A multifunctional enzyme regulation network function balance robustness analysis system

Abstract

This invention relates to the field of enzyme network analysis technology, specifically a robust system for analyzing the functional balance of a multifunctional enzyme regulatory network. The system includes a network topology analysis module, a graph generation module, a flux balance analysis module, a functional simulation module, a robustness curve fitting module, and a report generation module. It identifies key nodes and vulnerable paths in the target regulatory network; constructs a structural feature association graph; performs flux balance analysis on the target regulatory network to obtain functional flux distribution data; simulates the functional operation of the target regulatory network and quantifies the output efficiency of the simulation results to obtain the core function maintenance degree; fits the perturbation trend of the core function maintenance degree to obtain a functional balance robustness curve; and analyzes the decay mode of the functional balance robustness curve to generate a robustness analysis report of the target regulatory network. This invention can improve the efficiency of functional balance robustness analysis of a multifunctional enzyme regulatory network.

Description

Technical Field

[0001] This invention relates to the field of enzyme network analysis technology, and in particular to a robust analysis system for the functional balance of multifunctional enzyme regulatory networks. Background Technology

[0002] In the field of enzyme regulatory network analysis, robustness analysis of the functional balance of multifunctional enzyme regulatory networks is a key link in controlling the network's operational status and ensuring the stability of its core functions. However, existing technologies have not yet formed a systematic analytical logic from network structure analysis to feature map construction. This makes it impossible to accurately identify key nodes and vulnerable paths in the regulatory network, nor can it effectively integrate network topology attributes and flux characteristics. Consequently, it is difficult to construct feature maps that reflect the relationship between the network's core structure and functions. This results in a lack of accurate structural foundation for subsequent flux analysis and functional simulation, directly affecting the overall accuracy of robustness analysis.

[0003] In existing technologies, the flux balance analysis results deviate from the actual network operating state, and there is a lack of professional analytical capabilities for robustness curve decay patterns. As a result, the analysis results generated are difficult to objectively and comprehensively reflect the actual functional balance robustness characteristics of the control network. Summary of the Invention

[0004] To achieve the above objectives, the present invention provides a robust analysis system for the functional balance of a multifunctional enzyme regulatory network, characterized in that the system includes a network topology analysis module, a graph generation module, a flux balance analysis module, a functional simulation module, a robust curve fitting module, and a report generation module, wherein: The network topology analysis module is used to perform topology correlation analysis on the target control network and identify key nodes and vulnerable paths in the target control network. The graph generation module is used to embed network structure relationships between key nodes and vulnerable paths to obtain a structural feature association graph of the target regulation network. The flux balance analysis module is used to perform flux balance analysis on the target control network and obtain the functional flux distribution data of the target control network. The functional simulation module is used to simulate the functional operation of the target control network based on the structural feature correlation map and functional flux distribution data, and to quantify the output efficiency of the simulation results to obtain the core functional maintenance degree of the target control network. The robust curve fitting module is used to fit the perturbation trend of the core function maintenance degree to obtain the functional balance robustness curve of the target control network. The report generation module is used to analyze the decay mode of the functional balance robustness curve to generate a balance robustness analysis report of the target control network.

[0005] In a preferred embodiment, when the network topology analysis module performs topology correlation analysis on the target control network and identifies key nodes and vulnerable paths in the target control network, it is specifically used for: Acquire the topology connectivity data of the target control network; Measure the node influence of the topology connectivity data to obtain the node centrality index of the topology connectivity data; Based on the node centrality index, the nodes of the target control network are prioritized to obtain the key nodes of the target control network. Based on the topological connection relationship of the target control network, starting from the key node, the target control network is traversed to obtain the connection path of the target control network. Vulnerability risk assessment is performed on connectivity paths to identify vulnerable paths in the target control network.

[0006] In a preferred embodiment, when the graph generation module performs network structure relationship embedding on key nodes and vulnerable paths to obtain the structural feature association graph of the target regulation network, it is specifically used for: Using key nodes as graph nodes and vulnerable paths as graph connecting edges, an initial structural graph of the target regulation network is constructed. Two-dimensional statistical analysis was performed on key nodes to obtain the number of connections and the frequency of path traversal of key nodes; Historical flux fluctuation analysis is performed on vulnerable paths to obtain their historical flux fluctuation attributes. The number of connections and the frequency of path traversal are integrated into a set of topological attributes for the target control network; According to the preset mapping rules, joint attribute mapping is performed on the topological attribute set and historical flux fluctuation attributes to obtain the structural feature association map of the target control network.

[0007] In a preferred embodiment, when the map generation module performs joint attribute mapping on the topological attribute set and historical flux fluctuations according to preset mapping rules to obtain the structural feature association map of the target regulation network, it is specifically used for: A correlation matching analysis was performed on the topological attribute set and the historical flux fluctuation attributes to obtain the correspondence between the topological attribute set and the historical flux fluctuation attributes; Based on the correspondence, the topological attributes and historical flux fluctuation attributes are fused to obtain the joint attribute set of the target regulation network. Based on the preset mapping rules, the joint attribute set of points and edges is embedded into the initial structural graph to obtain the structural feature association graph of the target control network.

[0008] In a preferred embodiment, when the balance analysis module performs flux balance analysis on the target control network to obtain functional flux distribution data of the target control network, it is specifically used for: The topology of the target control network is analyzed to obtain the connection constraints and historical operating flux of the target control network. Based on connectivity constraints, a constrained flux analysis is performed on historical operational fluxes to obtain the steady-state flux distribution of the target control network. Based on the functional paths in the target control network, the path contribution of the steady-state flux distribution is analyzed to obtain the functional flux distribution data of the target control network.

[0009] In a preferred embodiment, when the balance analysis module performs path contribution analysis on the steady-state flux distribution based on the functional paths in the target control network to obtain the functional flux distribution data of the target control network, it is specifically used for: Functional pathway retrieval is performed on the target regulation network to obtain its functional paths. Based on the nodes and connecting edges of the functional path, the path local flux data of the functional path in the steady-state flux distribution are filtered out. Functional flux aggregation is performed on the local flux data of the path to obtain the functional flux distribution data of the target control network.

[0010] In a preferred embodiment, when the functional simulation module performs functional simulation of the target regulation network based on structural feature correlation maps and functional flux distribution data, it is specifically used for: Using structural feature correlation maps as the network topology framework and functional flux distribution data as the initial load, a dynamic operation simulation network for the target regulation network is constructed. Based on the relationship between nodes and edges in the dynamic simulation network, the internal dynamic control rules of the target control network are analyzed. Based on the internal dynamic control rules, the dynamic operation simulation network is iteratively updated. During the iterative state update process, the overall functional output flux of the dynamically running simulation network is continuously tracked; When the overall functional output flux reaches the convergence state, the final functional output flux of the dynamically running simulation network is recorded, and the final functional output flux is output as the simulation result.

