Optimization and Regulation Methods and Systems for Gene Switching Expression Processes Resisting Ribosome Number Perturbations

Abstract

This invention relates to the field of gene switching expression regulation technology, and in particular to a method and system for optimizing and regulating gene switching expression processes to resist ribosome number perturbations. The method includes: constructing a biological regulatory circuit based on the interactions between biomolecules in the switched expression of the regulated gene; constructing a mathematical equation describing the concentration changes of mRNA, sRNA-A, and GFP products according to the biological regulatory circuit; constructing a controller that enables the expression level of the regulated gene to resist ribosome perturbations in the cytoplasm; performing iterative calculations based on the controller to obtain a regulatory input value that ensures the concentration of the regulated gene's expression product meets stable conditions; and controlling the switched expression process of the regulated gene by regulating the input value, so as to maintain a stable concentration of the regulated gene's expression product even under fluctuations in the number of ribosomes in the cell ribosomes. This invention can effectively improve the stability and flexibility of the gene switching expression process and significantly enhance regulatory efficiency.

Description

Technical Field

[0001] This invention relates to the field of gene switching expression process regulation technology, and in particular to a method and system for optimizing and regulating gene switching expression process to resist perturbations in ribosome number. Background Technology

[0002] In the field of bioengineering, gene expression is influenced by a variety of factors in the cellular environment, which can lead to frequent switching of gene expression states during different reactions. For example, when the strength of the transcription promoter increases, a gene may switch from its current transcriptional state to a high-transcriptional state; or, under conditions of active cell growth and proliferation, in order to maintain a sufficient amount of functional proteins, the cell may reduce protein degradation, thus entering a low-degradation state. Therefore, the dynamic switching between multiple modes during gene expression is a very common phenomenon.

[0003] Current technologies for regulating gene switching expression processes have the following drawbacks:

[0004] First, the cost is high: relying on a large number of repetitive experiments to determine the amount of input to be controlled greatly increases the cost of control, involving the consumption of human, material and other resources.

[0005] Second, the regulatory efficiency is low: every time the gene expression state switches modes, a new regulatory input must be selected through experimentation, which is a cumbersome process and results in low regulatory efficiency.

[0006] Third, it lacks flexibility and universality: the designed regulatory inputs can only guarantee stability under fixed conditions, and are difficult to adapt to the dynamic changes of the system such as the intracellular environment. It has poor universality under different environmental conditions and lacks the ability to flexibly respond to changes. Summary of the Invention

[0007] To address the aforementioned technical problems, this invention provides a method and system for optimizing and regulating gene switching expression processes to resist perturbations in ribosome number. The regulation method includes the following steps:

[0008] S1: Based on the interaction between mRNA, the process product of regulated gene switching expression, and biomolecules such as ribosomes and sRNA-A, a biological regulatory loop for gene switching expression is constructed.

[0009] S2: Based on the biological regulatory circuit, construct a mathematical equation to describe the relationship between the concentration changes of mRNA, sRNA-A and GFP products;

[0010] S3: Based on the aforementioned mathematical equation, construct a controller that enables the expression level of regulated genes to resist disturbances caused by fluctuations in the number of available ribosomes in the cytoplasm;

[0011] S4: Based on the controller, perform iterative calculations to obtain dynamically updated regulatory input values ​​where the concentration of the expression product of the regulated gene meets stable conditions under an environment where the number of ribosomes in the cytoplasm fluctuates.

[0012] S5: By controlling the switching expression process of regulated genes through the amount of regulatory input after each update, it can maintain a stable concentration of the expression products of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

[0013] In one embodiment of the present invention, in S1, the method for constructing the biological regulatory circuit of the gene switching expression process is as follows:

[0014] The gene encoding the ECF32 protein is embedded into the expression sequence of a regulated gene, the expression product of which includes GFP protein and ECF32 protein. The ECF32 protein binds to the promoter PECF32 to form a transcription complex, which is transcribed to obtain sRNA. The sRNA is complementary to the target mRNA transcribed from the regulated gene to obtain double-stranded RNA.

[0015] In one embodiment of the present invention, in S2, the relational mathematical equation is as follows:

[0016]

[0017] Where x(t) = [m; s; y] describes the state during gene switching expression, m represents the concentration of mRNA, the final product of transcription, during gene switching expression, s represents the concentration of sRNA-A, the intermediate product of the constructed biological regulatory circuit, and y represents the concentration of the final protein product during the switching expression process; u(t) is the regulatory input in the regulatory circuit; B(x(t), t, r(t)) is the control coefficient matrix during gene switching expression; f[x(t), t, r(t)] is a nonlinear function; d represents the degree of fluctuation in the number of ribosomes in the cytoplasm; and r(t) represents the switching mode during gene switching expression.

