Method for realizing ultra-sensitive Brink control of delayed enzymatic reaction based on DNA strand displacement

Abstract

The application discloses a kind of based on DNA chain replacement's delayed enzymatic reaction ultra-sensitive Brink control implementation method, comprising: with single molecule and bimolecular chemical reaction to describe enzymatic reaction process, introduce time delay factor, obtain the enzymatic reaction process model with time delay;Brink controller based on CRN is constructed;The static mapping expression between the output of the Brink controller and the system output under steady-state condition is obtained, and then the analytical condition for ensuring the performance of the controller is obtained;The construction of Brink controller is realized using DNA strand displacement reaction;Through DNA strand displacement mechanism, and based on delay material and compensation mechanism, obtain time delay representation, apply the time delay representation to the DNA implementation of enzymatic reaction process model;At the same time, in combination with the constructed Brink controller, the control of rewritten enzymatic reaction process model is realized.The application does not involve subtraction operation in structure, reduces the number of abstract chemical reactions required for implementation, greatly simplifies the complexity of DNA implementation.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of feedback control of biological systems based on DNA strand displacement, and particularly relates to a method for implementing ultra-sensitive Brink control of delayed enzymatic reactions based on DNA strand displacement. BACKGROUND

[0002] Chemical reaction networks (CRNs) are often used to represent feedback control systems to reflect the performance of biomolecular feedback control circuits. At the same time, DNA molecules are widely considered as ideal engineering materials for constructing molecular devices based on CRNs. In particular, DNA strand displacement reactions have become a means for formally programming and analyzing DNA devices. Therefore, when designing applications such as biochemical controllers, it has become a major goal to construct CRNs to represent the dynamics of the system. Combined with the mechanism of DNA strand displacement, digital circuits, signal processing calculations and simulations, etc. can be further implemented. Existing controllers based on CRNs mostly use a double-track representation method, which directly leads to a substantial increase in the number of CRNs required for the implementation of the controller, and further increases the complexity of DNA implementation.

[0003] CRNs provide an abstract representation of complex biochemical processes, which provides an important premise for constructing chemical reaction network representations of various modules in control systems and reflecting the performance of biomolecular feedback control circuits. Samaniego, C.C., and Franco, E. in the article “Ultrasensitive molecular controllers for quasi-integral feedback” published in Cell Systems, 12(3), 272-288 in 2021, constructed a molecular controller, namely the Brink controller, using a modular design strategy, and applied it to regulate the expression of target RNA or protein. The modular strategy involved in the construction of the Brink controller is based on two design principles of using ultra-sensitive response and tunable threshold of response. In addition, Fern, J., Scalise, D., Cangialosi, A., Howie, D., Potters, L., and Schulman, R. in the article “DNA strand-displacement timer circuits” published in ACS synthetic biology, 6(2), 190-193 in 2017, constructed an abstract chemical reaction timer circuit that can coordinate different in vitro chemical events without external stimuli, for example, it can be used for pre-specified species for delayed release.

[0004] The existing CRNs-based controller has experienced a series of evolution such as PI controller, PID controller and nonlinear QSM controller, and the corresponding DNA implementation has also been completed. However, these controllers have subtraction operation between signals in structure, which makes the design of CRNs depend on the double-track representation method, increases the number of CRNs required for implementation, and further increases the difficulty of DNA implementation. SUMMARY

[0005] The present application aims to provide a DNA strand displacement-based ultra-sensitive biomolecular Brink controller implementation method, which realizes ultra-sensitive input-output response with as few chemical reactions as possible.

[0006] To achieve the above-mentioned purpose, the present application provides a DNA strand displacement-based delayed enzymatic reaction ultra-sensitive Brink control implementation method, comprising:

[0007] The enzymatic reaction process is described by using single-molecule and double-molecule chemical reactions, and a time delay factor is introduced to obtain a time-delayed enzymatic reaction process model;

[0008] A Brink controller based on CRNs is constructed;

[0009] A static mapping expression between the output of the Brink controller and the output of the system under steady-state conditions is obtained, and then an analytical condition for ensuring the performance of the controller is obtained;

[0010] The construction of the Brink controller is realized by using DNA strand displacement reaction;

[0011] The time delay representation method is obtained by DNA strand displacement mechanism and based on delay material and compensation mechanism, and the time delay representation method is applied to the DNA implementation of the enzymatic reaction process model; at the same time, the control of the rewritten enzymatic reaction process model is realized in combination with the constructed Brink controller.