[0011] In a preferred embodiment, when the functional simulation module performs output efficiency quantification on the simulation results to obtain the core functional maintenance of the target control network, it is specifically used for: Obtain the historical best output efficiency of the target control network; The ratio of the simulated result to the historical best output efficiency is determined as the simulated relative efficiency ratio of the target control network. Structural connectivity is evaluated on the structural feature association graph to obtain the topological connectivity coefficients of the structural feature association graph; Perform flux statistical analysis on the functional flux distribution data to obtain the critical path flux ratio of the functional flux distribution data; Based on the preset weight configuration, the relative efficiency ratio, topological connectivity coefficient and critical path throughput ratio after simulation are weighted and fused to obtain the core function maintenance degree of the target control network.

[0012] In a preferred embodiment, when the robust curve fitting module performs perturbation trend fitting on the core function maintenance degree to obtain the functional balance robustness curve of the target regulation network, it is specifically used for: The core function maintenance is subjected to simulated perturbation, and the perturbation response of the core function maintenance after the perturbation is recorded to obtain the dynamic response sequence of the core function maintenance after the perturbation. Nonlinear regression fitting is performed on the dynamic response sequence to obtain the initial fitting curve of the dynamic response sequence; The initial fitted curve is smoothed to obtain the functional balance robustness curve of the target regulatory network.

[0013] In a preferred embodiment, when the report generation module performs attenuation mode analysis on the functional balance robustness curve to generate a balance robustness analysis report of the target control network, it is specifically used for: Inflection point detection analysis is performed on the functional balance robustness curve to identify key decay characteristic points of the functional balance robustness curve; Based on the distribution of key decay characteristic points, the functional balance robustness curve is divided into trend intervals to obtain the decay stage and plateau period of the functional balance robustness curve. Based on the coordinate data of key attenuation feature points, the attenuation parameters of the attenuation stage are deconstructed to obtain the attenuation rate and attenuation amplitude of the attenuation stage. By combining the decay phase, plateau period, decay rate, and decay magnitude, a balance robustness analysis report of the target control network is generated.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention, through the systematic collaborative operation of six modules including network topology analysis, graph generation, and flux balance analysis, forms a complete analysis system from network structure analysis to robustness report generation. It accurately realizes core operations such as key node and vulnerable path identification, structural feature association graph construction, and functional flux distribution analysis. It progressively completes functional simulation, robust curve fitting, and decay mode analysis, making the robustness analysis of enzyme regulatory network functional balance a standardized process, effectively improving the overall efficiency and accuracy of the analysis work.

[0015] 2. Each module of this invention is designed to meet the core requirements of enzyme regulatory network analysis. Topology analysis lays the structural foundation for subsequent analysis, map generation realizes the fusion of structural and flux attributes, flux balance analysis provides accurate functional flux data, the functional simulation module quantifies the maintenance of core functions, robustness curve fitting intuitively reflects the functional change trend under perturbation, and the report generation module completes the systematic analysis of decay laws. This invention achieves the integrated realization of robustness analysis from structure to function, and from simulation to evaluation, providing scientific and comprehensive data analysis support for the stable operation and optimization of enzyme regulatory networks. Attached Figure Description

[0016] Figure 1 This is a system architecture diagram of a multifunctional enzyme regulatory network functional balance robustness analysis system provided in an embodiment of the present invention.

[0017] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments belong to some, but not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “said” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms, and “multiple” generally includes at least two unless the context clearly indicates otherwise.

[0020] Depending on the context, the word "if" or "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0021] Furthermore, the timing of the steps in the following method embodiments is merely an example and not a strict limitation.

[0022] In practice, the server-side equipment deployed in a multifunctional enzyme regulatory network functional balance robustness analysis system may consist of one or more devices. This system can be implemented as a business instance, a virtual machine, or hardware devices. For example, it can be implemented as a business instance deployed on one or more devices in a cloud node. Simply put, it can be understood as software deployed on a cloud node, providing a robust analysis system for multifunctional enzyme regulatory network functional balance to various user terminals. Alternatively, it can be implemented as a virtual machine deployed on one or more devices in a cloud node, with application software installed to manage each user terminal. Or, it can also be implemented as a server composed of numerous identical or different types of hardware devices, with one or more hardware devices configured to provide a robust analysis system for multifunctional enzyme regulatory network functional balance to various user terminals.

[0023] In terms of implementation, the robustness analysis system for the functional balance of a multifunctional enzyme regulatory network and the user terminal are mutually compatible. Specifically, if the system is implemented as an application installed on a cloud service platform, the user terminal acts as a client establishing a communication connection with that application; or if the system is implemented as a website, the user terminal acts as a webpage; or if the system is implemented as a cloud service platform, the user terminal acts as a mini-program within an instant messaging application.

[0024] like Figure 1 The figure shown is a system architecture diagram of a multifunctional enzyme regulatory network functional balance robustness analysis system provided in an embodiment of the present invention.

[0025] The robustness analysis system 100 for functional balance of a multifunctional enzyme regulatory network described in this invention can be located on a cloud server. In terms of implementation, it can be used as one or more service devices, or as an application installed in the cloud (e.g., a mobile service operator's server, server cluster, etc.), or it can be developed into a website. Depending on the functions implemented, the robustness analysis system 100 for functional balance of a multifunctional enzyme regulatory network may include a network topology analysis module 101, a graph generation module 102, a flux balance analysis module 103, a functional simulation module 104, a robustness curve fitting module 105, and a report generation module 106. The modules described in this invention can also be called units, referring to a series of computer program segments that can be executed by an electronic device's processor and perform a fixed function, stored in the electronic device's memory.

[0026] In this embodiment of the invention, in a robustness analysis system for the functional balance of a multifunctional enzyme regulatory network, each of the above-mentioned modules can be implemented independently and can call other modules. Here, "calling" can be understood as one module connecting to multiple modules of another type and providing corresponding services to those connected modules. In the robustness analysis system for the functional balance of a multifunctional enzyme regulatory network provided by this embodiment of the invention, the applicable scope of the system architecture can be adjusted by adding modules and directly calling them without modifying the program code, achieving cluster-based horizontal expansion to quickly and flexibly expand the system. In practical applications, the above modules can be set in the same device or different devices, or they can be set in a virtual device, such as a service instance in a cloud server.

[0027] The following describes, with reference to specific embodiments, each component and its specific workflow of a robust analysis system for the functional balance of a multifunctional enzyme regulatory network: The network topology analysis module 101 is used to perform topology correlation analysis on the target control network and identify key nodes and vulnerable paths in the target control network. In this embodiment of the invention, when the network topology analysis module performs topology correlation analysis on the target control network and identifies key nodes and vulnerable paths in the target control network, it is specifically used for: Acquire the topology connectivity data of the target control network; Measure the node influence of the topology connectivity data to obtain the node centrality index of the topology connectivity data; Based on the node centrality index, the nodes of the target control network are prioritized to obtain the key nodes of the target control network. Based on the topological connection relationship of the target control network, starting from the key node, the target control network is traversed to obtain the connection path of the target control network. Vulnerability risk assessment is performed on connectivity paths to identify vulnerable paths in the target control network.

