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

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 Pivot-Mediated Strand Displacement Reaction Technology

technical field

The invention relates to the fields of biological computing and artificial intelligence, and relates to a nonlinear neural network based on the technology of DNA fulcrum-mediated strand displacement reaction.

Background technique

In recent years, the size of semiconductor devices has reached the scale of several nanometers, but due to physical constraints, integrated circuits will not be able to continue to develop according to Moore's Law in the near future. It is in this context that computers with smaller microscopic dimensions have become the main object of computing demands. At present, the main platform for the realization of artificial intelligence is the electronic computer. Therefore, the development of artificial intelligence is bound to be limited by the development of the electronic computer's own performance. The electronic computer adopts a linear data placement mode and a serial information processing method, and this information storage and processing method will limit the computing speed of the computer, while the biological computer can realize the parallel processing and operation of information due to the advantages of the biochemical reaction itself. It has huge advantages for solving large-scale NP problems.

As a new semiconductor technology, semi-synthetic biology may lead to a whole new storage and computing paradigm 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 various DNA strands with complex structures. Under the catalysis of no biological enzymes, the DNA strand displacement reaction can be triggered at room temperature. The kinetic properties of the DNA fulcrum-mediated strand displacement reaction strictly follow the Watson–Crick base pairing principle, so its kinetic behavior is predictable and controllable, and is highly programmable and cascaded to achieve multiple complex functions, such as logic computing, analog computing, biosensors, and molecular walkers. The DNA strand displacement reaction can faithfully simulate the dynamics of any abstract chemical reaction network, construct logic gates and operation modules with computing functions, and realize distributed computing, becoming an important basis for realizing biological computers.

Artificial intelligence realizes the functions of reasoning, judgment and classification of the human brain by simulating the biological characteristics of information transmission between neurons. Compared with electronic devices, DNA computing uses the biological characteristics of molecular devices to realize the human brain. Therefore, the method of using DNA computing to realize artificial intelligence may be closer to the learning essence of the human brain, and it is more likely to realize the real human brain function.

SUMMARY OF THE INVENTION

The present invention designs a non-linear neural network based on DNA fulcrum-mediated strand displacement reaction technology, the neural network has a framework structure similar to BP neural network, and utilizes the compilability of DNA strand displacement reaction to construct a plurality of fluorescent markers. and cascade multiple reaction modules into the input layer, hidden layer and output layer of the network, and then build a complete neural network to realize the learning function of the standard quadratic function.

Part 1: Design of Nonlinear Neural Networks Based on Idealized Responses

The nonlinear neural network based on the DNA fulcrum-mediated strand displacement reaction technology is described in the following form:

where n=1,2,...,L; _j =1,2,...,M; Xi, _Yj , _Win and _Vnj are signal participants, the concentrations of Xi and _Yj characterize the _input data, _Win The concentrations of and V _nj represent the weights of the input layer and the hidden layer part; k _s , s=1, . . . , 14 are the reaction rates. As shown in Figure 2, the nonlinear neural network consists of three parts: the input layer, the hidden layer and the output layer, in which the responses (1), (2), (9) and (11) constitute the input layer, and the responses (3), (4), (5), (6), (10) and (12) constitute the hidden layer, and reactions (7), (8) and (13) constitute the output layer.

的微分方程为：According to idealized reactions (1)-(13), In, I′n, I″n and

The differential equation of is:

达到反应平衡时，有When In, I′n, I″n and

When the reaction equilibrium is reached, there is

The following equations (15) can be obtained:

Among them, y=ψ(*) represents the activation function. Since the right half of the quadratic function only meets the requirements of the activation function, and is easily realized by DNA strand displacement reaction, the activation function in the present invention is selected as the quadratic function y=x ² . right half.

Part II: DNA Implementation of Nonlinear Neural Networks

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 above-mentioned reaction module can be realized by the following DNA strand displacement reaction:

(1) catalytic reaction module 1:

它可由如下DNA链置换反应得到：The idealized reaction equation of Catalytic Reaction Module 1 is:

It can be obtained by the following DNA strand displacement reaction:

Wherein I _i is catalyzed, X _i is the signal DNA strand, Wi is the weight report chain A _i , Pa _i , _{Pci i and Pd i are the} auxiliary DNA strands, and the initial concentration of the auxiliary DNA strands is C _m , and satisfies C _m ≥ [X _i ] ₀ , [W _i ] ₀ , [I _i ] ₀ , [*] ₀ represents the initial concentration of *. The reaction rates qi and _ki satisfy qi _{≤ q m , ki = qi , and q m represents the maximum reaction rate} .

