Method for implementing a new biomolecular controller based on DNA strand displacement

Abstract

This invention discloses a method for implementing a novel biomolecular controller based on DNA strand substitution, comprising: modeling the enzymatic protein hydrolysis process using abstract chemical reactions; constructing a Brink controller BC based on a covalently modified cycle CMC; constructing a covalently modified cycle CMC-D with a direct positive self-regulating PAR structure; obtaining an improved Brink controller BC-DPAR using abstract CRNs; constructing a covalently modified cycle CMC-I with an indirect PAR structure; obtaining an improved Brink controller BC-IPAR using abstract CRNs; constructing an enzymatic protein hydrolysis model based on CRNs using a DNA strand substitution reaction; constructing controllers BC, BC-DPAR, and BC-IPAR respectively through the DNA strand substitution mechanism; and constructing different control schemes based on the differences between the controllers according to the enzymatic protein hydrolysis model. This invention utilizes the DNA strand substitution mechanism to realize control schemes for the enzymatic protein hydrolysis process under different controllers, which improves the output effect of hydrolysis products to a certain extent and can achieve the expected output level more quickly.

Description

Technical Field

[0001] This invention relates to the field of feedback control technology for chemical reaction networks in biological systems, and more specifically to a method for implementing a novel biomolecular controller based on DNA strand substitution. Background Technology

[0002] Chemical reaction networks (CRNs) are commonly used to represent feedback control systems to reflect the performance of biomolecular feedback control circuits. DNA molecules are also widely considered ideal engineering materials for constructing CRN-based molecular devices. Constructing CRNs to represent the dynamics of the system is a primary goal when designing applications such as biochemical controllers.

[0003] Existing patents related to CRNs and DNA strand displacement reactions mostly focus on logical operations and image encryption. Furthermore, most CRN-based controllers employ a dual-track representation method, which directly leads to a significant increase in the number of CRNs required for controller implementation, thus increasing the complexity of DNA implementation. CRNs provide an abstract representation of complex biochemical processes, which is an important prerequisite for constructing chemical reaction network representations of various modules in a control system and reflecting the performance of biomolecular feedback control circuits.

[0004] Currently, CRN-based controllers have evolved through a series of transformations, including PI controllers, PID controllers, and nonlinear QSM controllers. However, these controllers inherently involve subtraction operations between signals, making CRN design reliant on dual-track representation methods. This increases the number of CRNs required for implementation, significantly increasing the difficulty of implementing DNA. Summary of the Invention

[0005] The purpose of this invention is to design two novel biomolecular controllers based on DNA strand substitution: an improved Brink controller with direct positive self-regulating PAR (BC-DPAR) and an improved Brink controller with indirect positive self-regulating PAR (BC-IPAR), to achieve process control of enzymatic protein hydrolysis reactions, so that the hydrolysis products can reach the expected level.

[0006] To achieve the above objectives, this application proposes a method for implementing a novel biomolecular controller based on DNA strand substitution, comprising:

[0007] Modeling the enzymatic protein hydrolysis process using abstract chemical reactions;

[0008] A Brink controller based on covalently modified cyclic CMC is constructed, which can achieve ultrasensitive switching input and output response;

[0009] The covalent bond modification cycle is improved by combining it with the direct positive autoregulation PAR to construct the covalent bond modification cycle CMC-D with the direct PAR structure; based on CMC-D, the improved Brink controller BC-DPAR is obtained using abstract CRNs;

[0010] The covalent bond modification cycle is improved by combining it with the indirect positive autoregulation PAR to construct the covalent bond modification cycle CMC-I with the indirect PAR structure; based on CMC-I, the improved Brink controller BC-IPAR is obtained using abstract CRNs;

[0011] A CRN-based enzymatic protein hydrolysis model was constructed using DNA strand displacement reaction;

[0012] Controllers BC, BC-DPAR, and BC-IPAR were constructed using a DNA strand substitution mechanism. Based on the enzymatic protein hydrolysis model, different control schemes were constructed according to the differences in the controllers.

[0013] Compared with existing technologies, the technical solutions adopted in this invention have the following advantages: This invention constructs biochemical controllers using as few abstract chemical reactions as possible, proposing controllers BC-DPAR and BC-IPAR based on DNA strand substitution reactions. Compared with existing technologies, on the one hand, the two proposed controllers introduce PAR structures based on the Brink controller, thereby improving the stability of the ultrasensitive response; on the other hand, the proposed controllers circumvent the limitations of the dual-track representation method in CRNs design, do not involve the application of subtraction operations in the structure, reduce the number of abstract chemical reactions required for implementation, and greatly simplify the complexity of DNA implementation.