[0018] In one embodiment of the present invention, the switching probability of the switching mode r(t) in the gene switching expression process is as follows:

[0019]

[0020] Where r(t) = i represents the gene expression switching mode i at time t, and r(t + Δt) = j represents the switching from mode i to mode j at time (t + Δt), where Δt > 0, and for i, j ∈ N, i ≠ j, π ij >0, and Let n be a finite set of integers, where n is the total number of switching modes in the gene expression switching process; for each mode i, the following condition is satisfied:

[0021]

[0022] In one embodiment of the present invention, in S3, the method of constructing a controller that enables the expression level of the regulated gene to resist disturbances from fluctuations in the number of available ribosomes in the cytoplasm includes:

[0023] In a non-perfectly flat space, the hypothetical spacing is used to represent the distance between the trajectories of the final product GFP concentration change trajectory of any adjacent gene switching expression under different environments with different numbers of available ribosomes in the cytoplasm.

[0024] And based on the rate of change of the aforementioned spacing, a judgment condition for reaching a steady state during the switching expression of regulated genes is constructed.

[0025] In one embodiment of the present invention, in a non-perfectly flat space, a hypothetical spacing is used to represent the spacing between the trajectories of GFP concentration changes of any adjacent gene switching expression under different environments with varying numbers of available ribosomes in the cytoplasm, including:

[0026] When r(t) = i, the differential form of the relational mathematical equation in equation (1) can be expressed using the hypothetical spacing as:

[0027]

[0028] Where, δ x Indicates the imaginary spacing. For δ x The derivative of represents the hypothetical distance δ during the switching expression of any two adjacent genes. x The rate of change that is constantly updated over time; A i (x(t), t, i, d) represents the hypothetical spacing δ x A state change matrix that is continuously updated over time;

[0029] Let the controlled input u(t) = K i x(t), K i Representing the control gain to be designed, the differential form of the controlled input u(t) is expressed as:

[0030] δ u =K i δ x (4)

[0031] Substituting (4) into (3), we obtain the closed-loop representation of regulated gene expression:

[0032]

[0033] Introduce a regression matrix M in a non-perfectly flat space. i (t), and M i (t) is a positive definite and symmetric matrix, therefore, when the number of ribosomes available in the cytoplasm is different, the distance V(δ) between the trajectories of the switching expression product GFP concentration change trajectory is significant. x (t,i) represents the following:

[0034] V(δ x ,t,i)=δ x T M i (t)δ x (6).

[0035] In one embodiment of the present invention, the spacing V(δ) x The method for calculating the rate of change of (t,i) is as follows: by introducing a weak differential operator The spacing V(δ) is obtained x The rate of change of (t, i) is expressed as follows:

[0036]

[0037] in, Represents the regression matrix M i (t) is the update rate over time.

[0038] In one embodiment of the invention, based on the rate of change of the spacing The criteria for determining whether a regulated gene has reached a stable state during the process of switching expression are as follows:

[0039]

[0040] In one embodiment of the present invention, in S4, the method for obtaining the dynamically updated regulatory input value u(t) where the concentration of the expression product of the regulated gene meets the stable condition under conditions of fluctuating ribosome numbers in the cytoplasm is as follows:

[0041] S41: Construct the first set of positive definite matrices and the second set of positive definite matrices, where the expression for the first set of positive definite matrices is as follows:

[0042] (F i +G i ) T (F i +G i ) = F i T F i +G i T F i +Fi T G i +G i T G i (9)

[0043] And let the positive definite matrix Q i =T i T T i The expression for the second set of positive definite matrices is as follows:

[0044] K t T Q i K i =K i T T i T T i K i (10)

[0045] S42: The judgment condition described in equation (8) includes K. i The item must meet the following conditions:

[0046] K i T B i T M i +M i B i K i <0 (11)

[0047] S43: Transform inequality (11) including:

[0048] The last term G in expression (9) T G equals the last term K in equation (10). i T T i T T i K i Solve for G i The expression:

[0049] G i =T i K i (12)

[0050] From equation (12), we can obtain G i T F i =K i T T i T Ti K i Let K i T T i T T i K i =K i T B i T M i Solve for F i The expression:

[0051] F i =(T i T ) -1 B i T M i (13)

[0052] From equation (13), we can obtain:

[0053] F i T F i =M i B i (T i ) -1 (T i T ) -1 B i T M i =M i B i Q i -1 B i T M i (14)

[0054] Let F i +G i =0, then T i K i +(T i T ) -1 B i T M i =0, so that Q i =T i T T i The control feedback gain K is obtained. i The calculation expression:

[0055] K i =-Q i-1 B i T M i (15)

