Optimization method for design of ultra-sensitive quasi-fuzzy molecular controller based on CRNs

Abstract

The invention relates to the technical field of biomolecule control, in particular to a CRNs-based ultra-sensitive quasi-fuzzy molecular controller design and optimization method, which comprises the following steps: S1, establishing a kinetic model for simulating a phosphorylation biochemical process through an abstract chemical reaction network CRNs; s2, constructing a molecular logic arithmetic unit with ultra-sensitive response characteristics based on a one-way covalent modification circulation mechanism; s3, constructing a quasi-fuzzy PI controller QFPI by adopting a double-track covalent modification cycle structure, and performing nonlinear control logic on a similar T-S fuzzy rule through modular CRNs; and S4, carrying out monorail and simplified design on the initial quasi-fuzzy controller, providing an M-QFPI optimization scheme, and overcoming the defect of finite-time regulation and control while increasing the reaction quantity of biochemical molecules. According to the invention, ultra-sensitive response is realized by using a covalent modification cycle structure, and an ideal addition logic arithmetic unit process is described by using a simple chemical reaction, so that the response time and the adjustment time of a biochemical molecule control strategy are remarkably reduced, and overshoot of a biochemical molecule controller is inhibited.

Description

Technical Field

[0001] This invention relates to the field of biochemical molecular control technology, specifically to a design and optimization method for an ultrasensitive quasi-fuzzy molecular controller based on CRNs. Background Technology

[0002] Control theory originated from conceptual and generalized design strategies to improve the stability and robustness of systems, including mechanical devices, electrical systems, space systems, and chemical molecular processes. With the continuous development of intelligent control, fuzzy control mechanisms have gradually emerged and attracted widespread attention due to their effectiveness in controlling complex nonlinear systems. Against this backdrop, ultrasensitive response is considered a feasible method for designing controllers with short settling times. Ultrasensitive response, as a common reaction in biochemical processes, significantly reduces reaction time due to its sensitivity, serving as an efficient design paradigm. With the increasing application of control theory in synthetic biology, how to realize fuzzy control strategies with ultrasensitive responses at the molecular level is a worthwhile area of ​​consideration.

[0003] Existing CRN-based controllers have undergone a series of evolutions, from the initial PI controller to the QSM controller and then to the nonlinear Brink controller. However, the early traditional linear control strategy design relied on the dual-track representation method, which resulted in unsatisfactory response time, settling time, and overshoot; moreover, the previous single-track covalent modified loop had the limitation of finite-time control.

[0004] Based on this, the present invention provides a design and optimization method for an ultrasensitive quasi-fuzzy molecular controller based on CRNs to solve the above-mentioned technical problems. Summary of the Invention

[0005] The purpose of this invention is to provide a design and optimization method for an ultrasensitive quasi-fuzzy molecular controller based on CRNs. This invention uses a covalently modified cyclic structure to achieve an ultrasensitive response and uses a simple form of chemical reaction to describe the ideal additive logic operation process, thereby significantly reducing the response time and settling time of the biochemical molecular control strategy and suppressing the overshoot of the biochemical molecular controller.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] This invention provides a design and optimization method for an ultrasensitive quasi-fuzzy molecular controller based on CRNs, comprising the following steps:

[0008] S1: A kinetic model simulating the biochemical process of phosphorylation is established using abstract chemical reaction networks (CRNs).

[0009] S2: Constructing a molecular logic operator with ultrasensitive response characteristics based on a unidirectional covalent modification cycle mechanism;

[0010] S3: A quasi-fuzzy PI controller QFPI is constructed using a dual-track covalently modified loop structure, and nonlinear control logic is applied to TS-like fuzzy rules through modular CRNs;

[0011] S4: The initial quasi-fuzzy controller is designed to be single-tracked and simplified, and an M-QFPI optimization scheme is proposed to overcome the limitation of finite time control while increasing the number of biochemical molecular reactions.

[0012] The CRNs model for the phosphorylation reaction in S1 is expressed as follows:

[0013]

[0014] Where V1, V2, V3, and V4 represent the reaction rates of the phosphorylation process, U represents the output of the intermediate species as a controller, B, D, and F represent the substrates, S represents the activating enzyme, and V and Y represent the enzyme-substrate complex and the product, respectively.

