consists of four nucleotides A, T, G, C, which convert DNA into multiple DNA strands with complex structures. Under the catalysis of no biological enzyme, the DNA strand displacement reaction can be triggered at room temperature. The kinetic property of the DNA fulcrum-mediated strand displacement reaction strictly follows the Watson-Crick base pairing principle, so that the kinetic behavior is predictable and controllable, the high programmability and the high cascading performance can be realized, and various complex functions such as logic calculation, analog calculation, biosensors, molecular walkers and the like can be realized. The DNA strand displacement reaction can faithfully simulate the dynamics of any abstract chemical reaction network to construct a logic gate and an operation module with a calculation function, realize distributed calculation and become an important base for realizing a biological computer.
Artificial intelligence realizes the functions of reasoning, judging, classifying and the like of the human brain through the simulation of biological characteristics of information transfer modes among neurons, and compared with an electronic device, DNA calculation realizes partial functions of the human brain by utilizing the biological characteristics of a molecular device, so that the method for realizing artificial intelligence by utilizing the DNA calculation is probably closer to the learning essence of the human brain and is more likely to realize the real functions of the human brain.
Disclosure of Invention
The invention designs a nonlinear neural network based on a DNA fulcrum mediated strand displacement reaction technology, the neural network has a frame structure similar to a BP neural network, a plurality of reaction modules with fluorescent labels are constructed by utilizing the compilability of DNA strand displacement reaction, and the reaction modules are cascaded into an input layer, a hidden layer and an output layer of the network, so that a complete neural network is built, and the learning function of a standard quadratic function is realized.
A first part: design of nonlinear neural network based on idealized reaction
A nonlinear neural network based on a DNA pivot mediated strand displacement reaction technology is described as follows:
Figure BDA0003459564930000021
Figure BDA0003459564930000022
Figure BDA0003459564930000023
Figure BDA0003459564930000024
Figure BDA0003459564930000025
Figure BDA0003459564930000026
Figure BDA0003459564930000027
Figure BDA0003459564930000028
Figure BDA0003459564930000029
Figure BDA00034595649300000210
Figure BDA00034595649300000211
Figure BDA0003459564930000031
Figure BDA0003459564930000032
wherein n is 1,2, …, L; j ═ 1,2, …, M; xi、Yj、WinAnd VnjAs signal participants, XiAnd YjConcentration of (2) characterizes the input data, WinAnd VnjThe concentration of (b) represents the weight of the input layer and the hidden layer; k is a radical ofsAnd s is 1, …,14 is the reaction rate. As shown in fig. 2, the nonlinear neural network is composed of three parts, i.e., an input layer, a hidden layer and an output layer, wherein reactions (1), (2), (9) and (11) constitute the input layer, reactions (3), (4), (5), (6), (10) and (12) constitute the hidden layer, and reactions (7), (8) and (13) constitute the output layer.
According to idealized reactions (1) to (13), In, I 'n, I' n, and
Figure BDA0003459564930000033
the differential equation of (a) is:
Figure BDA0003459564930000034
when In, I 'n, I' n and
Figure BDA0003459564930000035
when the reaction equilibrium is reached, the reaction is carried out
Figure BDA0003459564930000036
The following equation set (15) can be obtained:
Figure BDA0003459564930000041
wherein y (═ ψ (—) represents the activation function, and since the right half of the quadratic function only satisfies the requirement of the activation function and is easily realized by the DNA strand displacement reaction, the activation function is selected as the quadratic function y ═ x in the present invention2The right half of (a).
A second part: DNA implementation of nonlinear neural networks
The reaction equations (1) to (13) are composed of different reaction modules, wherein equations (1) and (5) belong to the catalytic reaction module 1; equations (1) and (5) belong to catalytic reaction module 1; equations (2), (4), (6) and (8) belong to the degradation reaction module; equations (9) and (10) belong to the regulation reaction module 1; equations (11) - (13) belong to the catalytic reaction module 2. The reaction module can be realized by the following DNA strand displacement reaction:
(I) catalytic reaction module 1:
the idealized reaction equation for the catalytic reaction module 1 is:
Figure BDA0003459564930000042
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000043
wherein IiIs catalyzed by XiAs a signal DNA strand, WiAs weight report chain Ai、Pai、PciAnd PdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Xi]0,[Wi]0,[Ii]0，[*]0Initial concentration is indicated. Reaction rate qiAnd kiSatisfy qi≤qm，ki＝qi，qmIndicating the maximum reaction rate.