[0028] Read the structured data file or relational database table corresponding to the target control network. The structured data file can be in CSV or JSON format, and the database table must contain a node table and a connection table. Extract the unique identifier of each node from the node table. This identifier can be a numeric number or a character name, ensuring that each node's identifier is unique. Extract the direct connection association information between each node and other nodes from the connection table. The connection direction must be clearly marked as unidirectional or bidirectional. Unidirectional connections must specify the specific direction from the current node to the target node, while bidirectional connections are marked as having no fixed direction. The connection status must be clearly recorded as normal connectivity, temporary interruption, or permanent restriction. Group the extracted node information and association information according to the node's unique identifier. For each node, list the identifiers of all its directly connected nodes, the connection direction, and the connection status, ensuring that each direct connection relationship is completely recorded. Finally, form topology connection data arranged in order by node and containing all direct connection details.

[0029] The total number of directly connected nodes for each node in the topology connection data is calculated. When identifying intermediate bridge paths, first list all non-directly connected node pairs in the network for that node. Then, check each non-directly connected node pair for a path that connects them solely through that node without any other intermediate nodes. Such paths are considered intermediate bridge paths for that node. Count all paths that meet this condition to obtain the number of intermediate bridge paths. Since both data are equally important, add the total number of directly connected nodes to the number of intermediate bridge paths; the resulting combined value is the node centrality index for that node.

[0030] First, calculate the sum of node centrality indices for all nodes. Divide this sum by the total number of nodes in the target control network to obtain the average value of all node centrality indices. Then, multiply this average value by 1.2 to determine the node centrality screening threshold. Following the order of node unique identifiers, compare the node centrality index of each node with the screening threshold. If a node's node centrality index is equal to or greater than the screening threshold, its unique identifier is included in the critical node set. The critical node set is presented as a list containing all node identifiers that meet the criteria, thus clearly identifying the critical nodes of the target control network.

[0031] Arrange the key nodes in ascending order of their unique identifiers, and use each key node as a starting point. Based on the direct connections recorded in the topology connection data, find all directly connected adjacent nodes of the starting key node and treat these adjacent nodes as first-level traversal nodes. Then, using each first-level traversal node as a new starting point, continue searching for all untraversed directly connected nodes in the topology connection data and treat them as second-level traversal nodes. Repeat this process until there are no new untraversed directly connected nodes at a certain level. During the traversal, record the node identifiers traversed at each step in the connection order, forming a complete node connection sequence from the starting key node to the final untraversed node. Each such sequence is a connected path. After all key nodes have been traversed, collect all complete node connection sequences to form the connected paths of the target control network.

[0032] First, calculate the average node centrality index for each connected path, which is the sum of the node centrality indices of all nodes in each path divided by the number of nodes in that path. Then, sum the average node centrality indices of all connected paths and divide by the total number of connected paths to obtain the average node centrality index of all connected paths. Multiply this average value by 0.8 to determine the threshold for the average node centrality index. The historical anomaly count threshold is set to 3 times. Extract the operation records of each connected path from the historical operation log of the target control network. The connection interruption judgment criterion is that the connection status of any two adjacent nodes in the path is recorded as interrupted. The connection efficiency reduction judgment criterion is that the throughput transmission rate of the path is lower than 50% of the normal level. Count the cumulative number of times each path meets the above two conditions during historical operation, which is the historical anomaly count of the path. For each connected path, compare its average node centrality index with the preset average node centrality index threshold and its historical anomaly count with the preset historical anomaly count threshold. If the average node centrality index of a connected path is lower than the preset threshold and the historical anomaly count is higher than the preset threshold, then the path is identified as a vulnerable path of the target control network.

[0033] The graph generation module 102 is used to embed network structure relationships between key nodes and vulnerable paths to obtain a structural feature association graph of the target regulation network. In this embodiment of the invention, when the graph generation module performs network structure relationship embedding on key nodes and vulnerable paths to obtain the structural feature association graph of the target regulation network, it is specifically used for: Using key nodes as graph nodes and vulnerable paths as graph connecting edges, an initial structural graph of the target regulation network is constructed. Two-dimensional statistical analysis was performed on key nodes to obtain the number of connections and the frequency of path traversal of key nodes; Historical flux fluctuation analysis is performed on vulnerable paths to obtain their historical flux fluctuation attributes. The number of connections and the frequency of path traversal are integrated into a set of topological attributes for the target control network; According to the preset mapping rules, joint attribute mapping is performed on the topological attribute set and historical flux fluctuation attributes to obtain the structural feature association map of the target control network.

[0034] When the map generation module performs joint attribute mapping on the topological attribute set and historical flux fluctuations according to preset mapping rules to obtain the structural feature association map of the target regulation network, it is specifically used for: A correlation matching analysis was performed on the topological attribute set and the historical flux fluctuation attributes to obtain the correspondence between the topological attribute set and the historical flux fluctuation attributes; Based on the correspondence, the topological attributes and historical flux fluctuation attributes are fused to obtain the joint attribute set of the target regulation network. Based on the preset mapping rules, the joint attribute set of points and edges is embedded into the initial structural graph to obtain the structural feature association graph of the target control network.

[0035] Each critical node identified by the network topology analysis module is treated as an independent node in the graph, occupying a fixed position and clearly labeled with its unique identifier. Complete path information for each vulnerable path is extracted, and the unique identifiers of all critical nodes within that path are identified. Based on these identifiers, connecting edges are constructed in the graph: if a vulnerable path contains only two critical nodes, a connecting edge is directly established between these two nodes, labeled with the corresponding vulnerable path identifier; if a vulnerable path contains three or more critical nodes, consecutive connecting edges are established between adjacent critical nodes in the order they appear in the path, each labeled with the same vulnerable path identifier. This ensures that the node connections of each vulnerable path are completely and accurately represented in the graph, ultimately forming an initial structural graph that intuitively reflects the connections between critical nodes and vulnerable paths.

[0036] For each critical node, first extract all vulnerable paths containing its unique identifier. Then, analyze the adjacent nodes of each such path: adjacent nodes must be directly connected to the critical node in the path and have no other critical nodes in between. Count the total number of such adjacent critical nodes. Even if the same adjacent critical node is directly connected to the critical node in multiple paths, it is only counted once. This count is the connection count of the critical node. Simultaneously, inventory all vulnerable paths. Paths containing the unique identifier of the critical node are included in the statistics. The total number of paths counted is the path traversal frequency of the critical node. Perform these two data statistics for all nodes in order of their unique identifiers to ensure that each critical node corresponds to a clear connection count and path traversal frequency.