(II) Catalytic reaction module 2:

它可由如下DNA链置换反应得到：The idealized reaction equation of Catalytic Reaction Module 2 is:

It can be obtained by the following DNA strand displacement reaction:

wherein I _i is catalyzed, X _i is the signal DNA strand, Ga _i , E _i , F _i , Gd _i , Ge _i , _Ji and _Ki are the auxiliary DNA strands, and the initial concentration of the auxiliary DNA strands is C _m , and Satisfy C _m ≥[Y _i ] ₀ , [I _i ] ₀ ; the reaction rate qi satisfies qi _{≤ q m ,} and _{ki =} qi _.

(III) Degradation reaction module:

它可由如下DNA链置换反应得到：The idealized reaction equation of degradation reaction module 2 is:

It can be obtained by the following DNA strand displacement reaction:

Wherein I _i is degraded, Fa _i , C _i , Fc _i and Fd _i are auxiliary DNA chains, and the initial concentration of the auxiliary DNA chains is C _m , and satisfies C _m ≥ [Y _i ] ₀ , [I _i ] ₀ ; The reaction rate qi satisfies qi _{≤q m} , and _{ki =} qi _.

(IV) Regulating reaction module 1:

它可由如下DNA链置换反应得到：The idealized reaction equation for tuning reaction module 1 is:

It can be obtained by the following DNA strand displacement reaction:

The concentration of Wi is adjusted, Ea _i and _Ebi are signal DNA strands, and the concentrations between them satisfy [W _i ] ₀ << [Eb _i ] ₀ and [Ea _i ] ₀ << [ _{Eb i ] 0} ; the reaction rate satisfies ka _i =qa _i and kb _i =qb _i .

(V) Adjustment reaction module 2:

它可由如下DNA链置换反应得到：The idealized reaction equation of the adjustment reaction module 2 is:

It can be obtained by the following DNA strand displacement reaction:

The concentration of Yi is adjusted, La _i and Lb _i are signal DNA strands, and the concentration between them satisfies [Y _i ] ₀ , [La _i ] ₀ <<[Lb _i ] ₀ ; the reaction rate satisfies kx _{i =} qx _i and ky _i =qy _i .

Part 3: Training of Linear Neural Networks

其中权值w_i及输入x_i(i＝1,2,…,N)皆为实数，由于权值和输入的数值由DNA链的浓度表示，因此w_i,x_i≥0。The present invention utilizes nonlinear neural network to learn standard quadratic function

The weight _wi and the input _xi ( _i =1, ₂ , .

(1) Normalization of training data

The training of the neural network consists of multiple rounds of training. One round of training consists of K groups of training data, and the training data group is disrupted to obtain another round of training data. The first round of training data is represented by X _i =[ _xi (1,1), _xi (2,1),..., _xi (K,1)], then the data can be normalized as follows:

middle

及

为神经网络的输入信号DNA链的初始浓度设定。x _i (k,l) represents the i-th data of the k-th group of data of the l-th training, where k=1,2,...,K, l=1,2,...,Λ, ρ>0 are adjustment parameters ,

and

Set the initial concentration of DNA strands for the input signal to the neural network.

(2) Training evaluation of neural network

In the lth training, the relative error e _l (k) is defined as follows:

in

及

表示经过第l次训练以后，得到的输入层和隐藏层的权值。

and

Indicates the weights of the input layer and the hidden layer obtained after the lth training.

To evaluate the results of this training, the average relative error is defined as follows:

After many training sessions, when the average relative error reaches the target value, the training is stopped.

Table 1 The concentration of DNA strands and the setting of the reaction rate.

Table 2 The structure of the nonlinear neural network, and the idealized reactions and DNA realizations corresponding to each part.

Beneficial effects of the present invention:

In the previous neural network design based on DNA computing, the setting of weights requires the participation of electronic computers or a known database to complete. The network itself cannot realize the updating and calculation of weights, but only realizes some kind of neural network. Function. The invention utilizes the dynamic characteristics and self-adaptive characteristics of the DNA strand displacement reaction network itself, and does not rely on a certain algorithm to realize the update of the weight value and the learning function of the neural network.