[0014] Furthermore, based on the enzymatic protein hydrolysis reaction, a CRN-based enzymatic protein hydrolysis model was constructed. Considering the transformation representation between CRNs and DNA reactions, control schemes for the enzymatic protein hydrolysis process under different controllers (including controllers BC, BC-DPAR, and BC-IPAR) were implemented using the DNA strand substitution mechanism. Compared to the BC control scheme, the BC-DPAR and BC-IPAR schemes for the enzymatic protein hydrolysis process improved the output of hydrolysis products to a certain extent, achieving the expected output level more quickly. Among them, the BC-DPAR control scheme showed a regulatory effect closer to the ideal control effect. Attached Figure Description

[0015] Figure 1 A diagram representing a model of enzymatic protein hydrolysis;

[0016] Figure 2 A framework diagram for modifying covalent bonds in a loop;

[0017] Figure 3 A representation diagram of CRNs covalently modified cycles;

[0018] Figure 4 This is a control block diagram based on the Brink controller;

[0019] Figure 5 A CMC-D framework diagram with direct positive self-regulation;

[0020] Figure 6 A diagram representing the CMC-D chemical reaction network with direct positive self-regulation;

[0021] Figure 7 The control block diagram is for the controller BC-DPAR with direct positive self-adjustment.

[0022] Figure 8 This is a CMC-I framework diagram with indirect positive self-regulation;

[0023] Figure 9 A diagram representing the CMC-I chemical reaction network with indirect positive self-regulation;

[0024] Figure 10 The control block diagram is for the BC-IPAR controller with indirect positive self-adjustment.

[0025] Figure 11 For the reaction A schematic diagram of DNA implementation;

[0026] Figure 12 For the reaction A schematic diagram of DNA implementation;

[0027] Figure 13 For the reaction A schematic diagram of DNA implementation;

[0028] Figure 14 The trajectory tracking response diagrams are shown for the protein hydrolysis reaction process under two conditions (a) and (b) in the BC, BC-IPAR and BC-DPAR control schemes. Detailed Implementation

[0029] 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.

[0030] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0031] Example 1

[0032] This embodiment proposes two novel controllers based on CRNs and DNA strand substitution reactions: an improved Brink controller with a direct positive self-regulating PAR (BC-DPAR) and an improved Brink controller with an indirect positive self-regulating PAR (BC-IPAR). Performance analysis is conducted from the perspectives of implementation principle, mechanism of action, and simulation. Furthermore, an enzymatic protein hydrolysis process is modeled using abstract chemical reactions, leading to a CRN-based enzymatic protein hydrolysis model. Next, the proposed protein hydrolysis model is integrated with the controllers BC, BC-DPAR, and BC-IPAR, respectively. The feasibility of the DNA implementation of the control scheme is verified using a DNA strand substitution reaction. Corresponding control schemes are then designed to achieve process control of the enzymatic protein hydrolysis reaction, ensuring that the hydrolysis products reach the expected levels. The implementation method specifically includes:

[0033] S1. Modeling the enzymatic protein hydrolysis process using an abstract chemical reaction yields the following representation:

[0034]

[0035]

[0036]

[0037] Where parameters k1 and k2 represent the catalytic rate, and k3 represents the degradation rate; X P and X E X represents protein and enzyme, respectively. P:E and X A These represent the protein-enzyme complex and the hydrolysis product (protein hydrolysis product, i.e., amino acids or polypeptides), respectively. Figure 1 As shown; X W It represents the substance—water; reaction Used to describe the degradation process of amino acids or peptides;

[0038] Combining the mass action dynamics MAK, the corresponding set of ordinary differential equations ODEs is:

[0039]

[0040]

[0041]

[0042]

[0043] in,[·] t Indicates the chemical concentration of ·;

[0044] Based on the above system of equations, the following results are obtained:

[0045]

[0046] Indicates X E +X P:E The total mass is conserved, i.e., X Total =X E +X P:E .