[0037] Flux data for each vulnerable path is extracted from the operational log database of the target control network. This database records the real-time flux values ​​of each path within each network operation cycle. A fixed statistical period is set for the most recent 100 network operation cycles, meaning flux data is extracted from the 100 network operation records most recent to the current analysis time. For each vulnerable path, its flux data within the 100 operation cycles is arranged in ascending order of value. The maximum value is the maximum flux value for that path, and the minimum value is the minimum flux value. The criterion for determining flux value changes is that the difference between the flux data of the later operation cycle and the flux data of the previous operation cycle is not equal to 0. Flux data from two adjacent cycles are compared sequentially, and the cumulative number of times the difference is not equal to 0 is counted. The maximum flux value, minimum flux value, and cumulative number of flux changes are then integrated into a set of data in a fixed order. This set of data represents the historical flux fluctuation attribute of each vulnerable path.

[0038] Arrange the key nodes in ascending order of their unique identifiers. Create a dedicated data entry for each key node, clearly marking its unique identifier within the entry. The number of connections and the frequency of path traversal for that node are then entered into the designated locations within the entry, ensuring that these two data points for each key node are strictly bound to its unique identifier, preventing data confusion or omissions. Summarize all the dedicated data entries for all key nodes in the order they are arranged to form a unified set. This set constitutes the topology attribute set of the target control network. Each data entry within this set can be quickly located to its corresponding key node using its unique identifier.

[0039] Each key node data entry in the topology attribute set is traversed. Based on the unique identifier of the key node within the entry, a comprehensive search is performed on the vulnerable path list of the target control network to filter out all vulnerable paths whose path information contains the unique identifier. These paths are the vulnerable paths formed by the key node. An attribute association list is established for each key node data entry. The historical flux fluctuation attributes corresponding to the filtered vulnerable paths are filled into the association list one by one. Each historical flux fluctuation attribute is labeled with the unique identifier of the corresponding vulnerable path, clarifying which historical flux fluctuation attributes of vulnerable paths correspond to the topology attributes of each key node, forming a clear and traceable correspondence between the topology attribute set and the historical flux fluctuation attributes.

[0040] Based on the established correspondences, data entries for each key node and their associated historical flux fluctuation attributes are merged to create a point-edge association data table. This table includes fields such as the key node's unique identifier, number of connections, path traversal frequency, vulnerable path's unique identifier, maximum flux value, minimum flux value, and cumulative flux change count. The corresponding data is then filled into these fields one by one, ensuring that each point-edge association data table fully encompasses both the topological attributes of the key node and the historical flux fluctuation attributes of its associated vulnerable paths. All point-edge association data tables corresponding to key nodes are arranged in ascending order of the key node's unique identifier and aggregated to form a unified dataset. This dataset constitutes the point-edge joint attribute set of the target control network.

[0041] The pre-defined mapping rules clearly stipulate that: key node attribute data such as the unique identifier of key nodes, the number of connections, and the frequency of path traversal in each table of the point-edge joint attribute set correspond to the uniquely identified graph nodes in the initial structural graph; vulnerable path attribute data such as the unique identifier of vulnerable paths, the maximum flux value, the minimum flux value, and the cumulative number of flux changes in each table correspond to the uniquely identified graph connecting edges in the initial structural graph. Following these rules, each table of the point-edge joint attribute set is processed one by one. The key node attribute data in the table is attached to the graph nodes with the corresponding unique identifiers in the initial structural graph using annotations. Similarly, vulnerable path attribute data is attached to the graph connecting edges with the corresponding unique identifiers in the initial structural graph using the same annotations. The annotation information is clear and readable, ensuring that the initial structural graph not only contains the connection relationships between nodes and edges but also fully carries the corresponding attribute information, ultimately yielding the structural feature association graph of the target control network.

[0042] The flux balance analysis module 103 is used to perform flux balance analysis on the target control network and obtain the functional flux distribution data of the target control network. In this embodiment of the invention, when the balance analysis module performs flux balance analysis on the target control network to obtain the functional flux distribution data of the target control network, it is specifically used for: The topology of the target control network is analyzed to obtain the connection constraints and historical operating flux of the target control network. Based on connectivity constraints, a constrained flux analysis is performed on historical operational fluxes to obtain the steady-state flux distribution of the target control network. Based on the functional paths in the target control network, the path contribution of the steady-state flux distribution is analyzed to obtain the functional flux distribution data of the target control network.

[0043] When the balance analysis module performs path contribution analysis on the steady-state flux distribution based on the functional paths in the target control network to obtain the functional flux distribution data of the target control network, it is specifically used for: Functional pathway retrieval is performed on the target regulation network to obtain its functional paths. Based on the nodes and connecting edges of the functional path, the path local flux data of the functional path in the steady-state flux distribution are filtered out. Functional flux aggregation is performed on the local flux data of the path to obtain the functional flux distribution data of the target control network.

[0044] Identify the unique identifiers of all nodes in the target control network. These identifiers can be numerical codes or character combinations, ensuring that each node's identifier is unique and points directly to its corresponding node. Confirm the type of each connection edge between nodes. Unidirectional connections must clearly indicate the throughput direction, while bidirectional connections are marked as having no fixed transmission direction. Consult the target control network's design parameter documents or historical maximum load test records to determine the throughput limit for each connection edge. This limit is the maximum throughput that the connection edge can handle under stable operating conditions, and the value must be clearly specified. These rules and numerical restrictions, including the unique identifier correspondence between nodes, connection edge types and transmission directions, and the specific throughput limit for each connection edge, together constitute the connection constraints of the target control network. Flux records are extracted from the operational database of the target control network. The operational database stores data sequentially according to the operational cycle. Each record contains the operational cycle number, the connection edge identifier, and the real-time flux value of the connection edge within that operational cycle. The flux records of these 100 operational cycles are classified according to the connection edge identifier. Each connection edge identifier corresponds to a set containing 100 real-time flux values. This set is the historical operational flux of the target control network.

[0045] For each connection edge's historical operational throughput data, real-time throughput values ​​are extracted sequentially according to the operational cycle number. Each value is compared with the throughput transmission limit of that connection edge. If the real-time throughput value is greater than the transmission limit, it is determined to be an abnormal throughput value and is removed. If the real-time throughput value is less than or equal to the transmission limit, it is retained as a valid throughput value. For the retained valid throughput values, the cumulative arithmetic mean is calculated sequentially, starting from the first valid value, according to the operational cycle number: first, the average of the first two valid values ​​is calculated, then the third valid value is added to calculate a new average, and so on. After each calculation, the difference between the current average value and the previous average value is calculated. When the difference between the average value obtained from 10 consecutive calculations and the previous average value is less than 0.01, subsequent calculations are stopped. The latest average value at this point is the steady-state throughput value of that connection edge. The steady-state flux values ​​of all connected edges are organized according to their corresponding connected edge identifiers. Then, based on the one-to-one correspondence between the connected edge identifiers and the connected edge positions in the network topology, each steady-state flux value is precisely matched to its corresponding position in the topology, forming a complete steady-state flux distribution of the target control network that reflects the steady-state flux status of each connected edge in the network.