Description of drawings

Figure 1 is a flow chart of the present invention.

Figure 2. Framework diagram of nonlinear neural network.

Figure 3 Catalyzes the main DNA strand displacement reaction of Reaction Module 1.

Figure 4 Catalyzes the main DNA strand displacement reaction of Reaction Module 2.

Figure 5. The main DNA strand displacement reaction of the degradation reaction module.

Figure 6 Modulates the DNA strand displacement reaction of reaction module 1.

Figure 7 Modulates the DNA strand displacement reaction of reaction module 2.

Figure 8 DNA encoding of data chains I _i , Xi , Wi _{, A i and} Pd _{i .}

Figure 9 DNA coding of data _chains Yi, _Ki , _Gai and _Gei .

Figure 10 DNA coding of data links Fa _i and Fd _i .

Figure 11 DNA coding of data links Ea _i and La _i .

Figure 12. Update trajectory of weights.

Figure 13 Evolution of the mean relative error with the number of training sessions.

Figure 14. Total number of training sessions required in different rounds of training.

Figure 15 Evolution of relative error with test data.

Detailed ways

The implementation of the present invention is carried out on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the protection scope of the present invention is not limited to the following examples.

The detailed steps are as follows:

1. Design of Nonlinear Neural Network Based on Idealized Response

The idealized chemical reaction network of the nonlinear neural network proposed by the present invention can be described in the following form:

where n=1,2,...,L; _j =1,2,...,M; Xi, _Yj , _Win and _Vnj are signal participants, the concentrations of Xi and _Yj characterize the _input data, _Win The concentrations of and V _nj represent the weights of the input layer and the hidden layer part; k _s , s=1, . . . , 14 are the reaction rates. As shown in Figure 2, the nonlinear neural network consists of three parts: the input layer, the hidden layer and the output layer, in which the responses (1), (2), (9) and (11) constitute the input layer, and the responses (3), (4), (5), (6), (10) and (12) constitute the hidden layer, and reactions (7), (8) and (13) constitute the output layer.

的微分方程为：According to idealized reactions (1)-(13), In, I′n, I″n and

The differential equation of is:

达到反应平衡时，有When In, I′n, I″n and

When the reaction equilibrium is reached, there is

The following equations (15) can be obtained:

Among them, y=ψ(*) represents the activation function. Since the right half of the quadratic function only meets the requirements of the activation function, and is easily realized by DNA strand displacement reaction, the activation function in the present invention is selected as the quadratic function y=x ² . right half.

2. Design of data chain and reaction module

(1) catalytic reaction module 1:

它可由如下DNA链置换反应得到：The idealized reaction equation of Catalytic Reaction Module 1 is:

It can be obtained by the following DNA strand displacement reaction:

Wherein I _i is catalyzed, X _i is the signal DNA strand, Wi is the weight report chain A _i , Pa _i , _{Pci i and Pd i are the} auxiliary DNA strands, and the initial concentration of the auxiliary DNA strands is C _m , and satisfies C _m ≥ [X _i ] ₀ , [W _i ] ₀ , [I _i ] ₀ , [*] ₀ represents the initial concentration of *. The reaction rates qi and _ki satisfy qi _{≤ q m , ki = qi , and q m represents the maximum reaction rate} . The DNA codes of the data chains I _i , Xi , Wi , A _i and Pd _i are shown in Figure 8 _, and the main DNA strand displacement reaction process of the catalytic reaction module ₁ is shown in Figure 3 .

(II) Catalytic reaction module 2:

它可由如下DNA链置换反应得到：The idealized reaction equation of Catalytic Reaction Module 2 is:

It can be obtained by the following DNA strand displacement reaction:

where I _i is catalyzed, Y _i is the signal DNA strand, Ga _i , E _i , F _i , Gd _i , Ge _i , _Ji and _Ki are the auxiliary DNA strands, and the initial concentration of the auxiliary DNA strands is C _m , and Satisfy C _m ≥[Y _i ] ₀ , [I _i ] ₀ ; the reaction rate qi satisfies qi _{≤ q m ,} and _{ki =} qi _. The DNA codes of the data chains _Yi , _{Ki, Ga i and} Ge _i are shown in Figure 9, and the main DNA strand displacement reaction process of the catalytic reaction module 2 is shown in Figure 4.