[0012] Further, the enzymatic reaction process is described by using single-molecule and double-molecule chemical reactions, specifically:

[0013]

[0014]

[0015]

[0016] Among them, S and B represent substrate and enzyme respectively, and X and P represent enzyme-substrate complex and output material respectively.

[0017] Further, the time-delayed enzymatic reaction process model is constructed, specifically:

[0018]

[0019]

[0020]

[0021]

[0022] where the parameter τ represents the cumulative time delay present in the production of output species P.

[0023] Further, the controller based on CRNs is represented as:

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] where the parameters R and Y are the inputs to the Brink controller, and U represents the output; the parameter k c , θ c and α c represent the catalytic rates, γ c and β c represent the binding rates, and φ c represents the degradation rate; in addition, the parameter R produces species R r , which then reacts with U * to form U; the parameter Y produces species R y , which then reacts with U to form U * ; simultaneously, the signals R r and R y bind to form the complex R r ·R y , which does not interact with any other species, i.e. there is a reverse acting functional mechanism between the two different input parameters R and Y of the Brink controller; the Brink controller uses the signals R r and R y as activator and deactivator, respectively;

[0032] The corresponding ODEs equations for the mass action kinetics MAK are:

[0033]

[0034]

[0035]

[0036]

[0037] From the differential equation, (d[U * ] t / dt)+(d[U] t / dt)=0 indicates that the total mass of U+U * is conserved in time evolution.

[0038] Further, the static mapping expression between the Brink controller output and the system output under steady-state condition is obtained, specifically:

[0039] Assuming that the Brink controller has achieved a steady-state output, the following results are obtained:

[0040] k c [R] t -γ c [R r ] t [R y ] t -φ c [R r ] t -α c [R r ] t [U * ] t =0

[0041] θ c [Y] t -γ c [R r ] t [R y ] t -φ c [R y ] t -β c [R y ] t [U] t =0

[0042] -α c [R r ] t [U * ] t +β c[R y ] t [U] t = 0

[0043] Assuming that the reference input R of the Brink controller is constant, the following constraint condition is obtained:

[0044]

[0045] wherein the signal represents the concentration of the substance · in the steady state.

[0046] Further, the construction of the Brink controller is realized by using the DNA strand displacement reaction, specifically: let i, x, y, z be variables, wherein i∈(1, 2,..., 12), x∈(1, 2,..., 8), y∈(1, 2, 3, 4), z∈(1, 2,..., 9);

[0047] For the reactions and there is the same DSD implementation mechanism; the two reactions are converted to:

[0048]

[0049]

[0050] Meanwhile, there is also a same implementation mechanism between the reactions and , which is converted to:

[0051]

[0052] For the reactions and , the corresponding DNA implementation is

[0053]

[0054]

[0055]

[0056] wherein G x , T x and L y all represent auxiliary substances participating in the reaction, O z and H y represent intermediate products, and B y represents inert waste produced by the reaction which does not interact with other substances; in addition, C max represents the initial concentration of the auxiliary substance, and q maxq represents the maximum rate of strand displacement i q represents the rate of reaction achieved by the corresponding DNA.

[0057] Further, the time delay representation is obtained by the DNA strand displacement mechanism and based on the delayed substance and compensation mechanism, specifically:

[0058] The time delay is represented by a circuit composed of two simultaneous abstract chemical reactions, which is realized based on the participation of delayed substance D and described by the following reactions:

[0059]

[0060]

[0061] wherein, the parameter k prod and k delay are rate constants; in the first stage, substance O is produced at a constant rate; in the second stage, when substance O combines with delayed substance D, it is rapidly converted into waste The time of consumption of substance D by substance O is taken as the delay time, and the delay effect depends on the initial concentration of delayed substance D;

[0062] Further, the time delay representation is applied to the DNA implementation of the enzymatic reaction process model, so the enzymatic reaction model is rewritten as:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068] wherein, k delay1 represents the rate of delayed reaction; combined with mass action kinetics, the following results are obtained:

[0069]

[0070]

[0071]

[0072]

[0073]

[0074] Further, combined with the constructed Brink controller, the control of the rewritten enzymatic reaction process model is realized, specifically:

[0075] The reaction is converted to:

[0076]

[0077] The degradation reaction is converted to:

[0078]

[0079] In addition, the reaction is converted to:

[0080]

[0081] For the reversible reaction In the design of DNA implementation, the original reaction form is maintained.

