Determination of high sensitivity parameters of enzyme constrained metabolic network model and its optimization method

Abstract

The application discloses a high-sensitivity parameter determination and optimization method of an enzyme-constrained metabolic network model. First, a sensitivity analysis method is used to sort parameters in the model according to contributions to comparative growth rate prediction results from high to low, and parameters with higher contributions are selected for optimization. Then, a differential evolution algorithm with an adaptive mutation strategy is used for parameter optimization. The algorithm can adaptively select a mutation strategy to improve optimization efficiency. Comparative growth rate data under different growth conditions are obtained from a database, and part of the training set is selected from the data. Finally, a performance evaluation result of the optimized model is obtained through a flux variability and phase plane analysis method. The high-sensitivity parameter is a turnover number kcat parameter of an enzyme.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of biotechnology and information technology, and relates to the parameter sensitivity analysis of enzyme turnover number (kcat) in enzyme-constrained genome-scale metabolic networks, and a method for parameter optimization of high-sensitivity kcat sets using a difference evolution algorithm with an adaptive mutation strategy. Background Technology

[0002] Genome-scale metabolic network models (GSMMs) are powerful tools for characterizing cellular metabolic processes, systematically representing the relationships between metabolic reactions, metabolites, and proteins within cells. The core of a GSMM is a stoichiometric matrix composed of the relationships between metabolites and reactions. Rows in the matrix represent metabolites involved in microbial metabolism, and columns represent metabolic reactions. Positive coefficients in the matrix indicate that a reaction produces that metabolite, while negative coefficients indicate that a reaction consumes that metabolite. Typically, constraint-based solving algorithms can be used to construct linear programming models of GSMMs to study the relationship between genotype and phenotype. Flux balance analysis is commonly used for phenotypic prediction in GSMMs. This method, based on the steady-state assumption that metabolite concentrations do not change over time, defines a single-objective linear programming problem with the optimization objective of maximizing the specific growth rate. The solution yields a set of flux distributions. Improving the reliability and accuracy of these flux distributions can provide significant assistance for future digital cell-guided metabolic engineering.

[0003] To improve the simulation accuracy of GSMM (Genome-Scale Metabolic Network Model), enzyme-constrained genome-scale metabolic network model (ecGSMM) has been proposed. It is believed to effectively constrain reaction flux in GSMM by limiting enzyme dosage, thereby improving simulation accuracy. ecGSMM can be broadly divided into two parts: the GSMM itself and the enzyme turnover number (kcat). The enzyme turnover number (kcat) is a crucial kinetic parameter in the model. Using the enzyme's kcat value to expand the stoichiometric matrix of the GSMM allows for a very intuitive integration of proteomics data. As a parameter in the model, different kcat values ​​lead to different model phenotypic results, directly affecting prediction accuracy. Typically, in vitro measured kcat values ​​are used in metabolic models. However, due to the significant differences in enzyme kinetic parameters between in vivo and in vitro, and the fact that in vitro kcat cannot fully reflect the in vivo activity of yeast enzymes, the reliability of existing kcat values ​​has been questioned.

[0004] With the introduction of the whole-cell digital model concept, the importance of metabolic networks has further increased, and the requirements for the results of metabolic network models are becoming increasingly stringent. Therefore, to address the uncertainty of kcat in the model, parameter optimization methods can be considered. Using the parameter sizes in the database as a reference, optimization is performed within a certain range to make the model's prediction results more accurate. Since the number of kcat parameters in ecGSMM is very large, optimizing multiple parameters simultaneously would reduce optimization efficiency and make the optimization process more difficult. Therefore, sensitivity analysis is considered to select a subset of key kcats in the model. Sensitivity analysis involves proportionally changing the size of each parameter and calculating their impact on the objective function. Parameters are ranked according to their magnitude of influence; parameters with greater influence are considered more sensitive parameters in the model. Low-sensitivity parameters contribute little to the model performance or can be ignored. Therefore, when optimizing parameters, sensitivity analysis is first performed on all kcats in the model, and only the highly sensitive enzyme turnover number needs to be optimized.