(III) Degradation reaction module:

它可由如下DNA链置换反应得到：The idealized reaction equation of the degradation reaction module is:

It can be obtained by the following DNA strand displacement reaction:

Wherein I _i is degraded, Fa _i , C _i , Fc _i and Fd _i are auxiliary DNA chains, and the initial concentration of the auxiliary DNA chains is C _m , and satisfies C _m ≥ [Y _i ] ₀ , [I _i ] ₀ ; The reaction rate qi satisfies qi _{≤q m} , and _{ki =} qi _. The DNA codes of the data chains Fa _i and Fd _i are shown in Figure 10, and the main DNA strand displacement reaction process of the degradation reaction module is shown in Figure 5.

(IV) Regulating reaction module 1:

它可由如下DNA链置换反应得到：The idealized reaction equation for tuning reaction module 1 is:

It can be obtained by the following DNA strand displacement reaction:

The concentration of Wi is adjusted, Ea _i and _Ebi are signal DNA strands, and the concentrations between them satisfy [W _i ] ₀ << [Eb _i ] ₀ and [Ea _i ] ₀ << [ _{Eb i ] 0} ; the reaction rate satisfies ka _i =qa _i and kb _i =qb _i . The DNA code of the data chain Ea _i is shown in Figure 11(a), and the main DNA strand displacement reaction process of the degradation reaction module is shown in Figure 6.

(V) Adjustment reaction module 2:

它可由如下DNA链置换反应得到：The idealized reaction equation of the adjustment reaction module 2 is:

It can be obtained by the following DNA strand displacement reaction:

The concentration of Yi is adjusted, La _i and Lb _i are signal DNA strands, and the concentration between them satisfies [Y _i ] ₀ , [La _i ] ₀ <<[Lb _i ] ₀ ; the reaction rate satisfies kx _{i =} qx _i and ky _i =qy _i . The DNA code of the data chain La _i is shown in Figure 11(b), and the main DNA strand displacement reaction process of the degradation reaction module is shown in Figure 7.

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.

3. Training and testing of nonlinear neural networks

其中权值w_i及输入x_i(i＝1,2,…,N)皆为实数，由于权值和输入的数值由DNA链的浓度表示，因此w_i,x_i≥0。The present invention utilizes nonlinear neural network to learn standard quadratic function

The weight _wi and the input _xi ( _i =1, ₂ , .

(1) Normalization of training data

The training of the neural network consists of multiple rounds of training. Completing one training target is called one round of training. One round of training includes multiple trainings. One training consists of K groups of training data. One round of training data. The first training data of a certain round of training is represented by X _i =[x _i (1,1), _xi (2,1),..., _xi (K,1)], then the data can be processed as follows Normalized:

in

及

为神经网络的输入信号DNA链的初始浓度设定。x _i (k,l) represents the i-th data of the k-th group of data of the l-th training, where k=1,2,...,K, l=1,2,...,Λ, ρ>0 are adjustment parameters ,

and

Set the initial concentration of DNA strands for the input signal to the neural network.

(2) Training evaluation of neural network

In the lth training, the relative error e _l (k) is defined as follows:

in

及

表示经过第l次训练以后，得到的输入层和隐藏层的权值。

and

Indicates the weights of the input layer and the hidden layer obtained after the lth training.

To evaluate the results of this training, the average relative error is defined as follows:

After many training sessions, when the average relative error reaches the target value, the training is stopped.

Taking a nonlinear neural network with 3 input nodes as an example, the training and evaluation of a neural network based on DNA strand displacement reaction are described:

The original data of the test are X ₁ =[0.23,0.26,0.29,...,2.30], X ₂ =[0.31,0.32,0.33,...,1.00] and X ₃ =[0.23,0.26,0.29,...,2.30] in total 70 groups of data, the value of ρ is ρ=2. The initial concentration of DNA strands and the initial settings of the reaction rate are shown in Table 1. Figure 12 shows the updated trajectory of the weights in 30 rounds of training.

As shown in Figure 13, in the 30 rounds of training, after the first 30 trainings, the average relative error was higher than the target value by 5%, but after 31 trainings, the average relative error of some rounds of training reached the target value, after 43 training After training times, the average relative error of all rounds of training is at or below the target value, that is, the training target is achieved.