[0056] Therefore, based on inequality (11), we can rearrange to obtain:

[0057] K i T B i T M i +M i B i K i =(F i +G i ) T (F i +G i )-2M i B i Q i -1 B i T M i <0 (16)

[0058] Let P i =2Q i -1 P i It is a constant positive quantitative parameter. According to equation (15), the final control feedback gain K is obtained. i The calculation expression:

[0059] K i =-0.5P i B i T M i (17)

[0060] S44: Substituting equation (16) into equation (8) yields the following linear matrix inequality:

[0061]

[0062] Multiply both sides of each term in equation (18) by M. i -1 We can obtain:

[0063]

[0064] Let W i =M i -1 , For W i The derivative of can be used to simplify equation (18):

[0065]

[0066] The final control feedback gain K i The calculation expression:

[0067] K i =-0.5P i B i T W i (twenty one)

[0068] Equations (20) and (21) are solved iteratively to obtain the control regression matrix M. i and quantitative parameter P i The control regression matrix M obtained in each iteration i and quantitative parameter P i Substituting into equation (17), we obtain the control feedback gain K. i Using the control feedback gain K i Update the control input u(t).

[0069] Based on the same inventive concept, the present invention also provides a gene switching expression process optimization and regulation system resistant to ribosome number perturbation, characterized in that it is used to implement the steps of the gene switching expression process optimization and regulation method resistant to ribosome number perturbation as described in any one of claims 1 to 9, wherein the gene switching expression process optimization and regulation system resistant to ribosome number perturbation includes the following modules:

[0070] The regulatory circuit construction module is used to construct the biological regulatory circuit of gene switching expression process based on the interaction between mRNA, the process product of regulated gene switching expression, and biomolecules such as ribosomes and sRNA-A.

[0071] The product concentration change correlation module is used to construct mathematical equations describing the relationship between the concentration changes of mRNA, sRNA-A and GFP products based on the biological regulatory circuit.

[0072] A controller design module is used to construct a controller based on the relational mathematical equation that enables the expression level of the regulated gene to resist disturbances from fluctuations in the number of available ribosomes in the cytoplasm.

[0073] The regulation input value solving module is used to perform iterative calculations based on the controller to obtain dynamically updated regulation input values ​​where the concentration of the expression product of the regulated gene meets the stable conditions under the environment of fluctuating ribosome numbers in the cytoplasm.

[0074] The gene regulation optimization module is used to control the switching expression process of regulated genes through the updated regulatory input, so as to maintain the stable concentration of the expression products of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

[0075] The technical solution of the present invention has the following advantages compared with the prior art:

[0076] Based on the ability to measure mRNA, sRNA-A, and GFP concentrations, this invention introduces control theory from engineering into the regulation of gene switching expression. By monitoring changes in GFP concentration and the magnitude of ribosome number perturbations during gene switching expression, a biological regulatory circuit model of gene switching expression is used to construct mathematical equations describing the rate of change in the concentrations of intermediate products (mRNA, sRNA-A) and the final product GFP. The required regulatory input values ​​are flexibly calculated in a nonlinear space using hypothetical intervals, thus eliminating the reliance on numerous repeated experiments. This invention significantly improves the efficiency, applicability, and stability of the gene switching expression regulation process, making it more precise and efficient. Attached Figure Description

[0077] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein...

[0078] Figure 1 This is a schematic diagram of a method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations, provided in Embodiment 1 of the present invention.

[0079] Figure 2 This is a graph showing the trajectory of changes in the concentrations of expression products GFP protein, mRNA, and sRNA-A when the number of ribosomes fluctuates;

[0080] Figure 3 This is a robust result of the gene switching expression process;

[0081] Figure 4 This is a schematic diagram illustrating the switching between different modes during gene expression.

[0082] Figure 5 This is a schematic diagram of a gene switching expression process optimization and regulation system that resists ribosome number perturbation provided in Embodiment 2 of the present invention;

[0083] Explanation of the reference numerals in the instruction manual: 100, Regulatory loop construction module; 200, Correlation module for changes in the concentration of each product; 300, Controller design module; 400, Regulatory input value solving module; 500, Gene regulation optimization module. Detailed Implementation

[0084] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0085] Example 1

[0086] like Figure 1 As shown, this invention provides a method for optimizing and regulating gene switching expression processes to resist perturbations in ribosome number. The method includes the following steps:

[0087] S1: Based on the interaction between mRNA, the process product of regulated gene switching expression, and biomolecules such as ribosomes and sRNA-A, a biological regulatory loop for gene switching expression is constructed.