[0047] S2. Construct a Brink controller based on covalent bond modified cycles, which can achieve ultra-sensitive on / off input / output response;

[0048] Reference Figure 2 The basic framework of the covalent modification cycle (CMC) shown in the figure can be represented as follows:

[0049]

[0050]

[0051]

[0052]

[0053] Among them, activator X a With inactive substance U * Combined and converted into active substance U; deactivator X d It binds to the active substance U and converts it into the inactive substance U. * ; parameter k b1 k c1 k b2 and k c2 All represent the corresponding reaction rates;

[0054] Figure 3 The chemical reaction network diagram in the CMC visually illustrates the relationships between substances and multiple reactions in the chemical reaction set;

[0055] The corresponding ODEs can be obtained as follows:

[0056]

[0057]

[0058]

[0059]

[0060]

[0061]

[0062] From the above system of equations, we obtain:

[0063]

[0064]

[0065]

[0066] It indicates that C1+X a C2+X d , and C1+C2+U * The total mass of +U remains conserved throughout the entire evolution process.

[0067] The most significant feature of the Brink controller in its CRN design is that it does not involve subtraction operations, thus avoiding the limitations of the dual-track representation method. For example... Figure 4 As shown, the Brink controller based on a covalently modified loop structure is represented as follows:

[0068]

[0069]

[0070]

[0071]

[0072]

[0073]

[0074]

[0075] Where R and Y are the inputs to the Brink controller, and U represents the controller output; parameter k c θ c and α c Indicates catalytic rate, γ c and β c φ represents the binding rate. cIndicates the degradation rate; substance R r and R y Combined to form complex R r ·R y This complex does not interact with any other substance; furthermore, R produces substance R. r Then with U * The reaction produces U, while Y produces substance R. y Then it reacts with U to form U * ;

[0076] Based on MAK theory, the corresponding ODEs equation is:

[0077]

[0078]

[0079]

[0080]

[0081] From the above system of equations, we can obtain:

[0082]

[0083] It indicates U+U * The total mass of U is conserved over time, i.e., U Total =U * +U.

[0084] S3. Improve the covalent bond modification cycle by combining it with the direct positive autoregulation PAR to construct the covalent bond modification cycle CMC-D with the direct PAR structure; based on CMC-D, use abstract CRNs to obtain the improved Brink controller BC-DPAR;

[0085] Figure 5 The composition structure of CMC-D is shown, which can be represented as:

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] Among them, inactive substance U * With X a They combine to form U, but U and X d The reaction forms U * In addition, the following structure also exists in CMC-D: inactive substance U * Under the influence of substance U, it is converted into U, i.e., the reaction U * +U→C3→U+U; parameter k b1 k b2 and k b3 k represents the binding rate. c1 k c2 and k c3 Both represent dissociation rates;

[0093] Figure 6 The chemical reaction network diagram in the CMC-D visually illustrates the connections between substances and multiple reactions in the chemical reaction set;

[0094] The corresponding ODEs are:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102] Obtained from ODEs:

[0103]

[0104]

[0105]

[0106] It indicates that C1+X a C2+X d and C1+C2+C3+U * The total mass of +U is conserved.

[0107] in accordance with Figure 7 The structures shown indicate that the controller BC and BC-DPAR differ structurally. Compared to controller BC, the substance U in BC-DPAR...* It can be converted into substance U under the action of substance U, that is, the reaction. The corresponding CRNs are represented as follows:

[0108]

[0109]

[0110]

[0111]

[0112]

[0113]

[0114]

[0115]

[0116] parameter k c θ c and α c Indicates catalytic rate, γ c β c and μ c φ represents the binding rate. c Indicates the degradation rate;

[0117] Based on MAK theory, the corresponding ODEs equation is:

[0118]

[0119]

[0120]

[0121]

[0122] The result obtained from the above system of equations is (d[U) * ] t / dt)+(d[U) t / dt)=0 indicates U+U * The total mass is conserved, i.e., U Total =U * +U.

[0123] S4. Improve the covalent bond modification loop by combining it with the indirect positive autoregulation PAR to construct the covalent bond modification loop CMC-I with the indirect PAR structure; based on CMC-I, use abstract CRNs to obtain the improved Brink controller BC-IPAR;

[0124] Figure 8 The compositional structure of CMC-I is shown, which exhibits a unique mechanism: in the reaction of substance U and activator X... a Under the influence of the inactive substance U * It can be converted into U, that is, the reaction U + X a →C3+U * →C4→U+U.