[0046] The functional definition document of the target control network is consulted. This document clearly records the core functions that the network must implement and marks a list of key nodes for each core function. The list details the unique identifiers of all nodes necessary to implement the function. Based on the list of key nodes for each function, a continuous sequence of connecting edges is retrieved in the topology of the target control network. First, the start and end nodes of the function are determined. These start and end nodes are specified by the functional definition document and both belong to the list of key nodes. Then, a continuous sequence of connecting edges is found that starts from the start node, passes through other key nodes in the list in sequence, without omissions or the insertion of additional non-key nodes, and the nodes are directly connected according to the topological relationship through connecting edges without any other node gaps. This sequence must enable the complete transmission of throughput from the start node, through all key nodes, and to the end node. Such a continuous sequence of connecting edges is the functional path of the core function corresponding to the target control network.

[0047] For each functional path, all unique node identifiers and connection edge identifiers are extracted sequentially according to the throughput transmission order. An identifier list for the functional path is constructed in the order of node identifier – connection edge identifier – node identifier, ensuring that all identifiers in the list are complete and in the correct order. In the steady-state flux distribution, matching items are searched one by one according to the order of the connection edge identifiers in the identifier list. Steady-state flux values ​​that completely match the connection edge identifiers in the list are found. Each found steady-state flux value is arranged according to the order of its corresponding connection edge in the functional path identifier list, ensuring that each steady-state flux value corresponds precisely to a connection edge in the functional path, without misalignment or omission. This set of sequentially arranged steady-state flux values ​​constitutes the path local flux data for that functional path.

[0048] For each functional path, a summation operation is performed on the local flux data. The steady-state flux values ​​corresponding to all connecting edges in the path identifier list are accumulated one by one, ensuring that the steady-state flux value of each connecting edge is included without duplication or omission. The final accumulated result is the total flux value of the functional path. The total flux values ​​are then categorized and organized according to the unique identifier of each functional path. This unique identifier consists of a combination of numbers or characters. A unique entry is created for each functional path, containing four items: the unique identifier of the functional path, the unique identifiers of all key nodes participating in the path, the specific number of connecting edges in the path, and the total flux value of the path. All functional path entries are arranged in ascending order of their unique identifiers, with numerical numbers in ascending order and character combinations in alphabetical order, forming a clearly structured and complete structured functional flux distribution data for the target control network.

[0049] The functional simulation module 104 is used to simulate the functional operation of the target control network based on the structural feature correlation map and functional flux distribution data, and to quantify the output efficiency of the simulation results to obtain the core functional maintenance degree of the target control network. In this embodiment of the invention, when the functional simulation module performs functional simulation of the target regulation network based on structural feature correlation maps and functional flux distribution data, it is specifically used for: Using structural feature correlation maps as the network topology framework and functional flux distribution data as the initial load, a dynamic operation simulation network for the target regulation network is constructed. Based on the relationship between nodes and edges in the dynamic simulation network, the internal dynamic control rules of the target control network are analyzed. Based on the internal dynamic control rules, the dynamic operation simulation network is iteratively updated. During the iterative state update process, the overall functional output flux of the dynamically running simulation network is continuously tracked; When the overall functional output flux reaches the convergence state, the final functional output flux of the dynamically running simulation network is recorded, and the final functional output flux is output as the simulation result.

[0050] When the functional simulation module performs output efficiency quantification on the simulation results to obtain the core functional maintenance degree of the target control network, it is specifically used for: Obtain the historical best output efficiency of the target control network; The ratio of the simulated result to the historical best output efficiency is determined as the simulated relative efficiency ratio of the target control network. Structural connectivity is evaluated on the structural feature association graph to obtain the topological connectivity coefficients of the structural feature association graph; Perform flux statistical analysis on the functional flux distribution data to obtain the critical path flux ratio of the functional flux distribution data; Based on the preset weight configuration, the relative efficiency ratio, topological connectivity coefficient and critical path throughput ratio after simulation are weighted and fused to obtain the core function maintenance degree of the target control network.

[0051] Based on the nodes, edges, and corresponding attribute information in the structural feature association graph, the connection relationships between nodes, the transmission characteristics of edges, and various attribute data are fully preserved to form a network topology framework for a dynamic operation simulation network. The total flux value of each functional path in the functional flux distribution data is evenly distributed according to the sum of the number of nodes and edges contained in the path. Each node and each edge receives the same initial flux load value, ultimately constructing a dynamic operation simulation network that can reflect the target control network structure and initial flux state.

[0052] This paper comprehensively analyzes the relationships between nodes and edges in a dynamically simulated network, including the number of connections to a node, the frequency of path traversal, the historical flux fluctuation attributes of edges, and transmission direction restrictions. It analyzes the logic of how nodes distribute received flux to their connected edges. A node distributes its total received flux equally to all connected edges based on its number of connections. Edges limit their current transmission flux based on the explicit flux upper limit value in their historical flux fluctuation attributes. Edges strictly transmit flux to the next node according to the marked transmission direction. These explicit and executable logics are organized into the internal dynamic control rules of the target control network.

[0053] According to the internal dynamic control rules, the flux values ​​received by each node from all connected edges in the dynamic simulation network are first aggregated to obtain the total flux currently received by each node. The node then equally distributes the total flux according to its number of connections, with each connected edge receiving the same share of flux. Each edge checks its historical flux fluctuation attribute to confirm that the allocated flux does not exceed the upper limit, and then transmits the flux to the next node in the transmission direction, completing one network state update. Based on the network state after the last update, the above flux allocation and transmission process is repeated to continuously iterate and update the state of the dynamic simulation network.

[0054] After each iteration of the dynamically running simulation network, the flux values ​​received by all endpoint nodes in the network are collected. These endpoint nodes are the functional output terminal nodes explicitly defined in the functional definition document. The flux values ​​of all endpoint nodes are summed to obtain the overall functional output flux for the current iteration. A correspondence table between the iteration number and the overall functional output flux is established, recording the sequence number of each iteration and its corresponding overall functional output flux value to form a complete flux tracking record, ensuring a clear understanding of the changes in the overall functional output flux throughout the entire process.

[0055] The criteria for determining convergence are based on the operational characteristics of the target regulatory network and industry analysis needs. The setting of ten consecutive iterations stems from the analysis and summary of historical iteration data of a large number of enzyme regulatory networks with different structures. After repeated testing and verification, this number of iterations can effectively eliminate the random fluctuations of a single iteration and ensure the stability of the determination results. The setting of a change amplitude not exceeding 0.1% is based on the actual application accuracy requirements of enzyme regulatory network functional output and is formulated in conjunction with the conventional convergence criteria of similar analysis systems. This amplitude can ensure that the overall functional output flux remains at a stable level. The change amplitude is obtained by dividing the difference between the subsequent overall functional output flux value and the previous overall functional output flux value by the previous overall functional output flux value. When the change amplitude calculated for ten consecutive iterations all meets the requirement of not exceeding 0.1%, the overall functional output flux is determined to have reached convergence. At this time, the overall functional output flux corresponding to the last iteration is recorded. This value is the final functional output flux of the dynamically running simulation network and is output as the simulation result.