[0088] S2: Based on the biological regulatory circuit, construct a mathematical equation to describe the relationship between the concentration changes of mRNA, sRNA-A and GFP products;

[0089] S3: Based on the aforementioned mathematical equation, construct a controller that enables the expression level of regulated genes to resist disturbances caused by fluctuations in the number of available ribosomes in the cytoplasm;

[0090] S4: Based on the controller, perform iterative calculations to obtain dynamically updated regulatory input values ​​where the concentration of the expression product of the regulated gene meets stable conditions under an environment where the number of ribosomes in the cytoplasm fluctuates.

[0091] S5: By controlling the switching expression process of regulated genes through the amount of regulatory input after each update, it can maintain a stable concentration of the expression products of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

[0092] As can be seen from the above technical solutions, this invention constructs a targeted biological regulatory loop by deeply analyzing the biomolecular interactions between mRNA, a process product of regulated gene switching expression, and ribosomes and sRNA-A. This allows for precise regulation of gene expression by closely linking it to key biomolecules in the gene switching process, achieving accurate regulation from the root and avoiding the blindness and inaccuracy of traditional regulatory methods. The mathematical equations describing the concentration changes among mRNA, sRNA-A, and GFP products based on the constructed biological regulatory loop can quantitatively describe the dynamic changes in the concentration of each substance during gene switching expression. This quantitative approach helps to deeply understand the intrinsic laws of gene expression. Through mathematical models, gene expression under different conditions can be predicted and simulated in advance, thereby enabling more targeted regulatory strategies. The dynamically updated regulatory input values ​​obtained through iterative calculations of the designed controller can be flexibly adjusted according to real-time changes in the number of ribosomes in the cell. This dynamic optimization method allows the regulatory process to adapt to changes in the intracellular environment in real time, always maintaining an optimal regulatory state.

[0093] Furthermore, in S1, the method for constructing the biological regulatory circuit of the gene switching expression process is as follows:

[0094] The gene encoding the ECF32 protein is embedded into the expression sequence of a regulated gene, the expression product of which includes GFP protein and ECF32 protein. The ECF32 protein binds to the promoter PECF32 to form a transcription complex, which is transcribed to obtain sRNA. The sRNA is complementary to the target mRNA transcribed from the regulated gene to obtain double-stranded RNA.

[0095] In step S2, based on the biological regulatory circuit, a mathematical equation is constructed to describe the relationship between the concentration changes of mRNA, sRNA-A, and GFP products, as follows:

[0096]

[0097] Where x(t) = [m; s; y] describes the state during gene switching expression, m represents the concentration of mRNA, the final product of transcription, during gene switching expression, s represents the concentration of sRNA-A, the intermediate product of the constructed biological regulatory loop, and y represents the concentration of the final protein product during the switching expression process; u(t) is the regulatory input in the regulatory loop; B(x(t), t, r(t)) is the control coefficient matrix during gene switching expression; f[x(t), t, r(t)] is a nonlinear function; d represents the degree of fluctuation in the number of ribosomes in the cytoplasm; and r(t) represents the switching mode of gene switching expression. The switching probability of the switching mode r(t) during the gene switching expression process is as follows:

[0098]

[0099] Where r(t) = i represents the gene expression switching mode i at time t, and r(t + Δt) = j represents the switching from mode i to mode j at time (t + Δt), where Δt > 0, and for i, j ∈ N, i ≠ j, π ij >0, and Let n be a finite set of integers, where n is the total number of switching modes in the gene expression switching process; for each mode i, the following condition is satisfied:

[0100]

[0101] In step S3, the method for constructing a controller that enables the expression level of the regulated gene to resist perturbations from fluctuations in the number of available ribosomes in the cytoplasm includes:

[0102] In a non-perfectly flat space, the hypothetical spacing is used to represent the distance between the trajectories of the final product GFP concentration change trajectory of any adjacent gene switching expression under different environments with different numbers of available ribosomes in the cytoplasm.

[0103] And based on the rate of change of the aforementioned spacing, a judgment condition for reaching a steady state during the switching expression of regulated genes is constructed.

[0104] Designing a controller in a non-perfectly flat space presents challenges. When the number of available free ribosomes in the cytoplasm varies, the distance between any two adjacent trajectories of GFP concentration changes is not necessarily a straight line, necessitating the calculation of the arc length. This increases computational complexity. However, by treating a small local space within the non-perfectly flat space as a perfectly flat space, the distance between each trajectory describing GFP concentration changes can be approximated as a straight line within this locally flat space.