Figure 14 shows the total number of training times required to achieve the training goal in 30 rounds of training. Obviously, the training times are concentrated in 30 to 40 times.

(3) Test of neural network

In order to make the test data and training data fall in the same range, the training data needs to be normalized as shown in formula (24):

in

x' _i (k) represents the i-th data in the k-th group of data, and the test data consists of X' _i =[x' _i (1),x' _i (2),...,x' _i (K')] It means that there are K' groups of test data. The data used in each test is the same, but the weight update used is different. That is, the p-th test uses the weight update obtained after the p-th round of training. Obviously, the number of tests is different from that of training. The number of rounds is the same.

The test relative error is defined as:

in

e′ _k (p) represents the relative error of the k-th group of data _in the p-th test, and Win (p) and V _n1 (p) are the weight update results obtained after the corresponding p-th round of training.

Still take the nonlinear neural network with 3 input nodes as an example to illustrate the test results of the neural network based on DNA strand displacement reaction:

Select the 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], a total of 30 sets of test data, as shown in Figure 15, in the 30 tests, except for the first set of test data, the average relative errors of the remaining 29 sets of data are all within the allowable error range, indicating that the DNA strand replacement is based on DNA strand replacement. The reactive neural network 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:

wherein n is 1,2, …, L; j ═ 1,2, …, M; x_i、Y_j、W_inAnd V_njAs signal participants, X_iAnd Y_jConcentration of (2) characterizes the input data, W_inAnd V_njThe concentration of (b) represents the weight of the input layer and the hidden layer; k is a radical of_sAnd 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:

it can be obtained by the following DNA strand displacement reaction:

wherein I_iIs catalyzed by X_iAs a signal DNA strand, W_iAs weight report chain A_i、Pa_i、Pc_iAnd Pd_iIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C_mAnd satisfy C_m≥[X_i]₀,[W_i]₀,[I_i]₀，[*]₀Initial ofStarting concentration; reaction rate q_iAnd k_iSatisfy q_i≤q_m，k_i＝q_i，q_mRepresents the maximum reaction rate;

(II) catalytic reaction Module 2:

the idealized reaction equation for the catalytic reaction module 2 is:

it can be obtained by the following DNA strand displacement reaction:

wherein I_iIs catalyzed by X_iAs a signal DNA strand, Ga_i,E_i,F_i,Gd_i,Ge_i,J_iAnd K_iIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C_mAnd satisfy C_m≥[Y_i]₀,[I_i]₀(ii) a Reaction rate q_iSatisfy q_i≤q_m，k_i＝q_i；

(III) degradation reaction module:

the idealized reaction equation for the degradation reaction module 2 is:

it can be obtained by the following DNA strand displacement reaction:

wherein I_iIs degraded, Fa_i,C_i,Fc_iAnd Fd_iIs an auxiliary DNA strand, and the initial concentration of the auxiliary DNA strand is C_mAnd satisfy C_m≥[Y_i]₀,[I_i]₀(ii) a Reaction rate q_iSatisfy q_i≤q_m，k_i＝q_i；

(IV) adjusting the reaction module 1:

the idealized reaction equation for tuning the reaction module 1 is:

it can be obtained by the following DNA strand displacement reaction:

wherein W_iIs adjusted, Ea_iAnd Eb_iIs a signal DNA strand, and the concentration between them satisfies [ W_i]₀＜＜[Eb_i]₀And [ Ea_i]₀＜＜[Eb_i]₀(ii) a The reaction rate satisfies ka_i＝qa_iAnd kb_i＝qb_i；

(V) adjusting the reaction module 2:

the idealized reaction equation for the tuning reaction module 2 is:

it can be obtained by the following DNA strand displacement reaction:

wherein Y is_iIs adjusted in concentration of La_iAnd Lb_iIs a signal DNA strand, and the concentration between them satisfies [ Y_i]₀,[La_i]₀＜＜[Lb_i]₀(ii) a The reaction rate satisfies kx_i＝qx_iAnd ky_i＝qy_i。

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 X_i＝[x_i(1,1),x_i(2,1),…,x_i(K,1)]To show, the data normalization can be performed as follows:

wherein

x_i(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,

and

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 defined_l(k) The following were used:

wherein

W_inAnd V_n1Representing 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:

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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