[0082] Further, the DSD mechanism is used to realize the adjustment of the enzymatic reaction process model based on the Brink controller, and the proposed DNA strand displacement expression about time delay is improved, specifically: the consumption of substance P in the enzymatic reaction is compensated by the following reaction mechanism, so as to realize the expected yield of output substance P:

[0083]

[0084]

[0085] Wherein, k pro1 and k pro2 are reaction rate constants, and F is an additional reaction substance; combined with mass action kinetics, the corresponding ordinary differential equations ODEs are obtained:

[0086]

[0087]

[0088] In addition, the reaction is converted to:

[0089]

[0090] The reaction is converted to:

[0091]

[0092] Compared with existing technologies, the technical solutions adopted in this invention have the following advantages: the Brink controller avoids the limitations of the bi-regular representation method in CRNs design, does not involve subtraction operations in its structure, reduces the number of abstract chemical reactions required for implementation, and greatly simplifies the complexity of DNA implementation. Furthermore, taking enzymatic reactions as a background, a time delay factor is introduced, thereby constructing a delayed enzymatic reaction model based on CRNs; considering the transformation representation between CRNs and DNA reactions, a representation scheme for time delay in DNA strand substitution reactions is proposed. Finally, the enzymatic reaction process control under the Brink controller is achieved using the DNA strand substitution mechanism. Under both zero-delay and non-zero-delay conditions, the output substances of the enzymatic reaction process can approach the target level in a quasi-steady state. Attached Figure Description

[0093] Figure 1 An abstract representation of the various chemical substances involved in enzyme-catalyzed reactions;

[0094] Figure 2 This is a schematic diagram of the biomolecular control system under the Brink controller.

[0095] Figure 3 This is a diagram illustrating the regulation of an idealized enzymatic reaction process under Brink control based on DNA strand substitution.

[0096] Figure 4 for Figure 3 Graph showing the long-term regulation results of related experiments;

[0097] Figure 5 This is a process regulation diagram of a non-zero-delay enzymatic reaction under Brink control based on DNA strand substitution.

[0098] Figure 6 The process regulation results of the enzymatic reaction under Brink control when the initial concentration of substance D1 is set to 1.1 nM;

[0099] Figure 7 The diagram shows the process regulation results of the enzymatic reaction under Brink's control when the initial concentration of substance D1 is set to 1.1 nM and the initial concentration of substance F is set to 1.3 nM. Detailed Implementation

[0100] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit the application; that is, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0101] The following detailed description of embodiments of the application provided in the accompanying drawings is not intended to limit the scope of the application, but merely represents selected embodiments of the application. Based upon the embodiments of the application, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts are within the scope of protection of the application.

[0102] Embodiment 1

[0103] The embodiment provides an implementation method of delayed enzyme reaction super-sensitive Brink control based on DNA strand displacement, and specifically comprises the following steps.

[0104] S1: a single molecule and a double molecule chemical reaction are used to describe the enzyme reaction process, and the following expression can be obtained:

[0105]

[0106]

[0107]

[0108] Wherein, S and B represent a substrate and an enzyme respectively, and X and P represent an enzyme-substrate complex and a product respectively, as shown in the following formula: Figure 1

[0109] Considering that the enzyme reaction process is susceptible to factors such as temperature and pH value, the enzyme activity in the above reaction will change, and then the production efficiency of the product in the enzyme reaction is affected. In addition, the accumulation of the substrate S also needs a certain time (according to the reaction It can be known that S is affected by the input flux U). In order to more accurately simulate the reaction process, a delay factor τ is introduced in the reaction model, and a time-delayed enzyme reaction process model is constructed:

[0110]

[0111]

[0112]

[0113]

[0114] Wherein, the parameter τ represents the accumulated time delay in the process of producing the output substance P;

[0115] S2: a Brink controller based on CRNs is constructed;

[0116] ​In particular, compared to a controller based on dual-rail representation such as the QSM controller, the Brink controller directly reduces the number of CRNs required to achieve ultra- sensitive input-output response in design, since it does not involve the use of a subtraction module, reducing the complexity of DNA implementation.