[0125] The CMC-I structure is represented as follows:

[0126]

[0127]

[0128]

[0129]

[0130]

[0131]

[0132]

[0133] Where the parameter k b1 k b2 k b3 and k b4 k represents the binding rate. c1 k c2 and k c4 Both represent dissociation rates;

[0134] Figure 9 The chemical reaction network diagram in the CMC-I visually illustrates the connections between substances and multiple reactions in the chemical reaction set;

[0135] In addition, the corresponding ODEs are:

[0136]

[0137]

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144] Obtained from ODEs:

[0145]

[0146]

[0147]

[0148] It indicates that C1+C3+X a C2+X d and C1+C2+C3+C4+U * The total mass of +U is conserved.

[0149] Figure 10 The block diagram of the controller BC-IPAR is shown. In the controller BC-IPAR, substance U * and R r Under the influence of U, it can be converted into substance U, i.e., the reaction. The Brink controller BC-IPAR is represented as:

[0150]

[0151]

[0152]

[0153]

[0154]

[0155]

[0156]

[0157]

[0158] Where; parameter k c θ c and α c Indicates catalytic rate, γ c β c and δ c φ represents the binding rate. c Indicates the degradation rate;

[0159] Based on MAK theory, the corresponding ODEs equations are given:

[0160]

[0161]

[0162]

[0163]

[0164] The result obtained from the above system of equations is (d[U) * ] t / dt)+(d[U) t / dt)=0 indicates U+U * The total mass is conserved, i.e., U Total =U * +U.

[0165] S5. Construct an enzymatic protein hydrolysis model based on CRNs using DNA strand substitution reactions, specifically:

[0166] For the reaction (Refer to Figure 11 Transformed into:

[0167]

[0168] At the same time, the reaction (Refer to Figure 12 The transformation is expressed as:

[0169]

[0170] For degradation reaction (Refer to Figure 13 For example, the corresponding DNA implementation is represented as:

[0171]

[0172] Among them, G x T x and L y Both refer to the auxiliary substances that participate in the reaction, O z and H y Spn represents an intermediate product, while C represents an inert waste product that does not interact with other substances produced by the reaction. max q represents the initial concentration of the auxiliary substance. max q represents the reaction rate of maximum chain displacement. i Indicates the reaction rate achieved by the corresponding DNA; cofactor G x and T xAll are consumed irreversibly; variables i∈(1,2,...,13), n∈(1,2,...,21), x∈(1,2,...,6), y∈(1,2,...,7), z∈(1,2,...,10).

[0173] S6. Controllers BC, BC-DPAR, and BC-IPAR are obtained through DNA strand substitution mechanism; based on the enzymatic protein hydrolysis model, different control schemes are constructed according to the differences of the controllers.

[0174] The reaction in the Brink controller BC and There is a common DNA strand substitution mechanism between them; these two reactions are transformed into:

[0175]

[0176]

[0177] For the reaction and The same DNA strand substitution mechanism also exists between them; these two reactions are transformed into:

[0178]

[0179] reaction and Transform into:

[0180]

[0181]

[0182]

[0183] The difference between the improved Brink controller BC-DPAR with a direct PAR structure and the controller BC lies in the reaction mechanism. Its corresponding DNA implementation is represented as:

[0184]

[0185] The difference between the improved Brink controller BC-IPAR with indirect PAR structure and the controller BC lies in the reaction mechanism. It can be abstractly represented as:

[0186] U * +R r →U * ·R r

[0187] U+U* ·R r →U+U

[0188] The two formulas above can be expressed as:

[0189]

[0190]

[0191] Finally, DNA-based controllers (including BC, BC-IPAR, and BC-DPAR) and enzymatic protein hydrolysis models were integrated to construct three different regulatory schemes. Tables 1 and 2 provide all reaction rates involved in the CRN-based controllers and enzymatic protein hydrolysis process models. For the controllers involved in this work, the signal R... r R y and R r ·R y The initial value of R is set to zero, i.e., R r0 =R y0 =[R r ·R y ]0=0nM.

[0192] Table 1. Parametric representation of controllers BC, BC-DPAR, and BC-IPA

[0193]

[0194] Table 2. Parameter representation of the enzyme-catalyzed protein hydrolysis reaction model.

[0195]

[0196] The parameter μ in Table 1 c Reaction with BC-DPAR controller Related to the parameter δ c Reaction with BC-IPAR controller Related. There is a common point among the controllers BC, BC-DPAR, and BC-IPAR, namely U. Total =U * +U.