[0105] To allow for the use of a consistent metric to calculate the distances in the local micro-spaces along each trajectory, a hypothetical spacing is used to represent the distance between the trajectories of changes in the concentration of the final product GFP from any adjacent gene switching expression under conditions of varying availability of ribosomes in the cytoplasm. This spacing includes:

[0106] When r(t) = i, the differential form of the relational mathematical equation in equation (1) can be expressed using the hypothetical spacing as:

[0107]

[0108] Where, δ x Indicates the imaginary spacing. For δx The derivative of represents the hypothetical distance δ during the switching expression of any two adjacent genes. x The rate of change that is constantly updated over time; A i (x(t), t, i, d) represents the hypothetical spacing δ x A state change matrix that is continuously updated over time;

[0109] Let the controlled input u(t) = K i x(t), K i Representing the control gain to be designed, the differential form of the controlled input u(t) is expressed as:

[0110] δ u =K i δ x (4)

[0111] Substituting (4) into (3), we obtain the closed-loop representation of regulated gene expression:

[0112]

[0113] Introduce a regression matrix M in a non-perfectly flat space. i (t), and M i (t) is a positive definite and symmetric matrix, therefore, when the number of ribosomes available in the cytoplasm is different, the distance V(δ) between the trajectories of the switching expression product GFP concentration change trajectory is significant. x (t,i) represents the following:

[0114] V(δ x ,t,i)=δ x T M i (t)δ x (6).

[0115] In one embodiment of the present invention, the spacing V(δ) x The method for calculating the rate of change of (t,i) is as follows: by introducing a weak differential operator The spacing V(δ) is obtained x The rate of change of (t, i) is expressed as follows:

[0116]

[0117] in, Represents the regression matrix M i (t) is the update rate over time.

[0118] Furthermore, to ensure the stability of GFP gene expression during switching processes, even when the number of available ribosomes in the cytoplasm fluctuates to varying degrees, it is necessary to guarantee the rate of change of the spacing described in equation (7). If the expression of the regulated gene is consistently negative, then the criterion for reaching a stationary state during the process of switching expression is:

[0119]

[0120] When the above conditions are met, the distance between any two adjacent GFP concentration change trajectories will gradually decrease in an environment with varying degrees of perturbation caused by the number of ribosomes. Therefore, even if the GFP gene is subjected to different perturbations during the switching expression process, it can return to the same stable expression concentration trajectory.

[0121] In step S4, the method for obtaining the dynamically updated regulatory input value u(t) where the concentration of the expression product of the regulated gene meets the stable condition under conditions of fluctuating ribosome numbers in the cytoplasm is as follows:

[0122] S41: Construct the first set of positive definite matrices and the second set of positive definite matrices, where the expression for the first set of positive definite matrices is as follows:

[0123] (F i +G i ) T (F i +G i ) = F i T F i +G i T F i +F i T G i +G i T G i (9)

[0124] And let the positive definite matrix Q i =T i T T i The expression for the second set of positive definite matrices is as follows:

[0125] K i T Q i K i =K i T T i T T i Ki (10)

[0126] S42: The judgment condition described in equation (8) includes K. i The item must meet the following conditions:

[0127] K i T B i T M i +M i B i K i <0 (11)

[0128] S43: Transform inequality (11) including:

[0129] The last term G in expression (9) T G equals the last term K in equation (10). i T T i T T i K i Solve for G i The expression:

[0130] G i =T i K i (12)

[0131] From equation (12), we can obtain G i T F i =K i T T i T T i K i Let K i T T i T T i K i =K i T B i T M i Solve for F i The expression:

[0132] F i =(T i T ) -1 B i T M i (13)

[0133] From equation (13), we can obtain:

[0134] F i T F i =M i B i (T i ) -1 (T i T ) -1 B i T M i =M i B i Q i -1 B i T M i (14)

[0135] Let F i +G i =0, then T i K i +(T i T ) -1 B i T M i =0, so that Q i =T i T T i The control feedback gain K is obtained. i The calculation expression:

[0136] K i =-Q i -1 B i T M i (15)

[0137] Therefore, based on inequality (11), we can rearrange to obtain:

[0138] K i T B i T M i +M i B i K i =(F i +G i ) T (F i +G i )-F i T Fi -K i T Q i K i

[0139] =(F i +G i ) T (F i +G i )-2M i B i Q i -1 B i T M i <0 (16)

[0140] Let P i =2Q i -1 P i It is a constant positive quantitative parameter. According to equation (15), the final control feedback gain K is obtained. i The calculation expression:

[0141] K i =-0.5P i B i T M i (17)

[0142] S44: Substituting equation (16) into equation (8) yields the following linear matrix inequality:

[0143]

[0144] Multiply both sides of each term in equation (18) by M. i -1 We can obtain:

[0145]

[0146] Let W i =M i -1 , For W i The derivative of can be used to simplify equation (18):

[0147]

[0148] The final control feedback gain K i The calculation expression:

[0149] K i =-0.5P i Bi T W i (twenty one)

[0150] It can be observed that inequality (20) can be continuously updated according to the changes in time and GFP concentration, therefore the obtained regression matrix M i and quantitative parameter P i It can also continuously change with time and GFP concentration. Correspondingly, the final calculated control feedback gain K... i This also becomes a continuously updated dynamic value at every moment. Leveraging this characteristic, the controller can regulate the dynamic changes in GFP gene expression during the switching process through continuous real-time adjustments, thereby effectively resisting disturbances caused by fluctuations in ribosome count and ensuring the stability and accuracy of the gene switching expression process.