(II) catalytic reaction Module 2:
the idealized reaction equation for the catalytic reaction module 2 is:
Figure BDA0003459564930000051
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000052
wherein IiIs catalyzed by XiAs a signal DNA strand, Gai,Ei,Fi,Gdi,Gei,JiAnd KiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi。
(III) degradation reaction module:
the idealized reaction equation for the degradation reaction module 2 is:
Figure BDA0003459564930000053
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000054
wherein IiIs degraded, Fai,Ci,FciAnd FdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi。
(IV) adjusting the reaction module 1:
the idealized reaction equation for tuning the reaction module 1 is:
Figure BDA0003459564930000061
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000062
wherein WiIs adjusted, EaiAnd EbiIs a signal DNA strand, and the concentration between them satisfies [ Wi]0＜＜[Ebi]0And [ Eai]0＜＜[Ebi]0(ii) a The reaction rate satisfies kai＝qaiAnd kbi＝qbi。
(V) adjusting the reaction module 2:
the idealized reaction equation for the tuning reaction module 2 is:
Figure BDA0003459564930000063
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000064
wherein Y isiIs adjusted in concentration of LaiAnd LbiIs a signal DNA strand, and the concentration between them satisfies [ Yi]0,[Lai]0＜＜[Lbi]0(ii) a The reaction rate satisfies kxi＝qxiAnd kyi＝qyi。
And a third part: training of linear neural networks
The invention utilizes nonlinear neural network to learn standard quadratic function
Figure BDA0003459564930000065
Figure BDA0003459564930000066
Wherein the weight value wiAnd input xi(i-1, 2, …, N) are all real numbers, and w is the weight and the input value represented by the concentration of the DNA strandi,xi≥0。
(1) Normalization processing of training data
The training of the neural network is composed of a plurality of rounds of training, one round of training is composed of K sets of training data, the training data set is disordered, and the other round of training data is obtained. The first round of training data is composed of Xi＝[xi(1,1),xi(2,1),…,xi(K,1)]To show, the data normalization can be performed as follows:
Figure BDA0003459564930000071
in
Figure BDA0003459564930000072
xi(K, l) denotes the ith data of the kth group of data of the l training, where K is 1,2, …, K, l is 1,2, …, Λ, ρ > 0 is the tuning parameter,
Figure BDA0003459564930000073
and
Figure BDA0003459564930000074
the initial concentration of the input signal DNA chain of the neural network is set.
(2) Training evaluation of neural networks
In the first training, a relative error e is definedl(k) Such asThe following:
Figure BDA0003459564930000075
wherein
Figure BDA0003459564930000076
Figure BDA0003459564930000077
And
Figure BDA0003459564930000078
and representing the weight values of the input layer and the hidden layer obtained after the first training.
To evaluate the training results, the mean relative error is defined as follows:
Figure BDA0003459564930000079
after a plurality of times of training, when the average relative error reaches the target value, the training is stopped.
Table 1 setting of the concentration of DNA strands and reaction rate.
Figure BDA0003459564930000081
Table 2 structure of the nonlinear neural network, and idealized response and DNA realization for each part.
Figure BDA0003459564930000082
Figure BDA0003459564930000091
Figure BDA0003459564930000101
The invention has the beneficial effects that:
in the prior neural network design based on DNA calculation, the setting of the weight needs the participation of an electronic computer or a known database to be completed, and the network itself can not realize the updating and calculation of the weight and only realizes the function of a certain neural network. The invention realizes the updating of weight and the learning function of a neural network by utilizing the dynamic characteristics and the self-adaptive characteristics of a DNA strand displacement reaction network and not depending on a certain algorithm.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a block diagram of a non-linear neural network.
FIG. 3 catalyzes the main DNA strand displacement reaction of the reaction module 1.
FIG. 4 catalyzes the main DNA strand displacement reaction of the reaction module 2.