[0117] The Brink controller is characterized by the design of CRNs that circumvents the limitations of the dual-rail representation method. As shown in Figure 2 , parameters R and Y are inputs of the Brink controller, and U represents the output. Parameters k c , θ c and α c represent catalytic rates, γ c and β c represent binding rates, and φ c represents degradation rate. In addition, R can produce R r , which then reacts with U * to form U, while Y can produce R y , which then reacts with U to form U * . At the same time, substances R r and R y combine to form a complex R r ·R y , which does not interact with any other substance, i.e. there is a functional mechanism of reverse action between the two different inputs R and Y of the Brink controller. Figure 2 The modules highlighted in r and y are part of the covalent modification cycle, in which the Brink controller takes signal R r and R y as activator and deactivator, respectively. The corresponding CRNs can be represented as follows:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125] In combination with the mass action kinetics MAK, the corresponding ODEs equations are:

[0126]

[0127]

[0128]

[0129]

[0130] From the differential equation, we have (d[U * ] t / dt)+(d[U] t / dt)=0, which indicates that the total mass of U+U * is conserved in time evolution.

[0131] S3: Obtain the static mapping expression between the Brink controller output and the system output under steady-state condition, and then obtain the analytical condition for guaranteeing the controller performance;

[0132] Specifically, assuming that the Brink controller has realized the steady-state output, the following results can be obtained:

[0133] k c [R] t -γ c [R r ] t [R y ] t -φ c [R r ] t -α c [R r ] t [U * ] t =0

[0134] θ c [Y] t -γ c [R r ] t [R y ] t -φ c [R y ] t -β c [R y ] t [U] t =0

[0135] -α c [R r ] t [U * ] t +β c [R y ] t [U]t = 0

[0136] Assuming the reference input R of the Brink controller is constant, the following equation constraint can be obtained:

[0137]

[0138] where the signal represents the concentration of substance · in the steady state.

[0139] Compared with the QSM controller which also can achieve ultra-sensitive response, the steady state equilibrium condition of the Brink controller is only related to two variables R r and R y , and the factors affecting the final output result are relatively less. The reduction of the number of variables contained in the steady state regulation equation constraint is conducive to maintaining the ideal steady state output, thereby simplifying the control structure and reducing the complexity of the controller design.

[0140] S4: Constructing the Brink controller by using DNA strand displacement reaction;

[0141] Specifically, let i, x, y, z be variables, where i ∈ (1, 2,..., 12), x ∈ (1, 2,..., 8), y ∈ (1, 2, 3, 4), z ∈ (1, 2,..., 9); for the G x , T x and L y involved in the following DNA implementation, they all represent auxiliary substances participating in the reaction, O z and H y represent intermediate products, B y represents the inert waste produced by the reaction which does not interact with other substances; in addition, C max represents the initial concentration of the auxiliary substance, q max represents the maximum strand displacement reaction rate, q i represents the reaction rate of the corresponding DNA implementation;

[0142] There is the same DSD implementation mechanism between the reactions and . The two reactions can be converted to:

[0143]

[0144]

[0145] At the same time, there is also a same implementation mechanism between the reactions and , which can be converted to:

[0146]

[0147] For reactions and the corresponding DNA implementation is expressed as:

[0148]

[0149]

[0150]

[0151] S5: Through the DNA strand displacement mechanism, and based on the delay material and compensation mechanism to obtain the time delay representation, the time delay representation is applied to the DNA implementation of the enzymatic reaction process model; at the same time, combined with the constructed Brink controller, the control of the rewritten enzymatic reaction process model is realized.

[0152] Specifically, in order to use DNA strand displacement reaction to represent time delay, two circuits composed of abstract chemical reactions occurring simultaneously are designed to represent time delay; the implementation of this mechanism is based on the participation of delay material. It can be described by the following reactions:

[0153]

[0154]

[0155] Where, parameters k prod and k delay are rate constants. In the first stage, substance O is produced at a constant rate; in the second stage, when O combines with delay material D, it is rapidly converted into waste The mechanism takes the time for substance O to consume substance D as the delay time, and its delay effect depends on the initial concentration of delay material D.

[0156] Rewrite the delay enzymatic reaction model as:

[0157]

[0158]

[0159]

[0160]

[0161]

[0162] Where, k delay1 represents the delay reaction rate. Combined with mass action kinetics MAK, the following results can be obtained:

[0163]

[0164]

[0165]

[0166]

[0167]

[0168] Using the DNA strand displacement reaction mechanism, the reaction is converted to:

[0169]

[0170] The degradation reaction is converted to:

[0171]

[0172] In addition, the square reaction is converted to:

[0173]

[0174] For the reversible reaction In the design of DNA implementation, the original reaction form can be maintained.