[0151] Equations (20) and (21) are solved iteratively to obtain the control regression matrix M. i and quantitative parameter P i The control regression matrix M obtained in each iteration i and quantitative parameter P i Substituting into equation (17), we obtain the control feedback gain K. i Using the control feedback gain K i Update the control input u(t).

[0152] When the method proposed in this invention is applied to the switching expression process of the GFP gene, the mathematical model can be expressed as follows through analysis of the biological regulatory circuit:

[0153] dx1=(u-θ*x1*x2)-δ*x1

[0154] dx2=(TS*u_u*x3-θ*x1*x2)-δ*x2

[0155] dx3=R*(x1 / K p )*(1-d)-γ*x3

[0156] Where x1, x2, and x3 represent the concentrations of GFP / ECF32 mRNA (m), sRNA (s), and protein (y) generated by the regulated gene, respectively; u represents the transcription promoter strength of the regulated gene; θ represents the degradation rate of the mRNA-sRNA complex; the RNA degradation rate is denoted as δ; TS represents the promoter strength of the sRNA; u represents the control input to be designed; R represents the translation rate of the regulated gene; K prepresents the dissociation constant of the ribosome binding site for the protein of regulated gene expression; γ represents the degradation rate of the protein produced by the regulated gene; d represents the reduction ratio of available ribosomes in the cell, and 0 < d < 1. When d = 0, it means that the number of ribosomes does not fluctuate; the larger d is, the greater the fluctuation of the number of free ribosomes available in the cell.

[0157] The initial state of the selected system is [0; 0; 0] T , the strength u of the transcription promoter is 15, and the perturbation amount from the ribosome number is added at the middle time of the simulation, and the value is: d = 0.3. However, in the case of active cell growth and proliferation, in order to maintain more functional proteins, the cell may reduce the degradation of proteins, which will cause the gene switching expression process to enter the low degradation state. At this time, the degradation rate of the GFP protein switches from γ to 0.01 from 0.02; the degradation rate δ of the unstable double-stranded RNA switches from 0.05 to 0.02. And the switching probability of the GFP gene between the two modes is:

[0158]

[0159] To make the evaluation of the robustness of gene expression in the regulated transcription device more intuitive, the following formula for calculating the system robustness is proposed:

[0160]

[0161] The exact differential form of the system model is obtained through Equation (5), and then the mathematical equation inequality (20) is solved to obtain the control regression matrix M i and the quantitative parameter P i , and then substitute them into Equation (21) to find the control feedback gain K at the next time i .

[0162] Figure 2 Shows the change of the state trajectory of the gene switching expression process when facing ribosome perturbation. With the control feedback gain K designed by the present invention i , the expression process can be effectively regulated. In Figure 2 , the three trajectories from top to bottom respectively represent the concentration change trends of the product protein GFP, the intermediate product mRNA-A, and sRNA-A. It can be clearly seen that even if the ribosome number changes dynamically at the middle time, the concentration of the product protein GFP does not show a significant attenuation oscillation phenomenon.

[0163] To further illustrate this phenomenon, it can be found from Figure 3 that during the switching expression process of the GFP gene, the robustness of its expression process can reach 91.478%. In addition, Figure 4This demonstrates the switching between different modes during GFP gene expression.

[0164] Based on the above, this method, grounded in the ability to measure mRNA, sRNA-A, and GFP concentrations, determines the feedback control gain suitable for the GFP gene switching expression process through mathematical models and theoretical calculations, thus eliminating the reliance on numerous repeated experiments. Simultaneously, it flexibly calculates the required regulatory input values ​​based on the magnitude of ribosomal perturbation and the GFP concentration. This method significantly improves the efficiency, applicability, and stability of the gene switching expression regulation process, making it more precise and efficient. Compared to traditional methods that rely on numerous repeated experiments to select control variables, this optimized gene switching expression regulation strategy can dynamically calculate regulatory parameters based on the amplitude of ribosomal perturbation without requiring extensive experimental data. This method not only significantly reduces experimental costs but also effectively improves regulatory efficiency, providing a more efficient and flexible solution for gene expression regulation.