[0005] In parameter optimization, the Differential Evolutionary Algorithm (DEA) is considered one of the effective methods. DEA is a simple and efficient heuristic parallel search algorithm for solving problems, possessing advantages such as fast convergence, few and simple control parameters, robust optimization results, and is a population-based global search algorithm. In the early stages of evolution, the large differences between individuals in the population result in a large perturbation, allowing the algorithm to search over a wide range. In the later stages of evolution, the algorithm tends to converge, the differences between individuals decrease, and the algorithm searches in the vicinity of individuals, exhibiting strong local search capabilities. DEA's ability to learn from individuals in the population gives it unparalleled performance compared to other evolutionary algorithms.

[0006] Considering that the parameter set after sensitivity analysis may still have a high dimensionality, an optimization strategy suitable for high-dimensional searches is adopted. In differential evolution algorithms, the mutation strategy is considered to directly affect the search direction and efficiency, and different mutation strategies are suitable for different search environments. Therefore, in a complex high-dimensional search space, using a single mutation strategy may reduce search efficiency. Thus, a differential evolution algorithm with an adaptive mutation strategy is employed. In each iteration, the mutation strategy of an individual is determined by the performance of each mutation strategy; that is, the better the mutation strategy, the larger the proportion of iterations, while the smaller the number of poorly performing mutation strategies. This ensures that the mutation strategy used in each iteration yields better results.

[0007] Finally, we analyzed the performance of the optimized models. We calculated the specific growth rate prediction error, model flux variability analysis, and phase plane analysis under various growth conditions. The flux variability analysis, by fixing the objective function and calculating a series of linear programming problems, determined the upper and lower bounds of each reaction in the model. The smaller the difference between the upper and lower bounds, the fewer suboptimal solutions the model might find near the optimal solution, indicating better model stability. Phase plane analysis analyzes how the optimal phenotype of interest will respond to changes in environmental conditions. By stepwise changing the nutrient uptake rate and fixing different reaction conditions, different specific growth rate results were obtained. A phase plane for cell growth was generated, which effectively represents the different stages of cell growth. Summary of the Invention

[0008] The purpose of this invention is to first use sensitivity analysis to select highly sensitive parameters kcat in the enzyme-constrained metabolic network model, and then optimize the model using a differential evolution algorithm with an adaptive mutation strategy to improve the model's various performance aspects.

[0009] To achieve the above-mentioned objectives, the specific technical solution of this invention is as follows:

[0010] A method for determining and optimizing high-sensitivity parameters of an enzyme-constrained metabolic network model is proposed. First, the parameters in the model are sorted from high to low according to their contribution to the growth rate prediction results using sensitivity analysis. Parameters with higher contributions are selected for optimization. Then, a differential evolution algorithm with an adaptive mutation strategy is used for parameter optimization. This algorithm can adaptively select mutation strategies to improve optimization efficiency. Specific growth rate data under different growth conditions are obtained from a database, and a portion of the training set is randomly selected. Finally, the performance of the optimized model is evaluated using flux variability and phase plane analysis methods.

[0011] The high-sensitivity parameter mentioned above is the enzyme turnover number (kcat) parameter, which is an important parameter in enzyme-constrained metabolic network models. The kcat parameter directly affects the performance of the metabolic network in various aspects, and optimizing kcat can improve the model's performance. However, since there are a large number of kcat parameters in the model, and optimizing high-dimensional parameters can affect optimization efficiency, using sensitivity analysis to identify parameters that contribute significantly to improving model performance and optimizing them can significantly improve efficiency.

[0012] Differential evolution algorithms employing adaptive mutation strategies can improve the optimization efficiency of evolutionary algorithms in high-dimensional problems, while avoiding the situation where a single mutation strategy cannot adjust the global search capability and the local search capability in real time in the later stages of evolution, thus causing the search to stagnate.

[0013] Furthermore, the sensitivity analysis is performed by comparing the results of multiple flux balance analyses:

[0014] The flux balance analysis described above can be expressed by the following formula:

[0015]

[0016] Where μ is the specific growth rate; S is the stoichiometric matrix of the microbial metabolic network; v is the vector composed of all reaction fluxes in the metabolic network; and u and l are the vectors composed of the upper and lower limits of reaction fluxes.

[0017] The parameter modification percentages were determined to be 50%, 90%, 110%, 150%, and 0% of the original values. For each kcat parameter modification, flux balance analysis was performed to obtain predicted specific growth rates under different growth conditions after parameter changes. The obtained specific growth rate predictions were then compared with specific growth rate data under different conditions in the database to calculate the error.