[0015] The chemical reaction in the molecular logic operator in S2 is represented as follows:

[0016]

[0017] And based on the dynamics of mass action, its ordinary differential equation is obtained:

[0018]

[0019] Where K1 and K2 represent catalytic rates, K3 represents degradation rates, and K p and K d Indicates catalytic enzymes, U and U * These are the substrate and product of the catalytic reaction, respectively.

[0020] The control logic of the quasi-fuzzy PI controller QFPI in S3 is equivalent to the following TS-type fuzzy rule:

[0021]

[0022] in, These are the error E and the integral result ΔE, respectively, representing the outputs of the QFPI controller under different conditions. This represents the components of the error E. This represents the component of the integral result ΔE.

[0023] The QFPI controller in S3 implements the fuzzy control rule through the following chemical reaction, specifically as follows:

[0024]

[0025] Where E1, E2, E3, and E4 are the inputs to the controller, R1, R2, R3, and R4 are the catalytic reaction rates, U is the output of the controller, and RARP is the production waste.

[0026] And based on the dynamics of mass action, its ordinary differential equation is established, specifically expressed as:

[0027]

[0028]

[0029] Where R is the reference value, RA represents the reference value component, Y is the output value, RY represents the output value component, kc, θc, mc, αc and βc represent the reaction rates of catalysis, degradation, and annihilation, respectively.

[0030] The chemical reaction in the M-QFPI optimization scheme in S4 is specifically represented as follows:

[0031]

[0032] Where X1, X2, X3, and X4 represent the fractional products of RA and RY, and C and C # These are the substrate and product of the catalytic reaction, respectively.

[0033] The dual-track covalent modification cycle structure in S3 is a chemical reaction network of dual-track covalent modification cycles, defined as a dual-track ultrasensitive response. When the input exceeds a certain threshold, the output increases rapidly, shortening the rise time and settling time of the quasi-fuzzy PI controller QFPI.

[0034] The ultrasensitive molecular logic arithmetic unit constructed in S2 can shorten the adjustment time of the control system by more than 62.1% compared with the traditional dual-track arithmetic logic, and can suppress overshoot with an overshoot of 0.

[0035] Compared with the prior art, the beneficial effects of the present invention are:

[0036] 1. This invention achieves ultrasensitive response by using covalently modified cyclic structures, and describes the ideal additive logic operation process with a simple form of chemical reaction, thereby significantly reducing the response time and adjustment time of biochemical molecular control strategies and suppressing the overshoot of biochemical molecular controllers.

[0037] 2. This invention utilizes a dual-track covalent modification cycle—a chemical reaction network employing a dual-track (four-chain) covalent modification cycle structure—to enable the molecular pathway to rapidly increase the output when the input exceeds a certain threshold.

[0038] 3. This invention realizes an ultrasensitive quasi-fuzzy PI molecular controller through a modular design paradigm, and realizes an ultrasensitive quasi-fuzzy control strategy based on CRNs through a dual-track covalently modified loop, making the convergence speed of the control strategy faster and better.

[0039] 4. This invention constructs a biochemical controller using as few abstract chemical reactions as possible, without involving the application of logical operations in its structure, and overcomes the limitations of finite-time regulation in covalent modification cycles.

[0040] 5. This invention provides a new method for the modular design of biochemical molecules by using CRNs to design a reaction model with phosphorylation reaction as the background. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the phosphorylation reaction with interference in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention.

[0042] Figure 2 This is a diagram of the ultrasensitive logic unit framework in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs of the present invention.

[0043] Figure 3 This is a diagram of the ultrasensitive quasi-fuzzy molecular controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs of the present invention.

[0044] Figure 4 This is a block diagram of the QFPI controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention.

[0045] Figure 5 This is a block diagram of the M-QFPI controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention.

[0046] Figure 6 The diagram shows the closed-loop response curve of the PI controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention.

[0047] Figure 7 This is a closed-loop response curve of the QFPI controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs of the present invention.