FIG. 5 major DNA strand displacement reactions of the degradation reaction module.
FIG. 6 regulates the DNA strand displacement reaction of the reaction module 1.
FIG. 7 regulates the DNA strand displacement reaction of the reaction module 2.
FIG. 8 data chain Ii、Xi、Wi、AiAnd PdiThe DNA of (1) encodes.
FIG. 9 data chain Yi、Ki、GaiAnd GeiThe DNA of (1) encodes.
FIG. 10 data chain FaiAnd FdiThe DNA of (1) encodes.
FIG. 11 data chain EaiAnd LaiThe DNA of (1) encodes.
FIG. 12 is a trace of updating the weights.
FIG. 13 averages the evolution of relative error with training times.
Fig. 14 total number of training rounds required in different rounds of training.
FIG. 15 evolution of relative error with test data.
Detailed Description
The invention is implemented on the premise of the technical scheme of the invention, and a detailed implementation mode and a specific operation process are given, but the protection scope of the invention is not limited by the following examples.
The detailed steps are as follows:
design of nonlinear neural network based on idealized reaction
The idealized chemical reaction network of the nonlinear neural network proposed by the present invention can be described in the form:
Figure BDA0003459564930000111
Figure BDA0003459564930000112
Figure BDA0003459564930000113
Figure BDA0003459564930000114
Figure BDA0003459564930000115
Figure BDA0003459564930000116
Figure BDA0003459564930000117
Figure BDA0003459564930000118
Figure BDA0003459564930000119
Figure BDA00034595649300001110
Figure BDA00034595649300001111
Figure BDA0003459564930000121
Figure BDA0003459564930000122
wherein n is 1,2, …, L; j ═ 1,2, …, M; xi、Yj、WinAnd VnjAs signal participants, XiAnd YjConcentration of (2) characterizes the input data, WinAnd VnjThe concentration of (b) represents the weight of the input layer and the hidden layer; k is a radical ofsAnd s is 1, …,14 is the reaction rate. As shown in fig. 2, the nonlinear neural network is composed of three parts, i.e., an input layer, a hidden layer and an output layer, wherein reactions (1), (2), (9) and (11) constitute the input layer, reactions (3), (4), (5), (6), (10) and (12) constitute the hidden layer, and reactions (7), (8) and (13) constitute the output layer.
According to idealized reactions (1) to (13), In, I 'n, I' n, and
Figure BDA0003459564930000123
the differential equation of (a) is:
Figure BDA0003459564930000124
when In, I 'n, I' n and
Figure BDA0003459564930000125
when the reaction equilibrium is reached, the reaction is carried out
Figure BDA0003459564930000126
The following equation set (15) can be obtained:
Figure BDA0003459564930000131
wherein y (═ ψ (—) represents the activation function, and since the right half of the quadratic function only satisfies the requirement of the activation function and is easily realized by the DNA strand displacement reaction, the activation function is selected as the quadratic function y ═ x in the present invention2The right half of (a).
Design of data chain and reaction module
(I) Catalytic reaction module 1:
the idealized reaction equation for the catalytic reaction module 1 is:
Figure BDA0003459564930000132
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000133
wherein IiIs catalyzed by XiAs a signal DNA strand, WiAs weight report chain Ai、Pai、PciAnd PdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Xi]0,[Wi]0,[Ii]0，[*]0Initial concentration is indicated. Reaction rate qiAnd kiSatisfy qi≤qm，ki＝qi，qmIndicating the maximum reaction rate. Data linkIi、Xi、Wi、AiAnd PdiThe DNA code of (1) is shown in FIG. 8, and the main DNA strand displacement reaction process of the catalytic reaction module 1 is shown in FIG. 3.
(II) catalytic reaction Module 2:
the idealized reaction equation for the catalytic reaction module 2 is:
Figure BDA0003459564930000141
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000142
wherein IiIs catalyzed, YiAs a signal DNA strand, Gai,Ei,Fi,Gdi,Gei,JiAnd KiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi. Data chain Yi、Ki、GaiAnd GeiThe DNA code of (2) is shown in FIG. 9, and the main DNA strand displacement reaction process of the catalytic reaction module 2 is shown in FIG. 4.