[0018]

[0019] Where μ is the specific growth rate reference value in the database. The specific growth rate prediction result is obtained by calculating after changing a certain kcat. Defined as the average relative error under a given growth condition after changing a certain kcat.

[0020] Furthermore, the high sensitivity parameter is determined based on the average relative error calculated after changing each kcat. The corresponding value for each kcat is... Sort the values ​​from highest to lowest. The larger the value, the greater the influence of the kcat on the model, and the higher its sensitivity to the model. A comprehensive comparison of strategies for changing different parameter ratios during sensitivity analysis is performed, and a search is conducted among five ranking results to find the parameter set that encompasses all highly sensitive kcats.

[0021] Furthermore, there exists a critical value to help determine the high-sensitivity parameter. The calculation results can span many orders of magnitude, demonstrating significant differences in sensitivity between different parameters. To search for as many high-sensitivity parameters as possible while avoiding a still large number of selected parameters, there exists a... The critical value is used to determine the high sensitivity parameter. It is believed that when... In 10 -9 Up to 10 -10 If a high-sensitivity parameter exists within the range, the critical value that can be reached can be calculated. If In 10 -10If so, it is considered to have a low contribution to the model and cannot be considered a high-sensitivity parameter; if higher than 10 -10 When this is the case, it can be considered a high-sensitivity parameter. In the context of... After sorting, you can use them in relation to 10 -10 The magnitude relationship can determine the set of high-sensitivity parameters.

[0022] Furthermore, a differential evolution algorithm with an adaptive mutation strategy is used to optimize the obtained high-sensitivity parameter set. The differential evolution algorithm has advantages such as fast convergence, few and simple control parameters, and robust optimization results, and is considered one of the effective swarm intelligence search algorithms. Therefore, an intelligent optimization approach is considered to determine the optimization values ​​of the high-dimensional optimization variables. An adaptive mutation strategy is applied in the differential evolution algorithm to alleviate the search stagnation problem that may occur when calculating high-dimensional problems. An appropriate mutation strategy is automatically selected for calculation based on the performance of each mutation strategy, avoiding the inability of a single mutation strategy to balance the global and local search capabilities during iteration. The optimal mutation strategy can be automatically evaluated to balance the search capabilities during iteration, improving the efficiency of search optimization.

[0023] Furthermore, sensitivity analysis was performed on the enzyme turnover number kcat in the enzyme-constrained metabolic network model, yielding a set of highly sensitive parameters. This reduced the dimensionality of the optimization problem and improved optimization efficiency. A differential evolution algorithm with an adaptive mutation strategy was used for parameter optimization, which facilitates the adoption of more reasonable mutation strategies in high-dimensional optimization problems, resulting in better optimization performance. The optimized model was evaluated from multiple perspectives, assessing the performance improvements in various aspects. This demonstrates that there is room for optimization of the enzyme turnover number kcat, providing optimization ideas and directions for other enzyme-constrained metabolic network models already constructed in other cells.

[0024] Compared with existing technologies, the method of the present invention has the following advantages and beneficial effects: (1) Sensitivity analysis of the enzyme turnover number kcat in the enzyme-constrained metabolic network model was performed, and a set of highly sensitive parameters was obtained, which reduced the dimension of the optimization problem and improved the optimization efficiency; (2) Differential evolution algorithm with adaptive mutation strategy was used for parameter optimization, which is conducive to adopting a more reasonable mutation strategy in high-dimensional optimization problems, thereby making the optimization results perform better; (3) The performance of the optimized new model was evaluated from multiple perspectives, and the performance improvement of the new model in various aspects was evaluated; (4) It shows that there is room for optimization of enzyme turnover number kcat, and provides optimization ideas and directions for enzyme-constrained metabolic network models that have been constructed in other cells. Attached Figure Description

[0025] Figure 1 The overall flowchart of the optimization algorithm in this invention;

[0026] Figure 2 Sensitivity analysis results of kcat parameters in the Saccharomyces cerevisiae enzyme-constrained metabolic network model;

[0027] Figure 3 The iterative results diagram and the specific growth rate prediction result diagram of the optimization algorithm in this invention;

[0028] Figure 4 Flux variability analysis diagram of the optimized model in this invention;

[0029] Figure 5 Phase plane analysis diagram of the optimized model in this invention. Detailed Implementation

[0030] The present invention will be further illustrated by the following examples:

[0031] The present invention provides a method for determining and optimizing high-sensitivity parameters of an enzyme-constrained metabolic network model, comprising the following steps:

[0032] Step 1: Perform sensitivity analysis on the parameters within the model, change the parameters within the model to predict the specific growth rate, and select the set of parameters with high sensitivity.