[0165] Example 2

[0166] Based on the same inventive concept as in Example 1, this invention also provides a gene switching expression process optimization and regulation system resistant to ribosome number perturbations, used to implement the steps of the gene switching expression process optimization and regulation method resistant to ribosome number perturbations described in Example 1. Figure 5 As shown, the gene switching expression process optimization and regulation system that resists ribosome number perturbation includes the following modules:

[0167] The regulatory circuit construction module 100 is used to construct a biological regulatory circuit for the gene switching expression process based on the interaction between the process product mRNA in the regulated gene switching expression and the biomolecules ribosome and sRNA-A.

[0168] The product concentration change correlation module 200 is used to construct mathematical equations describing the relationship between the concentration changes of mRNA, sRNA-A and GFP products based on the biological regulatory circuit.

[0169] The controller design module 300 is used to construct a controller based on the relational mathematical equation, which enables the expression level of the regulated gene to resist disturbances from fluctuations in the number of available ribosomes in the cytoplasm.

[0170] The regulation input value solving module 400 is used to perform iterative calculations based on the controller to obtain dynamically updated regulation input values ​​where the concentration of the expression product of the regulated gene meets the stable conditions under the environment of fluctuating number of ribosomes in the cytoplasm.

[0171] The gene regulation optimization module 500 is used to control the switching expression process of regulated genes through the regulatory input amount after each update, so as to maintain the stable concentration of the expression product of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

[0172] This embodiment proposes a gene switching expression process optimization and regulation system to resist ribosome number perturbation. This system is used to implement the aforementioned gene switching expression process optimization and regulation method to resist ribosome number perturbation. Therefore, the specific implementation of the gene switching expression process optimization and regulation system to resist ribosome number perturbation can be found in the embodiment section of the aforementioned gene switching expression process optimization and regulation method to resist ribosome number perturbation. For example, the regulation loop construction module 100, the product concentration change correlation module 200, the controller design module 300, the regulation input value solving module 400, and the gene regulation optimization module 500 are respectively used to implement steps S1, S2, S3, S4, and S5 in the gene switching expression process optimization and regulation method to resist ribosome number perturbation described in Embodiment 1. Therefore, its specific implementation can be referred to the description of the corresponding embodiments. To avoid redundancy, it will not be repeated here.

[0173] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0174] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0175] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0176] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0177] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for optimizing and regulating gene switching expression processes to resist perturbations in ribosome number, characterized in that, Includes the following steps: S1: Based on the interaction between mRNA, the process product of regulated gene switching expression, and biomolecules such as ribosomes and sRNA-A, a biological regulatory loop for gene switching expression is constructed. S2: Based on the aforementioned biological regulatory circuit, construct the mathematical equations describing the relationship between the concentration changes of mRNA, sRNA-A, and GFP products, as follows: (1)； in, Used to describe the state during gene switching expression. This indicates the concentration of mRNA, the final product of the transcription phase, during gene switching expression. This indicates the concentration of sRNA-A, an intermediate product of the constructed biological regulatory circuit. This indicates the concentration of the final protein product in the switching expression process; This refers to the control quantity to be input into the control loop; This is the control coefficient matrix for the gene switching expression process; It is a nonlinear function; This indicates the degree of fluctuation in the number of ribosomes in the cytoplasm; This indicates the switching mode in the gene expression switching process; S3: Based on the aforementioned mathematical equation, a controller is constructed that enables the expression level of regulated genes to resist disturbances caused by fluctuations in the number of available ribosomes in the cytoplasm, the method comprising: In a non-perfectly flat space, hypothetical spacing is used to represent the distance between the trajectories of GFP concentration changes in the final product of any adjacent gene switching expression under different environments with varying numbers of available ribosomes in the cytoplasm. This includes: exist Then, using the hypothetical spacing, the differential form of the relational mathematical equation in equation (1) can be expressed as: = + (3)； in, Indicates the imaginary spacing. for The derivative of represents the hypothetical distance during the switching expression of any two adjacent genes. The rate of change that updates over time; Indicates imaginary spacing A state change matrix that is constantly updated over time; i represents the switching mode of the gene expression switching process; Control the input volume , This represents the control gain to be designed, and the control input quantity is obtained. The differential form is expressed as: (4); Substituting (4) into (3), we obtain the closed-loop representation of regulated gene expression: (5)； Introducing a regression matrix in a non-perfectly flat space ,and The matrix is ​​positive definite and symmetric, therefore the spacing between the trajectories of GFP concentration changes when the number of available ribosomes in the cytoplasm varies. It is expressed as follows: (6)； And based on the rate of change of the aforementioned spacing, a judgment condition for reaching a steady state during the switching expression of regulated genes is constructed; S4: Based on the controller, perform iterative calculations to obtain dynamically updated regulatory input values ​​where the concentration of the expression product of the regulated gene meets stable conditions under an environment where the number of ribosomes in the cytoplasm fluctuates. S5: By controlling the switching expression process of regulated genes through the amount of regulatory input after each update, it can maintain a stable concentration of the expression products of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