(III) degradation reaction module:
the idealized reaction equation for the degradation reaction module is:
Figure BDA0003459564930000143
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000144
wherein IiIs degraded, Fai,Ci,FciAnd FdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi. Data link FaiAnd FdiThe DNA code of (a) is shown in FIG. 10, and the main DNA strand displacement reaction process of the degradation reaction module is shown in FIG. 5.
(IV) adjusting the reaction module 1:
the idealized reaction equation for tuning the reaction module 1 is:
Figure BDA0003459564930000151
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000152
wherein WiIs adjusted, EaiAnd EbiIs a signal DNA strand, and the concentration between them satisfies [ Wi]0＜＜[Ebi]0And [ Eai]0＜＜[Ebi]0(ii) a The reaction rate satisfies kai＝qaiAnd kbi＝qbi. Data chain EaiThe DNA code of (a) is shown in FIG. 11, and the main DNA strand displacement reaction process of the degradation reaction module is shown in FIG. 6.
(V) adjusting the reaction module 2:
the idealized reaction equation for the tuning reaction module 2 is:
Figure BDA0003459564930000153
it can be obtained by the following DNA strand displacement reaction:
Figure BDA0003459564930000154
wherein Y isiIs adjusted in concentration of LaiAnd LbiIs a signal DNA strand, and the concentration between them satisfies [ Yi]0,[Lai]0＜＜[Lbi]0(ii) a The reaction rate is satisfiedkxi＝qxiAnd kyi＝qyi. Data link LaiThe DNA code of (a) is shown in FIG. 11(b), and the main DNA strand displacement reaction process of the degradation reaction module is shown in FIG. 7.
The reaction equations (1) to (13) are composed of different reaction modules, wherein equations (1) and (5) belong to the catalytic reaction module 1; equations (1) and (5) belong to catalytic reaction module 1; equations (2), (4), (6) and (8) belong to the degradation reaction module; equations (9) and (10) belong to the regulation reaction module 1; equations (11) - (13) belong to the catalytic reaction module 2.
Three, training and testing of nonlinear neural network
The invention utilizes nonlinear neural network to learn standard quadratic function
Figure BDA0003459564930000161
Figure BDA0003459564930000162
Wherein the weight value wiAnd input xi(i-1, 2, …, N) are all real numbers, and w is the weight and the input value represented by the concentration of the DNA strandi,xi≥0。
(1) Normalization processing of training data
The training of the neural network is formed by multiple rounds of training, one round of training is called as one round of training when one round of training is completed, wherein one round of training comprises multiple times of training, one round of training is formed by K groups of training data, and the training data group is randomly disturbed to obtain another round of training data or another round of training data. The first training data of a certain round of training is composed of Xi＝[xi(1,1),xi(2,1),…,xi(K,1)]To show, the data normalization can be performed as follows:
Figure BDA0003459564930000163
wherein
Figure BDA0003459564930000164
xi(K, l) denotes the ith data of the kth group of data of the l training, where K is 1,2, …, K, l is 1,2, …, Λ, ρ > 0 is the tuning parameter,
Figure BDA0003459564930000165
and
Figure BDA0003459564930000166
the initial concentration of the input signal DNA chain of the neural network is set.
(2) Training evaluation of neural networks
In the first training, a relative error e is definedl(k) The following were used:
Figure BDA0003459564930000167
wherein
Figure BDA0003459564930000171
Figure BDA0003459564930000172
And
Figure BDA0003459564930000173
and representing the weight values of the input layer and the hidden layer obtained after the first training.
To evaluate the training results, the mean relative error is defined as follows:
Figure BDA0003459564930000174
after a plurality of times of training, when the average relative error reaches the target value, the training is stopped.
The training and evaluation of a neural network based on DNA strand displacement reaction is illustrated by taking a nonlinear neural network of 3 input nodes as an example:
the original data of the test is X1＝[0.23,0.26,0.29,…,2.30]、X2＝[0.31,0.32,0.33,…,1.00]And X3＝[0.23,0.26,0.29,…,2.30]In 70 sets of data, ρ is 2. The initial concentrations of the DNA strands and the initial settings of the reaction rates are shown in Table 1. Fig. 12 shows the update trajectory of the weights in 30 rounds of training.