[0033] Step 2: Construct an optimizer using a differential evolution algorithm with an adaptive mutation strategy, perform iterative optimization calculations on a highly sensitive parameter set, and set the scope of the optimization search.

[0034] Step 3: Replace the optimized parameters into the original model, and perform specific growth rate error calculation, flux variability analysis, and phase plane analysis on the new model.

[0035] Specifically, for the sensitivity analysis described in step 1, the percentages of parameter changes were first determined to be 50%, 90%, 110%, 150%, and 0% of the original values. For each kcat parameter, a flux balance analysis was performed to obtain the predicted specific growth rate under different growth conditions after parameter changes.

[0036] Specifically, the flux balance analysis described in step 1 can be expressed by the following formula:

[0037]

[0038] Where μ is the specific growth rate; S is the stoichiometric matrix of the microbial metabolic network; v is the vector composed of all reaction fluxes in the metabolic network; and u and l are the vectors composed of the upper and lower limits of reaction fluxes.

[0039] Furthermore, the error is calculated between the obtained specific growth rate prediction results and the specific growth rate data under different conditions in the database:

[0040]

[0041] Where μ is the specific growth rate reference value in the database. The specific growth rate prediction result is obtained by calculating after changing a certain kcat. Defined as the average relative error under a given growth condition after changing a certain kcat.

[0042] Specifically, the high-sensitivity parameter set in step 1 is selected by sorting the parameters from highest to lowest based on the average relative error of each kcat. This set includes kcat parameters that have a significant impact on the model's specific growth rate.

[0043] Specifically, for the differential evolution algorithm with adaptive mutation strategy in step 2, there are five main mutation strategies: DE / rand / 1, DE / rand / 2, DE / best / 2, DE / current-to-best / 1, and DE / current-to-best / 2.

[0044]

[0045]

[0046]

[0047]

[0048]

[0049] Where r1, r2, r3, r4, r5 ∈ {1, 2, ..., NP} are different numbers randomly selected from the population catalog, and F ∈ [0, 1] is a random control parameter. It is the optimal individual in generation G.

[0050] Furthermore, the overall process of step 2 is as follows:

[0051] (1) Initialization: Randomly generate an initial population in the feasible solution space. Considering that the kcat measured in vitro still has some reference value, each kcat is initialized... cat The upper and lower bounds of the search are defined as [0.1k]. cat 1000k cat Determine the population size NP, crossover probability CR, and maximum number of iterations G. max Set the current generation to G=0 and Gs =0.2×G max Set the initial number of individuals for each mutation strategy:

[0052]

[0053] (2) Adaptive mutation strategy operator: If G < G s Considering that DE / rand / 1 has good global search properties, a single mutation strategy is adopted in the initial stage of the algorithm. If G = G s Then, the five mutation strategies DE / rand / 1, DE / rand / 2, DE / best / 2, DE / current-to-best / 1, and DE / current-to-best / 2 are randomly assigned to all individuals, and the number of each mutation strategy is [number missing]. If G > G s Calculate the average fitness function for each mutation strategy. Obtain the mutation strategies with the maximum and minimum average fitness. The method for updating the number of individuals for each mutation strategy is as follows:

[0054]

[0055] Among them, if It is the worst strategy and If the value is 1, then the number of individuals for the second worst strategy decreases by one, and so on. This ensures the number of individuals for each mutation strategy is [not specified].

[0056] (3) Boundary operations:

[0057]

[0058] Among them, B j ∈[0,1] is a random number.

[0059] (4) Cross operation:

[0060]

[0061] Among them, R j ∈[0,1] is a random number.

[0062] (5) Select operation:

[0063]

[0064] (6) Repeat steps 2-5 until the maximum number of iterations is reached.