[0048] Figure 8 The closed-loop response curves of the M-QFPI controller, Brink controller, and BC-DPAR controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs of this invention are shown.

[0049] Figure 9 This is a quantitative representation of the substrate U* concentration of the Brink controller in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs of the present invention.

[0050] Figure 10 This is a quantitative representation of the substrate C* concentration controlled by M-QFPI in the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention.

[0051] Figure 11 This is a flowchart illustrating the design and optimization method of an ultrasensitive quasi-fuzzy molecular controller based on CRNs according to the present invention. Detailed Implementation

[0052] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0053] Example:

[0054] like Figures 1-11 As shown, this embodiment provides an optimization method for designing an ultrasensitive quasi-fuzzy molecular controller based on CRNs, including the following steps:

[0055] S1: A kinetic model simulating the biochemical process of phosphorylation is established using abstract chemical reaction networks (CRNs).

[0056] S2: Constructing a molecular logic operator with ultrasensitive response characteristics based on a unidirectional covalent modification cycle mechanism;

[0057] S3: A quasi-fuzzy PI controller QFPI is constructed using a dual-track covalently modified loop structure, and nonlinear control logic is applied to TS-like fuzzy rules through modular CRNs;

[0058] S4: The initial quasi-fuzzy controller is designed to be single-tracked and simplified. An M-QFPI optimization scheme is proposed to overcome the limitations of finite-time regulation while reducing the number of DNA strands and reactions.

[0059] The CRNs model for phosphorylation in S1 is expressed as:

[0060]

[0061] Where V1, V2, V3, and V4 represent the reaction rates of the phosphorylation process, U represents the output of the intermediate species as a controller, B, D, and F represent the substrates, S represents the activating enzyme, and V and Y represent the enzyme-substrate complex and the product, respectively.

[0062] The chemical reaction in the molecular logic operator of S2 is represented as follows:

[0063]

[0064] And based on the dynamics of mass action, its ordinary differential equation is obtained:

[0065]

[0066] Where K1 and K2 represent catalytic rates, K3 represents degradation rates, and K p and K d Indicates catalytic enzymes, U and U * These are the substrate and product of the catalytic reaction, respectively.

[0067] The control logic of the quasi-fuzzy PI controller QFPI in S3 is equivalent to the following TS-type fuzzy rule:

[0068]

[0069] in, These are the error E and the integral result ΔE, respectively, representing the outputs of the QFPI controller under different conditions. This represents the components of the error E. This represents the component of the integral result ΔE.

[0070] In S3, the QFPI controller implements fuzzy control rules through the following chemical reaction, specifically as follows:

[0071]

[0072] Where E1, E2, E3, and E4 are the inputs to the controller, R1, R2, R3, and R4 are the catalytic reaction rates, U is the output of the controller, and RARP is the production waste.

[0073] And based on the dynamics of mass action, its ordinary differential equation is established, specifically expressed as:

[0074]

[0075] Where R is the reference value, RA represents the reference value component, Y is the output value, RY represents the output value component, kc, θc, mc, αc and βc represent the reaction rates of catalysis, degradation, and annihilation, respectively.

[0076] The chemical reactions in the M-QFPI optimization scheme in S4 are specifically represented as follows:

[0077]

[0078] Where X1, X2, X3, and X4 represent the fractional products of RA and RY, and C and C # These are the substrate and product of the catalytic reaction, respectively.

[0079] The dual-track covalent modification loop structure in S3 is a chemical reaction network of dual-track covalent modification loops, defined as a dual-track ultrasensitive response. When the input exceeds a certain threshold, the output increases rapidly, shortening the rise time and settling time of the quasi-fuzzy PI controller QFPI.

[0080] The ultrasensitive molecular logic arithmetic unit constructed in S2 can reduce the adjustment time of the control system by more than 62.1% compared with the traditional dual-track arithmetic logic, and can suppress overshoot with an overshoot of 0.