As shown in fig. 13, in 30 rounds of training, the average relative error was higher than the target value by 5% in the first 30 rounds of training, but after 31 rounds of training, the average relative error of some rounds of training reached the target value, and after 43 rounds of training, the average relative error of all rounds of training reached or was lower than the target value, i.e., the training target was achieved.
Fig. 14 shows the total number of training sessions required to achieve the training goal in 30 training rounds, and it is clear that the number of training sessions is concentrated in 30 to 40 sessions.
(3) Testing of neural networks
In order to make the test data and the training data fall in the same range, the training data needs to be normalized as shown in equation (24):
Figure BDA0003459564930000175
wherein
Figure BDA0003459564930000181
x′i(k) Representing the ith data in the kth group of data, and the test data is X'i＝[x′i(1),x′i(2),…,x′i(K′)]In the K' test data sets, the data used in each test is the same, but the weight updates used are different, that is, the weight updates obtained after the p-th round of training are used in the p-th test, and obviously, the number of tests is the same as the number of rounds of training.
The test relative error is defined as:
Figure BDA0003459564930000182
wherein
Figure BDA0003459564930000183
e′k(p) represents the relative error of the kth set of data in the p test, Win(p) and Vn1And (p) is a weight value updating result obtained after the corresponding p-th round of training.
Taking a nonlinear neural network with 3 input nodes as an example, the test result of the neural network based on the DNA strand displacement reaction is illustrated:
selecting original test data as X'1＝[0.5,0.7,0.9,…,6.5]、X′2＝[0.25,0.30,0.35,…,1.70]And X'3＝[0.4,0.7,1.0,…,9.1]In 30 test data sets, as shown in fig. 15, the average of the relative errors of the remaining 29 test data sets, except the first test data set, is within the allowable error range in 30 tests, which indicates that the neural network based on DNA strand displacement reaction has better test results.

Claims (3)

1. A nonlinear neural network based on a DNA pivot mediated strand displacement reaction technology is characterized by being described in the following form:
Figure FDA0003459564920000011
Figure FDA0003459564920000012
Figure FDA0003459564920000013
Figure FDA0003459564920000014
Figure FDA0003459564920000015
Figure FDA0003459564920000016
Figure FDA0003459564920000017
Figure FDA0003459564920000018
Figure FDA0003459564920000019
Figure FDA00034595649200000110
Figure FDA00034595649200000111
Figure FDA00034595649200000112
Figure FDA00034595649200000113
wherein n is 1,2, …, L; j ═ 1,2, …, M; xi、Yj、WinAnd VnjAs signal participants, XiAnd YjConcentration of (2) characterizes the input data, WinAnd VnjThe concentration of (b) represents the weight of the input layer and the hidden layer; k is a radical ofsAnd s is 1, …,14 is the reaction rate; the nonlinear neural network is composed of an input layer, a hidden layer and an output layer, wherein reactions (1), (2), (9) and (11) form the input layer, reactions (3), (4), (5), (6), (10) and (12) form the hidden layer, and reactions (7), (8) and (13) form the output layer.