[0065] Specifically, for the flux variability analysis in step 3, the flux variability value for each reaction is calculated according to the formula:

[0066] flux variability i =max flux i -min flux i

[0067] Where, max flux i and min flux i This is achieved by modifying the objective function using FBA, and by limiting the specific growth rate to within 1% of the maximum specific growth rate during the solution process. This involves solving the following series of linear programming problems:

[0068]

[0069] Among them, v i Let μ represent each reaction in the model, and μ be the specific growth rate.

[0070] Specifically, for the phase plane analysis in step 3, glucose and oxygen are used as independent variables to determine how the specific growth rate changes with glucose and oxygen. The glucose and oxygen uptake rates in the model are fixed, and the glucose and oxygen uptake reaction rates are increased in increments of 0.2 mmol / g DWh from 0 mmol / g DWh to 10 mmol / g DWh. Calculations are then performed to obtain the predicted maximum specific growth rate under different conditions. Phase plane diagrams of specific growth rate, glucose uptake, and oxygen uptake are plotted to observe the growth simulation results under different growth conditions.

[0071] For the 4261 enzyme turnover kcat parameters in the enzyme-constrained metabolic network model ecYeast 8.3.4 of Saccharomyces cerevisiae, 230 specific growth rate samples of Saccharomyces cerevisiae under different growth conditions were first collected from the database, and 150 samples were randomly selected to construct the training set. Sensitivity analysis was used to reduce the dimensionality of the 4261-dimensional kcat parameters, extracting parameters that showed high sensitivity in predicting the specific growth rate. The extracted high-sensitivity parameters were then optimized using a differential evolution algorithm with an adaptive mutation strategy. The performance of the optimized parameters and model was analyzed using flux variability analysis and phase plane analysis. Figure 1 The overall flowchart for optimizing the algorithm.

[0072] 1. Determination of high sensitivity parameters

[0073] Sensitivity analysis was performed on each kcat in the model across five scales. Based on the calculated... The values ​​revealed that they spanned multiple orders of magnitude. This implies that they hold different roles in the model, with some kcat values ​​playing a more crucial role. Therefore, we based... For different magnitudes, the number of kcat instances at different magnitudes was statistically analyzed, and a cumulative count curve was plotted. See [link / reference]. Figure 2 .

[0074] exist Figure 2 In the process, it was found that 10 appeared in all cases. -9 Up to 10 -10 The number of kcat instances changed abruptly. We analyzed five cases in 10... -9 The results generated five sets, with kcat set sizes of 1723, 495, 489, 636, and 669 for kcat scaling factors of 0, 0.5, 0.9, 1.1, and 1.5, respectively. To obtain as many of the more contributing kcats as possible, we took the union of these five sets, resulting in 1759 highly sensitive kcats, representing 41.3% of all kcats.

[0075] 2. Parameter Optimization of Differential Evolution Algorithm Based on Adaptive Mutation Strategy

[0076] Considering that the fitness function of each individual requires numerous linear programming calculations in evolutionary computation, we set the population size NP = 40, the crossover probability CR = 0.7, and the maximum number of iterations to 2000 generations. This is to achieve G... s =0.2×G max Previously, within the initial 400 generations of iteration, a DE / rand / 1 mutation strategy with good global search capabilities was used to maximize the search scope. After 400 generations, an appropriate mutation strategy was automatically selected for evolutionary computation based on the rules of an adaptive mutation strategy. After reaching the maximum number of iterations, the optimal model was selected for evaluation. Due to the randomness of evolutionary computation, the optimal solution obtained in each optimization may be different. Therefore, five repeated experiments were conducted, with 150 data points randomly selected from 230 nutrient combinations as the training set for each optimization to verify the stability of the method. The iteration curve of the optimization computation is shown below. Figure 3 As shown.

[0077] The optimized parameters were then incorporated into the original model. To further examine the improvement in the new model's performance in predicting specific growth rates, the new model was simulated in all 230 different Saccharomyces cerevisiae growth environments. The errors were calculated, and prediction plots were generated, as shown below. Figure 3 As shown, the training errors of the five optimizations were 22.4%, 25.6%, 28.2%, 26.7%, and 24.6%, respectively, and their errors on the entire dataset reached 29.2%, 26.0%, 26.2%, 26.5%, and 29.4%, respectively. This represents an improvement in accuracy compared to the original model's 41.9%.