[0081] In this embodiment, an optimization method for designing an ultrasensitive quasi-fuzzy molecular controller based on CRNs is described below: First, S1: A kinetic model simulating the biochemical process of phosphorylation is established using abstract chemical reaction networks (CRNs); the CRNs model of the phosphorylation reaction is represented as:

[0082]

[0083] in, , , and The values ​​represent the reaction rate of the phosphorylation process, U represents the output of the intermediate species as a controller, B, D, and F represent the substrate, S represents the activating enzyme, and V and Y represent the enzyme-substrate complex and product, respectively. From a molecular perspective, the robustness of the control system can be simulated by utilizing the cascade failure mechanism of perturbations in the biochemical network. For example... Figure 1 As shown, the controller output species U and F are converted into activator S, which binds to substrate B to form complex V. Subsequently, substrate V decomposes into the corresponding product Y and substrate B. S2: A molecular logic operator with ultrasensitive response characteristics is constructed based on a unidirectional covalent modification cycle mechanism. Compared with traditional dual-track operation logic, the constructed ultrasensitive molecular logic operator can shorten the settling time of the control system by more than 62.1% and suppress overshoot, with an overshoot of 0. The chemical reaction of the molecular logic operator is represented as follows:

[0084]

[0085] And based on the dynamics of mass action, its ordinary differential equation is obtained:

[0086]

[0087] Where K1 and K2 represent catalytic rates, K3 represents degradation rates, and K p and K d Indicates catalytic enzymes, U and U * These are the catalytic reaction substrate and product, respectively. Secondly, S3: A quasi-fuzzy PI controller (QFPI) is constructed using a dual-track covalently modified cyclic structure. Modular CRNs are used to apply nonlinear control logic to TS-like fuzzy rules. As a two-dimensional fuzzy controller, the quasi-fuzzy PI controller employs linear rules, resulting in the general form of the Mamdani-type fuzzy language: if (E is E) i )and(ΔE is E j then(U is U) F(i,j) In this context, E and ΔE represent the proportional gain signal and integral signal, respectively, and i and j represent the signal components. The dual-track covalent modification loop structure is a chemical reaction network of dual-track covalent modification loops, defined as a dual-track ultrasensitive response. When the input exceeds a certain threshold, the output increases rapidly, shortening the rise time and settling time of the quasi-fuzzy PI controller QFPI. The control logic of the quasi-fuzzy PI controller QFPI is equivalent to the following TS-type fuzzy rule:

[0088]

[0089] in, These are the error E and the integral result ΔE, respectively, representing the outputs of the QFPI controller under different conditions. This represents the components of the error E. This represents the component of the integral result ΔE. The QFPI controller in S3 implements the fuzzy control rule through the following chemical reaction, specifically expressed as:

[0090]

[0091] Where E1, E2, E3, and E4 are the inputs to the controller, R1, R2, R3, and R4 are the catalytic reaction rates, U is the output of the controller, and RARP is the production waste; ① and its ordinary differential equation is established based on mass action kinetics, specifically expressed as:

[0092]

[0093] Where R is the reference value, RA represents the reference value component, Y is the output value, RY represents the output value component, kc, θc, mc, αc and βc represent the reaction rates of catalysis, degradation, and annihilation, respectively. ② For the QFPI controller, using the dual-track notation, assuming the QFPI control system has reached steady-state output, the left-hand side of the expression can be set to zero, expressed as:

[0094]

[0095] K2[RA]t-αc[E3]t[U # ]t=0

[0096] K2[RY]t-βc[E4]t[U]t=0

[0097] βc[E3]t[U]t-βc[E4]t[U]t=0

[0098] αc[E1]t[U # ]t+ac[E2]t[U # ]t=0

[0099] ③Assuming the reference input R of the QFPI controller is constant and remains unchanged during the adjustment period, it can be expressed as:

[0100]

[0101] The output of the control process is obtained under steady state:

[0102]

[0103] ④ When the QFPI control system U reaches the ideal steady-state output, that is, the condition is met. Represented as:

[0104]