[0056] The historical operation record database of the target control network is retrieved. This database comprehensively stores relevant data for all operating cycles since the network was put into use. The overall functional output flux data corresponding to all historical operating cycles is extracted from the database. All extracted flux data are sorted by value, and the flux data with the highest value is selected. This value is the historical optimal output efficiency of the target control network.

[0057] The final output throughput value corresponding to the simulation result is divided by the historical best output efficiency value. The setting of retaining four decimal places during the calculation is to achieve a balance between ensuring computational accuracy and controlling the data processing burden. Referring to the conventional accuracy range of enzyme regulatory network throughput data, and after testing in multiple sets of different simulation scenarios, four decimal places can accurately distinguish efficiency differences under different scenarios, while avoiding data redundancy caused by too many decimal places. The resulting calculation result is the simulated relative efficiency ratio of the target regulatory network.

[0058] The total number of nodes in the structural feature association graph is calculated by multiplying the total number of nodes by one to determine the total number of possible node pairs in the network. Then, each node in the graph is checked to ensure that there is at least one connected path consisting of an edge. A connected path requires nodes to be directly or indirectly connected by an edge without interruption. The total number of node pairs meeting this condition is counted. The ratio of the total number of node pairs with connected paths to the total number of all possible node pairs is the topological connectivity coefficient of the structural feature association graph.

[0059] The total flux values ​​of all functional paths in the functional flux distribution data are sorted in descending order. The top 20% of functional paths after sorting are selected as critical paths. This proportion is based on the statistical regularity of functional flux distribution and has been verified through functional analysis of a large number of different types of enzyme regulatory networks. The paths selected by this proportion provide stable support for the core functions of the network, meet the industry's standard for critical path selection, and are reproducible. The total flux values ​​of all critical paths are summed, and then the total flux values ​​of all functional paths in the functional flux distribution data are summed again. The ratio obtained by dividing the sum of the total flux values ​​of critical paths by the sum of the total flux values ​​of all functional paths is the critical path flux proportion in the functional flux distribution data.

[0060] In the preset weight configuration, the simulated relative efficiency ratio accounts for 50%, the topology connectivity coefficient accounts for 30%, and the critical path flux ratio accounts for 20%. This configuration is derived from analyzing the impact of each indicator on the maintenance of core functions: the simulated relative efficiency ratio directly reflects the degree of fit between the network's current functional output and its historical stable state, and is the core manifestation of core function maintenance; the topology connectivity coefficient represents the integrity and stability of the network structure, and is the basic condition for the continuous operation of core functions; the critical path flux ratio reflects the support effect of the core path on the overall function. This weight configuration has been verified through testing on multiple enzyme regulation networks with different structures and functional types, and can objectively integrate information from various dimensions to ensure the rationality of the core function maintenance assessment results. The simulated relative efficiency ratio, topology connectivity coefficient, and critical path flux ratio are multiplied by 50%, 30%, and 20% respectively to obtain three weighted values. The sum of these three weighted values ​​is the core function maintenance of the target regulation network.

[0061] The robust curve fitting module 105 is used to fit the perturbation trend of the core function maintenance degree to obtain the functional balance robustness curve of the target regulation network. In this embodiment of the invention, when the robust curve fitting module performs perturbation trend fitting on the core function maintenance degree to obtain the functional balance robustness curve of the target control network, it is specifically used for: The core function maintenance is subjected to simulated perturbation, and the perturbation response of the core function maintenance after the perturbation is recorded to obtain the dynamic response sequence of the core function maintenance after the perturbation. Nonlinear regression fitting is performed on the dynamic response sequence to obtain the initial fitting curve of the dynamic response sequence; The initial fitted curve is smoothed to obtain the functional balance robustness curve of the target regulatory network.

[0062] Using the core function maintenance degree obtained from the functional simulation module as the perturbation benchmark, the influencing factors of the core function maintenance degree are clearly defined as the critical path throughput efficiency, node connection stability, and edge throughput upper limit. These three factors all come from the calculation logic of the core function maintenance degree in the functional simulation module and are the core variables affecting network function maintenance. The perturbation gradient is set to 5% of the benchmark value. This gradient is based on the intensity range of common external disturbances in enzyme regulation networks. Common external disturbances in enzyme regulation networks include environmental fluctuations and changes in enzyme activity. The intensity range of such disturbances is usually between 5% and 50%. After testing and verification with 50 groups of enzyme regulation networks with different structures and functional types, this gradient can cover the main perturbation scenarios and accurately capture the response law of core function maintenance degree. The perturbation range increases from 5% to 50% of the benchmark value, with a total of ten equal-gradient perturbation levels. The perturbation intensity corresponding to each level is 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, and 50% of the benchmark value, respectively. For each disturbance level, three types of influencing factors are adjusted synchronously according to the disturbance intensity corresponding to that level: the throughput efficiency of the critical path is reduced by a corresponding proportion according to the disturbance intensity, and the throughput efficiency of all critical paths under a 5% disturbance level is adjusted to 95% of the baseline value; node connectivity stability is achieved by adjusting the node connectivity probability, which is 100% under the baseline state and adjusted to 95% under a 5% disturbance level; the throughput limit of edges is reduced by a corresponding proportion according to the disturbance intensity, and the throughput limit of all edges under a 5% disturbance level is adjusted to 95% of the baseline value. After the adjustment, the complete operation flow of the functional simulation module is re-executed, i.e., from building a dynamic simulation network, iteratively updating the state, to obtaining the final functional output throughput, and then calculating the core function maintenance value under that disturbance level through weighted fusion. Each disturbance level and the corresponding core function maintenance value are arranged in ascending order of disturbance intensity to form a dynamic response sequence of the core function maintenance after the disturbance, which includes the disturbance level, disturbance intensity, and corresponding core function maintenance value. Each data item in the sequence corresponds one-to-one with the adjusted influencing factor parameters to ensure traceability.