[0197] For the driving signal U in the enzymatic proteolysis process, consider two cases: U = 0 nM and U = 1 nM. The proposed enzymatic proteolysis model is combined with controllers BC, BC-DPAR, and BC-IPAR, and the results are as follows: Figure 14 As shown. Additionally, using adjustment time as a metric, for... Figure 14 The output curves of the protein hydrolysis product yield were quantified, and the results are shown in Table 3.

[0198] Table 3. Parameterized analysis of the actual outputs of the enzymatic proteolysis models under controllers BC, BC-IPAR, and BC-DPAR.

[0199]

[0200] Compare Table 3 with Figure 14 Combining these, the following results can be obtained. On the one hand, the settling times of controllers BC and BC-IPAR at U = 0 nM are 1.2 × 10⁻⁶. 3 s and 8.0×10 2 At U = 1 nM, the adjustment time for BC and BC-IPAR is almost the same, approximately 8.5 × 10⁻⁶. 2 From a numerical perspective, compared to the BC control scheme, the proposed BC-IPAR scheme can reach the expected output level in a shorter time. On the other hand, the settling times of controllers BC and BC-DPAR at U = 0 nM are 8.5 × 10⁻⁶. 2 s and 6.5×10 2 At U = 1 nM, the adjustment time for BC and BC-DPAR is 1.2 × 10⁻⁶ s, while at U = 1 nM, the adjustment time for BC and BC-DPAR is 1.2 × 10⁻⁶ s. 3 s and 5.2×10 2 Compared to the BC control scheme, the proposed BC-DPAR scheme can achieve rapid and stable output of protein hydrolysates. Furthermore, the BC-DPAR controller exhibits better regulatory capability, shorter settling time, and faster steady-state output than the BC-IPAR controller. In summary, the proposed BC-DPAR and BC-IPAR schemes for enzymatic protein hydrolysis improve the output of hydrolysates to some extent compared to existing BC schemes. Among the proposed schemes, the DNA strand substitution-based BC-DPAR control scheme achieves a regulatory effect closer to the expected ideal result.

[0201] The entire implementation of this invention utilizes CRNs and DNA strand substitution reactions as analytical schemes to realize and verify the feasibility and effectiveness of the proposed control scheme. The key to the entire control scheme lies in the construction of CRNs for controllers BC-DPAR and BC-IPAR, the modeling of the enzymatic protein hydrolysis reaction, and the conversion between CRNs and DNA strand substitution reactions. The construction of controllers BC-DPAR and BC-IPAR is based on covalently modified loops and positively self-regulating PARs, differing only in the structural application of direct and indirect PARs, respectively. Performance analysis of the proposed controllers is conducted from the perspectives of implementation principle, mechanism of action, and simulation. Furthermore, combining DNA strand substitution representation, enzymatic protein hydrolysis reaction control schemes under different controllers (including controllers BC, BC-DPAR, and BC-IPAR) are constructed using DNA reactions.

[0202] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A method for implementing a novel biomolecular controller based on DNA strand substitution, characterized in that, include: Modeling the enzymatic protein hydrolysis process using abstract chemical reactions; A Brink controller based on covalently modified cyclic CMC is constructed, which can achieve ultrasensitive switching input and output response; The covalent bond modification cycle was improved by combining it with direct positive autoregulation PAR to construct the covalent bond modification cycle CMC-D with a direct PAR structure; Based on CMC-D, an improved Brink controller BC-DPAR is obtained using abstract CRNs; The covalent bond modification cycle is improved by combining it with the indirect positive autoregulation PAR to construct the covalent bond modification cycle CMC-I with the indirect PAR structure; based on CMC-I, the improved Brink controller BC-IPAR is obtained using abstract CRNs; A CRN-based enzymatic protein hydrolysis model was constructed using DNA strand displacement reaction; Controllers BC, BC-DPAR, and BC-IPAR were constructed using a DNA strand substitution mechanism. Based on the enzymatic protein hydrolysis model, different control schemes were constructed according to the differences between the controllers. The covalently modified cycle CMC-D with a direct PAR structure is represented as: in, As a deactivating agent, Activator; inactive substance and Combine to form active substances But active substances and Reaction formation In addition, CMC-D also contains the following structures: inactive substances. In active substances Transformed into That is, reaction ;parameter , and Indicates the binding rate, , and Both represent dissociation rates; The corresponding ODEs are: Obtained from ODEs: which indicates that , and the total mass is conserved; Improve the substances in the Brink controller BC-DPAR In matter Transformed into matter under the action That is, reaction The corresponding CRNs are represented as follows: parameter , and Indicates the catalytic rate. , and Indicates the binding rate, Indicates the degradation rate; Based on MAK theory, the corresponding ODEs equation is: The result is obtained from the above system of equations. show The total mass is conserved, that is... , and It is the input to the Brink controller, the substance. and Combine to form a complex ; The covalently modified cycle CMC-I with the indirect PAR structure is represented as follows: Among them, in active substances and activator Under the action of inactive substances Transformed into active substances That is, reaction ;parameter , , and Indicates the binding rate, , and Both represent dissociation rates; In addition, the corresponding ODEs are: Obtained from ODEs: It indicates , and The total mass is conserved; The improved Brink controller BC-IPAR is represented as follows: Among them, inactive substances and matter In active substances Under the action of [something], it is transformed into active substances. That is, reaction ;parameter Indicates the binding rate; Based on MAK theory, the corresponding ODEs equations are given: The result is obtained from the above system of equations. show The total mass is conserved, that is... .