2. The method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations according to claim 1, characterized in that, In S1, the method for constructing the biological regulatory circuit of gene switching expression process is as follows: The gene encoding the ECF32 protein is embedded into the expression sequence of a regulated gene, the expression product of which includes GFP protein and ECF32 protein. The ECF32 protein binds to the promoter PECF32 to form a transcription complex, which is transcribed to obtain sRNA. The sRNA is complementary to the target mRNA transcribed from the regulated gene to obtain double-stranded RNA.

3. The method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations according to claim 1, characterized in that, The switching mode of the gene switching expression process The transition probabilities are as follows: (2)； in, Indicates in The switching mode of gene expression switching process at a given time is as follows: , Indicates in At this moment, by pattern Switch to mode , ,for ,and N = {1, 2, 3, ..., n} is a finite set of integers, and n is the total number of switching modes in the gene expression switching process; for each mode i, the following condition is satisfied: .

4. The method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations according to claim 1, characterized in that, The spacing The rate of change is calculated by introducing a weak differential operator. The spacing is obtained. The rate of change is expressed as follows: (7)； in, Representing the regression matrix Update rate over time.

5. The method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations according to claim 4, characterized in that, According to the rate of change of the spacing The criteria for determining whether a regulated gene has reached a stable state during the switching expression process are as follows: (8)。 6. The method for optimizing and regulating gene switching expression processes to resist ribosome number perturbations according to claim 5, characterized in that, In S4, the dynamically updated regulatory input values ​​were obtained, ensuring that the concentration of the expression product of the regulated gene met the stable conditions under conditions of fluctuating ribosome numbers in the cytoplasm. The method is as follows: S41: Construct the first set of positive definite matrices and the second set of positive definite matrices, where the expression for the first set of positive definite matrices is as follows: (9) And let the positive definite matrix The expression for the second set of positive definite matrices is as follows: (10)； S42: The inclusion of the judgment condition described in equation (8) The item must meet the following conditions: (11)； S43: Transform inequality (11) including: The last term in expression (9) Equals the last term in equation (10) Solve The expression: = (12) From equation (12), we can obtain = ,make Solve The expression: = (13); From equation (13), we can obtain: = = (14); make =0, then we have ,make To obtain the control feedback gain The calculation expression: =- (15); Therefore, based on inequality (11), we can simplify to obtain: = - (16); make , It is a constant positive quantitative parameter. According to equation (15), the control feedback gain is obtained. The calculation expression: =- (17); S44: Substituting equation (16) into equation (8) yields the following linear matrix inequality: (18); Multiply both sides of each term in equation (18) We can obtain: (19); make = , for The derivative of can be used to simplify equation (18): (20); The final control feedback gain The calculation expression: =- (twenty one); Equations (20) and (21) are solved iteratively to obtain the control regression matrix. and quantitative parameters The control regression matrix obtained in each iteration and quantitative parameters Substituting into equation (17), we obtain the control feedback gain. Utilizing the control feedback gain Update and regulate input volume .

7. A gene switching expression process optimization and regulation system resistant to ribosome number perturbations, characterized in that, The steps for implementing the method for optimizing and regulating gene switching expression processes against ribosome number perturbations as described in any one of claims 1 to 6, wherein the system for optimizing and regulating gene switching expression processes against ribosome number perturbations comprises the following modules: The regulatory circuit construction module is used to construct the biological regulatory circuit of gene switching expression process based on the interaction between mRNA, the process product of regulated gene switching expression, and biomolecules such as ribosomes and sRNA-A. The product concentration change correlation module is used to construct mathematical equations describing the relationship between the concentration changes of mRNA, sRNA-A and GFP products based on the biological regulatory circuit. A controller design module is used to construct a controller based on the relational mathematical equation that enables the expression level of the regulated gene to resist disturbances from fluctuations in the number of available ribosomes in the cytoplasm. The regulation input value solving module is used to perform iterative calculations based on the controller to obtain dynamically updated regulation input values ​​where the concentration of the expression product of the regulated gene meets the stable conditions under the environment of fluctuating ribosome numbers in the cytoplasm. The gene regulation optimization module is used to control the switching expression process of regulated genes through the updated regulatory input, so as to maintain the stable concentration of the expression products of regulated genes even when the number of ribosomes in the cell nucleus fluctuates.

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