[0105] Assume the process reaches a steady-state output and satisfies... Determine the conditions that need to be met from ④, including If the process reaches a steady-state output, then the equation... In this case, the concentrations of R and Y are both 0, because E = 0, therefore The ultrasensitive quasi-fuzzy controller utilizes CRNs with an approximate switching structure that has an ultrasensitive response. It can realize fuzzy control logic through activation / deactivation: (1) When the error component E is positive, increase the concentration of the controller's output U; otherwise, decrease the concentration of the output U. (2) When the error transformation component ΔE is positive, decrease the concentration of the controller's output U; otherwise, increase the concentration of the output U. Finally, S4: The initial quasi-fuzzy controller is single-tracked and simplified, and an M-QFPI optimization scheme is proposed to overcome the finite-time regulation defect while reducing the number of DNA strands and reactions. The chemical reaction of the M-QFPI optimization scheme is specifically expressed as:

[0106]

[0107] Where X1, X2, X3, and X4 represent the fractional products of RA and RY, and C and C # These are the catalytic reaction substrate and product, respectively. When the M-QFPI control system reaches its ideal steady-state output, the controller's output concentration satisfies the following relationship, specifically expressed as follows: ① Further analysis of the M-QFPI controller based on the single-track representation method is as follows:

[0108]

[0109]

[0110] ②Assuming that the M-QFPI control has reached steady-state output, the left side of the equation can be set to zero, specifically expressed as:

[0111]

[0112] K2[RA]t-αc[X3]t[C # ]t=0

[0113] K2[RY]t-αc[X4]t[C]t=0

[0114] βc([X2]t+[X4]t)[C]t-αc([X1]t+[X3]t)[C # ]t=0

[0115] αc([X1]t+[X3]t)[C # ]t-βc([X2]t+[X4]t)[C]t=0

[0116] ③ Assuming the reference input R of the M-QFPI controller is constant and remains unchanged during the adjustment period, specifically expressed as:

[0117]

[0118] The output of the control process is obtained under steady state:

[0119]

[0120] in,

[0121] ④ When the M-QFPI control system reaches the ideal steady-state output, that is, when the condition is met. Specifically, it is expressed as follows:

[0122]

[0123] Assume the process reaches a steady-state output and satisfies... Determine the conditions that need to be met from ④, including If the process reaches a steady-state output, then the equation... In the middle, the concentrations of RA and RY are both 0, so Compared to the QFPI controller, the M-QFPI optimization scheme can reduce rise time by more than 99.2% and settling time by more than 98%. Compared to the Brink controller, it reduces rise time by more than 88.8% and settling time by more than 86.8%, while avoiding finite-time control failure caused by substrate depletion.

[0124]

[0125] Table 1. Parametric Representation of M-PI and PI Controllers

[0126]

[0127] Table 2 Comparison of Control Performance between M-PI and PI Controllers

[0128] Table 2 shows that the arithmetic logic unit (ALU) using a covalently modified cyclic unidirectional structure can effectively reduce the settling time of the controller by taking advantage of the ultrasensitive response, reducing it from 234727.2 s to 88908.9 s, a reduction of 62.1%, and suppressing overshoot. The design and implementation of the covalently modified cyclic unidirectional structure ALU further promotes the modular design of biochemical molecular controllers. This section demonstrates the closed-loop control performance of the quasi-fuzzy controller with ultrasensitive response. Compared with M-PI, QFPI approximates the fuzzy control function through the structure of an approximate switch with ultrasensitive response. The closed-loop dynamic response of the M-PI controller and the QFPI controller is studied through numerical comparison. The parameter definitions of the M-PI control strategy and the QFPI control strategy based on CRNs are shown in Table V. For a clearer comparison, Table 3 again provides the parameters of the M-PI control strategy.

[0129]

[0130] Table 3. Parametric Representation of QFPI and M-PI Controllers

[0131] This invention aims to construct a modular molecular quasi-fuzzy controller, which not only meets the time performance requirements of biochemical molecular controllers but also promotes the modular design of molecular controllers. Compared with the M-PI control strategy, under the same parameters, the rise time of the QFPI strategy decreased by 5984.4 s from 88908.9 s, a reduction of 93.2%, and the settling time decreased from 109581 s to 7038 s, a reduction of 94%. Specific parameters are shown in Table 4.