2. The method for implementing the novel biomolecular controller based on DNA strand substitution according to claim 1, characterized in that, The process of enzymatic protein hydrolysis is modeled using abstract chemical reactions, specifically as follows: Where parameters and Indicates the catalytic rate. Indicates the degradation rate; and They represent proteins and enzymes, respectively. and These represent the protein-enzyme complex and the hydrolysis product, respectively. It represents the substance—water; reaction Used to describe the degradation process of amino acids or peptides; Combining the mass action dynamics MAK, the corresponding set of ordinary differential equations ODEs is: wherein represents the chemical concentration of Based on the above system of equations, the following results are obtained: It is shown that the total mass of is conserved, i.e. .

3. The method for implementing the novel biomolecular controller based on DNA strand substitution according to claim 1, characterized in that, Covalent bond modified cycle (CMC) is represented as: Among them, activator With inactive substances Combined and transformed into active substances. Deactivating agent With active substances Combined and transformed into inactive substances. ; The corresponding ODEs are: From the above system of equations, we obtain: It indicates , ,and Its total mass remains conserved throughout the entire evolution process.

4. The method for implementing the novel biomolecular controller based on DNA strand substitution according to claim 3, characterized in that, The Brink controller based on a covalently modified loop structure is represented as: in, and It is the input to the Brink controller, and Indicates controller output; substance and Combine to form a complex This complex does not interact with any other substance; furthermore, Produced substances , and then with Reaction formation ,and Produced substances , and then with Reaction formation ; Based on MAK theory, the corresponding ODEs equation is: From the above system of equations, we can obtain: It is shown that the total mass of the system is conserved in time evolution, i.e. .

5. The method for implementing the novel biomolecular controller based on DNA strand substitution according to claim 1, characterized in that, A CRN-based enzymatic protein hydrolysis model was constructed using DNA strand substitution reactions, specifically as follows: For the reaction is converted to: At the same time, the reaction The transformation is represented as: For the degradation reaction the corresponding DNA implementation is expressed as: in, and They represent proteins and enzymes, respectively. and These represent the protein-enzyme complex and the hydrolysis product, respectively; parameters and Indicates the catalytic rate. Indicates the degradation rate; , and All of these refer to auxiliary substances that participate in the reaction. and Indicates intermediate product. This refers to inert waste produced by the reaction that does not interact with other substances; Indicates the initial concentration of the auxiliary substance. This indicates the reaction rate of maximum chain displacement. Indicates the reaction rate achieved by the corresponding DNA; auxiliary substances and All are irreversibly consumed; variables , , , , .

6. The method for implementing the novel biomolecular controller based on DNA strand substitution according to claim 5, characterized in that, The reaction in the Brink controller BC and There is a common DNA strand substitution mechanism between them; these two reactions are transformed into: For the reaction and there is also the same DNA strand displacement implementation mechanism; both reactions are transformed into: Reactions , and , are converted to: The improved Brink controller BC-DPAR with direct PAR structure differs from the controller BC in the reaction mechanism ; its corresponding DNA implementation is represented as: The difference between the Brink controller BC-IPAR with its indirect PAR structure and the controller BC lies in their reaction mechanism. ; It can be abstractly represented as: The two formulas above can be expressed as: 。

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