[0063] Each disturbance level in the dynamic response sequence is used as the x-axis value, representing the percentage of disturbance intensity corresponding to that level: level 1 corresponds to 5%, level 2 to 10%, and subsequent levels correspond sequentially according to disturbance intensity. The corresponding core function maintenance value is used as the y-axis value. All corresponding coordinate points are marked in a two-dimensional Cartesian coordinate system, with each coordinate point labeled with its corresponding disturbance intensity and core function maintenance value. By analyzing the distribution trend of the coordinate points point by point, it is clear that the overall law of core function maintenance changing with disturbance intensity is a gradient decrease, and the curve shape must strictly follow this decreasing trend. When adjusting the curve, first connect adjacent coordinate points to form a preliminary polygonal line, then analyze the changing trend of the polygonal line segment by segment: if there is no abrupt change in the slope of the polygonal line between adjacent coordinate points (the criterion for abrupt change is that the difference in slope between two adjacent polygonal lines exceeds 10%), then maintain the polygonal line shape; if abrupt change occurs, fine-tune the curve curvature to make the transition of the abrupt segment natural. When the difference in slope between two polygonal lines is 15%, the curve curvature can be adjusted at the middle position of the abrupt segment to make the curve smoothly transition from the first slope to the second slope, ensuring that the curve can pass through or closely approximate all coordinate points and fully reflect the changing characteristics of the dynamic response sequence. During the adjustment process, after each segment of the curve is modified, the fit between the curve segment and the coordinate points before and after it must be rechecked to ensure that no coordinate point deviates from the curve by more than 2%. The degree of deviation is the difference between the ordinate of the coordinate point and the ordinate of the corresponding abscissa of the curve divided by the ordinate of the coordinate point. Finally, an initial fitting curve for the dynamic response sequence that can accurately characterize the changing characteristics of the dynamic response sequence is obtained.

[0064] The slope difference threshold for continuous smoothing is set at 3%. This threshold is based on industry standards for curve smoothness; the smoothing threshold for robust curves of similar networks is typically between 2% and 4%. Considering the practical application scenarios of robust curves for enzyme-regulated networks, subsequent analysis of attenuation parameters based on the curve requires a smooth curve without obvious inflection points to determine this threshold. The slope is calculated as follows: Take two adjacent coordinate points on the initial fitted curve, subtract the ordinate value of the previous point from the ordinate value of the subsequent point, and then divide by the subtraction of the abscissa value of the previous point from the abscissa value of the subsequent point to obtain the slope between the two points. After calculating the slopes of all adjacent pairs of points, compare the slopes of adjacent pairs one by one in order of coordinate points: if the difference between the slope of the subsequent pair and the slope of the previous pair exceeds 3%, then add a new coordinate point at the midpoint between the adjacent coordinate points corresponding to these two slopes. The abscissa value of the new coordinate point is the average of the abscissa values ​​of the two adjacent points, and the ordinate value is the average of the ordinate values ​​of the two adjacent points. After adding new coordinate points, reconnect all coordinate points in x-axis order to form a new curve. Calculate the slope between all adjacent coordinate points again using the same method, and check the difference between adjacent slopes. Repeat the process of adding coordinate points, reconnecting curves, and calculating and checking slope differences until the slope difference between all adjacent coordinate points does not exceed 3%, and no two consecutive slope differences between three coordinate points on the curve are close to 3%, with the difference between 2.8% and 3%. This finally yields the functional balance robustness curve of the target control network.

[0065] The report generation module 106 is used to perform attenuation mode analysis on the functional balance robustness curve to generate a balance robustness analysis report of the target control network.

[0066] In this embodiment of the invention, when the report generation module performs attenuation mode analysis on the functional balance robustness curve to generate a balance robustness analysis report of the target control network, it is specifically used for: Inflection point detection analysis is performed on the functional balance robustness curve to identify key decay characteristic points of the functional balance robustness curve; Based on the distribution of key decay characteristic points, the functional balance robustness curve is divided into trend intervals to obtain the decay stage and plateau period of the functional balance robustness curve. Based on the coordinate data of key attenuation feature points, the attenuation parameters of the attenuation stage are deconstructed to obtain the attenuation rate and attenuation amplitude of the attenuation stage. By combining the decay phase, plateau period, decay rate, and decay magnitude, a balance robustness analysis report of the target control network is generated.

[0067] The slope change threshold is set at 10%. This threshold is determined by referencing industry-standard inflection point detection for robustness curves of similar networks and combining it with the decay characteristic analysis of the functional balance robustness curve of enzyme regulatory networks. Multiple tests have verified its accurate identification of abrupt change points in the curve trend. The slope between two adjacent coordinate points on the functional balance robustness curve is calculated, and the difference between the current slope and the previous slope is compared sequentially. If the difference exceeds 10%, the starting coordinate point of the current segment is the key decay characteristic point, indicating a significant change in the curve's decay trend. This process is repeated throughout the entire functional balance robustness curve, recording all coordinate points that meet the criteria, thus completing the identification of key decay characteristic points on the functional balance robustness curve.

[0068] Using the identified key decay feature points as dividing points, the functional balance robustness curve is divided into multiple continuous intervals. Each interval begins at the previous key decay feature point and ends at the next. The slope between all adjacent coordinate points within each interval is calculated, and the arithmetic mean of these slopes is taken as the average slope of that interval. The threshold for determining the absolute value of the average slope is set to 0.5%, based on the stable fluctuation range of the core function maintenance of the enzyme regulatory network, ensuring effective differentiation between stable and decaying states. If the absolute value of the average slope of an interval exceeds 0.5%, the interval is considered a decay phase; if the absolute value of the average slope does not exceed 0.5%, the interval is considered a plateau phase. This standard is used to classify all intervals, resulting in the decay phase and plateau phase of the functional balance robustness curve.

[0069] For each attenuation stage, the coordinates of key attenuation feature points at the beginning and end of the stage are extracted. The coordinate data directly uses the x-coordinate and y-coordinate values ​​of the key attenuation feature points recorded in the inflection point detection analysis. The attenuation rate is obtained by subtracting the y-coordinate value at the beginning from the y-coordinate value at the end, and then dividing by the difference between the x-coordinate values ​​at the end and the x-coordinate values ​​at the beginning. This calculation method is based on the physical meaning of the curve slope and can intuitively reflect the rate of change in the attenuation stage. The attenuation magnitude is obtained by subtracting the y-coordinate value at the end from the y-coordinate value at the beginning, and then dividing by the y-coordinate value at the beginning. This calculation method can clearly define the relative decrease in the maintenance of core functions in the attenuation stage. The parameters for each attenuation stage are calculated using this method to obtain the attenuation rate and attenuation magnitude for each stage.

[0070] The data related to the divided decay stages and plateau periods are systematically organized, and each stage is arranged in ascending order of its horizontal axis value. Each stage must clearly indicate its start and end coordinates, average slope, and coordinates of key decay characteristic points. The decay rate and decay magnitude corresponding to each decay stage are summarized, and the calculation basis and units of each parameter are added. This data is then organized into structured tables, supplemented with textual descriptions explaining the functional balance robustness characteristics of each stage, the significance of key nodes, and the overall decay law. Finally, a complete document containing data tables, textual explanations, and curve diagrams is generated; this document constitutes the balance robustness analysis report of the target control network.