2. The nonlinear neural network based on the DNA pivot mediated strand displacement reaction technology according to claim 1, wherein the reaction equations (1) - (13) are composed of different reaction modules, wherein equations (1) and (5) belong to catalytic reaction module 1; equations (1) and (5) belong to catalytic reaction module 1; equations (2), (4), (6) and (8) belong to the degradation reaction module; equations (9) and (10) belong to the regulation reaction module 1; equations (11) - (13) belong to the catalytic reaction module 2; the reaction module can be realized by the following DNA strand displacement reaction:
(I) catalytic reaction module 1:
the idealized reaction equation for the catalytic reaction module 1 is:
Figure FDA0003459564920000021
it can be obtained by the following DNA strand displacement reaction:
Figure FDA0003459564920000022
wherein IiIs catalyzed by XiAs a signal DNA strand, WiAs weight report chain Ai、Pai、PciAnd PdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Xi]0,[Wi]0,[Ii]0，[*]0Initial ofStarting concentration; reaction rate qiAnd kiSatisfy qi≤qm，ki＝qi，qmRepresents the maximum reaction rate;
(II) catalytic reaction Module 2:
the idealized reaction equation for the catalytic reaction module 2 is:
Figure FDA0003459564920000023
it can be obtained by the following DNA strand displacement reaction:
Figure FDA0003459564920000031
wherein IiIs catalyzed by XiAs a signal DNA strand, Gai,Ei,Fi,Gdi,Gei,JiAnd KiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi；
(III) degradation reaction module:
the idealized reaction equation for the degradation reaction module 2 is:
Figure FDA0003459564920000032
it can be obtained by the following DNA strand displacement reaction:
Figure FDA0003459564920000033
wherein IiIs degraded, Fai,Ci,FciAnd FdiIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is CmAnd satisfy Cm≥[Yi]0,[Ii]0(ii) a Reaction rate qiSatisfy qi≤qm，ki＝qi；
(IV) adjusting the reaction module 1:
the idealized reaction equation for tuning the reaction module 1 is:
Figure FDA0003459564920000034
it can be obtained by the following DNA strand displacement reaction:
Figure FDA0003459564920000035
wherein WiIs adjusted, EaiAnd EbiIs a signal DNA strand, and the concentration between them satisfies [ Wi]0＜＜[Ebi]0And [ Eai]0＜＜[Ebi]0(ii) a The reaction rate satisfies kai＝qaiAnd kbi＝qbi；
(V) adjusting the reaction module 2:
the idealized reaction equation for the tuning reaction module 2 is:
Figure FDA0003459564920000041
it can be obtained by the following DNA strand displacement reaction:
Figure FDA0003459564920000042
wherein Y isiIs adjusted in concentration of LaiAnd LbiIs a signal DNA strand, and the concentration between them satisfies [ Yi]0,[Lai]0＜＜[Lbi]0(ii) a The reaction rate satisfies kxi＝qxiAnd kyi＝qyi。
3. The nonlinear neural network based on the DNA pivot mediated strand displacement reaction technology as claimed in claim 1 or 2, characterized in that the nonlinear neural network is trained as follows:
(1) normalization processing of training data
Training of the neural network consists of multiple rounds of training, one round of training consists of K sets of training data, and the training data set is disordered to obtain another round of training data; the first round of training data is composed of Xi＝[xi(1,1),xi(2,1),…,xi(K,1)]To show, the data normalization can be performed as follows:
Figure FDA0003459564920000043
wherein
Figure FDA0003459564920000044
xi(K, l) denotes the ith data of the kth group of data of the l round of training, where K is 1,2, …, K, l is 1,2, …, Λ, ρ is a positive adjustment parameter,
Figure FDA0003459564920000051
and
Figure FDA0003459564920000052
setting the initial concentration of the input signal DNA chain of the neural network;
(2) training evaluation of neural networks
In a round of training, a relative error e is definedl(k) The following were used:
Figure FDA0003459564920000053
wherein
Figure FDA0003459564920000054
WinAnd Vn1Representing the weight of the input layer and the weight of the hidden layer obtained after the training of the current round;
to evaluate the training results of the current round, the mean relative error was defined as follows:
Figure FDA0003459564920000055
after the training is performed for a plurality of rounds, the training is stopped when the average relative error reaches the target value.
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CN115834788A (en) * 2022-11-16 2023-03-21 安阳师范学院 Color image encryption method for visualized DNA fulcrum-mediated strand displacement reaction
CN116844642A (en) * 2023-07-03 2023-10-03 燕山大学 Novel linear machine learning method based on DNA hybridization reaction technology
CN117057405A (en) * 2023-08-22 2023-11-14 燕山大学 DNA molecular learning machine method based on novel excitation function

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Publication number Priority date Publication date Assignee Title
CN115834788A (en) * 2022-11-16 2023-03-21 安阳师范学院 Color image encryption method for visualized DNA fulcrum-mediated strand displacement reaction
CN115834788B (en) * 2022-11-16 2023-06-09 安阳师范学院 Color image encryption method for visualized DNA pivot point-mediated strand displacement reaction
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CN116844642B (en) * 2023-07-03 2024-03-29 燕山大学 Novel linear machine learning method based on DNA hybridization reaction technology
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