[0078] 3. Model performance evaluation and analysis based on flux variability and phase plane

[0079] Flux variability can intuitively demonstrate the stability of a model. In flux variability analysis curves, a slope further to the left indicates that more fluxes have a smaller range of variation. This suggests that when solving optimization problems, the number of optimal or near-optimal solutions will decrease, demonstrating better stability. The flux variability of the optimized model was calculated using the formula, and the results are as follows: Figure 4 As shown, the overlap of the five calculation results for each optimization strategy is very high. Their variability analysis curves are basically consistent and appear to the left of the original model curve. This indicates that the five optimization results all have an improving effect on model variability, and also shows that although the parameters obtained in each optimization are different due to randomness, their improvement on model performance has good stability.

[0080] The optimized model was subjected to phase plane analysis to further analyze its performance. The main focus was on the effects of glucose and oxygen on the specific growth rate, and relevant phase planes were plotted, such as... Figure 5 As shown. For Figure 5 Analysis of all phase planes revealed that they can be divided into four sub-planes, each representing a different growth stage of the brewer's yeast. Figure 5 In this model, the connections between the various sub-phase planes are smoother, indicating that the model can effectively represent the transitions between cellular metabolic stages. Furthermore, their smaller areas at the top plateau phase suggest that the model can simulate more cell growth during secondary metabolic stages, making it more suitable for studying the transitions between cellular metabolic stages.

[0081] The sensitivity analysis in this invention involves comparing the results of multiple flux balance analyses. This method uses sensitivity analysis to identify the set of parameters that contribute significantly to model performance as variables to be optimized. Using specific growth rate datasets under different conditions as the training set, a differential evolution algorithm with an adaptive mutation strategy is employed to optimize the parameters. First, sensitivity analysis is performed on the model parameters, changing their magnitudes at multiple scales and calculating the changes in specific growth rate under various growth conditions. The set of parameters that maximizes the change in specific growth rate is selected. Then, a portion of the specific growth rate dataset under different conditions is randomly selected as the training set for the optimization problem. Next, a differential evolution algorithm with an adaptive mutation strategy is constructed to optimize the selected parameters. The mutation strategy for each individual parameter is determined by the performance of the strategy itself, ensuring that a more suitable mutation strategy is adopted in each iteration. Finally, the optimized parameters are updated in the original model. The error in specific growth rate prediction under various growth conditions, the flux variability analysis, and the phase plane analysis of the model are calculated, and the performance of the optimized parameters and the new model is evaluated.

[0082] In summary, the method of this invention can extract highly sensitive enzyme turnover parameters from enzyme-constrained metabolic network models, avoiding the problem of low optimization efficiency caused by excessive dimensionality. Furthermore, the use of an adaptive mutation strategy-based differential evolution algorithm for parameter optimization improves the efficiency of the optimization solution, and multiple experiments verify the stability of the method. Finally, flux variability and phase plane analysis are used to evaluate the performance of the new model, demonstrating that this method can effectively improve various performance aspects of the model. This provides a feasible approach for further improving the simulation accuracy of metabolic models, thereby facilitating the exploration of cellular metabolic processes.