[0175] It should be noted that all reaction rates, substrate values involved in the Brink controller based on CRNs and enzymatic processes are shown in Table 1 and Table 2, and the feasible values are Cmax=1000nM, qmax=10 7 / M / s. For the Brink controller, the initial values of signals R r ,R y and R r ·R y are set to zero, i.e. R r0 =R y0 =[R r ·R y ]0=0nM.

[0176] Table 1 Parameter representation of the enzymatic reaction process model

[0177]

[0178] In addition, the initial concentrations of substances X and P in the enzymatic reaction are set to zero, i.e. X0=P0=0nM. Then the related experiments are designed and the results are analyzed.

[0179] Table 2 Parameterization of the Brink controller

[0180]

[0181] 1) No delay

[0182] For the enzymatic reaction process, a fixed constant is chosen for the expected concentration of the output substance P, i.e., the reference signal R is set to 4.0 nM. At this time, an ideal enzymatic reaction model is analyzed, i.e., the initial concentration of D1 is zero. The corresponding experimental results are shown in Figure 3 Figure 3 In , the output signal Y, i.e., the actual concentration of substance P, gradually tends to the ideal output concentration and remains in a stable output state over time.

[0183] Figure 3 It is worth noting that Figure 4 the adjustment results shown can only indicate that the ideal output state can be reached within a limited time. In fact, if the simulation time is long enough, the entire adjustment will collapse, causing the ideal output state to transition to another state, as shown in Figure 4 The phenomenon observed in

[0184] 2) Non-zero delay

[0185] Next, the enzymatic reaction process with a non-zero delay is analyzed, i.e., the initial concentration of substance D1 is not zero. The delay reaction rate k delay1 is set to 1.0 x 10 2 s -1 The initial concentration of the delay substance D1 is set to three different values, i.e., 0.5 nM, 0.8 nM, and 1.0 nM, and the system response under the corresponding conditions is shown in Figure 5 According to the parameters shown in Table 3, as the substance concentration increases, the delay effect of the system response becomes more obvious. [D1]0 represents the initial concentration of substance D1.

[0186] Table 3 Parameterization of non-zero delay model adjustment results

[0187]

[0188] However, the above delay mechanism is achieved by consuming the delay substance, which to some extent requires the participation and consumption of the output substance P. For DNA-based enzymatic reactions with time delay, this makes the actual output of the output substance P lower than the expected level. Figure 5 The effect shown may not be obvious, but when D1 = 1.1 nM, the output response of the entire system is as follows​Figure 6

[0189] To solve this problem, the following reaction mechanism is designed to compensate for the consumption of substance P in the reaction , so as to achieve the expected output of substance P.

[0190]

[0191]

[0192] where k pro1 and k pro2 are reaction rate constants, and F is an additional reaction substance. Combined with mass action kinetics MAK, the corresponding ordinary differential equations ODEs can be obtained:

[0193]

[0194]

[0195] In addition, the reaction can be converted to:

[0196]

[0197] The reaction can be converted to:

[0198]

[0199] For the above redesigned control scheme, the corresponding adjustment results are shown in Figure 7 . The reaction rate k pro1 is set to 6.2×10 -5 s -1 , and the reaction rate k pro2 is set to 3.0×10 -5 s -1 .

[0200] Figure 7 The curve of the actual output of substance P in the reaction Figure 6 is significantly different from the results of. With the passage of time, the other curve can gradually approach the expected concentration of substance P. This difference is due to the construction of the compensation mechanism, which adds chemical substance F. Therefore, the representation of time delay DNA strand displacement based on delay substance and compensation mechanism is feasible, and under the action of the Brink controller, the enzymatic reaction process can achieve the expected output results.

[0201] The Brink controller in the present application avoids the limitation of the double-track representation method, so that the required CRNs, DNA reactions and the number of DNA chains are greatly reduced, and the complexity of DNA implementation is reduced.

[0202] The foregoing description of specific exemplary embodiments of the application has been presented for the purposes of illustration and description. It is not intended to be exhaustive or to limit the application to the precise form disclosed, and various modifications and variations are possible in light of the above teachings. It is intended that the application embrace all alternatives, modifications, and variations as can be included within the scope of the present application which is defined by the claims and their equivalents.