[0071] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0072] This application embodiment can acquire and process relevant data based on artificial intelligence technology. Artificial intelligence is the theory, method, technology, and application system that uses digital computers or machines controlled by digital computers to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use that knowledge to obtain optimal results.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A multifunctional enzyme regulatory network functional balance robustness analysis system, characterized by, The system includes a network topology analysis module, a graph generation module, a flux balance analysis module, a functional simulation module, a robust curve fitting module, and a report generation module, wherein: The network topology analysis module is used to perform topology correlation analysis on the target control network and identify key nodes and vulnerable paths in the target control network. The graph generation module is used to embed network structure relationships between key nodes and vulnerable paths to obtain a structural feature association graph of the target regulation network. The flux balance analysis module is used to perform flux balance analysis on the target control network and obtain the functional flux distribution data of the target control network. The functional simulation module is used to simulate the functional operation of the target control network based on the structural feature correlation map and functional flux distribution data, and to quantify the output efficiency of the simulation results to obtain the core functional maintenance degree of the target control network. The robust curve fitting module is used to fit the perturbation trend of the core function maintenance degree to obtain the functional balance robustness curve of the target control network. The report generation module is used to analyze the decay mode of the functional balance robustness curve to generate a balance robustness analysis report of the target control network.

2. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When performing topological correlation analysis on the target control network and identifying key nodes and vulnerable paths in the target control network, the network topology analysis module is specifically used for: Acquire the topology connectivity data of the target control network; Measure the node influence of the topology connectivity data to obtain the node centrality index of the topology connectivity data; Based on the node centrality index, the nodes of the target control network are prioritized to obtain the key nodes of the target control network. Based on the topological connection relationship of the target control network, starting from the key node, the target control network is traversed to obtain the connection path of the target control network. Vulnerability risk assessment is performed on connectivity paths to identify vulnerable paths in the target control network.

3. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When the graph generation module performs network structure relationship embedding on key nodes and vulnerable paths to obtain the structural feature association graph of the target regulation network, it is specifically used for: Using key nodes as graph nodes and vulnerable paths as graph connecting edges, an initial structural graph of the target regulation network is constructed. Two-dimensional statistical analysis was performed on key nodes to obtain the number of connections and the frequency of path traversal of key nodes; Historical flux fluctuation analysis is performed on vulnerable paths to obtain their historical flux fluctuation attributes. The number of connections and the frequency of path traversal are integrated into a set of topological attributes for the target control network; According to the preset mapping rules, joint attribute mapping is performed on the topological attribute set and historical flux fluctuation attributes to obtain the structural feature association map of the target control network.

4. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 3, characterized in that, When the map generation module performs joint attribute mapping on the topological attribute set and historical flux fluctuations according to preset mapping rules to obtain the structural feature association map of the target regulation network, it is specifically used for: A correlation matching analysis was performed on the topological attribute set and the historical flux fluctuation attributes to obtain the correspondence between the topological attribute set and the historical flux fluctuation attributes; Based on the correspondence, the topological attributes and historical flux fluctuation attributes are fused to obtain the joint attribute set of the target regulation network. Based on the preset mapping rules, the joint attribute set of points and edges is embedded into the initial structural graph to obtain the structural feature association graph of the target control network.

5. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When performing flux balance analysis on the target control network to obtain the functional flux distribution data of the target control network, the balance analysis module is specifically used for: The topology of the target control network is analyzed to obtain the connection constraints and historical operating flux of the target control network. Based on connectivity constraints, a constrained flux analysis is performed on historical operational fluxes to obtain the steady-state flux distribution of the target control network. Based on the functional paths in the target control network, the path contribution of the steady-state flux distribution is analyzed to obtain the functional flux distribution data of the target control network.

6. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When the balance analysis module performs path contribution analysis on the steady-state flux distribution based on the functional paths in the target control network to obtain the functional flux distribution data of the target control network, it is specifically used for: Functional pathway retrieval is performed on the target regulation network to obtain its functional paths. Based on the nodes and connecting edges of the functional path, the path local flux data of the functional path in the steady-state flux distribution are filtered out. Functional flux aggregation is performed on the local flux data of the path to obtain the functional flux distribution data of the target control network.

7. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When the functional simulation module performs functional operation simulation of the target regulation network based on structural feature correlation maps and functional flux distribution data, it is specifically used for: Using structural feature correlation maps as the network topology framework and functional flux distribution data as the initial load, a dynamic operation simulation network for the target regulation network is constructed. Based on the relationship between nodes and edges in the dynamic simulation network, the internal dynamic control rules of the target control network are analyzed. Based on the internal dynamic control rules, the dynamic operation simulation network is iteratively updated. During the iterative state update process, the overall functional output flux of the dynamically running simulation network is continuously tracked; When the overall functional output flux reaches the convergence state, the final functional output flux of the dynamically running simulation network is recorded, and the final functional output flux is output as the simulation result.

8. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When the functional simulation module performs output efficiency quantification on the simulation results to obtain the core functional maintenance degree of the target control network, it is specifically used for: Obtain the historical best output efficiency of the target control network; The ratio of the simulated result to the historical best output efficiency is determined as the simulated relative efficiency ratio of the target control network. Structural connectivity is evaluated on the structural feature association graph to obtain the topological connectivity coefficients of the structural feature association graph; Perform flux statistical analysis on the functional flux distribution data to obtain the critical path flux ratio of the functional flux distribution data; Based on the preset weight configuration, the relative efficiency ratio, topological connectivity coefficient and critical path throughput ratio after simulation are weighted and fused to obtain the core function maintenance degree of the target control network.

9. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, The robust curve fitting module, when performing perturbation trend fitting on the core function maintenance degree to obtain the functional balance robustness curve of the target control network, is specifically used for: The core function maintenance is subjected to simulated perturbation, and the perturbation response of the core function maintenance after the perturbation is recorded to obtain the dynamic response sequence of the core function maintenance after the perturbation. Nonlinear regression fitting is performed on the dynamic response sequence to obtain the initial fitting curve of the dynamic response sequence; The initial fitted curve is smoothed to obtain the functional balance robustness curve of the target regulatory network.

10. The robustness analysis system for functional balance of a multifunctional enzyme regulatory network as described in claim 1, characterized in that, When the report generation module performs attenuation mode analysis on the functional balance robustness curve to generate a balance robustness analysis report for the target control network, it is specifically used for: Inflection point detection analysis is performed on the functional balance robustness curve to identify key decay characteristic points of the functional balance robustness curve; Based on the distribution of key decay characteristic points, the functional balance robustness curve is divided into trend intervals to obtain the decay stage and plateau period of the functional balance robustness curve. Based on the coordinate data of key attenuation feature points, the attenuation parameters of the attenuation stage are deconstructed to obtain the attenuation rate and attenuation amplitude of the attenuation stage. By combining the decay phase, plateau period, decay rate, and decay magnitude, a balance robustness analysis report of the target control network is generated.

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