Claims

1. A method for determining and optimizing high-sensitivity parameters of an enzyme-constrained metabolic network model, characterized in that, First, the parameters in the model are sorted from high to low according to their contribution to the growth rate prediction results using sensitivity analysis. The parameters with higher contributions are selected for optimization. Then, the differential evolution algorithm with an adaptive mutation strategy is used to optimize the parameters. It can adaptively select the mutation strategy to improve the optimization efficiency. The specific growth rate data under different growth conditions are obtained from the database and a portion of the training set is randomly selected. Finally, the performance evaluation results of the optimized model are obtained through flux variability and phase plane analysis. The high sensitivity parameter mentioned above is the enzyme turnover number kcat parameter; The sensitivity analysis is performed by comparing the results of multiple flux balance analyses: The flux balance analysis described above can be expressed by the following formula: ， Where μ is the specific growth rate; S is the stoichiometric matrix of the microbial metabolic network; v is the vector composed of all reaction fluxes in the metabolic network; and u and l are the vectors composed of the upper and lower limits of reaction fluxes. By varying the proportions of each kcat parameter, flux balance analysis was performed to obtain predicted specific growth rates under different growth conditions after parameter changes. The obtained specific growth rate predictions were then compared with specific growth rate data under different conditions in the database to calculate the error. ， Where μ is the specific growth rate reference value in the database. The specific growth rate prediction result is obtained by calculating after changing a certain kcat; Defined as the average relative error under a given growth condition after changing a certain kcat; The sensitivity analysis first determined that the percentages of parameter changes were 50%, 90%, 110%, 150%, and 0% of the original values. Then, for each kcat parameter, flux balance analysis was performed to obtain the predicted specific growth rate under different growth conditions after parameter changes. The high sensitivity parameter is determined based on the average relative error calculated after changing each kcat; the corresponding parameter for each kcat is... Sort the values ​​from highest to lowest. The larger the value, the greater the influence of kcat on the model, and the higher its sensitivity to the model. There exists a critical value to help determine the high-sensitivity parameter. The critical value is used to determine the high sensitivity parameter; when exist Within the range, a high-sensitivity parameter exists that allows for the calculation of the critical value to be reached; if exist If so, it is considered to have a low contribution to the model and cannot be considered a high-sensitivity parameter; if Higher than When it is, it is considered a high-sensitivity parameter; when it is... After sorting, based on their relationship with The magnitude relationship determines the set of high-sensitivity parameters; The differential evolution algorithm for the adaptive mutation strategy has five mutation strategies: DE / rand / 1, DE / rand / 2, DE / best / 2, DE / current-to-best / 1, and DE / current-to-best / 2: "DE / rand / 1": "DE / rand / 2": "DE / best / 2": "DE / current-to-best / 1": "DE / current-to-best / 2": ， Where r1, r2, r3, r4, r5 ∈ {1, 2, ..., NP} are different numbers randomly selected from the population catalog, and F ∈ [0, 1] is a random control parameter. It is the optimal individual in generation G.

2. The method for determining and optimizing high-sensitivity parameters of the enzyme-constrained metabolic network model according to claim 1, characterized in that, The differential evolution algorithm of the adaptive mutation strategy, (1) initialization operation: randomly generate an initial population in the feasible solution space; set each The upper and lower bounds of the search are defined as [0.1]. 1000 Determine the population size NP, crossover probability CR, and maximum number of iterations Gmax; set the current generation to G=0 and... Set the initial number of individuals for each mutation strategy: ； (2) Adaptive mutation strategy operator: If G < Considering that DE / rand / 1 has good global search properties, a single mutation strategy is adopted in the initial stage of the algorithm; if G = Then, the five mutation strategies DE / rand / 1, DE / rand / 2, DE / best / 2, DE / current-to-best / 1, and DE / current-to-best / 2 are randomly assigned to all individuals, and the number of each mutation strategy is [number missing]. If G > Calculate the average fitness function for each mutation strategy; obtain the mutation strategies with the maximum and minimum average fitness; the method for updating the number of individuals for each mutation strategy is as follows: ， Among them, if It is the worst strategy and If the value is 1, then the number of individuals for the second worst strategy decreases by one, and so on; this ensures the number of individuals for each mutation strategy. ; (3) Boundary operations: ， in, It is a random number; (4) Cross operation: ， in, It is a random number; (5) Select operation: ， (6) Repeat steps 2-5 until the maximum number of iterations is reached.

3. The method for determining and optimizing high-sensitivity parameters of the enzyme-constrained metabolic network model according to claim 1, characterized in that, The flux variability analysis calculates the flux variability for each reaction using the following formula: ， in, This is achieved by modifying the objective function using FBA, and by limiting the specific growth rate to within 1% of the maximum specific growth rate during the solution process. This involves solving the following series of linear programming problems: ， in, Let μ represent each reaction in the model, and μ be the specific growth rate.

4. The method for determining and optimizing high-sensitivity parameters of the enzyme-constrained metabolic network model according to claim 1, characterized in that, The phase plane analysis, using glucose and oxygen as independent variables, obtained the specific growth rate as a function of glucose and oxygen. The glucose and oxygen uptake rates of the model were fixed, and the glucose and oxygen uptake reaction rates were increased in increments of 0.2 mmol / g DW h from 0 mmol / g DW h to 10 mmol / g DW h. Calculations were performed to obtain the predicted maximum specific growth rate under different conditions. Phase plane diagrams of specific growth rate, glucose uptake, and oxygen uptake were plotted to observe the growth simulation results of the model under different growth conditions.

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