Claims

1. A method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution, characterized in that, include: Enzyme-catalyzed reaction processes are described using unimolecular and bimolecular chemical reactions, and a time delay factor is introduced to obtain an enzyme-catalyzed reaction process model with a time delay. Build a Brink controller based on CRNs; Obtain the static mapping expression between the output of the Brink controller and the system output under steady-state conditions, and then obtain the analytical conditions that guarantee the controller performance; The Brink controller was constructed using a DNA strand substitution reaction. By employing a DNA strand substitution mechanism and obtaining a time delay representation based on delay substances and compensation mechanisms, the time delay representation is applied to the DNA implementation of the enzymatic reaction process model. Simultaneously, combined with the constructed Brink controller, the rewritten enzymatic reaction process model is controlled. The static mapping expression between the Brink controller output and the system output under steady-state conditions is obtained as follows: Assuming the Brink controller has achieved steady-state output, the following results are obtained: Assuming the Brink controller reference input If is a constant, then the following constraints are obtained: Among them, signal Represents matter in steady state Concentration; parameters and It is the input to the Brink controller. Indicates output; parameters , and Indicates the catalytic rate. and Indicates the binding rate, Indicates the degradation rate; in addition, parameters Produced substances , and then with Reaction formation ;parameter Produced substances , and then with Reaction formation At the same time, the signal and Combine to form a complex The complex does not interact with any other substance, i.e., at two different input parameters of the Brink controller. and There is a reverse action mechanism between them; the Brink controller will... and They act as activators and deactivators, respectively.

2. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 1, characterized in that, Enzyme-catalyzed reaction processes are described using unimolecular and bimolecular chemical reactions, specifically as follows: in, and They represent the substrate and the enzyme, respectively. and These represent the enzyme-substrate complex and the output substance, respectively.

3. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 2, characterized in that, A model of an enzyme-catalyzed reaction process with a time delay is constructed, specifically as follows: Among them, parameters Indicates the production of output substances The cumulative time delay that exists in the process.

4. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 1, characterized in that, A controller based on CRNs is represented as follows: Combining the mass action dynamics MAK, the corresponding ODEs equations are: Obtained from differential equations show The total mass remains conserved over time.

5. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 2, characterized in that, The Brink controller was constructed using a DNA strand substitution reaction, specifically as follows: Let... , , , Let be a variable, where , , , ; For the reaction and Both share the same DSD implementation mechanism; these two reactions are transformed into: At the same time, in the reaction and There is also a common implementation mechanism between them, which can be represented as: For the reaction , and In other words, the corresponding DNA implementation is represented as: in, , and Indicates the auxiliary substances that participate in the reaction. and Indicates intermediate product. This refers to inert waste products produced by the reaction that do not interact with other substances; furthermore, Indicates the initial concentration of the auxiliary substance. This indicates the reaction rate of maximum chain displacement. This indicates the reaction rate achieved by the corresponding DNA.

6. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 1, characterized in that, The time delay representation is obtained through DNA strand substitution mechanism and based on delaying substances and compensation mechanisms, specifically as follows: The time delay is represented by a circuit consisting of two simultaneous abstract chemical reactions, and its implementation is based on delay substances. The participation can be described by the following response: Among them, parameters and It is the rate constant; in the first stage, matter Produced at a constant rate; in the second stage, when matter... With delayed substances When combined, it will quickly turn into waste. ; with matter Consumable materials The time is used as the delay time, and its delay effect depends on the delaying substance. The initial concentration.

7. The method for achieving ultrasensitive control of the biomolecule Brink based on DNA strand substitution according to claim 1, characterized in that, Applying the aforementioned time delay representation to the DNA implementation of the enzyme-catalyzed reaction process model, the enzyme-catalyzed reaction model is thus rewritten as follows: in, This represents the delayed reaction rate; combined with mass action kinetics (MAK), the following results are obtained: 。 8. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 5, characterized in that, By combining the constructed Brink controller, the rewritten enzymatic reaction process model is controlled, specifically as follows: The reaction Transform into: Degradation reaction Transformed into: In addition, the reaction Transform into: For reversible reactions When designing DNA implementations, the original reaction form is preserved.

9. The method for achieving ultrasensitive Brink control of a delayed enzymatic reaction based on DNA strand substitution according to claim 5, characterized in that, The DSD mechanism is used to regulate the enzyme-catalyzed reaction process model based on the Brink controller, and the proposed representation of DNA strand substitution with respect to time delay is improved. Specifically, the following reaction mechanism is used to compensate for the enzyme-catalyzed reaction... Stage matter The consumption of substances, thereby achieving the output of materials. Expected output: in, and All are reaction rate constants. For the additional reactants; combined with mass action kinetics (MAK), the corresponding ordinary differential equations ODEs are obtained: In addition, the reaction Transform into: reaction Transform into: 。

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