[0132]

[0133] Table 4 Comparison of Control Performance between M-PI and PI Controllers

[0134] To verify the performance of the logic unit with ultra-sensitive response, this section compares the M-QFPI controller with the QFPI controller and the Brink controller. All reaction rates and total substrate values ​​involved in the CRN-based M-QFPI and Brink control strategies are shown in Table 5.

[0135]

[0136] Table 5. Parametric Representation of M-QFPI and Brink Controller

[0137]

[0138] Table 6. Comparison of control performance between M-QFPI, QFPI, and Brink controllers.

[0139] exist Figure 9 In the M-QFPI controller, the rise time and settling time decreased to 42.6s and 55.6s, respectively. Compared with the QFPI controller, the rise time was reduced by 99.2% and the settling time by 98%, and overshoot was eliminated. Compared with the Brink controller, the rise time was reduced by 88.8% and the settling time by 86.8%, with no overshoot. Compared with the BC-DPAR, the rise time was reduced by 81.2% and the settling time by 79%, with no overshoot. Specific parameters are shown in Table 6.

[0140] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0141] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A design and optimization method for an ultrasensitive quasi-fuzzy molecular controller based on CRNs, characterized in that, Includes the following steps: S1: A kinetic model simulating the biochemical process of phosphorylation is established using abstract chemical reaction networks (CRNs). S2: Constructing a molecular logic operator with ultrasensitive response characteristics based on a unidirectional covalent modification cycle mechanism; S3: A quasi-fuzzy PI controller QFPI is constructed using a dual-track covalently modified loop structure, and nonlinear control logic is applied to TS-like fuzzy rules through modular CRNs; S4: The initial quasi-fuzzy controller is designed to be single-tracked and simplified. An M-QFPI optimization scheme is proposed to overcome the limitations of finite-time regulation while reducing the number of biochemical molecular reactions.

2. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The CRNs model for the phosphorylation reaction in S1 is expressed as follows: Where V1, V2, V3, and V4 represent the reaction rates of the phosphorylation process, U represents the output of the intermediate species as a controller, B, D, and F represent the substrates, S represents the activating enzyme, and V and Y represent the enzyme-substrate complex and the product, respectively.

3. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The chemical reaction in the molecular logic operator in S2 is represented as follows: And based on the dynamics of mass action, its ordinary differential equation is obtained: Where K1 and K2 represent catalytic rates, K3 represents degradation rates, and K p and K d Indicates catalytic enzymes, U and U * These are the substrate and product of the catalytic reaction, respectively.

4. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The control logic of the quasi-fuzzy PI controller QFPI in S3 is equivalent to the following TS-type fuzzy rule: in, These are the error E and the integral result ΔE, respectively, representing the outputs of the QFPI controller under different conditions. This represents the components of the error E. This represents the component of the integral result ΔE.

5. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 4, characterized in that, The QFPI controller in S3 implements the fuzzy control rule through the following chemical reaction, specifically as follows: Where E1, E2, E3, and E4 are the inputs to the controller, R1, R2, R3, and R4 are the catalytic reaction rates, U is the output of the controller, and RARP is the production waste. And based on the dynamics of mass action, its ordinary differential equation is established, specifically expressed as: Where R is the reference value, RA represents the reference value component, Y is the output value, RY represents the output value component, kc, θc, mc, αc and βc represent the reaction rates of catalysis, degradation, and annihilation, respectively.

6. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The chemical reaction in the M-QFPI optimization scheme in S4 is specifically represented as follows: Where X1, X2, X3, and X4 represent the fractional products of RA and RY, and C and C # These are the substrate and product of the catalytic reaction, respectively.

7. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The dual-track covalent modification cycle structure in S3 is a chemical reaction network of dual-track covalent modification cycles, defined as a dual-track ultrasensitive response. When the input exceeds a certain threshold, the output increases rapidly, shortening the rise time and settling time of the quasi-fuzzy PI controller QFPI.

8. The design and optimization method of a CRNs-based ultrasensitive quasi-fuzzy molecular controller according to claim 1, characterized in that, The ultrasensitive molecular logic arithmetic unit constructed in S2 can shorten the adjustment time of the control system by more than 62.1% compared with the traditional dual-track arithmetic logic, and can suppress overshoot with an overshoot of 0.

Images